FR2761553A1 - Image data compression and decompression method - Google Patents

Abstract

The method involves, for each elementary subset which does not have the minimum dimension, an iteration of a sequence of steps having a division suitability estimation step during which a suitability for division of the elementary subset is estimated. The suitability estimate does not meet predetermined so-called "quality" criteria, a step of "supplementary partitioning" of the subset into so-called "intermediate" elementary subsets (Ki). A "construction" step in which, for each elementary subset resulting from the last partitioning step, n working subsets (Li) are considered, n being non-zero, and an elementary mapping of the n working subsets in the elementary subset under consideration is constructed by determining the parameters (ai, b) of the elementary mapping so as to make contractive a so-called "first type" global mapping. For the set of data, the global mapping belongs to the group of mappings composed of multidimensional mappings and non-linear mappings. The restrictions of the global mapping to the elementary subsets being composed of the elementary mappings. The fixed point of the global mapping constitutes an approximation of all or part of this set, allow the use of a method of successive approximations (407-410) converging towards the fixed point of the global contractive mapping. The set of parameters determined, and, when a supplementary partitioning step has taken place, so-called "partitioning" information, representing each the supplementary partitioning, jointly constitutes a primary representation of the set of data.

Description

The present invention relates, in general, to a method and a

  device for data processing, including representation, generation, restitution, regeneration or processing

iterative data.

  More particularly, the present invention relates to the transmission (ie the remote representation) and / or the storage (that is to say the representation in a memory) of data, with or without compression thereof. These data can advantageously be constituted by digital or analog data of an image or sequence of images, and / or digital or analog data relating to sound (music, speech, etc.), and / or digital data. or analogs relating to any mono or multidimensional signal. More generally, the present invention

  aims at the representation of any mono or multidimensional data.

  Before explaining the objectives and means of the invention, the following definitions are given below: "Data set": any set of data representing physical quantities (most often voltage levels) that can represent themselves other physically measurable or measurable quantities. In privileged applications, the data sets concerned are images, sound or mono- or multidimensional signals, etc. In the application concerning image processing, the "image" will sometimes be targeted in place of of the "image-related" data set What will be discussed below about "images" or "sub-images"

  is respectively applicable to "data sets" or "sub-

  o data sets "and vice versa.

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  "Data representation": any "processing" of a set of data of a given type, resulting in the perfect or imperfect transformation of said data set, into another type. Example: the data may consist of the 256 gray levels of the pixels of an image, their representation consisting of a series of binary words that can be stored or transmitted; reciprocally, the representation of the data constituted by said binary words may consist of their transformation

  to retrieve data of the same type as the original data.

  "Primary representation": conventionally, any processing resulting in the transformation of data of a first type to data of a second type. In this case, we will speak of a "primary processing" of the "Secondary Representation" data: by convention, the transformation of data of the second type resulting from a primary treatment. We will speak in

this case of "secondary treatment".

  "Data restitution": special case of a secondary representation in which the data of the second type are transformed into

  data of the first type. This restitution can be perfect or imperfect.

  A "metric space" is a set of elements with a functional distance that is symmetrical, positive and satisfies the triangular inequality. This space is "complete" when it contains all the endpoints of

all the convergent suites.

  A "Lipschitzian application": an application that transforms the points of a metric space into the same space and for which the set of ratios of the distance of two elements transformed by the said

  application, on the distance of the two said elements, is bounded.

  A "contractive application" or "contraction": a Lipschitzian application for which the smallest of the majorities (contraction factor) of said set of ratios is less than unity. However, in the sense of the present invention, all the convergent applications are contractive,

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  that is to say having a fixed point (thus allowing the implementation

  successive approximations) in a subset of the metric space.

  A "similarity" is a Lipschitzian application for which the ratio of the distance of two transformed elements over the distance of said elements is a fixed quantity. A linear similarity is a "similarity". A "contractive similarity" is a Lipschitzian application for which the ratio of the distance of two elements transformed over the distance

  said elements is a fixed quantity strictly less than unity.

  The "fixed point" of a contraction of a complete metric space in the same space (or a subset of that space in itself)

  is the only element that is left invariant by said contractive application.

  The "construction" of a contractive application on a set of data consists in constituting a family of contractions able to transform the data and to select the parameters of one of the aforementioned

  contractions to satisfy one or more predetermined conditions.

  The "successive approximation method" makes it possible to approach iteratively as closely as one wishes, the fixed point of a contraction. Starting from an arbitrary element, it applies on the latter said contraction. The same contraction is then applied to the previously obtained transform. By reiterating this process we are approaching

  successively and inevitably from the fixed point of contraction.

  "A better approximation" of an element in a metric space is a point in a subset of candidates, which are themselves

  points of said space, which minimizes the distance to said element.

  "A good approximation" of an element in a metric space is a point of a subset of that space that is close with

  a predetermined error of a better predetermined approximation.

  In the state of the art, various methods of

  image representation, with compression, using the so-called "fractal" technique.

  US-A-5,065,447 discloses a method and a device for processing or compression image storage.

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  data relating to the initial image. In this method, the data relating to the initial image are divided, that is to say that the image is divided into a plurality of sub-elementary images (called "domain blocks"). This method then consists in generating an ordered dictionary of a set of reference picture frames (called "range blocks") constituted from image portions of predetermined size having undergone a certain number of predetermined operations such as rotation and reversal. according to various axes of symmetry. Then, for each elementary subimage, a comparison is made with all the reference sub-images of the dictionary and o10 is selected in the dictionary the most similar reference sub image of the sub-image considered. Finally, the method consists of processing or storing parametric information relating to the addresses of the reference sub images selected in the dictionary, to represent

  each of the original elementary subimages.

  It is through this set of operations that the method described in this document makes it possible to obtain a first representation of the image with

data compression.

  To carry out, from said parametric information, the restitution of the initial image, the method and the device described in this document, carry out the following operations: starting from an arbitrary initial image, steps are performed similar to those above, that is to say that one partitions the initial arbitrary image and that one constitutes a dictionary starting from the elementary subimages of this one. However, the dictionary is constituted only partially by performing for each sub-image only the predetermined operation corresponding to the address

  concerned of the dictionary for the position of the sub-image considered.

  The data thus obtained are used to repeat this process until the difference between two images consecutively obtained is less than a predetermined threshold. The image obtained last

  place is then an approximation of the initial image.

  This method, interesting theoretically, has the major disadvantage that it is sometimes difficult to practice industrially with the means known to date. Indeed, each image must give rise to a long analysis with constitution of a particularly important dictionary, the sub-elementary images of the image to be stored or transmitted being all compared to each of the reference sub images contained in the dictionary. The inventors, who carried out simulations, thus found that for some images of average size and resolution (512 x 512 pixels at 3 x 256 color levels) the processing time for the compression was of the order of 1000 at 2000 seconds on a workstation, about half an hour. Such a treatment time is

  obviously prohibitive for almost any industrial application.

  Document WO-A-93/17519 discloses another method and device for processing images with compression of data relating to the initial image. In this method the data relating to the initial image are also partitioned, that is to say that the image is divided into a plurality of sub-elementary images (called "domains"). In this method, a set of fractal transforms linking the sub-images is then determined to the set of initial data, that is to say that the initial image is searched for a portion of image similar to the image. considered minimal, so as to minimize the error between the initial data and the approximated data thus obtained. The coefficients of the set of fractal transformations thus made constitute the first representation of the initial image. To carry out the restitution of the image, the method and the device described in this document proceed to search for the fixed points of the elementary fractal transformations whose coefficients have been received without, however, explaining how this search is performed. The initial image is

  thus restored by proceeding to a meeting of the restored sub-images.

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  This method is also interesting theoretically.

  However, the inventors have noted significant degradation of the

quality of the rendered image.

  The inventors have sought to develop a method of data processing of the same kind as the processes of the state of the art analyzed above, but having better performance both in terms of the quality of the data returned than in terms of treatment speed. In the course of their research, the inventors discovered that the

  why the processes described in US-A-5,065,447 and WO-A-

  93/17519 have the aforementioned defects is due to the fact that the two processes involve geometric transformations of portions of images consisting essentially of contractive similarities (construction of

  dictionary in US-A-5,065,447 and fractal transformation in WO-A-

  93/17519). They have in fact been able to highlight that in both cases this is the implementation of an idea widely shared by the person skilled in the art concerned by the fractal compression at the time of filing of the present application, idea according to which the images would, whatever their origin, consist essentially of elements or parts presenting between them

  important degrees of resemblance.

  In fact, the performance of WO-A-93/17519 is very low in terms of the quality of the image restored because the inventors have discovered that the capabilities of restitution of contractive similarities are very limited contrary to the belief of said men of art on the date of filing of the

this request.

  Similarly, the performance of US-A-5,065,447 is very limited in terms of processing time. As the restitution capacities of

  contractive similarities are inherently limited, the author of US-A-

  5,065,447 is brought to the realization of an important dictionary which is built on the basis of numerous transformations of sub-images in the process according to US-A-5,065,447: it is indeed to artificially increase the

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  elements of similarity, which certainly makes it possible to significantly improve the

  image quality restored, but at the expense of computing time.

  The inventors have therefore sought to produce a method and a device for the processing of data, in particular images, making it possible to obtain better performances than the state of the art mentioned above both in terms of the quality of the data or the quality of the data. image than that of the speed of calculation, and likely to lead to a significant compression of

  data to be transmitted or stored.

  Furthermore, when, as is commonplace, an image to be processed has substantially uniform ranges and other ranges where at least one of the components varies rapidly from pixel to pixel, processing parameters the image as a whole is inappropriate, either because they provide too high quality treatment in the most uniform areas, or because they imply too low quality treatment in more complex. The inventors have therefore sought to optimize, depending on the local complexity of the image to be processed,

  treatment parameters used locally.

  The methods and devices of the invention solve this problem. In a general manner, the present invention firstly aims at a method for primary processing of a set of data representative of physical quantities, a primary treatment method taking into account a minimum dimension and comprising an "initial partition" step at during which, said set of data is partitioned into so-called "initial elementary" subsets, a primary treatment method characterized in that it comprises a) for each elementary subset that does not have said minimum dimension, at least one iteration of a sequence of steps comprising:

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  a divide opportunity estimation step during which an opportunity is estimated for dividing said elementary subset, and when the opportunity estimate does not meet predetermined criteria known as "quality" criteria, a step of "complementary partition" of said subset into elementary subsets called "intermediate", b) a step of "construction" in which, for each subset

  elementary elements resulting from the last stage of partition, we consider n

  working sets, n being non-zero, and one constructs an elementary application of the n subsets of work in the elementary subset considered by determining the parameters of the elementary application so as to: contractive a global application called "de first type "for said set of data, a global application belonging to the application group consisting of multidimensional applications and non-linear applications, the restrictions of the global application to the elementary subsets consisting of said elementary applications, the fixed point of the global application constituting an approximation of all or part of this set, to allow the implementation of a method of successive approximations converging towards the fixed point of said global contractive application; the set of parameters thus determined, as well as, when at least one complementary partitioning step has taken place, a so-called "partition" information representative of each said complementary partition constituting

  together a primary representation of said data set.

  In general, the present invention then aims at a device for primary processing of a set of data representative of physical quantities, characterized in that it comprises: data input means to be processed;

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  means for outputting parameters and partition information; first logical means for transforming the data to be processed into parameters and partition information, said first logical means comprising: partitioning means adapted to partition said set of data into "elementary subsets"; "estimate" adapted, for each elementary subset that does not have said minimum dimension, to estimate an opportunity of division of said elementary subset, said partition means being, furthermore, adapted to partition each elementary subset which has not said minimum dimension and whose division opportunity estimate does not meet predetermined quality criteria, in so-called "intermediate elementary" subassemblies and adapted "construction" means: to build an application so-called "global contractive" whose fixed point constitutes an approximation of all or part of this set of data, by determining the parameters of each elementary application of n work subsets associated with each elementary subset resulting from the last partition, n being non-zero, in said elementary subset, the restrictions of the global application to elementary subsets being constituted of said elementary applications, said global application belonging to the application group consisting of multidimensional applications and non-linear applications, so as to allow the implementation of a method of successive approximations converging towards the fixed point of said global contractive application; to deliver on the output means the parameters thus determined, as well as, when at least one elementary subset has been partitioned, a so-called "partition" information, representative of

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  each said complementary partition, jointly constituting a

  primary representation of said data set.

  Thanks to these provisions, the present invention achieves the objectives

outlined above.

  It should be noted first of all that it has been discovered that, in a general manner, in accordance with the invention, in order to process, and in particular to represent, a set of initial data representative of physical quantities, in particular with compression of said initial data, it suffices to construct, by appropriate means, a global contractive application,

o10 acting on said data.

  Another important feature of the invention resides in the fact that in order to construct said global contractive application it is necessary to implement at least one application belonging to the group of applications consisting of multidimensional applications and non-linear applications. In doing so, we exclude any recourse to mathematical transformations belonging to the class of the contractive similarities, which

  avoids the disadvantages noted above.

  However, to construct said global contractive application acting on the data, one skilled in the art has at his disposal a very wide range of mathematical tools from which he can draw. It can therefore choose among those tools those that are most favorable to performance, for example in conjunction with the type of data to be represented or the particular application targeted. Such a possibility does not exist in the state of the art analyzed above and is very advantageous. Thus, for example, in the case of local processing of the image, by partitioning the latter into elementary subimages, the skilled person may choose, for local processing, applications that are not necessarily contractive , which gives him an important choice in the possibilities of local treatment of the image and thus leaves him a great freedom. In particular, it will be able to choose at the local level Lipschitzian applications which will enable it to facilitate the

  implementation of the contractive nature of the global application.

  In addition, the implementation of a method of successive approximations, leaves the skilled person the freedom to choose the final difference between

  said fixed point and the data thus restored or generated.

  The estimation step allows the device to estimate or measure the local complexity of the data set in the elementary subset, and the complexity of the processing to be applied thereto. A division opportunity being estimated, it is checked during the estimation step if this opportunity meets predetermined criteria called "quality". When the division opportunity meets these criteria, which usually means that lo the local complexity of the dataset can be handled properly

  without any additional division, no division is made on the sub-division.

  elementary set. On the other hand, when the division opportunity does not meet the said criteria, this generally means that the local complexity is greater than what can be correctly handled without complementary division, a complementary partitioning step is performed, the elementary subsets resulting from this partition being processed in turn. The method of the invention is thus adaptive according to the values of the data set, which makes it possible to deal with more than

  finesse the local variations between these data.

  Indeed, it will first be noted that the method and the device allow a representation of a set of data, especially those

  related to an image, possibly with significant compression.

  Moreover, considering the number of successive partitions defining an elementary subset and constructing each elementary application considered from working subsets, the quality of the restitution is significantly improved, and this to the extent that the partition number is high. Of course, the calculation time increases with the

  number of additional partitions used to define each

  elementary sets but this computation time, even for a relatively large number, is much less than the computation time associated with the construction

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  of a dictionary and to the analysis of the image on the basis described in the document

US Patent 5,065,447.

  Moreover, by avoiding the constitution of a dictionary and the long analysis described in US-A-5.065.447, and thanks to the features of the present invention, the processing of an image is significantly accelerated compared to the US document. supra. By implementing their preferred embodiment, the inventors have found that for an image of 512 × 512 pixels at 3 × 256 color levels, the processing time was of the order of less than 100 seconds on a station working; they have every reason to believe that improvements made in the process and device succinctly defined above will make it possible to obtain

  improved performance in speed.

  Note further that since the basic applications built belong to the application group consisting of multidimensional applications and non-linear applications, applications are avoided.

  belonging to the class of similarities, with the advantages observed above.

  According to particular features, in the primary treatment method as succinctly set forth above, for at least one iteration of said sequence of steps, the opportunity estimate determined during the estimation step of opportunity consists of a measurement of a predetermined statistical magnitude applied to the data of the elementary subset considered. Preferably, the measured statistical magnitude is

  the variance of the elementary subset considered.

  Correlatively, according to particular features, in the primary treatment device as briefly described above, the estimation means are adapted to measure a predetermined statistical magnitude applied to the data of the elementary subset considered. Preferably, the measured statistical magnitude is the variance

  of the elementary subset considered.

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  Thanks to each of these provisions, the determination of the opportunity estimate is easy and implements only functions

  of addition, multiplication and division.

