Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T9/00—Image coding
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T9/00—Image coding
  • G06T9/001—Model-based coding, e.g. wire frame
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
  • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/50—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using predictive coding
  • H04N19/503—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using predictive coding involving temporal prediction
  • H04N19/51—Motion estimation or motion compensation
  • H04N19/537—Motion estimation other than block-based
  • H04N19/54—Motion estimation other than block-based using feature points or meshes

Definitions

• Image coding and decoding methods and devices using nested meshes, program, signal and corresponding application are described in detail below.
• the field of the invention is that of coding of images, with a view in particular to their transmission or their storage. More specifically, the invention relates to an improvement in hierarchical coding techniques, implementing a hierarchy of nested meshes.
• a mesh is conventionally defined by a set of vertices and oriented faces (Figure 1) defining a topology.
• Such meshes are for example used in computer graphics, to model three-dimensional objects with limited geometric complexity.
• the approximation of a mesh M consists in finding a mesh M 'whose geometric complexity is less than that of the mesh M, and which best approaches the geometry of M.
• the mesh M ′ consists of a succession of nested meshes, each corresponding to a level of detail, or hierarchical level, so as to allow a progressive reconstruction of the images and a simplified coding.
• the nodal values of the mesh are optimized to minimize the quadratic reconstruction error. These nodal values are then quantified and coded.
• Such a method makes it possible to achieve effective compression rates and to limit the visual degradations which correspond here more to smoothing effects, less unpleasant for the human eye. This is linked to the good continuity properties of the reconstructed surfaces thanks to the mesh approximation.
• this scheme is suitable for video. Indeed, the meshes triangulars are more flexible and efficient for estimating movement.
• the wavelet bases used are constructed as a tensor product of one-dimensional wavelets. This induces a limitation of the capacity to represent certain structures by favoring certain directions. These faults specific to image coding methods by sub-bands have led to favoring a representation of the image based on nested triangular meshes.
• E.Quak suggests using the two techniques simultaneously, by associating at each level of the mesh a base of complementary wavelets by giving conditions on the edges. It thus constructs an explicit base of prondelets on a triangular mesh. This technique is intended for the representation and compression of digital 3D terrain models.
• Annex 2 recalls the general principle and the main lines of the functioning of the coding method based on a hierarchy of meshes. nested.
• a vertex is on the border between a refined zone and an unrefined zone, one cannot choose an optimal value for this vertex for the two resolutions.
• choosing one of the values of one of the optimization levels will only allow optimal reconstruction on the region corresponding to this level of refinement.
• this sub-optimality of the representation also constitutes a drawback in the context of a scalable coding scheme. Indeed, it does not make it possible to provide the optimal quality of reconstruction for intermediate bit rates.
• the invention particularly aims to overcome these drawbacks of the state of the art.
• an objective of the invention is to provide a scalable image coding technique and a corresponding decoding technique allowing optimal reconstruction quality to be obtained at each reconstruction level.
• Another objective of the invention is to provide such coding and decoding techniques which require a limited bit rate, for each level of reconstruction.
• the invention also aims to provide such coding and decoding techniques, which make it possible to efficiently process several images having the same structure (same size and same reference mesh). Yet another object of the invention is to provide a data and signal structure which makes it possible to optimize the bit rate necessary for the transmission and storage of images coded in this way.
• At at least level n of decomposition (with the exception of the first level of decomposition), only image coefficients are expressed expressed in a base of functions defined in a space orthogonal to the space corresponding to the level previous n-1 decomposition, said functions being chosen so that said image coefficients make it possible to optimize for said level n of decomposition the information already transmitted for the previous level n-1 of decomposition, so as to produce a reconstructed image , representative of said source image, with a quality of reproduction optimized for said level n of decomposition.
• V n V n _, ⁇ W ,,. ! , or :
• V n . Is the space associated with the level n-1 of decomposition;
• W n . ! is a space orthogonal to V n . l5 and we associate to said space V n on the one hand a base of piecewise affine functions ⁇ n , and on the other hand a base formed by the combination of two orthogonal bases:
• An advantage of such a method lies in the better statistical distribution of the value of the coefficients allowing a reduction in the cost of coding.
• the new method makes it possible to carry out a first representation of the image from these only coefficients optimal for this level of resolution.
• the first coefficients correspond to the value for these vertices optimized for the finest level of refinement of the mesh (one thus has sub-optimality).
• said pre-wavelet functions are wavelet functions, orthogonal to each other.
• each of said pre-wavelet functions has a narrow support, limited to a predefined number of vertices of said mesh located in the vicinity of a reference vertex for said function.
• said pre-wavelet functions are one-dimensional.
• each of said pre-wavelet functions is advantageously determined by taking into account the position in said mesh of at least one edge carrying a new vertex of said mesh, to which said function will be assigned.
• Vi (p) is the set of vertices neighboring vertex j in the mesh of new p.
• said pre-wavelet functions are multidimensional. These can in particular be functions of the "box spline" type.
• the determination of the image coefficients at a mesh level n is based on the resolution of a linear system:
• the coding method of the invention comprises: a preliminary step of determining bases of function ⁇ n and ⁇ n of reference, for a predetermined image structure; an image coding step, systematically using said reference bases ⁇ n and ⁇ n , for any image having said predetermined image structure.
• the coding of a set of images of the same type is thus particularly simplified.
• the invention also relates to a method of constructing function bases for the hierarchical coding of source images using a hierarchical mesh defining at least two nested spaces, each corresponding to a level n of decomposition of said mesh.
• a mathematical space of representation of an image V such that N . ⁇ V ⁇ ⁇ W ⁇ where: - V n . ⁇ is the space associated with the level n-1 of decomposition;
• the invention also relates to the image coding devices, implementing the coding method and / or construction of bases described above.
• the invention relates to a device for coding at least one source image implementing a hierarchical mesh defining at least two nested spaces, each corresponding to a level n of decomposition of said mesh, in which to at least one level n of decomposition (with the exception of the first level of decomposition), it associates only image coefficients expressed in a base of functions defined in a space orthogonal to the space corresponding to the previous level n-1 of decomposition, said functions being chosen so that said image coefficients make it possible to optimize for said level of decomposition the information already transmitted for the previous level n-1 of decomposition, so as to produce a reconstructed image, representative of said source image, with a quality of optimized rendering for said level n of decomposition.
• the invention also relates to a method for decoding coded images using the coding method and / or construction of bases described above.
• Such a decoding method decodes images coded in the form of image coefficients obtained by the implementation of a hierarchical mesh defining at least two nested spaces, each corresponding to a level n of decomposition of said mesh, according to a coding associating , at at least one level n of decomposition (with the exception of the first level of decomposition), only image coefficients expressed in a function base defined in a space orthogonal to the space corresponding to the previous level n-1 of decomposition, said functions being chosen so that said image coefficients make it possible to optimize for said level n of decomposition the information already transmitted for the previous level n-1 of decomposition, so as to produce a reconstructed image representative of said image source, with a quality of reproduction optimized for said level n of decomposition.
• such a decoding method comprises: a prior step of receiving and / or storing databases of reference functions, for at least one predetermined image structure; an image decoding step, using the bases of reference functions corresponding to the image structure of the image to be decoded. Again, this simplifies the processing and limits the amount of data to be transmitted, for a series of images.
• the invention also relates to a device for decoding coded images, characterized in that it implements the decoding method described above.
• the invention also relates to a computer program for coding and / or decoding of images, characterized in that it comprises program instructions allowing the implementation of the coding method and / or of the decoding method described above.
• the invention further relates to an image data signal, comprising a first part comprising data representative of at least one set of reference function bases, for at least one predetermined image structure, and a second part comprising data representative of at least two images coded using one of said sets of reference function bases.
• said first part comprises at least two sets of bases of reference functions, corresponding to distinct image structures, and in that each image of said second part comprises information allowing the selection of one of said sets of bases. of reference functions.