  According to other particular features, at least one iteration of said sequence of steps is carried out after a construction step, the opportunity estimation step comprising an operation of measuring a difference between, on the one hand, the data of the elementary subset and, secondly, the restriction of the overall contractive application under construction to the elementary subset considered, and, when a complementary partitioning step of the elementary subset is performed, it is followed by a new construction step taking into account said complementary partition. Preferably, the difference measurement operation,

  consists of a distance measurement operation.

  Correlatively, according to particular characteristics of the primary treatment device as succinctly set forth above: the construction means having constructed a global contractive application, the estimation means are adapted to measure a difference between, on the one hand, the data of the basic subset and, on the other hand, the

  restriction of the overall contractive application under construction to the sub-

  elementary set considered, and in that - when the partition means realize a complementary partition, the means of construction are adapted to build a new application

  global contractive taking into account said complementary partition.

  Preferably, to measure said difference, the estimation means

  take into account a measure of distance.

  Thanks to these provisions, it is the adaptation of the overall contractive application to the data of the elementary subset considered is estimated, which better reflects the result to be expected of a treatment of

  the primary representation determined according to the invention.

  According to particular features, the predetermined quality criteria are to compare said measurement with a value

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  predetermined. Preferentially, the opportunity estimate meets the predetermined quality criteria when said measurement is less than said

predetermined value.

  Correlatively, according to particular features of the primary treatment device as succinctly set forth above, the estimation means are adapted to compare said measurement with a predetermined value to determine whether the predetermined quality criteria are met. Preferably, the estimation means are adapted to determine that the opportunity estimate meets the predetermined criteria of

  quality when said measurement is less than said predetermined value.

  Thanks to these provisions, the application of the quality criteria is

particularly simple.

  According to another of its aspects, the present invention aims at a method of secondary processing of a set of parameters associated with at least one partition information, resulting from a primary processing of a first set of data, a secondary treatment method characterized in that it comprises: a step of determining dimensions of elementary subsets constituting a partition of a second set of data, step taking

  account the presence of partition information corresponding to the said sub-

  sets, each elementary application corresponding to an elementary subassembly being determined by at least one parameter of said set of parameters, and - an "iterative calculation" step during which, from said set of parameters and said dimensions, it implements on the second set of data, a method of successive approximations converging towards the fixed point of a global contractive application called "second type", the restrictions of the global application to the elementary subsets consisting of said elementary applications, by implementing, for this purpose, at least one application belonging to the group

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  applications consisting of multidimensional applications and

non-linear applications.

  Correlatively, in another of its aspects, the present invention aims a secondary data processing device suitable for the secondary processing of a set of parameters associated with at least one partition information, resulting from the primary processing of initial data carried out by a user. primary treatment device, characterized in that it comprises: input means of the parameters and partition information; data output means; second logical means for transforming the parameters and partition information into data; said second logic means comprising: - "determination" means of dimensions adapted to determine dimensions of elementary subsets constituting a partition of a second set of data, taking into account the presence of partition information corresponding to said sub-sets -sets, each elementary application corresponding to an elementary subset being determined by at least one parameter of said set of parameters, and - means of "iterative computation" adapted to implement, from said set of parameters and said dimensions, a method of successive approximations converging towards the fixed point of a so-called "second type" global contractive application comprising said elementary applications, by implementing, for this purpose, at least one application belonging to the application group consisting of the applications multidimensional and nonlinear applications, said fixed point c constituting a secondary representation of said set of initial data, and delivering the data thus calculated on the means

Release.

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  With these provisions, it is possible to perform a secondary processing of a set of data comprising a set of parameters resulting from the primary processing of initial data in a relatively simple manner since it suffices to implement a method of successive approximations, in itself - even known, converging towards the fixed point of a global contractive application. The convergence process thus implemented makes it possible to approach a representation of the initial data set. One can, advantageously, set an error threshold, from which it will be considered that the precision required for the representation of the whole

  o10 initial data is reached.

  In the hypothesis, implemented in the preferred embodiment, o the global contractive application used during the primary treatment and the overall contractive application used during the secondary treatment are identical, the representation of all the initial data to which results after the secondary treatment is actually a restitution of said initial data, with, if necessary, the predetermined error mentioned above. Thus, if the initial data set is relative to an image, the primary processing makes it possible to transform and / or compress this data, for example for storage or transmission, and the

  secondary treatment can restore them.

  In the hypothesis that the global contractive application implemented during the primary treatment and the global contractive application implemented during the secondary treatment are of distinct types, the secondary representation does not constitute any restitution of the initial data but constitutes in reality a transformation of these. This will be the case for example when an initial image in color has been the subject of a primary treatment and is then represented by an image at a gray level: in both cases it is indeed the same image, however the data relating to the image obtained at the end of the secondary treatment are no longer of the same type

as initial data.

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  Thanks to these provisions, the successive approximation method used for the secondary treatment is implemented in a particularly simple manner from the parameters obtained at the end of the primary treatment. The inventors have been able to observe, in the field of image processing with compression, the performances both in terms of the quality of

  the restored image than that of the processing speed recalled above.

  The advantages outlined above with regard to supplementary partitions relate, in a similar way, to the quality of the secondary processing, the partition information making it possible to reconstitute the elementary subassemblies of different dimensions used during

primary treatment.

  Another aspect of the invention combines, within one and the same treatment method, a primary treatment phase and a secondary treatment phase. These arrangements may be particularly advantageous in the case where it is desired to transform data of one type into data of another type. Thus, for example, in some image processing applications, it may be useful to be able to transform a color image into a grayscale image. According to this aspect of the invention, such a transformation will consist, on the one hand, in a primary treatment of the color image, followed (immediately or not) by a secondary treatment, of the parameters thus obtained, during which a contractive application so-called "second type" (different from the global contractive application implemented during the primary treatment) will be implemented so as to restore a different type of image, in the example cited, a level image of

  Grey. This is an example of "complex processing".

  The invention also relates to a printer, a photocopier, a camera and a facsimile device comprising a device

  treatment as succinctly set forth above.

  The invention also relates to a memory that stores - parameters and partition information resulting from a primary treatment as succinctly described above and

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  instructions for a software allowing the implementation of a method of

  secondary treatment as succinctly set forth above.

  The advantages of these devices and memory being identical to

  those who are exposed above, they are not remembered here.

  The features, advantages and other objects of the invention

  will also be apparent from the description of the attached drawings in which:

  FIG. 1 schematically illustrates a partition of an image of 512 × 512 pixels in elementary subsets, consisting of squares of 32 × 32 pixels; FIG. 2 schematically illustrates a division of an image of 512 × 512 pixels in a slate covering, consisting of squares of 32 x 32 pixels, offset horizontally and vertically by 16 pixels,

  FIG. 3 schematically illustrates the arrangement of a subset

  elementary set Ki and its four working subsystems L ,, L, L3 and L4, which, in a first embodiment of the invention, are of identical size to that of the elementary subset K, and offset in both directions, with respect to said elementary subset, in a predetermined manner, FIG. 3A is similar to FIG. 3 and schematically illustrates a second preferred embodiment of the invention, in which

  which the arrangement of an elementary subset K, and its four subsets

  work sets L ,, L2, L3 and L4, each dimension of which is twice that of the associated elementary subset Ki, and which is shifted in both directions, with respect to said elementary subassembly, in a predetermined manner; FIG. 4 is a simplified block diagram of a particular embodiment of the device for primary processing of a data set, FIG. 5 is a block diagram of a device implementing the device of FIG. ,

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  FIG. 6 is a simplified block diagram of a particular embodiment of the device for secondary processing of a set of data; FIG. 7 is a block diagram of a device implementing the device of FIG. 6; FIG. 8 is a block diagram of a primary treatment and secondary treatment device; FIG. 9 is a block diagram of another primary treatment and secondary treatment device; FIG. 9A is a simplified block diagram of a particular embodiment of the processing device of FIG. 9; FIG. 10 is a simplified flow chart of compression of a 512 × 512 pixel color image implemented in the device of FIGS. 4, 9 and 9A; FIGS. 11, 12, 12A, 12B, 13, 14 and 15 are flow diagrams illustrating certain operations of the flowchart of FIG. FIG. 16 is a simplified flowchart for decompressing a put color image. implementation of In the device of FIGS. 6, 9 and 9A, FIG. 16A is a flowchart illustrating an operation of the flowchart of FIG. 16. FIGS. 17, 17A and 17B are flowcharts illustrating an operation of the flowchart of FIG. 16. - Figure 18 is a flowchart of a program of

  configuration implemented in the device of Figure 9A.

  FIGS. 19 and 20 are flowcharts illustrating certain operations of the flowchart of FIG. 10 and one of its variants, and FIG. 21A is a representation of a succession of partitions of elementary subsets; Fig. 21B is a partition and parameter information structure representation 30 representing this succession of partitions and - Fig. 21C is a representation of the organization of

  parameters and partition information resulting from primary processing.

  This description is divided into five parts:

  - the first part deals with the general description of the process.

  This part is divided into three sections: In the first section relates to the general theory underlying the invention. It sets forth the mathematical concepts underlying, in a general way, the invention as it can be understood in its most general terms; 10. the second section, in particular in support of FIGS. 1 to 3, shows certain particular characteristics of the first embodiment of the method allowing the primary processing of the data of an image of 512 × 512 pixels resulting in the compression of it. This section explains more particularly the structure of the multidimensional application chosen in this particular mode of implementation and the means allowing to

  calculate the coefficients of this application.

  the third section describes the particular characteristics of the first embodiment of the method of secondary representation of the data of the image, and in particular the restitution of the data thereof to

  from the compressed data obtained after a primary treatment.

  This section discusses the approximation method

  successive implementation here to do this.

  - the second part relates to the description of a first mode of

  realization of a treatment device and it is divided into six sections:

  * the first section deals with the description of a treatment device

  primary of a data set, the second section relates to a device for secondary processing of a set of parameters resulting from the primary processing of initial data. Such a device makes it possible, for example, to restore the image 3 o compressed by the primary treatment device,

  * the third section relates to the description of a device incorporating at the same time

  a primary treatment device and a secondary treatment device,

  * the fourth section deals with the description of a particular organizational chart of

  compression of a 512 x 512 pixel color image implemented in the logic means of the primary processing device,

  * the fifth section relates to the description of two embodiments

  a decompression flowchart implemented in the logic means included in the secondary processing device, and

  ò the sixth section deals with the description of the organization chart of the program

  configuration of the device incorporating a primary treatment device

  and a secondary treatment device.

  - the third part deals with the description of the mode of

  preferred embodiment, implementing work subsets having a size different from that of the corresponding elementary subset. In this part, only the modifications which are made to the embodiment described in the second part are described; in the fourth part, an embodiment variant is described, one of which implements a global contractive application composed of non-linear applications. In this fourth part only the modified elements are exposed with respect to those of the embodiment described in the second part; and in the fifth part, there is described an embodiment variant implementing a quality criterion measured with the help of

the overall contractive application.

  1. General description of the process

  The method as implemented in the first embodiment of the present invention will now be described with reference to FIGS. 1 to 3.

  invention. This description will be made in support of the above figures and a

  number of mathematical concepts belonging in a way

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  general to the theory of analysis and more particularly to those of the

  topology and functional analysis.

  In this particular embodiment, it is proposed to compress the data relating to an image, to arrive at a "primary representation" thereof, then to restore the initial data, that is to say to perform a "secondary representation" "compressed data to obtain a set of data of the same type as the initial data with a predetermined maximum deviation between the data as well as

  restituted and initial data.

  To fix the ideas, here is considered a color image of 512 x 512 pixels with three components, one of luminance and two of chrominance, each having 256 levels. In general, such a color image is captured in the form of three components relating to the three fundamental colors, red, green and blue, and then converted, using conversion matrices well known to those skilled in the art, into components.

luminance and chrominance.

  This digital image requires 512 x 512 x 24 bits to store either, without data compression, 6 Mbit. In order to measure the difference between the initial image and the restored image, it is considered the square root of the mean square deviation, averaged over all the pixels and all the components (classically noted RMSE). The effectiveness of a compression algorithm is expressed

  by the link between the compression ratio obtained for a given difference (RMSE).

  The particular embodiment described here makes it possible to obtain the following efficiency

Table 1

  Number of iterations at RMSE bits / pixel decompression

- 7 7 - 15 0.75

-8 5- 10 1.50

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6 - 8 4 - 8 2.25

7-9 3-7 3.00

7 - 10 2 - 5 4.50

  General theory underlying the invention

  The representation of a set of data, representing

  even physical quantities, such as the data relating to the image described above, especially when it is desired to compress these data on the occasion of said representation, can be analyzed as an approximation

of all the data.

  The invention proceeds from the demonstration, by the inventors, that the fixed point theory can be implemented to achieve such

the approximation.

  It is considered that the approximation of a set of initial data is an operation consisting in searching in a family of candidates for the representation, the candidate (s) which minimizes (s) a predetermined criterion. Most often, the criterion is expressed by a distance between two elements of a metric space, which can be expressed by the following equation: d: (g, h) E x E ---> d (g , h) e R (1) o: - d is the distance function, 2 o - E is a metric space,

  -R + is the set of real positives or zero.

  - g, h are elements of the metric space E, that is to say of the space which contains all the applications of a given domain of definition

  Q c Rq in a Rx application domain.

  The data to be processed are applications of Q c RI 'in' ": g. ' (x, y) E Q c Rq - * g (x, y) E R "

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* O Rq and Rd are produced spaces of R of a given number (n or d) of

  dimensions. The data set to be processed is a metric space E given.

  It will be noted that for example in the context of a 512 x 512 color image at 3 x 256 levels of each of the three components, the data of the initial image are constituted by a correspondence table which at each position (x, y) in the definition domain [0.511] x [0.511] associates three positive values of levels of the luminance components, Y, of red chrominance, Cr, and of blue chrominance, Cb, between 0 and 255. It is observed that these data of the initial image actually constitute an application f EE of a domain of the space R2 in a domain of the space R3 g: (x, y) e [0.511] x [0.511] c R2 -> [ 0, 255] 3 c R3 The problem of the approximation of a set of data to be processed fe E therefore consists in finding in a family of candidates for the representation G c E the candidate or candidates g * in G which minimize the distance (1). This is expressed by the following equation: ## EQU1 ## These candidates belong to the set: PG (f) = g * e GI d (f, g *) = inf (.f, g) xgEGX, (2) o: - Pt is the metric projection operator,

  - inf {...} is the largest of the minorities of the set considered ....

  In the following, it is assumed that the metric space is complete, which guarantees the existence of a single fixed point for each contraction of

the metric space in itself.

  The inventors have shown that candidates for representation can be defined as fixed points relating to contractions, a family of contractions being jointly determined. Under these conditions, the search for the best approximation amounts to determining the fixed point relating to the contraction minimizing said predetermined error criterion.

in this family of contractions.

  These conditions can be expressed as follows:? A E ci (X): d (f, a *) <d (fJ, a), Va Ea (X) (3) oc (X) is the extension to a subset set of contractions X, (Xc ('ON (E)) of the link between a contraction and its fixed point This mathematical relation can be expressed as follows: a: TE (' ON (E) -> te E (4) is the fixed point of the contraction T (T (t) = 1), ('ON (E) the set of contractions of E. The approximation problem can, under these conditions, be reformulated as follows: it is a question of looking for the contraction whose fixed point

  is the best approximation of the initial data.

  It will be observed that in doing so the inventors have moved the problem to be solved since it is no longer a matter of looking for a candidate constituting in itself a better approximation but a

  contraction whose fixed point constitutes the best approximation.

  This can be expressed by the inequation:? T * e X: fc (T) d (f, (T *)) V IEX (5)

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  o X is a subset of contractions of E (X c CON (E)).

  The inventors have thus demonstrated that, in accordance with the general method discovered by them, the essential step to arrive at a representation of data to be processed, especially in the context of data compression, consists in: - constituting a family of contractions capable of transforming the data, and - selecting the parameters of one of said contractions so as to satisfy one or more predetermined conditions, in this case minimizing the distance between the initial data and the fixed point constituting the best

  approximation of said initial data.

  This is, according to the invention, a step of

  "construction" of the global contractive application.

  Then, according to the invention, the parameters thus determined must allow, for the restitution of the initial set of data, the implementation of a method of successive approximations converging towards the fixed point of said representative global contractive transformant of said set of initial data, which allows for the reasons explained above to restore with the best approximation

set of data to process.

  It will be observed that for the implementation of the general method according to the invention, and in particular in the step of constructing the global contractive application, the skilled person has, to constitute the family of contractions capable of transforming the data, a wide range of mathematical application choices in the application group consisting of multidimensional applications and nonlinear applications. In the embodiment described hereinafter, the overall contraction will be piecewise constructed, and for each piece a specific multidimensional linear application will be used. He could use other applications, for example

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  example of non-linear applications. The general method, a particular embodiment of which will be described in detail below, thus makes it possible to

  many possibilities of data processing, in order to represent them.

  We will now describe the means used in the particular embodiment to build the overall contractive application. The inventors have shown that in order to find a contraction whose fixed point constitutes the best approximation of the

  initial data, it was first necessary to search for a constituent candidate

  even a good approximation, which is a practical approach to

solve such a problem.

  The inventors have demonstrated that said practical approach can consist in finding the contraction which minimizes the distance between the initial and transformed data, taking into account a factor of

estimated contraction.

  This reformulation of the problem to be solved can be expressed by the following main optimization problem:? EX d) = min | d [. e - X (6) I - co 1 - con (T) to con (T) is the contraction factor of the contractive application 7: As, in reality, it is sometimes difficult to find the contraction factor of the As a global application, the inventors have found that, in these hypotheses, it is sufficient to solve a simplified optimization problem under which it is necessary to find a global contraction that minimizes the distance between the initial data and their transform. We will observe here

  that the factor l / 1-con (T) is no longer taken into account.

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  This simplified optimization problem is expressed as follows: T EX: d (f, T (f)) = min (Jf, T (f) "T e X. (7)

  First mode of primary processing of image data.

  According to an important characteristic of one of the aspects of the invention as implemented here, the overall contraction is constructed in pieces. To do this, a "partitioning" step is performed of all the data relating to the image, during which said partition is partitioned

  set in m "elementary subsets".

  In the particular embodiment which relates to the treatment

  image, in a general way, we partition the initial image, in m sub-

  elementary images, also called "elementary subsets"

  for the sake of clarity of the description.

  We will recall here that in a general way a "partition" of the metric space Q. amounts to defining the set T = {KiKi c Qui = I .... m} OK /, .. Km are sub- defined in said metric space Q. to meet the following four conditions: 1) the subsets K, must be closed, which is expressed by

Ki adh Ki, i = 1, ..., m.

  2) none of the subsets K, can have an empty interior,

  what is expressed by: int Ki = 0, i = 1 ... i.m.

  2 5 3) their union must produce the closure of the metric space Q considered, which is expressed by: adhQ = UK, I = 1 4) the interiors of each subset K, must be disjoint two by two, what is expressed by:

int K, hint K, = 0 i, .I = l, ..., m, i j.

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  It will also be noted here that the partition of an initial datum of a given type (ge E) returns, in a general way, to define a restriction g K, for each subset Ki of the partition T. This characteristic allows, advantageously, to facilitate the work of constructing the global contraction, by bringing this work back to that of finding elementary mathematical transformations whose object is to allow the restitution of the elementary subset Ki. Indeed, by definition, the subsets of data have less data than the initial set, and therefore it is significantly easier to find mathematical transformations to retrieve these data, again being specified that the set mathematical transformations must, at the level of the whole image, constitute a

global contractive application.

  Consequently, the global contractive application T is thus constructed per piece, each piece being, in accordance with this aspect of

  the invention, a Lipstchizian application.

  It will be observed here, moreover, that these elementary Lipstchizean applications are not necessarily contractive, and that at this level also, thanks to the invention, the person skilled in the art has at his disposal a wide range of mathematical applications to him. to process the data

relating to subsets.

  Note however that in some cases, there will be no need to proceed to this partition, for example when the image gives rise to a

simple geometric structure.

  According to the aspect of the invention described here, for each of the n, sub-

  elementary sets (K1I ..., K ,,), we consider n work subsets (n = 4 in this embodiment). For each of the elementary ni subassemblies made during the partition, the application is built

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  3o Elemental Lipstchizean considered from these n subsets of work. In order to be able to consider the n subsets of work related to each of the m elementary subsets, a "division" of the initial set of data will be performed. This division = {Lú Li c, j = l .... of the data set, which is defined in the metric space Q, must respect the three following conditions: 1) the subsets Lj must be closed, what is expressed by: Lj = adh Lj, j = 1 ..... l 2) None of the subsets Lj can have an empty interior

which is expressed: int L É0, j = 1 ..., 1.

  3) Their union is included in the metric space Q, which is expressed by: U Lj c Q i = l It is observed at this stage that the division thus made includes, on the one hand, the partitions, such as they have been defined above, but also includes, on the other hand, what will be called a "slate covering" (notion known in English as "tiling") for which the Li subsets are likely to overlap, which is expressed by the equation

intL, qint L, 0, ij = 1, ..., l, i. /.

  In the first embodiment, the image of 512 x 512 pixels is, according to an initial partition, partitioned into 256 subsets

  elementary squares of 32 x 32 pixels (see Figure 1).

  According to a habit in the field of image processing, the data is organized as follows: - the coordinate reference point (0,0) is constituted by the point at the bottom left of the image;

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  - the columns (abscissa x) are numbered from left to right;

  - the lines (y-ordinate) are numbered from bottom to top.

  In Figure 1 is shown schematically in the ordinate the rank of some lines of the image and the abscissa the rank of some columns. For reasons of clarity, the scale used on the abscissa and the ordinate axis is not uniform. On the bottom left of Figure 1 the first 9 squares of 32 x 32 pixels are illustrated, so as to highlight the rows and columns constituting the border of the latter. The 32 x 32 pixel squares are an example of a domain partition

  Q = [0.511] x [0.511] where the image under consideration is defined.

  In the first embodiment, the division of the 512 x 512 pixel image into working subsets is illustrated in FIG. 2. It is similar to the partition of FIG. 1, except that the subassemblies of FIG. 32 x 32 pixels are shifted by 16 pixels in both directions, and in each direction of movement, relative to the elementary subsets. In this figure, which illustrates the lower left corner of the 512 x 512 pixel image, the elementary subsets resulting from the partition are shown in bold lines while the subsets of work resulting from the

  division are shown in dotted lines and are hatched.

  In FIG. 2, the work subsets affecting the edges of the image have not been shown. Many solutions exist for

  provide to each elemental subset that is not associated with sub-subsets

  sets of work entirely within the initial image, sub-

  substitution work sets.

  It is noted here that throughout the rest of the description, the choice

  such a solution is applied, as well to the working subsets for the primary treatment, for the secondary treatment and for the complex processing: the points of the subsets of work defined above which do not belong to the image, that is to say those whose at least one of the coordinates is negative, are fictitiously associated with an average value,

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  for example 127 for the luminance component and the possible

chrominance components.

  FIG. 3 illustrates how, in this first embodiment, each working subset Li is linked to a given elementary subset K,. The elementary subset K, having coordinates (v ,, y,) is shown in bold lines, while the corresponding work subsets are illustrated in dashed lines, the other subsets being outlined in fine lines. It is observed that, in this first embodiment, to each of the subsets Ki are connected four work subsets L, (numbered L ,, 10 ..., L4) offset by 16 pixels in both directions. It is actually the four subsets from the division that cover the elementary subset considered (from the partition). The expressions below show the coordinates of a subset Ki and subsets of

work L ,, ..., L4.

  Ki: [xi, x + 31] x [yi, y; + 31] Li: [xi-16, xi + 15] x [vi + 16, yi + 47] L2: x + 16, x + 47] x [yx + 16, xy + 47] L3: [xi-16, xi + 15] x [i-16, yi + 15] L4: [x, + 16, xi + 47] x [yi-16, yi + 15] It will be noted that, in this first embodiment, the subassemblies resulting from the division have the same dimensions as those resulting from the partition; moreover, in this first embodiment, the division of the image into working subassemblies does not constitute a slate recovery but a simple partition because the work subsets have a size identical to the sub-assemblies. -set and that the offset, between a subset of work and the corresponding elementary subset, is equal to one-half of the square subsets

Considered.

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  In particular, a second preferred embodiment will be described in particular with reference to FIG. 3A, in which, according to another aspect of the invention, the work subassemblies have a size different from that of the sub-assembly. elementary set to which they correspond, the division of the image thus resulting in a slate covering. We will now define the global application used in the

  particular embodiment described in support of Figures 2 and 3.

  We first recall that the global contractive application consists of taking an element g from the metric space E to transform it into an element T (g) of the same metric space E, which is expressed by T: g E E -> T (g) EE (8) The belonging of g to the space E (ge E) can also be expressed in the following way: g: (x, y) e Q c R -> g ( x, y) c IR "(9) Indeed, we observe that equation (9) only explains the type of special data considered: at each pair of values (xy) taken in the domain of definition (in In this case, the plane image Q2 c R2) corresponds to a value in the field of application Rd, that is to say three values among 256 levels of the three components, Y, Cr and Cb. In the field of image processing, the definition domain is R2, while the field of application is R, 3 since the color image has three components, one

  of luminance and two of chrominance.

  In the particular embodiment of FIGS. 2 and 3 described above,

  after and in accordance with another aspect of the invention, each "piece" of the global contractive application, that is to say a Lipschitzian elementary application, is a multilinear application of the type:

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  1, T (g) K: (x, y) E Ki -> [T (g)] (x, y) = Ea, (x, y) + h (10) / = 1 o: T (g) Ki the restriction of T (g) to the elementary subset K, n> 1 the dimension of the multilinear application a, ... a multiplicative coefficients h the translation factor L, ú the subsets of work, at a position predetermined by

  report to Ki and related to this subset.

  Thus in the example of FIG. 3, the values g (x, y) of the pixels of coordinates (x, y), are transformed as follows: [T (g)] (x, y) = a ,. g (x16, y + 16) + a2. g (x + 16, y + 16) + a3. g (x-16, y-16) + a4. g (x + 16, y-16) + h (1 Obis) o: g (x, y) is the value of the pixel (x, y) in the image g (x, y) is a pixel of the sub- elementary set K,

  g (x - 16, y + 16) is the value of the corresponding pixel in the sub-

work set L,

  g (x + 16, y + 16) is the value of the corresponding pixel in the sub-

work set L2

  g (x-16, y-16) is the value of the corresponding pixel in the sub-

L3 work set

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  g (x + 16, y - 16) is the value of the corresponding pixel in the sub-

  working set L4 aI, ..., a4 multiplicative coefficients

h the translation factor.

  It can be seen that equations (10) and (10a) above are of a linear and multidimensional nature, that is to say multilinear, the coefficients a, for j = 1, ..., n and b being respectively the multiplicative coefficients and the translation factor. The coefficients (a .... a ,,, b) are here the "parameters", in the sense of

  the invention, the elementary application relating to the subset K ,.

  The set of coefficients (al, .., an, h) K relative to the elementary ni subsets (Ki, ..., Km) constitutes, in this embodiment, "the set of

  parameters "of the overall contractive application, within the meaning of the invention.

  It is recalled that in the particular embodiment, n = 4, which means that only four subsets of work L ,. / = I .... n such as those defined in support of Figure 3, are related to each subset

elementary Ki.

  Thus, for each pair of values (xy) of a given elementary subset Ki, a value calculated from the multilinear equation (10) is associated (see the example of FIG. 3 and equation 10a). ). This is done

  for the set of m elementary subsets (K, ... K ,,,).

  We will now explain how the coefficients of the multilinear application a, j = l ..., n and h are determined for each of the elementary subsets of work K, To solve the problem of simplified optimization (7) it is necessary, d in general, for each elementary subset K ,. minimize the distance between the restriction to the elementary subset K, and its transformed by the overall contractive application. In other words, distances must be minimized:

36 2761553

  d (.fKi, T (f) lKi), i = ... (11) In the particular embodiment, a least squares minimization method is used in the presence of constraints, where the quantity to be minimized is the distance defined in equation (11) and is expressed as: [d (Ki, T (f) K,) 1 = z (o (xy) [T (f)] (x,)) (12) ) (xy) EKi lail <1, i = 1, -.-, n (13)

O p <1 / n.

  By minimizing the expression (12) under the constraints (13), each restriction of T (/) to Ki and at the same time the coefficients ai and

h of equation (10).

  The coefficients aj, b associated with each of the subsets K,

  constitute the primary representation of the initial data set.

  The problem of minimization according to the equations (10) and (12) under the constraints (13), in order to determine the coefficients (a, ..., h) for

  each Ki: i = 1, ..., m will be detailed below.

  For each elementary subset, we consider the objective function 4 K,: R.n + 1- R defined as follows: K (, I, ... (aa ,, h) = _, a ', (xy) - (Y) .. (x ,, ') +. (14) (xY) EK, J = I The constraint minimization problem is therefore to look for the (n + 1) values (al *, .., a , *, b) C c P. "which satisfy: K, min ..., c ,, a) min} v (a1a,>, h) | aa ,,, h) E CI (15) o

  C = {a (, .... a., B) l R "l | -I3 <a, <t3; i =; .... n ..

  Recall first that the resolution of a minimization problem without constraints is well known to those skilled in the art. It is in this case to minimize in general an objective function of the type: 1s P (ci, .... C.) F (xy) - ,, c., (X,.) + I ,, I +, (16) om is the number of parameters of the objective function and when (cI ... c ,, l) traverses all the space R '". The vector (cI *, .... nc, *) sought satisfies : Y (c *, .... c. *) = Min I, {(c1, c).)) (C., Cm) ..) c) "This vector (ci * .cc ,,, *) is characterized by the equation of Euler: 2 5 Y (ci, ... c *,) = o, (17)

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  o Y c ..., cm) is the derivative of Y (in the sense of Fréchet). It is a linear and continuous application of R "to R. This last equation is replaced here by the partial derivatives of IY at the point (c .... Cm, with respect to each variable. ) is characterized by: a 1 ((C Cm) = O, (18) i CI ..... C m. = .0..cm Taking into account the particular form of the functional (16), the equations ( 18) are equivalent to: ## EQU1 ## where

(x.y) eK {ni: l.i ..-

  Gm; == Gim: = Z g, (xy) i = 1 .....-? I (x, y) EK Gma = number of points (x, y) in K, Si = E gj (xy) F ( xy), i = I. - I (xy) EK

Sm = E F (xy).

(xy) EK

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  Equations (19) form a linear system of easy equations

  to be solved by various methods well known in mathematics.

  The resolution of the problem of minimization (15) of the functional (14) under the constraints (13) will comprise the following steps: a) Solving the problem of minimization without constraints of the functional (14) on pR "+" by the described method supra by equations (16) to (19) The solution will be noted (aI ..., n ,,, b) e R "b) Si (al, ..., an, b) e C, so if -3 <a, <[3; i = I ..., n then the solution sought for the problem described by equations (15) and (16) is found and therefore (a, * ... *, ban) = (.... ,,, b) c) If (ai ..., a1, b) e C, some constraints are violated. This will result in a disjoint partition of the set of indices {1, ..... n} = NVu UVu LV o - NV is the set of indices i E {1, ..., n} for which - , t3 <a, 3 - UV is the set of indices i {i, ..., n} for which [3 <a, - LV is the set of indices k E {1, ..., n} for which ak <-f3 So mathematically expressed: {1, ..., n = NV u UV u LV (20) NV = {{I, ...... Pn} -1 <a,} <. ... (21) {UV {= E {l ,, n}, <-} (22) LV = tE {1, .nk-} n ...... <(23)

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  In this case it is necessary to solve a problem of minimization without constraints described by the equations (16) to (19) where F (xy) = f (x, y) - 1 [g 4L (x, Y) + Y g. AT,. (X.) (24) jEU k EL 1 (c, ... cm) = ZrF (x, y) - mcj. gj (x,) +., (25) (x, y), K o DO m the number of indices in NV, gi = L, expresses that the j-e constant not violated concerns the coefficient a ,.

  The solution of the last problem (24) and (25) will be (c ... c ,,,).

  Finally, the solution sought for the problem with constraints will be a = c,: ij = 1 ..., m-1 oie NVI, (26) ak = ke UV, (27) a, * 1 = -1: I ELV, (28) b * = cm ,. (29) if however (26) respects the constraints. Otherwise, it will be necessary to reiterate

the process.

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  A flowchart allowing the partition of the 512 x 512 pixel image, its division and the calculation, for each of the elementary subspaces K,

  coefficients c, and b is described infra, in support of Figures 10 to 15.