• the data of said first part and / or of said second part are organized so as to allow progressive image reconstruction and / or with a predetermined reconstruction quality level.
• said images are coded according to a method implementing a hierarchical mesh defining at least two nested spaces, each corresponding to a level n of decomposition of said mesh, said reference functions being chosen so that said image coefficients make it possible to optimize for said level n of decomposition the information already transmitted for the previous level n-1 of decomposition, the coding of the images associating, at any level n of decomposition (with the exception of the first level of decomposition), only image coefficients expressed in a function base defined in a space orthogonal to the space corresponding to the previous level n-1 of decomposition, so as to produce a reconstructed image, representative of a source image, with an optimized quality of reproduction for said level n of decomposition.
• FIGS. 2 A to 2D show the different positions of an edge in a mesh, according to the Quark approach, discussed in Appendix 1;
• - Figure 3 is a simplified block diagram of the general principle of an embodiment of the invention
• - Figure 4 illustrates a k-disc taken into account for the calculation of the pre-wavelet functions, in an exemplary implementation of the invention
• FIG. 5 shows an example of signal structure exploiting the principle illustrated in Figure 3.
• the invention is therefore based in particular on the use of wavelets, or pre-wavelets, specific, based on the orthogonalisation of the complementary bases.
• box-spline type wavelets [2].
• the first are pre-wavelets on a triangular mesh whose significant coefficients are few.
• Box-spline wavelets are also constructed from meshes and represent a means of constructing two-dimensional wavelets that are not based on the tensor product of one-dimensional wavelet bases.
• the proposed method is an improvement on the previous method of mesh coding developed in [7]. It relates to the coding of still images but can also be applied to the coding of intra images in the context of video compression, in particular the codings using the meshes jointly for the intra surface approximation and the inter motion estimation.
• FIG. 3 therefore illustrates, in a simplified manner, the general principle of the invention.
• a nested mesh (311) of a type known per se, defining a plurality of spaces V n , each corresponding to a level of the mesh.
• orthogonal bases (312) are sought, according to the technique described in detail below.
• a coding step 32 proper which can be repeated several times (321) without returning to the calculation of the orthogonal bases.
• the matrices having been calculated once and for all.
• the image coefficients corresponding to each level of the mesh are calculated (323), using matrices, then we transmit (324), or store, the coefficients obtained.
• Decoding 33 performs the reverse operations. It has decoding matrices, which can be permanently installed in memory or which are received (331), for example at the start of a video stream, to initialize the decoder.
• the decoder On reception (332) of the coded coefficients, the decoder gradually reconstructs (333) each image up to the desired quality level.
• the signal comprises a first part 51 of initialization, which contains the bases of functions determined once and for all, and a second part 52 of image data, comprising coefficients determined using said bases.
• a reduced bit rate is thus obtained, the first part 51 being transmitted only once, at the start of the sequence.
• an identification system is provided for these. For each image or series of images, or simply when a change is necessary, data 521 of an image is transmitted in the preamble an identifier 5211 indicating the set of function bases to be used.
• a space V n is associated with each of the decomposition levels of the mesh.
• the invention is of course also applicable to the case where nested spaces V m to V are associated, with only the consecutive levels of decomposition m to l of the mesh, where m and / are any two integers.
• the principle of the invention described in the rest of this document can only be implemented for the decomposition levels 3 to 12 of the mesh, associated with nested spaces V 3 to V 12 .
• the affine base presented in appendix 2 is a special case of such bases where the polynomials considered are of degree 1, that is to say that the vector spaces in which one places oneself are limited to the affine functions by pieces and continuous overall.
• index p describes all the different resolutions and where N p denotes the dimension of W p .
• pre-wavelets These functions are called pre-wavelets.
• wavelets In the particular case where the basic functions of the same level are orthogonal to one another, they will be called wavelets.
• the obstacles encountered in the application of the proposed method come from the difficulty of exhibiting the bases ( ⁇ (p) i) whose functions have supports limited to a finite number and as small as possible of contiguous triangles at the reference vertex. Thus one cannot be satisfied with orthogonalising the initial base in an arbitrary way.
• the following sections give practical examples of application where the method can be applied.
• the coefficients obtained can be coded according to conventional methods. Note that in this case the orthogonality between two successive levels of resolution invalidates a differential coding: the coefficients obtained are directly quantified and coded by means of an arithmetic coder.
• the vector X being composed of the coordinates of approximation of the image in the new base.
• this property corresponds to the limitation of the support of the pre-wavelet functions used to a sufficiently small number of vertices.
• the matrix A being symmetric definite positive and presenting a significant number of null values, one then solves the linear system by a profile method.
• Algorithm 2 Filling the passage matrix C. Note that this method does not pose an implementation on the edges. In fact, the construction method of the pre-wavelets took into account the different possible configurations for any bounded mesh. 5. application with "box splines" 5.1 Description of the method The method can also be applied to other types of wavelet or pre-wavelet construction. We can thus construct explicit wavelet bases from nested spaces on which we have built a multi-resolution. A general method for constructing multidimensional wavelet databases is developed in [3]. The advantage of using such wavelets compared to wavelets constructed by tensor product lies in the better adaptation of the basic functions to the multi-dimensional framework.
• An edge is said to be interior if it delimits two triangles of the mesh, otherwise it is said to be exterior.
• the edge can be interior with its two interior vertices (a), interior with one of the two exterior vertices (b), interior with its two exterior vertices (c) or even itself exterior (d).
• the different cases are shown in figure2.
• Such a representation base therefore has the advantage of being suitable for multi-resolution and of being easy to use thanks to the small size of the support used.
• the same notations are used, also distinguishing the t x neighboring vertices of b, located to the left of the edge considered and t ⁇ the number of neighboring vertices of b, and located to the right of the edge.
• chroma bands For the chroma bands, a similar method can be applied. We can therefore consider the image as being a discretized representation of a parametric surface. We are interested here in the representation of this surface by a mesh.
• q ⁇ is the affine function taking the value 1 on the vertex i and such that the value in a point of one of the triangles of which i is the vertex is equal to the barycentric coordinate of this point with respect to vertex i (see figure 1).
• This function is therefore zero outside the triangular faces, one of the vertices of which is the vertex i.
• OC coefficients are calculated so as to minimize the quadratic error:
• the method uses a hierarchy of nested triangular meshes. We initially have a triangular mesh. One then adopts a rule of subdivision of the meshes. One can for example obtain the following meshes by inserting in the middle of each edge of the mesh a new vertex.
• Each triangle is in this case divided into 4 new triangles.
• This representation of the image is used so as to have successive approximations of the image, each corresponding to a given resolution.
• This hierarchy is then exploited by subdividing only the triangles whose quadratic reconstruction error is greater than a certain threshold. The value of this threshold partly determines the quality of reconstruction desired. We thus obtain a tree of subdivision of the hierarchy which must be transmitted to the coder and allows the decoder to determine which are the refined triangles.
• the first term of the sum corresponds to the N p vertices of the resolution level p and the second term of the sum corresponds to the new vertices inserted at the level p + 1.
• N p vertices we have:
• V ⁇ represents the set of vertices neighboring vertex i in the mesh
• the mean coefficients are subtracted from their coefficients.
• This representation makes it possible to exploit the spatial redundancies linked to the statistical correlation between close pixels in the image. Compression is carried out by quantifying these coefficients followed by adaptive arithmetic coding. Furthermore, the coefficients not belonging to any of the triangles selected in the adaptive refinement step are not coded; indeed don't refine a triangle amounts to considering that the coefficients of the vertices corresponding to the finer resolutions inside this triangle are the interpolated values, which is equivalent to assigning 0 to the coefficient ⁇ ; (p) .
• the method therefore makes it possible to obtain a simple coding scheme for still images by means of the use of a hierarchy of nested regular meshes. This provides effective compression rates. Furthermore, such a coding scheme is well suited to scalar transmission of the coefficients.

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