  It is observed here that, when all the elementary subsets have the same dimensions, a compromise must be made. Indeed, when these dimensions are too small, the compression ratio is limited since it is directly a function of the number of

  pixels that are represented by the five parameters associated with each sub-

  elementary set. On the other hand, when the dimensions of

  the elementary sets are important, the quality of the image reconstructed after a secondary treatment of these parameters, may be too limited for a comfortable exploitation of the reconstructed image, the smallest details

  may have been poorly treated during primary treatment.

  In an image, it is common for some areas to have very little detail and to be practically uniform, and for other areas of the image to be highly complex (which can be represented by the variance of the values of each pixel component of the image).

the area under consideration).

  The invention proposes, in addition to the implementation of the

  the above theory, a method of using sub-

  large elementary sets in the most uniform image areas and smaller elementary subsets

  in the least uniform image areas. For this purpose, for each sub-

  elementary set being processed, a criterion of complexity, called "quality", is determined and a partition opportunity estimate is

  performed. When this estimate does not meet the quality criterion, that is,

  say when the elementary subset considered is supposed to have a certain complexity, it is partitioned into smaller elementary subsets which are processed in turn, until a minimum dimension has been reached. In the embodiments described and shown, this partition consists of dividing the subset

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  elementary in four equal elementary subsets, homothetic in shape to that of the initial elementary subset and decalled between them

in each direction.

  First mode of secondary processing of compressed data. We will now describe a first embodiment of the method of secondary representation of a data set constituted by parameters resulting from a primary processing of data, according to the first embodiment of the treatment method.

primary described above.

  In this first embodiment, the parameters resulting from the primary treatment are subject to the secondary treatment, in order to restore,

  with the error rate mentioned above, the initial data.

  In other embodiments, one of which is described below, the purpose of secondary processing is to provide data of a different type than

that of the initial data.

  In a general manner, in the case of restitution of the initial data, an "iterative calculation" step is carried out during which, from said parameters (a1 ....., a), it is set to works a method of successive approximations converging towards the fixed point of the global contractive application (T) this fixed point constituting a representation

  of said initial data set (f E E).

  To implement the method of successive approximations in the context of a restitution, according to the first embodiment of the invention, an arbitrary set of data (xo e E) is applied to the contractive application. global (T *) as defined above (equations (8) and (10)). The same contraction (TM) is then applied to the resulting transform and this process is repeated until the distance

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  between two consecutive transforms is less than a given threshold. This is expressed by the following equation: T * (... T * (T (xo)) ....) = (T *) (X () (30) By applying q times the global contractive application on the result of the preceding transform, we obtain a good approximation of f which is expressed by: (T ') (x0) zf (31) the stop criterion of the iterations being expressed as follows: d ((T * )! (xo), (T *) I + I (xo)) <'(32) os is the tolerated deviation on a pixel multiplied by the number of pixels in the image. Note that to implement the global contractive application (T) amounts to performing the various partitions and divisions of the arbitrary image and successive transforms thereof, so as to be able to implement equation (10) for each of the elementary subsets of the partitions In particular, in support of FIGS. 16 and 17, there is described a flowchart for reproducing an image represented according to the first embodiment of the secondary treatment method of FIG.

The invention.

  In the foregoing description, the overall contractive application

  defined in equations (8) and (10) is used in the data restitution process. Indeed, as the purpose of the secondary treatment described above is, in this embodiment, to obtain a return as faithful as possible

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  initial data, it's the same overall contractive application that's

  used during the restitution stage.

  On the other hand, in the variant described below, in support of FIGS. 9, 9A, 18 and 19, it is desired to obtain, at the end of the secondary treatment, data of a type different from that of the initial data. another application

  global contractive, and / or another set of definition will be used.

  In general, the overall contractive application used during the primary treatment is called "first type"; the one used during the secondary treatment is called "second type". In the event of restitution of the initial data, the global second type contractive application is identical to that of the first type. In the case o during the secondary processing data of a type different from that of the initial data are obtained, the overall contractive application of second type will be different from that of

first type.

  2. Description of a first embodiment of a

  processing device Primary data set processing device A first embodiment of a device for processing a set of data representative of physical quantities and intended to allow a primary representation of said assembly by the implementation of the method described

supra.

  In this embodiment, which concerns a color image processing device, the data of the image at 512 × 512 pixels is inputted, while at the output the device delivers the parameters

  ai, i = 1, .... 4 and h and partition information, relating to each of the sub-

  sets constituting a partition of the image.

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  It should be noted here that the present invention is certainly not limited to a particular image format but allows the processing of images of any size. However, in one embodiment described and shown, the image processed and rendered is an image of 512 x 512 pixels with 256 levels on each of the three components Y, luminance, Cr, chrominance

red, and Cb, blue chrominance.

  In the block diagram of FIG. 4, the coding device carries the

general reference 500.

  It comprises, connected to a data and address bus, designated under the reference 501: a controller (ALU + CTR) 550 incorporating an arithmetic logic unit. This controller is constituted, in this embodiment, by a microprocessor of the type sold by the INTEL Company under the reference i486, a RAM RAM, bearing the reference 510. This memory comprises a number of registers which will be described. hereinafter and a rapidly addressable portion (cache) 514, a program memory 530, of the ROM type, a first register 560 of direct access random access memory (REG 1), a second register 570 of direct access random access memory ( REG 2), an input buffer (IBFR) 590, connected to an input connector 591 and an output buffer (OBFR) 580, connected to a connector of

exit 581.

  In the ROM 530 is recorded a program for processing the input data 591, with compression thereof in accordance with the method described above. The compression program, which relates to FIG. 4, reference 531, is described below with reference to FIGS.

, 19, 20 and 21.

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  All of the means 510, 530, 531, 550, 560 and 570 constitute here an embodiment of "first logical means of transformation" to the

sense of the invention.

  In a particular embodiment, all of these elements are incorporated into one and the same specific integrated circuit (ASIC). In this embodiment, the RAM RAM 510 includes, among others the following registers for the implementation of the program 531: - a register 511 (IM), for storing the image data, - a counter 513 (CNT) used as explained below (figure). the part 514 (CACHE) of the random access memory. This part is a portion of memory addressable very quickly, in which are, as is known, stored the most commonly used data at a given time. The portion (CACHE) 514 of the memory 510 comprises the following registers: a register 515 CSI intended to memorize, at a given instant, the coordinates of the elementary subset K, being processed, of the registers f (L, ) - f (L4) referenced 516 to 519, in which are recorded the values [f (Li)] (x, y) correspond to each point (xy)

  (level among 256 of the component being processed) of the sub-

  work sets LI - L4 associated with the elementary subset Ki considered,

  a register 520 for storing the coefficients a ;, a2. a, a.

  and b, relating to an elementary subset considered K ,, and a register 522 intended to keep dividing factors A corresponding to the number of complementary partitions made to obtain the elementary subset considered K ,,

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  - Registers 521 and 523 to 526, intended to preserve

  intermediate variables of a processing generating the sub-references

  elementary sets forming an initial partition of an image to be compressed, the register 560 (REG 1), intended to accumulate, for each elementary subset, the coefficients ap, a2, a3, a4 and 1h, as well as the possible

  partition information, relative to each work subset.

  register 570 (REG 2), intended to memorize the list of

  addresses of all elementary subsets K ,.

  FIG. 5 shows, respectively connected to the input and output means: a source 592 of uncompressed data, and means 582 users of compressed data.

  The source 592 may include many means within the reach of the skilled person. For example, it may consist of a hard disk drive or floppy disk or compact disks (known as initials CD-ROM). The data of the image to be compressed can therefore advantageously be recorded on the corresponding media: hard disk, floppy disk or CD-ROM (compact disk). This recording can be done

  2o in any manner known to those skilled in the art.

  The source 592 may also be constituted by a video interface capable of delivering the data of the image to be compressed at the input 591. The source 592 may also be constituted by means for receiving the data connected to a transmission network. the source 592 being capable of transforming the received data into a suitable format so that they can be presented at the input of the primary processing device. Similarly, the user means 582 may consist of means for storing the compressed image (hard disk, floppy disk, CM-ROM, etc.) or a simple interface intended to deliver the signal in a known format.

48 2761553

  video, to other user means, such as means for example to transmit this compressed image remotely or to store it. These means 582 may moreover consist in a transmission device of

  data connected to a telecommunications network.

  Device for secondary processing of a set of parameters resulting from the primary processing of initial data. In this embodiment, which relates to the image processing, the secondary processing device is able to restore, from the coefficients a1, a2, a3, a4 and b and partition information, relating to each

  elementary subsets, the initial image, in color.

  It is also capable of delivering the data relating to a grayscale image corresponding to an original image in colors. It is further adapted to provide an image having a number of elementary points different from the number of elementary points of the image processed by the primary processing device, these images being said to be of different definition or resolution. This output data of the secondary processing device is of a different type than the type of the data of the initial image that was the subject of the

primary treatment.

  In the block diagram of FIG. 6, the device for restitution or

  Iterative calculation carries the general reference 600.

  It comprises, connected to a data and address bus, designated under the reference 601: a controller (ALU + CTR) 650 incorporating an arithmetic logic unit. This controller is constituted, in this embodiment, by a microprocessor of the type sold by the company INTEL under the

reference i486.

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  a random access memory RAM, bearing the reference 610, which comprises a certain number of registers which will be described below and a part

  addressable quickly (called "cache memory") 614.

  a program memory 630, of the ROM type. In this memory, are recorded in particular: a program 631 for decompressing the data of the image presented at input 681 in order to reconstruct an approximation of the initial image of identical or different resolution, 10. a decompression program 632 image data for the reconstruction of a grayscale image instead of a color image, and

  a zoom factor z in a "z" register 628.

  The programs 631 and 632 implement the method described above and their organization charts are detailed below in support of the figures

16 to 17.

  a first register 560 with direct access (REG 1), and a second register 570 with direct access (REG 2) identical to those described in support of FIG. 4, an output buffer (OBFR) 690, connected to an output connector 691 and an input buffer (IBFR) 680, connected to a connector

681 input.

  The set of means 610, 630, 631, 650, 560, and 570 constitutes here an embodiment of "second logic means" within the meaning of the invention. The set of means 610, 630, 632, 650, 560 and 570 constitutes here another embodiment of "second logic means" within the meaning of the invention. In a particular embodiment, all of these elements are incorporated into one and the same specific integrated circuit (ASIC).

  suitable for secondary treatment.

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  In this embodiment, RAM RAM 610 includes, among others the following registers for the implementation of programs 631 and 632: - a register 511 (IM), described in support of Figure 4, - a register 621 (RE), for storing the data of an image, - a register (CHTY) 622, intended to differentiate the general secondary processing from a restitution, - a register (IT) 612 intended to memorize the current value of the o10 number of iterations performed to perform the secondary representation, - a register (p) 623 for storing the number of iterations to implement the successive approximation method for performing the secondary image processing, - a 513 counter (CNT) described in support of Figure 4. This counter is used here as explained below (Figure 16), - Part 614 (CACHE) of the RAM 610. This part is a part of addressable memory very quickly, in which are, as is known, stored the most commonly used data at a given time, the portion (CACHE) 614 of the memory 610 includes registers 515 to 520 and 627 respectively identical to the registers 515 to 520 and 522 described in the support of Figure 4,

  - the register 560 (REG 1), intended to store, for each subset

  elementary set, the coefficients a1, a2, u3, t14 and h and any partition information associated with this subset, and the register 570 (REG 2) for storing the list of

  addresses of all elementary subsets K ,.

  FIG. 7 shows, respectively connected to the input and output means: a source 682 of compressed data, and

  means 692 users of uncompressed data.

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  The source 682 may consist of storage means of the compressed image (hard disk, floppy disk, CD-ROM, etc.) or a simple interface intended to deliver them. The means 682 may also consist of a data reception system connected to a telecommunications network. The means 692 may consist, for example, of storage means of the decompressed data or of a simple interface delivering on its output the decompressed data. They may also consist of a device for transmitting the uncompressed data over a network of

Telecommunications.

  Description of a device incorporating a device

  primary treatment and a secondary treatment device In the block diagram of FIG. 8, a device incorporating a primary treatment device 500 and a secondary treatment device

  600 is shown and has the general reference 700.

  This device is capable of parallel processing of image compressions and decompressions. It is therefore composed of the devices described in support of FIGS. 4 and 6. It is in this case the primary treatment device 500 and the secondary treatment device

  600. This type of device is called "full-duplex".

  In another embodiment (half-duplex), the device can perform only primary treatment or secondary treatment but never at the same time. It can furthermore perform a "complex" treatment comprising a primary treatment and a secondary treatment carried out one after the other. The block diagram of such a device is represented in the

Figures 9 and 9A.

  This device which bears the reference 800 jointly comprises the resources of the devices 500 and 600 described above, avoiding duplication. Thus:

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  the registers of the random access memories 510 and 610 described above are incorporated in a same random access memory unit 810, the same read-only memory unit 830 incorporates the programs 531, 631 and 632 mentioned above and a configuration program 831; microprocessor 850 incorporates the means 550 and 650. The configuration program 831 which will be described below with the support of Figure 18 allows the device 800, to achieve: - a compression of the data of a color image, - a data decompression either to restore the initial color image, or to render it with a different resolution, or to deliver a corresponding gray-scale image, and - a complex processing for transforming an image

  is color in a grayscale image.

  Description of a particular flowchart of compression

  This flowchart is illustrated in FIG. 10. FIGS. 11 to 15 are flowcharts explaining certain operations of the flowchart of FIG.

compression of Figure 10.

  The flow charts of FIGS. 11 and 12 also detail operations of the decompression flow chart of FIGS. 16 and 17 which will be described below. References between the parameters refer to

steps of Figure 16.

  It is first recalled that the data relating to the image materialize an application as defined in equation (9) explained above. In the present case, for each pair of values (x, y) (column, line coordinates) taken in the definition domain (in this case at the 512 x 512 pixels) corresponds a value f / (x, y) in the field of application 3, PIR3 ', ie a value among 256 levels relative to each of the three

Y, Cr and Cb components.

  Three series of numbers, each corresponding to the level of one component (ie 512 x 512 = 262,144 values /(.l- l) per component), are organized by scanning the data of the image as follows: - the lines are scanned from left and right;

  - the lines are incremented from bottom to top.

  These three suites are here recorded in the uncompressed data source 592. They can be read on the input port 591 at the

microprocessor control 550.

  In 200, the registers (IM) 511, (CNT) 513 and the two registers (REG 1) 560 and (REG 2) 570 are initialized to the value

zero uniform.

  The files relating to the components Y, Cr and Cb are accessible separately and are provided in a predetermined order, namely: firstly the data of the image considered and relating to the luminance component (Y), then the data of the image relating to the red chrominance component (Cr) and finally the image data

  relating to the blue chrominance component (Cb).

  In 201, a first test is conducted to determine whether

  the counter (CNT) 513 is not equal to 3.

  If not, the program branches to step 202, during which: the counter 513 (CNT) is incremented by one unit; the microprocessor 550 will read on the input port 591 the

next component to be processed.

  Remember that each component, Y, Cr or Cb, is a sequence of 262,144 values f (x, y) corresponding to the level of the component considered for each of the pixels of the image. This suite is

54 2761553

loaded in the register (IM) 511.

  It should be remembered that, in this particular embodiment, each subset of work has as much data as the elementary subsets. The program then branches to step 204 (explained in FIG. 11), during which the initial partition of the image of 512 × 512 pixels will be performed in 256 elementary subsets K i, i = (, ..., 256) of 32 x 32 pixels. This partition is done by determining the

  coordinates (xy) of the lower left corners of each of the sub-m

  K sets, considered. Thus the subset K, illustrated in Figure 3, has coordinates (xi, y), which correspond to those of its lower left corner. Each of the addresses of the lower left corners of the 32 x 32 pixel blocks corresponds to a particular address in the list stored in

  the register (IM) 511 of the random access memory 510.

  The list of these addresses is loaded in the register (REG 2).

  With reference to FIG. 11, after an initialization of a counter constituted by the register i 521 relating to the index of the subsets K, in step 211, the program branches to the test 212 in which it is checked whether the list is complete or not. If not, the program branches to step 213 in which the division factor A, which counts each additional partition that is performed on an elementary subset, is initialized to zero and is determined a variable B as the quotient of an integer division of (i-1) by 16. The rest of the division (variable C () is stored in register 524. The values x, = (C * 32 and ,, = /; 32 are calculated in the course of the operation 214 and temporarily stored in the registers 525 and 526. These coordinates which are those of the lower left corner of the elementary subset K, considered, and the associated division factor A, are stored in memory in the variables (x, y) in the register 570 (REG 2) during the step 215. During the step 216 the counter i is incremented and the

  program then runs the test 212 again.

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  When the test 212 is positive, the program performs the test 205 (FIG. 10) during which it is checked whether the list registered in the register (REG 2) is empty or not. If not, this means that there are still elementary subsets K to be processed and the program is connected to step

206.

  At step 206, the first subset of the list registered in the register (REG 2) is deleted. This subset

  is stored in a CSI register 515 of the RAM 510 cache.

  The program then branches to step 207 detailed in FIG. 19 or, alternatively, in FIG. 20. During this step, a test 255 determines whether the elementary subset considered has the minimum dimensions, that is, in the embodiment described and shown, 2 times 2

pixels, or not.

  When the result of the test 255 is positive, the operation 250 consists in determining the four working sub-images Li associated with the subset of work under consideration. This operation 250 is detailed in FIG. 12. During the operation 250, starting from the address registered in the CSI register and the division factor A, the four neighboring work subassemblies L are searched for. ,, L2, L3, L4 (see Figure 3 for the subsets of work associated with the initial partition). For this purpose, the rule recalled above is applied - each work subset has the same dimensions as the elementary subset to which it is connected, or in each direction: 32 divided by 2 brought to the power A; and - each subset of work is shifted by one-half

  each direction, relative to the associated elementary subset.

  The purpose of the operation 250 is therefore to determine the values / (x, ia) of the component considered associated with each of the pixels of the work subsets L 1, L 2, L 3 and L 4 geometrically bound in a predetermined way to the elementary set considered K, the set of values f (ix.y) related to

56 2761553

  pixels of the subset LI (respectively L, L3 and L4) will be noted below

  (L,) (respectively (L2). (L3) and f (L4)).

  With reference to FIG. 12, for each elementary subset K i considered, the controller 550 reads in the register 570 (REG 2) the coordinates (x 1, y) of the lower left pixel of K 1 at the step 217. in step 218, the arithmetic unit 550 reads the values of the component considered for each pixel of the four work subsets L1 to L4, defined according to the following table: L ,: [xi-16 / 2A, x , - + 16 / 2A)] x [Yi + 16 / 2A, Yi-] + (3x16) / 2 '] L2: [x + 16 / 2A, x -1 + (3x16) / 2] x [Yi + 16 / 2A, Y 1 - + (3x] 6) / 2 "] L 3: [x-16 / 2A, x-1 + 16/2] x [- 16 / 2A, yi-] + I6 / 2 '] L4: [xi + 16 / 2A, x ij-1 + (3x16) / 2A] x [Yi- 16 / 2A Yi_1 + 16 / 2A] It can be seen here that each of the subsets of work here has the same number of pixels as the basic subset

considered, ie (32 / 2A) 2.

  Then, in step 219, the arithmetic unit 550 will seek, for the component, Y, Cr or Cb, during processing, the value corresponding to each of the (32 / 2'A) 2 pixels of LI (respectively L, L3 and L4) and stores all (32 / 2A) 2 values in the register 1 (L,) 516 (respectively 1 (L,)

  517, 1 (L3) 518 et./(L4) 519) of the cache 514).

  Following the operation 250 (FIG. 19), the program performs the operation 251 during which, in general, the parameters a, (in this case ap, a2, a3, a4) and h are calculated using the least squares method with the constraints described above (see equations 12 and 13).

  A simplified description of step 251 is given in

  the flowchart shown in Figure 13. It is recalled that to determine the coefficients a, a2, a3, a4 and h there is a problem of

57 2761553

  minimization of a functional under constraints. Supra it has been seen, in support of equations 14 to 29 that it amounts to iteratively solve two types of minimization problems without constraints. The explanations given above for a general case are put into practice for the determination of the four parameters ap, a2, a3, a4 and of the parameter h. In step 220, the first problem of minimization without constraints is solved. We minimize the functional: K, (ap ... Y) = (h (X, y) E Ki for values (a, ..., a4, b) going through all R5. the least squares method described above by equations (16) to (19) The unique solution to this problem (a ", ..., a4, b) in R5 is the solution of

linear system (19).

  As illustrated in FIG. 14, step 220 is subdivided into four

steps 230 - 233.

  During step 230, coefficients Gi, i = 1,..., 5, j = 1,... Are calculated using the following formulas: Gi 1 = [/ (L i)) (xy). [/ (Li)] (x y) i. = 1 4 (xy) EK, = G, = [(L)] (X y) ...... 4 (XjEK (x, .v) t, '

G55 = 322

  The coefficients [GB] constitute the matrix to be reversed in order to

  solve the linear system of equations (19).

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  The above formulas for determining the coefficients G., are as we see simple additions and multiplications implementing pixel values corresponding to the levels of the component considered, and this for each of the pixels of the elementary subset considered. Similarly, in step 231, the coefficients s.sub.S.sub.5 constituting the second member of the linear system are calculated. The formulas used are: S i, =) EK [(La)] (xy) L f (x, y) S5 = Y f (x, y) (x, y) eK The step 232 uses a classic inversion routine of a system of linear equations, in this case five unknowns. The linear system to be reversed is as follows: (G1 G21 G1 G41 G52 G52 G52 G52 G52 G2 G52 G52 G52 G52 G52 G53 G53 G53 G53 G53 G53 G53 G53 G53 The solution a / .., a4, h will be stored in step 233 in the

  register 520 of the part 514 (CACHE) of the random access memory 510.

  The program then proceeds to step 221 (Fig. 13) o, according to equations (20) to (23), a disjoint partition of the set of integers {1,2,3,4} in NV, UV is determined. and LV defined as

59 2761553

UV = j {c tl, ..., 4} l D <a,}

L V = te {1,, 4 <l <-

  The program then connects to test 222 in which it is checked whether the sets UV and LV are empty. If this test is positive, the values currently present in the register 520 constitute (step 224) the solution

the problem with constraints.

  In the negative, some constraints are active for the solution of the problem with constraints. In this case, (step 223, see FIG.

  there is a need to solve a limited problem.

  It is in this case to minimize under constraints the modified functional: o] y (ci, ... Cm) = z F (y - ci-. [Q- i) lx, i + CI (x, y ) = KI y i15 OF (x, y) = f (x, y) - E E) x, y ^) + E i (t)] (x, y), j6UI 'k el l'

  and m <4 since fewer constraints are active.

  The solution of this problem is (CI .... ',) and is obtained in

  considering equations (16) to (18) and solving the linear system (19).

  The solution of the initial problem with constraints is: ai = Cj:. = I ... m - 1 or i G NI, ak = e - k UV, a / = -: l e LV,

b = c.

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  Step 223 will be described in support of the flowchart of Fig. 15 assuming m = 3. The minimization problem without constraints described in step 223 which is subdivided into four steps 240 to 243. During step 240, coefficients H i = 1,..., 4, j = 1,. 4 by implementing the following formulas: Hji = 1 [(Li A (X, y) [(i] (X, .i 1, i ..... 3 (x, y) eK H4i = Hi4 = [ f (Li)] (Xy) (Xy) EK

H44 = 322

  The coefficients [H ,,] constitute the matrix to be reversed in order to

  solve the linear system of equations (19).

  o10 The above formulas for determining the coefficients Hij ,, are as we see simple additions and multiplications implementing pixel values corresponding to the levels of the component considered, and this for each of the pixels of the elementary subset considered . Similarly, in step 241, the coefficients T ,, T4, constituting the second member of the linear system, are calculated. The formulas used are: Ti = L (Li)] (x, y) F (x, y) ...... 3 (xy) eK T, = F (x, y) (xy) EK L Step 242 uses a conventional inversion routine of a system of linear equations, in this case 4 unknowns. The linear system to be reversed is as follows:

H1 H2, H3, H41 C1 T,

H, 2 H22 H32 H42 c2 = T2

H13 H23 H33 H43I 7K

H, 4 H24 H34 H44 74

  At the end of step 223, it is necessary to review whether the solution thus obtained still satisfies the constraints. To do this, step 221 and test 222 are executed again. This process is repeated until the test 222

be positive.

  In the course of the operation 251, the coefficients a ,, a..i, a4, b are recorded in the register 560 (REG 1). Then the test 205 is reiterated. It is observed here that since the elementary subset has minimum dimensions, no partition information is needed,

  since no additional partition can be made.

  When the result of the test 255 is negative, the operation 252 consists of

  to measure the variance of the levels of the component under consideration, in the

  elementary set considered. Then, operation 253 consists in determining

  a so-called "quality" criterion applicable to the elementary subset considered.

  Preferentially, the definition of the quality criterion consists of the definition

  a threshold below which the quality criterion is considered to be respected.

  Preferentially also, the value of the threshold takes into account the dimensions of the elementary subset considered. In the embodiment described and shown, this threshold is the function corresponding to the following table. Subset dimensions in pixels threshold 2x2 200 4 x 4 160 8x8 100 16 x 16 60 32 x 32 20

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  According to non-represented variants: the value of the threshold is constant irrespective of the dimensions of the elementary subsets or the value of the threshold is an inverse function of a dimension of the

  elementary subset considered.

  The test 254 determines whether the quality criterion is met or not.

  In the embodiment described and shown, it is respected when the measurement of the variance of the levels of the component considered is less than the value of the threshold which corresponds, in the table above, to the dimensions

  of the elementary subset considered.

  When the result of one of the tests 254 or 255 is positive, the operation 250 consists in determining the four working sub-images as explained above. Then, the operation 258 is identical to the operation 251, except that are stored in the register 560 (REG 1) successively partition information worth "0" since no additional partition has

  was performed and the coefficients a ,, a2, a3, a4, b. Then, the test 205 is reiterated.

  When the result of the test 254 is negative, the operation 256 consists of performing a complementary partition of the elementary subset considered. In the embodiment described and shown, this complementary partition consists in dividing each elementary subset into four equal square elementary subsets. For this purpose, during the operation 256, the coordinates of the four points defining the lower left corners of the list are added to the top of the list.

  four elementary subsets resulting from the complementary partition.

  To these coordinates are associated a division factor A which is equal to the division factor of the elementary subset that is partitioned, incremented by the value 1. In addition a partition information worth "1", since a complementary partition has been performed, is stored in the

register 560 (REG 1).

  Following the operation 256, the test 205 is reiterated.

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  It is observed here that, according to general characteristics of the invention, the primary treatment: - takes into account a minimum dimension, during step 255 and includes an "initial partition" step, operation 204, during which, the data set is partitioned into so-called "initial elementary" subsets (Ki), comprises: a) for each elementary subset that does not have said minimum dimension, at least one iteration of the sequence of operations 252 to 205, comprising: a divest opportunity estimation step, operation 253 and test 254, during which an opportunity of dividing said elementary subset is estimated, and when the opportunity estimate does not occur. does not meet the quality criteria, a step of "complementary partition" of said subset into elementary subsets called "intermediate" Ki, operation 256, b) a step of "construction", operations 258 or 251, during from which, for each of the elementary subsets Ki resulting from the last stage of partition, one considers n subsets of work Li, n being nonzero, and one constructs an elementary application of the n subsets of work

  in the elementary subset considered.

  In this regard, it should be noted that the parameters ai, b of the application element were determined in such a way as to: make a global application called "first type" contractive for said set of data, a global application belonging to the application group consisting of multidimensional applications and non-linear applications, the restrictions of the global application to the elementary subsets Ki being constituted by said elementary applications, the fixed point of the global application constituting an approximation of all or part of this set,

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  to allow the implementation of a method of successive approximations converging towards the fixed point of said application

overall contractive.

  The set of parameters ai, b thus determined, and when at least one complementary partitioning step has taken place, a so-called "partition" information, representative of each said complementary partition, then jointly constitutes a primary representation.

said set of data.

  FIGS. 21A, 21B and 21C illustrate the effect of the complementary partitions 1o which are performed on the elementary subsets

  from the initial partition or previous complementary partitions.

  For explanatory purposes, and as an exception to the general rules of the

  description, it is assumed that in the embodiment set forth in FIGS.

  21A to 21C, the minimum dimensions of the basic subsets are

  four times smaller than their maximum dimensions.

  FIG. 21A represents a part of an image, corresponding to twelve elementary subsets referenced B0 to B.1 resulting from the initial partition (operation 204, FIG. 11), in which: the elementary subset B. has undergone a complementary partition into four elementary subsets B1,0 to B1,3, - the elementary subset B13 has undergone a complementary partition into four elementary subsets B1,3,0 to B1,33, - the subset elementary B6 has undergone a complementary partition into four elementary subsets B6.0 to B6,3, 2 5 - the elementary subset B6,1 has undergone a complementary partition into four elementary subsets B6,1,0 to B6 , 1 3, and the elementary subset B11 has undergone a partition

  complementary in four elementary subsets B11 0 to B 1.3.

  Figure 21B illustrates, for elementary subsets as well

  3o partitioned, the partition information that is associated with the sub-

  elementary sets resulting from the initial partition (subsets for

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  which the value of the division factor A is zero) or to the subsets

  elementary elements resulting from complementary partitions.

  Thus, the elementary subsets B0, B2, B3, B4, B5, B7, B8, B9 and B1 are associated with zero partition information, the elementary subsets B1, B6 and B, 1 are associated with partition information. 1, their elementary subsets B1.0, B11 ,, B1 2, B6.0, B62, B63, B11.0, B11.1, B11.2 and B113 are associated with zero partition information, the subsets B1,3 and B6,1, are associated with partition information equal to "1" and the elementary subsets resulting from their 0a complementary partition are not associated with any partition information since the dimensions of these elementary subsets are the

minimum dimensions.

  The dimensions of all these elementary subsets can thus be defined unambiguously by the following partition information: FIG. 21C proposes a representation of the parameters a ,, a2, a3, a4 and b, which, together, are referenced here D and information from

  partition associated with them, using the sequence outlined above.

  It is observed that the sequence of the compressed data corresponding to the portion of the image represented in FIG. 21A comprises: a header, representing in particular the dimensions of the image (worth here 512 × 512 pixels) the initial dimensions of the sub elementary sets (corresponding here to 32 x 32 pixels) and the definition of the minimum dimensions of the elementary subsets (here corresponding to 2 x 2 pixels) and complementary processing information and the possible dimension ratio between the resolution of the luminance component and that of the chrominance components; - following the partition information presented above:

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  associated with any data that correspond to them, during the storage performed during steps 251 (without partition information) and 258 (with partition information), knowing that the partition information of 1 is not associated with any data. The set of operations 205-258 or 205-256 is reiterated as long as the memory (REG 2) is not empty. When the test 205 (FIG. 10) is positive, the program reconnects to the test 201 for the purpose of check if the counter (CNT) 513 is 1o or not equal to 3. If yes, it means that the three components have been processed. The program then connects to the complementary processing determination step 209, during which it is proceeded: on the one hand, to the determination of the utility or not to carry out a complementary smoothing treatment on the image resulting from a secondary processing of the parameters and information of partition and - on the other hand, to the storage of the header of the file of the parameters and information of partition, header including in particular the dimensions of the image, the maximum and minimum dimensions of the elementary subsets, the possible ratio of dimensions between the resolution of the luminance component and that of the chrominance components, and the complementary processing information representing the utility of said complementary processing. To determine this utility, several criteria can be

  used. The first is to compare the minimum dimension of the sub-

  one-dimensional elementary sets that serves as a threshold. When the minimum dimension is greater than the threshold dimension, this means that relatively large elementary subsets (for example 8 × 8 pixels) will be used even if the quality criterion, defined in step 253, is not not respected and it will therefore be beneficial to reduce the edge sensation affecting such elementary subsets. The second is to compare the thresholds used in the table defining the quality criterion with so-called "critical" values, predetermined thresholds. When the thresholds actually used are higher than these critical values, it means that the quality criterion is easily respected on large subset elementary subsets, subset whose edges can be visible. It is then again interesting to provide additional treatment. Then the end step 210 is performed. The parameters of the global down-application are associated with the partition information in the register (REG 1) 560. These parameters constitute a primary representation of the initial data that was stored in the

data source 592.

  The following performances were observed on a 512 x 512 pixel color image at 256 levels per component: 15. Starting data: 3x 512x512 x 8bit = 6291456 Number of incoming data: 3x 256x (4x64 + 10) ) = 204288 therefore: 2 o - compression ratio: 30 - number of bits per pixel: 0.78 Processing time:

3 x 256 x 80 msec.- 61 sec.

  (80msec = unitary calculation time of u1 ..... 4,)> Of course, the invention applies equally to the primary processing of grayscale images (having a single component) as well as

  that of color images (having several components).

  Description of two embodiments of a flowchart

decompression

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  The program flowchart 631 for reconstructing the data of the original color image will be described with reference to FIGS. 16 and 17. During the operation 400, FIG. 16, the registers (IM), (RE) and (IT) of the random access memory 610, the two memories (REG 1) 560 and (REG 2) 570 are initialized. , and counter (CNT) 513, at the value

zero uniform.

  The test 401 determines whether the content of the counter 513 (CNT) is or l0 not equal to 3. When the result of the test 401 is positive, the three components have been restored and the decompression program is finished. The

  program then performs the test 416 described below.

  If not, the program performs the operation 403 in which the compressed data of the input memory is loaded into the memory (REG 1) 560. It is recalled that the compressed data is formed of a series of five or six numbers, namely the coefficients al, a2, a3, a4 and b and, optionally, partition information relating to each elementary subset Ki. In the case of a 512 x 512 pixel color image, each component was compressed into suites during the

  primary treatment as implemented by the program 531 described above.

  This sequence of number sequences is loaded into (REG 1) 560.

  During the operation 420, the zoom factor z is read in the ROM 630. It is noted here that the selection of the zoom factor z can also be done by any means within the reach of the skilled person. In particular, it could be done by means of a switch (not shown) arranged on the housing of the secondary treatment device object of the present invention, multi-position switch each corresponding to a predetermined zoom factor. This switch would send the appropriate signals to the RAM RAM 610, so as to load the values indicated in a register not shown z. This initialization can

69 2761553

  also be made in similar conditions by means of a keyboard (not shown), with technical provisions not shown but

well known to those skilled in the art.

  The program then performs the operation 404, during which it is proceeded to the creation of the list of references of each elementary subset. It is in this case a list of coordinates (xi, yji) of the lower left pixel of each elementary subset K ,, whose number of pixels is ((zx 32) 12 /) 2 pixels, the division factor A being recalculated according to the partition information as exposed with the primary processing. This list is determined by taking into account the partition information that is associated with each elementary subset as well as the zoom factor z that is associated with the entire image resulting from the

secondary treatment.

  It is noted here that the zoom factor z is a multiplicative factor that applies to the dimensions of the reconstructed image during secondary processing from the parameters from an image processed during a primary compression process. This multiplicative factor also applies to the dimensions of each elementary subset, whether it comes from the initial partition or complementary partitions, and to each dimension of

  subset of work associated with one of these elementary subsets.

  When a ratio between the resolutions of the luminance components has been transmitted in the header, the zoom factor z is applied to the luminance and the product of the zoom factor z by said ratio is applied to the chrominance, such that all the data sets on

  which one rebuilds a component have the same resolution.

  According to the invention, no zoom factor z causes a pixel duplication forming the appearance, in the image

rebuilt, of uniform pavers.

  The program then branches to step 406 during which:

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  according to the mode of implementation of the invention described here, an initial arbitrary image is stored in the register (IM) 511 of the random access memory 610. In the present case of decompression of a color image where each component has 256 levels respectively having values 0 to 255, the register (IM) is initialized to the numerical value 128 (corresponding substantially to the average value between 0 and 255) for each pixel for the first component processed. For the following components, we use

  as initialization the result previously obtained.

  the register (IT) 612 is initialized with a value p) read in the first register 623 of the RAM 610. The number of iterations is recorded in the register (p), taking into account the desired RMSE (see table 1 above). of the

  general description of the process). The inventors have indeed found during

  of tests with the prototype that, to obtain a given RMSE from a compression ratio, a limited number of successive iterations during the approximation calculation was necessary. Typically: 2 <p <10; however for

  very complex images p can have a higher value.

  the counter (CNT) 513 is incremented by one unit.

  The program then executes a number p of iterations referenced

  on the loop 450 to allow the return of a component of the image.

  The program first connects to the 407 test during

  which one verifies if the contents of the register (IT) 612 is positive and not null.

  If the test 407 is positive, the program connects to the test 408 during which it is checked whether the list registered in (REG 2) 570 is empty or not. If the test 408 is negative, the program branches to step 410 and executes it until all the elementary subsets K,

have been treated.

  The detail of step 410 will now be described in FIG.

  Step 410 itself includes steps 411 to 415:

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  In step 411, the coordinates (xi, yi) corresponding to the elementary subset Ki considered are removed and copied into the CSI register 515. In parallel, the coefficients (a ,, ..., a4.hbrelatives to the elementary subset considered are copied from the register (REG 1) to the register 520 of the part 614 (CACHE) of the random access memory 610. The purpose of the step 412 is to determine the work subassemblies linked geometrically and in a predetermined manner to the elementary set Ki taken into account, taking into account that each working subassembly has the same dimensions as the elementary subset considered (thus taking into account the zoom factor z) and is shifted, relative to

  to this elementary subset, of a half-size.

  This step comprises the same operations as in step 250 described above with the support of Figure 12. The values / (L), / (L2). / (L,) and / (L4) relative pixels respectively to L ,, L2, L3 and L4 are respectively copied in the registers 516, 517, 518 and 519 of the part 614 (CACHE) of the

RAM 610.

  The program then branches to steps 413 and 414 in which for each pixel (x, y) of K the value úai. [F (Li)] (x, y) + i = 1 is calculated using coefficients stored in the register 520 and data f (L,) ..., f (L4) stored in the registers 516 to 519, (step 413) and

  stores (step 414) this value in the register (RE) 621 of the RAM 610.

  If the test 408 is positive, the contents of the register (RE) 621 are copied to the register (IM) 511, and the contents of the register (IT) 612 are decreased by one unit. The test 407 is again carried out. As long as this test is positive, it means that the number of iterations predicted by the number recorded in the

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  register (p), is not completed and operations 408 to 410 are repeated.

  When the test 407 is negative or zero, the number of iterations planned is completed, for the component being processed, and the program leaves the loop

  450. This component is therefore decompressed.

  Step 405 which consists of copying the contents of the register (IM) 511 into the output buffer (OBFR) 690 is carried out.

then branch to the 401 test.

  As long as the 401 test is negative, it means that there is at least

a component to decompress.

  It can be observed that for the second and the third components, the register (IM) 511 is not initialized again. The register (IM) has in fact the list of values corresponding to each pixel for the previously decompressed component. This value list is the initial arbitrary image for the next component. Figure 16A illustrates in this regard

the progress of step 406.

  However, according to a variant not shown, it is proceeded in parallel manner to the processing of the three components, Y, Cr and Cb, of the image, taking as initial data set, a set of

arbitrary data.

  It will be observed here that, according to general characteristics of the invention, the secondary treatment comprises: a step of determining dimensions of elementary subsets constituting a partition of a second set of data, operation 404, step taking into account account the presence of partition information corresponding to said subsets, each elementary application corresponding to an elementary subset being determined by at least one parameter of said set of parameters, and - an "iterative calculation" step, operation 450 or 407 at 410, during which, from said set of parameters and said dimensions, is implemented, on the second set of data, a method of successive approximations converging towards the fixed point of an application

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  global contractive, global application restrictions to subassemblies

  elementary Ki being constituted of said elementary applications.

  In FIG. 16A, during the test 430, the counter 513 (CNT) is tested. If its content is equal to zero, this means that it is the first component, that of luminance, and the register (IM) 511 is initialized to 128 for each pixel (step 431). The register (IT) is initialized to the value p

(step 432).

  If the content of the counter 513 (CNT) is greater than zero, it means that at least one component has been decompressed and in step 433 the register (IM) 511 is loaded with the contents of the register (RE). 621, that is to say with the values corresponding to the component previously decompressed. This makes it possible to decrease the number of iterations p by two units (see step 434 where the initialization is done (IT) at the value p-2) because the initial image is very close to the final image. The calculation time is decreased thanks to this

feature.

  The counter 513 (CNT) is then incremented by one unit (step 435). When all three components have been decompressed, the 401 test is positive. The test 416 then consists in determining whether: either the complementary processing information present in the header of the parameters and partition information is representative of a utility of performing a complementary processing, or the zoom factor z has a value that makes complementary processing useful (z being, for example, greater than or equal to 4)

2 5 or not.

  When the result of the test 416 is negative, the end step 402 is performed directly. When the result of the test 416 is positive, the operation 417 of complementary processing is performed. This operation 417 consists of an operation known to those skilled in the art under the name of "post-processing", which refers to a processing performed after the image decompression illustrated in FIG. 16. This processing comprises, in a known manner , filtering

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  space, intended to reduce the possible border sensation of the sub-

elementary sets.

  Preferentially, the parameters of this filtering are functions of the dimensions of the processed subset. For example, the dimensions of the filter used are proportional to those of the subset considered, on the one hand, and the number of pixels on which this filter applies is proportional to each dimension of the elementary subset considered, other share. According to each of these examples, the zoom factor intervenes in the parameterization of the

* additional treatment.

  At the end of the operation 417, the end step 402 is performed. During the end step 402, the data relating to each of the three components are, in turn, copied to the output buffer (OBFR) 690 where they are transferred to the data user means.

decompressed 682 (Figure 7).

  It is observed here that, in order to obtain a reconstructed image in grayscale, without color, it suffices to perform a primary treatment only on the data resulting from the primary treatment of the luminance of the color image, this limitation being elsewhere referred to as program 632.

  Description of the organization chart of the program

  configuration The diagram of the configuration program implemented in the device will now be described in support of FIG.

800 of Figures 9 and 9A.

  The configuration program is referenced 831 to

Figures 9A and 20.

  The device 800 illustrated in FIG. 9A has four modes of

  3 o operation which will be detailed below.

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  The operating mode of the apparatus is first selected (step 832). Mode selection is done by entering the MOD 822 register, a value equal to 0, 1 or 2 and in the register (CHTY) a value equal to 0 or 1. This recording can be done by any means within the range of the skilled person. In particular, it could be done by means of a switch arranged on the housing of the apparatus 800 at four positions each corresponding to the desired operating mode. This switch would send the appropriate signals to the RAM 810, so as to load the values indicated in the MOD or (CHTY) registers. This initialization can also be done under conditions

  similar by means of a keyboard, not shown in Figure 9A.

  In step 833, a first test is performed on the register MOD for the purpose of determining whether or not its content is equal to zero. If the test 833 is positive, it means that the mode of operation chosen is the first of those mentioned above and the program 531 is implemented from data supplied from the data source 810, the compressed data being delivered in output 881 to means data users

compressed 860 (Figure 9).

  If the test 833 is negative, a test is carried out at step 834.

  for the purpose of determining whether the contents of the MOD register are equal to 1.

  If the 834 test is positive, then an 840 test is performed on the

  register content (CHTY) for the purpose of determining whether or not it is 1.

  If the test 840 is negative, it means that the device of FIGS. 9 and 9A is in the second mode of operation, that is to say in the one where it is used for restoring the original data of a color image. from parameters (compressed data) and partition information, provided at input 881, from a source 861 (FIG. 9). The decompressed data output 892 of the device 800 is intended for

  means users of uncompressed data 820.

  If the test 840 is positive, this means that the device 800 is in the third mode of operation, that is to say the one where it is used to carry out a secondary processing of compressed data and to deliver data of another type. than that of the original data, in this case data relating to a gray-scale image corresponding to an original color image. In this case, the program 632 is implemented from parameters and partition information delivered by a compressed data source 861. The decompressed data is output 892 and

  fed to user means 820.

  If the test 834 is negative, it means that the content of the register MOD is equal to 2. The device 800, which is then in its fourth mode of operation, is used to transform a color image into a grayscale image. This is an example of a complex treatment within the meaning of the present invention, comprising a primary treatment phase and

a secondary treatment phase.

  Thus, in the embodiment described herein, in accordance with this aspect of the invention, the primary treatment and

  secondary treatment are implemented sequentially.

  The program 531 makes it possible, from data delivered by an uncompressed data source 810 on the input 891 of the device 800, to compress these data, in order to obtain parameters a ,. b, A relative to 20 each of the elementary subsets K, of the original image. These parameters and partition information are, in accordance with what has been described above with the support of FIG. 10, all present in the register (REG 1) 560 at the end of the program 531. The main program of FIG. so

  a direct connection at the end of step 404 of program 631 described above.

  The transformed data is then present on the buffer register (OBFR) 893 of the device 800 and transferred to the means 820 users of uncompressed data. These data are those relating to a gray-scale image corresponding to the color image whose data

  were transferred to device 800 from source 810.

  It will be noted that the subroutine comprising all the steps 404, 452, 406, 450, 405 and 402 of the program 632 constitutes here a particular embodiment of a secondary treatment method within the meaning of the invention. It is this particular sub-program that is implemented here as a result of program 631 to constitute an example of a treatment.

  "complex" within the meaning of the present invention.

  3. Description of a preferred variant implementing

  subassemblies of work having a size different from that of the corresponding elementary subset When the work subsets have the same dimension as the elementary subsets to which they are associated, and the contractive application is linear on each subset of work, the reconstructed image can only have in the elemental subset

  considered to be a greater complexity than the ones it has in each

work set.

  In addition, the convergence of the approximation method

  successive can be relatively slow.

  For these two reasons, and at least in the case of the implementation of multilinear contractive applications, it is preferable to use subassemblies of work having dimensions greater than those of

elementary subsets.

  Also, will now be described in support of Figures 3A, 10, 11, 12A, 13 to 16 and 17A, a preferred embodiment of the method and device described supra, wherein at least a subset of work has a size different from that of the corresponding elementary subset. In the particular embodiment of this variant, four subsets of work are associated with each elementary subset, these four subsets of work having dimensions greater than

  those of the corresponding elementary subset.

  The image to be processed is here an image of 512 x 512 pixels initially partitioned into square subsets of 32 x 32 pixels,

  in accordance with what has been described supra in support of Figure 1.

  We will now describe the initial division of the image into sub-

  work sets, knowing that each complementary partition of an elementary subset gives rise to the definition of working subsets of dimensions proportional to that of this elementary subset. The

  subassemblies are twice as large as sub-assemblies

  elementary sets, so that the 512 x 512 pixel image is divided into 64 x 64 pixel square subsets. However, in order to

  that to a given elementary subset correspond to four subsets

  sets (see Figure 3A), the offset used for the division of the image is 32 pixels, the division of the image then resulting in a

  slate recovery (in English "tiling").

  In FIG. 3A, the elementary subset K, whose coordinates (xiy) is illustrated in bold lines, while the subsets of

  corresponding work are shown in dotted lines, the other sub-items are

  sets being sketched in fine lines. It is observed that, in this embodiment, to each of the subsets Ki are connected four working subsets Li (numbered L ,, ..., L4) offset by 64 pixels in both directions and arranged symmetrically with respect to the subassembly. Ki considered. It is actually the four subsets derived from the division that cover the elementary subset considered (from the initial partition). The expressions below show the coordinates of a subset K, and work subsets L ,, .... L4, for all values of the division factor A.

Table 2

  Ki: [xi, xi-1 + (32 / 2A)] x [Yi, yi-1 + (32 / 2A)]

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  L1: [xi - (48 / 2A), x -1 + (16 / 2A) x [yi + (16/2), Yi -1 + (80/2 "')] L2: [xi + (16 / 2A), X -1 + (801 / 2A) x [yi + (16/2), yi -1 + (80 / 2A)] L3: [xi (48/2), xi -1 + (16 / 2A) ] x [yi - (48 / 2A), Yi -1 + (16/2)] L4: [xi + (16/2), x -1 + (80/2] x [yi - (48 / 2A) , y -1 + (16/2 ")] We recall here that the points of the subsets of work defined above that do not belong to the image, that is to say those whose one at least coordinates are negative, are fictitiously associated with a

  average value, for example 127, for each component.

  The compression and decompression devices used to implement this variant embodiment are similar to those described in support of FIGS. 4 and 6. However, the programs 531 and 631 are

  modified as will be explained below.

  With regard firstly to the compression program 531 is described supra with the aid of FIG. 10, its structure is preserved. Only changes the operation 250. This modified operation 250A will be described below in support of

of Figure 12A.

  At step 250A, the search for the four subsets

  neighboring work sets L ,, L2, L3, L4 (see FIG. 3A) from the address registered in the CSI register. For this purpose, the rule recalled above is applied. The purpose of step 250A is to determine the values f / (xy) of the component considered, associated with each of the pixels of the working subsets L ,, L2, L3, L4 geometrically linked and in a predetermined manner to the set elementary considered Ki. The set of f (xy) values related to the pixels of the subset L, (respectively L2, L3 and L4) will be noted hereinafter / '(L,) (respectively) / (L2), / (L3) and .f (L4)) according to the notation used above. The essential element that differentiates step 250A (FIG. 12A) from step 250 (FIG. 12) lies in the fact that the set of values

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  represented byj (Li), i = I, .... 4 relates to working subassemblies L ,. i =

  1, .... 4 which have a size different from that of the elementary subset K ,.

  In order to be able to carry out the comparison operations with the subassembly Ki, the sets (L,) must be brought to the same size. Several methods are available to those skilled in the art. In this embodiment where the size of the work subsets is 64 × 64 pixels and that of the elementary subsets of 32 × 32 pixels, a mean value per square of 4 pixels is retained. The set of these average values will be noted for a set of working Li considered: ÀL i2). The detailed organization chart of

  L0 this step is shown in Figure 12A.

  Referring to FIG. 12A at step 317, copy to the unit

  arithmetic 550 the coordinates (xi, y) of the lower left pixel of the subarray

  elementary set Ki as well as the division factor A, and stores them in the register (REG 2) 570. Next, the arithmetic unit 550 determines the coordinates of each pixel of each subset of

  work according to Table 2 as indicated in step 318.

  In step 319, the arithmetic unit 550 will seek, for the component being processed, the value corresponding to each of the (64 / 2A) 2 pixels of L1 (respectively L2, L3 and L4) and stores the set (64 / 2A ') 2 values in the register / (L,) 516 (respectively f / (L2) 517, / (I, /) 518 and

/ (L4) 519) of the cache 514.

  In step 320, arithmetic unit 550 processes each square of 2 x 2 values of J (L,) and substitutes a corresponding value of / 41, I) for register 516. In this embodiment the value of / ( l corresponding will be obtained by averaging the values of said square of 2 x 2 values of

  f (L /). The other sets.f (L2) ..., .. (L4) are then treated in the same way.

  In step 321, the values of f (L) ...... 1 (L4) are stored in the part 514 (CACHE) of the random access memory 510, in the registers./(L,) 516

at (L4) 519.

  The program then branches to step 208 (FIG. 13) during which, as indicated above, the parameters ai (in this case aI, a2, a3, a4) and b are calculated by implementing the method of least squares with the constraints described above (see equations 12 and 13). However, in this embodiment, the value of a will be smaller than the value. It is observed that this latter value is higher than that used in the first embodiment. Indeed, to the extent o,

  In the course of step 320, sub-records 516 to

  substitution work sets whose value of each pixel is calculated as the average of the values of four pixels of the initial image, a contractive application has already been made. The constraints applied to the contractivity of the global application that succeeds this substitution can, in

consequently, be reduced.

  The operation of the compression program is, for the rest, identical to the operation of the compression program 531 described above with the support of FIG. 10. The only difference being that in the registers

  516 to 519, are stored the values (L! /), ...,. (L4).

  In this alternative embodiment, the decompression program operates in a similar manner to the program 631 described above with reference to FIGS. 16 and 17. However, the operation 410 must be modified as

  discussed below and will be referenced as 410A, shown in FIG. 17A.

  The detail of step 410A is described in support of FIG. 17A.

  Step 410A itself comprises steps 459 to 465: Steps 459 and 460 are identical to steps 411 and 412 described above.

  (Figure 17), but they take into account, for the definition of the sub-

  elementary sets and subsets of work the multiplicative factor called "zoom" z which multiplies each of their dimension in a set of

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  data which itself has dimensions that are multiplied by this

zoom factor.

  The program then branches to steps 461, 462 and 463 in which the values f (L,) .... f (L4) are determined. Then at step 462 the values (L), L4, L4) are determined. To do this, the arithmetic unit 550 processes each square of 4 values of f (L,) and substitutes a corresponding value of <L / 2) for the register 516. In this embodiment, the value of (Lj) corresponds to is obtained by calculating the average of the values of said square or any other low-pass filtering well known to those skilled in the art. The other sets f (L2) ..., F (L4) are then treated in the same way. At the step of 463, for each pixel (x, y) of K, the value - a [t (t)] (xy) + / i = l is calculated using the coefficients of 520 and the data (Li) ...... 1 (L4) from 516 to 519, (step 462) and this step is memorized (step 463) at the corresponding pixel

  in the register (RE) 621 of the RAM 610.

  Finally, step 464 is identical to step 414 (FIG. 17).

  The operation of the modified decompression program as explained above in support of FIG. 17A is otherwise identical to the operation of the decompression program 631 described above.

of Figure 16.

  In this variant embodiment, it is also possible to carry out a complex process for transforming data, as described above with the support of FIG. 20, by implementing the programs of FIG.

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  compression 531 and decompression 631 modified as described above at

  the support of Figures 10, 11, 12A, 13, 14 and 17A.

  4. Description of a variant embodiment

  implement a global contractive application composed of non-linear applications In this variant embodiment of the methods and devices according to the invention, it is implemented a global contractive application

  composed of non-linear applications.

  In this variant embodiment, which also concerns compression and decompression of images, the image to be processed is also a

  image 512 x 512 pixels. This image is initially partitioned into

  elementary sets and divided into subsets of work the same

  way than what is described above in support of Figures 1 to 3.

  We will now define the global application used in a

  particular embodiment of this variant embodiment.

  According to this aspect of the invention, each "piece" of the global contractive application is a nonlinear Lipschitzian elementary application of the type: I1 T (f) Ki (x, y) E Ki -> [T (f )] (x, y) = a, [] ,, (xy) + / / = I i = 1 (10b) o: 1T (/) Ki the restriction of T (f) to the elementary subset K, g1 fJ.g. [/] are nonlinear transformations of f (gi e F (E, E) such as fractional or integer powers of

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  f (eg g [f] = / f) n> I the number of work subsets (n = 4 in this embodiment) a, ... a multiplicative coefficients b the translation factor LI ,. ..Ln the work subassemblies, at position predetermined by

  report to Ki and related to this subset.

  It can be seen that the above equation (10b) is nonlinear in nature, essentially because of the nonlinear transformations, g ,, the coefficients aj, j = 1, .... n and b being respectively the multiplicative coefficients and the translation factor. The coefficients (a ..., u, hb) are here the "parameters" within the meaning of the invention of the elementary application relating to the subset Ki. The set of coefficients (a1 .... an, b) Ki relating to the m elementary subsets (Ki .... Km) constitutes here also the "set of parameters" of

  the overall contractive application within the meaning of the invention.

  It is recalled that, in this embodiment, n = 4, which means that only four work subsets L / j I = ... 1 such as those defined in support of FIG. each subset

elementary Ki.

  Thus, for each pair of values (x, y) of a determined elementary subset K, a value calculated from the nonlinear equation (10b) is associated. This is done for the set of elementary ni subsets (K, ..., K ,,,) resulting from the initial partition as well as from

  2 5 additional partitions, as described supra.

  To solve the simplified optimization problem (see above, in particular equation (7)) which makes it possible to determine the coefficients of the nonlinear application ai, j = I, .... n and h for each of the subassemblies.

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  elementary work Ki, it is necessary, in general, for each sub-

  elementary set Ki, to minimize the distance between the restriction

  elementary set Ki and its transformed by the overall contractive application.

  In other words, it is necessary to minimize the distances d (f [Kii, T (f) [1Ki), i = I, ... m (11) In this respect, the theory put forward in support of

  equations (12) to (29) in the part relating to the general theory.

  Furthermore, it will be observed that, in a general manner in this variant embodiment, the method of secondary representation of the parameters resulting from the primary processing, of initial data, according to the variant described above, implements the general principles described. supra

  in support of equations (30) to (32).

  The compression and decompression devices used to implement this variant of embodiment are similar to those described above with reference to FIGS. 4 and 6. However, the programs 531 and 631

  are modified as will be explained below.

  With regard first of all to the compression program 531 described above with the support of FIG. 10, its structure is preserved. Only changes the step 251 relative to the calculations of the coefficients. This variant of step 251 (referenced as 251B) will now be described in particular in support of the

Figure 12B.

  Step 251B comprises steps 322 and 323 respectively identical to steps 217 and 218 described above with the support of FIG.

  step 324, the values (l) .... (L,) are read in the register (IM) 511.

  In step 325, the values g, 1 [f (L,) J, g, 4 [f '(L4) are determined by calculating the formula

g, [(L,) = (Li).

86 2761553

  Finally, in step 326, in the registers 516 to 519 of the part 514 (CACHE) of the random access memory 510, the values g1 [f (L)} are stored in memory 5 5 (g4 [f (L4)]. of the compression program with the modified operation 250 as just described is, for the remainder, identical

  operation of the program 531 described supra with the support of Figure 10.

  Similarly, in this alternative embodiment, the decompression program operates in a similar manner to the program 631 described above with the aid of FIGS. 16 and 17. However, the operation 410 must be modified as explained hereinafter. This new operation is referenced 410B and is illustrated

in Figure 17B.

  The detail of step 410B will now be described in support of FIG. 17B. Step 410B itself comprises steps 471 to 475: In step 471, the coordinates (x ,, yi) of the elementary subset Ki considered are removed and copied to the CSI register 515. The coefficients ( al ,.

  , a4, b, relating to subsets K, considered are copied from the register (REG 1) to the register 520 of part 614 (CACHE) of the .. DTD: RAM 610.

  The purpose of step 472 is to determine the geometrically and predetermined working subsets of the elementary set Ki considered. This step comprises the same operations as in step 250 described above with the support of FIG. 12. The values g1 [f], lg2 [], 2 g3 [f1] | and g4 I [f] 4 relative pixels respectively to LI, L2, L3 and L4 are respectively copied in the registers 516, 517, 518

and 519 (CACHE) 614.

  The program then branches to steps 473 and 474 in which for each pixel (xy) of K is calculated the value i = 1 4 ai [gl [] | / x y + using the coefficients kept in the register 520 and the data f (L) ..., f (L4) stored in the register 516 to 519, (step 474) and this value is stored at the corresponding pixel in the register (RE) 621 of the

RAM RAM 610.

  In this variant embodiment, it is also possible to carry out a complex process for transforming data as described above with the support of FIG. 20, by implementing modified compression programs 531 and decompression programs 631 as described herein. - top to

the support of Figures 12B and 17B.

  5. Description of a variant embodiment

  A quality criterion measured using the global contractive application is used. According to one variant, the quality criterion used to determine the necessity of performing a complementary partition is not, as shown next to FIG. 19, the comparison, on the one hand, of a statistical measurement made on the levels of the component considered in a basic subset with, on the other hand, a threshold, but the comparison of a measure of difference between, on the one hand, the image obtained after having

  applied a global contractive application, with this initial image.

  This variant is illustrated in FIG. 20, in which the tests and operations common to FIG. 19 bear the same references. In this variant, following the operation 206, the operation 250 is performed, taking into account the present value of the division factor A even if this value is not the value that will ultimately be associated with the sub-factor. -together

  basic element. Operation 250 determines, it is recalled, the sub-

  work sets associated with the elementary subset considered.

  Then, the operation 260 is identical to the operation 251 (FIG. 19) with the exception of the storage in the memory register 560 (REG 1). It therefore provides parameters of the overall contractive application, in the elementary subset considered. The test 255 succeeds the operation 260 and determines, as explained above, whether the elementary subset possesses

minimum dimensions or not.

  When the result of the test 255 is positive, the operation 263 consists in storing in the register 560 (REG 1) the five parameters determined during the operation 260, without associating them with partition information since no new additional partition did not take place. Then the test

205 is reiterated.

  When the result of the test 255 is negative, the operation consists in determining a so-called "quality" criterion applicable to the elementary subset considered. Preferentially, the definition of the quality criterion consists in defining a threshold below which the quality criterion is considered to be respected. Preferentially also, the value of the threshold takes into account the dimensions of the elementary subset considered. In the embodiment described and shown, this threshold is the function corresponding to the following table: subset size in pixels threshold 2x2 800 4 x 4 640 8x8 400 16 x 16 240 32 x 32 80 It is observed here that it is preferential to use a table

  corresponding to a decreasing function.

  The test 254 then determines whether the quality criterion is met or not. In the embodiment described is represented, it is respected when the measurement of the mean square deviation between the component considered and its image by the overall contractive application, a measurement restricted to the elementary subset considered, is less than the value of the threshold which corresponds, in the table above to the dimensions of the subset

basic element.

  When the result of the test 254 is negative, the operation 256 consists of performing a complementary partition of the elementary subset considered. In the embodiment described and shown, this complementary partition consists in dividing each elementary subset into four equal square elementary subsets. For this purpose, during the operation 256, it is added at the top of the list_soutimage the coordinates of the four points which define the lower left corners of the

  is four elementary subsets resulting from the complementary partition.

  To these coordinates is associated a division factor A which is equal to the division factor of the elementary subset that is partitioned, incremented by the value 1. Finally, partition information worth "1" is stored in the register 560. (REG 1) since an additional partition has

Has been carried out.

  When the result of the test 254 is positive, the five parameters determined during the operation 260 are stored in the register 560 (REG 1) with partition information equal to "0" since no partition

complementary took place.

  In the variant shown in FIG. 20, it is interesting to measure the average of the values of the mean squared difference of all the treated elementary subsets for which this difference is measured during the operation 254, to determine the utility of complementary treatment during secondary treatment: when this average is greater than a predetermined overall critical value, it is useful to

complementary treatment.

  It can be seen here that the variants presented with reference to FIGS. 19 and 20 are particularly well combined, while carrying out the operation

  262 of Figure 20 at the end of operations 258 of Figure 19.

  According to variants not shown, the complementary partitions are made by performing a non-homothetic cutting of the elementary subsets, such as for example a cutting into triangles, into two equal rectangles, successively forming

  two rectangles side-by-side horizontally or vertically, ...

  According to another variant, the zoom factor is not uniform. It can thus, for example, have a horizontal value, which serves as a multiplicative coefficient to the horizontal dimensions of the elementary subsets and a vertical value which serves as a multiplicative coefficient to the vertical dimensions of the elementary subsets. The zoom factor can also

  have a value that varies depending on the distance to the center of the image ...

  According to another variant, preferably, the zoom factor is different for the different components of the processed image. For example, the zoom factor is twice as much for each chrominance component as it is for the luminance component. In this case, a preliminary filtering is performed at the primary processing (i.e., compression), which splits the resolution of the chrominance components by a factor of two in each direction, giving each component of each pixel of the lower resolution image the average value of the corresponding component of four pixels of the original image. This factor is transmitted

  in the header in the form of the aforementioned ratio.

  At the same time, the number of initial data used for the reconstruction of the luminance component is, in each direction, twice that for each of the chrominance components. Indeed, it is common that the complexity of the chrominance components is less than that of the luminance component, on the one hand and that this

  complexity is less perceived by the human eye.

  In combination with this latter variant, the primary processing device is adapted to carry out, before the operations illustrated in FIG. 10, a filtering of the chrominance components in order to divide by two

  their resolution in each direction of the image.

  Of course, the present invention is in no way limited to the embodiments chosen and represented but encompasses, on the contrary,

  all variants within the reach of the skilled person.

92 2761553

Claims (52)

  A method for primary processing of a set of data (IM, f) representative of physical quantities, a primary processing method taking into account a minimum dimension and comprising an "initial partition" step (204) during which, partitioning said set of data into so-called "initial elementary" subsets (Ki), a primary processing method characterized in that it comprises: a) for each elementary subset that does not have said minimum dimension, at least one iteration of a sequence of steps comprising: a step of estimating division opportunity during   which an opportunity of dividing the said sub-   elementary set, and - when the opportunity estimate does not meet predetermined criteria known as "quality criteria", a step of "complementary partitioning" of said subset into elementary subsets called "intermediate" (Ki), b) a "construction" step (205 to 209) in which, for each of the two elementary subsets (Ki) resulting from the last partition step, n work subsets (Li) are considered, n being non-zero , and we build a   elementary application of the n subsets of work in the sub-   elementary set considered by determining the parameters (ai, b) of the elementary application so as to: 25. make a global application called "first type" contractive for said set of data, a global application belonging to the group of applications constituted by multidimensional applications and nonlinear applications, the restrictions of the global application to the elementary subsets (Ki) consisting of said elementary applications, the fixed point of the global application constituting an approximation of all or part of this set, to allow the implementation of a method of successive approximations (407 to 410) converging towards the fixed point of said global contractive application; the set of parameters (ai, b) thus determined, as well as, when at least one complementary partitioning step has taken place, a so-called "partition" information, representative of each said complementary partition, constituting   together a primary representation of said data set.   2. Primary processing method according to claim 1, characterized in that, for at least one iteration of said sequence of steps, the opportunity estimate determined during the opportunity estimation step consists of a measurement of a predetermined statistical magnitude   applied to the data of the elementary subset considered.   3. Primary treatment method according to claim 2,   characterized in that the measured statistical magnitude is the variance of the sub- elementary set considered.   4. Primary treatment method according to any one of   Claims 1 to 3, characterized in that at least one iteration of said   sequence of steps is performed after a construction step, the opportunity estimation step comprising an operation of measuring a difference between, on the one hand, the data of the elementary subset and, on the other hand, , the restriction of the overall contractive application in construction to the elementary subset considered, and, when a complementary partition step of the elementary subset is performed, it is followed by a new construction step taking into account said partition complementary. Primary treatment method according to claim 4, characterized in that the difference measuring operation consists of a distance measurement operation.   6. Primary treatment method according to any one of   Claims 2 to 5 characterized in that the predetermined quality criteria   compare said measurement to a predetermined value.   7. Primary processing method according to claim 6, characterized in that the opportunity estimate meets the predetermined quality criteria when said measurement is less than said predetermined value. 8. Primary treatment method according to any one of   Claims 1 to 7 characterized in that said overall contractive application   consists, at least partially, of Lipschitzian applications   elementary elements each related to an elementary subset (K,).   9. Primary treatment method according to any one of   Claims 1 to 8, characterized in that during the step of   construction, for each of said elementary subsets (Ki), n work subassemblies (Li) geometrically related to each other are taken into account.   predetermined manner to the elementary subset considered.   2 5 10. Primary treatment method according to claim 9, characterized in that at least one of the working subassemblies (L,) has   a different size of the corresponding elementary subset (Ki).   11. A method of secondary processing of a set of parameters (ai, b) associated with at least one partition information, resulting from a primary processing of a first set of data, secondary processing method characterized in that it comprises: a step of determining dimensions of elementary subsets constituting a partition of a second set of data, a step taking into account the presence of partition information corresponding to said subsets, each elementary application corresponding to a subset elementary set being determined by at least one parameter of said set of parameters, and - an "iterative computation" step (450) during which, from said set of parameters (ai, b) and said dimensions, it is implemented on the second set of data, a method of successive approximations (407 to 410) converging towards the fixed point of a global contractive application called " of the second type ", the restrictions of the global application to the elementary subsets (Ki) being constituted by said elementary applications, by implementing, for this purpose, at least one application belonging to the application group consisting of the applications   multidimensional and nonlinear applications.   12. Secondary treatment method according to claim 11,   characterized in that each elemental subset is related to n sub-   sets, n being non-zero, an elementary application of n   set of work in the basic subset being determined by   parameters of said set of parameters.   13. The secondary processing method as claimed in claim 12, characterized in that said partition information is representative of partitions of initial elementary subsets into subsets. intermediate elements.   14. A method of processing a set of data (IM, f) representative of physical quantities, comprising a primary treatment phase implementing a primary treatment method according to one of   any of claims I to 10 and a secondary treatment phase   implementing a secondary treatment method according to any one of   Claims 11 to 13, the secondary treatment phase   The set of parameters (ai, b) and partition information resulting from the primary treatment.   15. Method according to any one of claims 11 to 14,   characterized in that, during said "iterative calculation" step (450), said set of parameters (a ,, b) associated with partition information is taken into account, and, on the other hand, on the other hand, an arbitrary set of data, called the "initialization" set, and to carry out said so-called "second type" global contractive application: Cl) we partition the initialization set into elementary subsets (Ki), these subassemblies realizing the partition corresponding to said partition information; c2) for each of the elementary subsets (Ki) thus determined, the parameters (ai, b) of the elementary applications corresponding to the elementary subsets (Ki) are considered; resulting from the partition of the set of initial data, and implementing said elementary applications on the elementary subsets (Ki) of the initialization set; c3) gathering all the data obtained by the stakes; in implement elementary applications, this constituting an intermediate representation of said initial data, assigned an error; c4) repeating the operations c1-c3, taking as initialization set, said intermediate representation, so as to approach the fixed point of said global second type of contractive application; the finally obtained data set constituting a secondary representation (RE) of the data set that has been the subject of a primary treatment.   16. Process according to any one of claims 14 or 15,   characterized in that said global second type contractive application is   identical to said global first type contractive application.   17. A treatment method according to any one of   1o claims 11 to 16 wherein said parameters (ai, b) and said   Partition information is a primary representation of a multicomponent color image (Y, Cr, Cb), characterized in that, after an iterative computation step (450) on one of the components, the initialization of the component is used. iterative calculation step (450) relating to the component following the i secondary representation (RE) obtained at the end of the iterative calculation step   (450) relating to one of the components already dealt with.   18. A treatment method according to any one of   Claims 11 to 17, wherein said parameters (ai, b) and said   Partition information is a primary representation of a multicomponent color image (Y, Cr, Cb) characterized in that the iterative computation steps corresponding to said components implement initialization sets consisting of arbitrary data for the processing of data. parameters (ai, b) relating to each component and in that said iterative calculation steps implement a method of successive approximations (407 to 410) converging towards the fixed point of each contractive application   global component corresponding to each component.   19. Treatment method according to any one of   Claims 1 to 18, characterized in that it is suitable for determining   parameters (ai, b) and partition information of the contractive application 98 2761553   in order to allow the implementation, on a second set of data comprising a number of data different from the number of data of the first set, of a method of successive approximations (407 to 410) converging towards the fixed point of a global contractive application called "second type"; the set of parameters (ai, b) and partition information thus determined constituting a primary representation of said set of data. 20. Process of treatment according to claim 19, characterized in that: it comprises a step of "initial partition" (204) during which, said first set of data is partitioned into so-called "initial elementary" subsets ( Ki)   - during the construction stage (205 to 209), for each of the sub-   elementary sets (Ki), we determine the parameters (ai, b) of the elementary application which constitutes a restriction of the contractive application   overall audit of this elementary subset.   the successive approximation method carried out on the second set of data is allowed to take into account elementary subsets each corresponding to an elementary subset of the first set of data and comprising a number of data different from that of the first set of data; elementary subset of the first corresponding data set. 21. The processing method as claimed in claim 20, characterized in that the data numbers of the elementary subsets of the second data set are proportional to the data numbers of the elementary subsets of the first set of data which correspond respectively. 99 2761553   22. A treatment method according to any one of   claims 20 or 21, characterized in that:   - during the construction stage (205 to 209), for each of the sub-   elementary sets (Ki) resulting from the initial partition and any additional partitions, consider n work subsets (Li), and construct an elementary application of the n subsets of work in the elementary subset considered by determining the parameters (ai, b) of the elementary application, - the method of successive approximations carried out on the 10th set of data is allowed to take into account subsets of work each corresponding to a subset of work of the first set of data and having a different number of data than   of the working subset of the corresponding first data set.   23. The processing method as claimed in claim 22, characterized in that the data numbers of the work subsets of the second data set are proportional to the data numbers of the work subsets of the first set of data which correspond respectively.   24. Primary processing device (500) of a set of data (IM, f) representative of physical quantities, characterized in that it comprises: data input means (591) to be processed; output means (581) for parameters (a ,, b) and partition information; first logical means (510, 530, 531, 532, 550, 560, 570, 200 to 209) for transforming the data to be processed into parameters (a ,, b) and partition information; said first logic means including: 2761553   - "partition" means (204) adapted to partition said set of data into "elementary subsets" (Ki) - adapted "estimation" means, for each elementary subset that does not have said minimum dimension , estimating an opportunity of division of said elementary subset, said partitioning means being further adapted to partition each elementary subset that does not have said minimum dimension and whose division opportunity estimate does not respond to predetermined "quality" criteria, in so-called "intermediate elementary" subsets and - "construction" means (510, 530, 531, 550, 560, 570, 205 to 209) adapted to: construct an application so-called "first type" global contractive whose fixed point is an approximation of all or part of this data set, by determining the parameters of each elementary application of n subsets of t corresponding to each elementary subset resulting from the last partition, n being non-zero, in said elementary subset, the restrictions of the global application to the elementary subsets being constituted by said elementary applications, said global application belonging to the application group consisting of multidimensional applications and nonlinear applications, so as to allow the implementation of a method of successive approximations (407 to 410) converging towards the fixed point of said global contractive application; to output on the output means (581) the parameters (ai, b) thus determined, as well as, when at least one elementary subset has been partitioned, a so-called "partition" information representative of each said complementary partition , jointly constituting   O primary representation of said data set.   25. Primary processing device according to claim 24, characterized in that the estimation means are adapted to measure a predetermined statistical magnitude applied to the data of the subassembly. basic element.   Primary treatment device according to claim 25,   characterized in that the measured statistical magnitude is the variance of the sub- elementary set considered.   27. Primary treatment device according to any one of   Claims 24 to 26, characterized in that:   the construction means having constructed a global contractive application, the estimation means are adapted to measure a difference between, on the one hand, the data of the elementary subset and, on the other hand, the   restriction of the overall contractive application under construction to the sub-   elementary set considered, and in that - when the partition means realize a complementary partition, the means of construction are adapted to build a new application   global contractive taking into account said complementary partition.   28. Primary treatment device according to claim 27, characterized in that for measuring said difference, the estimation means   take into account a measure of distance.   29. Primary treatment device according to any one of   Claims 25 to 28, characterized in that the estimation means are   adapted to compare said measurement with a predetermined value for   determine whether the predetermined quality criteria are met.   30 30. Primary treatment device according to claim 29 characterized in that the estimation means are adapted to determine that 102 2761553   the opportunity estimate meets the predetermined quality criteria when   said measurement is less than said predetermined value.   31. Primary treatment device according to any one of   Claims 24 to 30, characterized in that the construction means (205   209) are adapted to constitute said global contractive application, at least partially, of elementary Lipschitzian applications related to elementary subsets (Ki).   32. Primary treatment device according to any one of   Claims 24 to 31, characterized in that the construction means (510,   530, 531, 550, 570, 205 to 209) are adapted to take into account for each of said elementary subsets (Ki), n work subsets (Li) geometrically linked in a predetermined manner to the subset basic element.   33. Primary treatment device according to any one of   Claims 24 to 32, characterized in that the construction means (510,   530, 531, 550, 570, 205 to 209) are adapted to take into account at least one of the subsets of work (L,) of a different size of the subset elementary (Ki) corresponding.   34. Primary treatment device according to any one of   Claims 24 to 33, characterized in that the first logical means   comprise: - a microprocessor (550); a read-only memory (530) comprising a primary data representation program, and a random access memory (510) comprising registers adapted to record modified variables during the execution of said program of primary representation. 103 2761553   35. Primary treatment device according to any one of   Claims 24 to 34, characterized in that it comprises:   - means of "construction" (510, 530, 531, 550, 560, 570, 205 to 209) adapted: to construct for each set of data to be processed, a global contractive application, called "first type" whose point stationary is an approximation of all or part of this set of data, by implementing, for this purpose, at least one application belonging to the group of applications 1o consisting of multidimensional applications and non-linear applications, so as to: implementing a method of successive approximations (407 to 410) converging towards the fixed point of said global down-link application, on a second data set having a number of data different from the number of data of the first data set; to output to the output means (581) the parameters (a 1, b) and partition information thus determined, these constituting a   primary representation of said data set.   36. A primary processing device according to claim 35, characterized in that said first logic means comprise "partition" means (204) adapted to partition said data set into "elementary subsets" (Ki), and in that that the means of construction are adapted, for each of the elementary subsets (Ki), to determine the parameters (ai, b) of the elementary application which constitutes a restriction of the global contractive application to said elementary subset, for allow the successive approximation method carried out on the second set of data to take into account elementary subsets each corresponding to an elementary subset of the first set of data and comprising a number of 104 2761553   different data than the elementary subset of the first set corresponding data.   37. The primary processing device as claimed in claim 36, characterized in that the data numbers of the elementary subsets of the second data set are proportional to the data numbers of the elementary subsets of the first set.   corresponding data respectively.   38. Primary treatment device according to any one of   Claims 35 to 37, characterized in that the means of construction are   adapted, for each of the elementary subsets (Ki) resulting from the initial partition step and any additional partitions, to take into account n work subsets (L,), and to construct a   elementary application of the n subsets of work in the sub-   elementary set considered by determining the parameters (ai, b) of the elementary application, to allow the method of successive approximations carried out on the second set of data, to take into account   subsets of work each corresponding to a subset   work set of the first set of data and having a different number of data from that of the work sub-set of the first corresponding data set.   39. Primary processing device according to claim 38, characterized in that the data numbers of the work subsets of the second data set are proportional to the data numbers of the work subsets of the first set of data. correspond to them respectively.   3 o 40. Secondary data processing device (600) suitable for secondary processing of a set of parameters (ai, b) 2761553   associated with at least one partition information, resulting from the primary processing of initial data (IM, f) carried out by a primary processing device, characterized in that it comprises: input means (681) of the parameters (ai , b) and partition information; data output means (691); second logic means (560, 570, 610, 630, 631, 632, 650, 400 to 410) for transforming the parameters (ai, b) and partition information into data; o 10 said second logic means comprising: - means for "determination" of dimensions adapted to determine dimensions of elementary subsets constituting a partition of a second set of data, taking into account the presence of partition information corresponding to said subsets, each elementary application corresponding to an elementary subset being determined by at least one parameter of said set of parameters, and - iterative calculating means (650, 450) adapted to implement, from said set of parameters (ai, b) and said dimensions, a method of successive approximations (407 to 410) converging towards the fixed point of a global contractive application called "second type" comprising said elementary applications, by implementing, for do this, at least one application belonging to the application group consisting of multidimensional applications and applications s nonlinear, said fixed point constituting a secondary representation (RE) of said set of initial data, and delivering the   data thus calculated on the output means.   41. Secondary treatment device according to claim 40,   characterized in that each elemental subset is related to n sub-   sets, n being non-zero, an elementary application of n   sets of work in the elemental subset being determined by   parameters of said set of parameters.   42. Device according to any one of claims 40 or 41,   characterized in that the elementary application, constructed for some at   least of said elementary subsets (Ki), is Lipschitzian.   43. Secondary treatment device according to any one of   claims 40 to 42, wherein said parameters (a ,, b) are a   1o primary representation of a multicomponent color image (Y, Cr, Cb) characterized in that said second logic means are adapted to provide the iterative calculation means (450) with an initialization set consisting of arbitrary data for processing parameters (ai, b) relating to a first component and, as initialization set for the processing of the following components, the secondary representation (RE) obtained at the end   the iterative calculation step (450) relating to one of the components already processed.   44. Secondary treatment device according to any one of   claims 40 to 43, wherein said parameters (a ,, b) are a   primary representation of a multicomponent color image (Y, Cr, Cb) characterized in that said second logic means are adapted to provide the iterative computation means (450) with an initialization set consisting of arbitrary data for the processing of data. parameters (ai, b) relating to each component and in that the iterative calculation means are adapted to implement in parallel the successive approximation methods (407 to 410) converging towards the fixed point of each global contractive application corresponding to each component.   45. A secondary treatment device according to any one of   Claims 40 to 44, characterized in that said second logic means   comprise: - a microprocessor (650), - a read-only memory (6comportant a program of secondary representation (RE) data, and a random access memory (610) having registers adapted to record modified variables during the execution of said   secondary representation program (ER).   46. A data processing device (700,800) incorporating a   device (500) according to one of claims 24 to 39 and a   Device (600) according to one of claims 40 to 45.   47. A data processing device according to claim 46, characterized in that said first and second logic means are incorporated in particular in: - a microprocessor (850), - a read-only memory (830) comprising at least one primary representation program data and a secondary representation (RE) program of data; a random access memory (810) comprising registers adapted to record modified variables during execution said programs.   48. Data processing device according to any one of   Claims 46 or 47, characterized in that said application   overall contractive second type is identical to said contractive application overall type.   49. Printer, characterized in that it comprises a device   treatment device according to any one of claims 40 to 48.   50. Photocopier, characterized in that it comprises a   treatment device according to one of claims 40 to 48.   51. A camera, characterized in that it comprises a   treatment device according to any of claims 24 to 48.   52. Facsimile device, characterized in that it comprises a   treatment device according to any of claims 24 to 48.