EP1800263A2

EP1800263A2 - Method for locally decoding a bit stream of wavelet coefficients

Info

Publication number: EP1800263A2
Application number: EP05792261A
Authority: EP
Inventors: Patrick Gioia; Loïc BOUGET
Original assignee: France Telecom SA
Current assignee: Orange SA
Priority date: 2004-10-14
Filing date: 2005-09-30
Publication date: 2007-06-27
Also published as: WO2006040270A3; WO2006040270A2; FR2876821A1; US8086054B2; US20080193027A1

Abstract

The invention concerns a method for decoding a data stream representing an object with at least three dimensions, associated with a basic mesh consisting of an assembly of facets defined by an assembly of vertices and ridges, and with wavelet coefficients corresponding to the local modifications of the basic mesh, indexed each by a vertex of the basic mesh. The invention is characterized in that, for at least some wavelet coefficients of the data stream, the method includes the following steps: determining an orientation of a ridge bearing the vertex indexing the wavelet coefficients, called orientation of the wavelet coefficient; determining, based on the orientation, an information for locating in the basic mesh at least one child of the wavelet coefficient, distinct locating rules being associated with each orientation, so as to extract a data stream of at least some of the wavelet coefficients, associated each with a locating information.

Description

Method for local decoding of a bitstream of wavelet coefficients 1. Field of the invention

The field of the invention is that of encoding images and objects in at least three dimensions. More precisely, the invention relates to the transmission of data representative of three-dimensional scenes or 3D objects, as well as their decoding, with a view to their subsequent reconstruction on a display screen. It can for example be used for the transmission of images or multimedia scenes via the Internet.

The invention finds particular applications in the field of adaptive representation of scenes (or scene objects) in three dimensions (3D) represented by meshes.

It fits more particularly in the framework of the decoding and the representation of objects of a graphic scene coded by meshes by means of methods known as "wavelet", putting in particular implemented wavelets of ^2nd generation, presented in the Wim Sweldens, entitled "The Lifting Scheme: A Construction of Second Generation Wavelets" (in English, "The Elevation Process: A Construction of Second Generation Wavelets"), SIAM Journal on Mathematical Analysis, Volume 29, Number 2 , pp. 511-546, 1998. 2. Solutions of the prior art

It is recalled that the so-called "wavelet" coding methods make it possible to represent a mesh as a succession of details added to a basic mesh. The general theory of this technique is described in particular in the article by M. Lounsbery, T. DeRose and J. Warren, "Multiresolution Analysis for Surfaces of Arbitrary Topological Type" (ACM Transaction on Graphics, Vol.16, No.1, pp. 34-73, January 1997).

The general principle of this technique is to develop a homeomorphism between an object to be encoded (such as a 3D mesh for example) and a simple mesh (more generally called "basic mesh") in a base of particular functions, called wavelets of second generation. According to this technique, a mesh is therefore represented by a series of coefficients that correspond to the coordinates in a wavelet basis of a parameterization of this mesh by a simple polyhedron.

Thus, an object coded according to such a technique is presented as the union of the two following elements: the basic mesh, which generally has few facets, and represents a coarse version of the object to be encoded; the wavelet coefficients, which are triplets of real numbers assigned simultaneously to a specific area of the base mesh and to a given subdivision level of this mesh. These wavelet coefficients represent the refinements to be made to the zone with which they are associated to converge towards the geometry of the initial object.

In order to be able to reconstruct a representation of the object coded on a display terminal, it is necessary to transmit to the latter, on the one hand, the basic mesh, and on the other hand the associated wavelet coefficients.

Several wavelet coefficient encoding techniques are known for their transmission to the display terminal, among which the so-called "zero-tree" coding technique presents particularly interesting results in terms of compression. Such a technique consists in describing a coding order of the wavelet coefficients, which is predetermined and known in advance of the transmitter and receiver terminals (for example of a server and a client display terminal). It thus makes it possible, during the transmission of wavelet coefficients, to avoid transmitting information relating to the ranges of coefficients which are not significant for the coding of the object under consideration. The cancellation of the non-significant coefficients thus makes it possible to reach a satisfactory level of compression.

The zero-tree coding techniques advantageously exploit the fact that the wavelet coefficients have, at the finest levels of detail, a smaller amplitude than the wavelet coefficients associated with the coarser subdivision levels.

Such "zero-tree" encodings are generally coupled to a coding

"bit plane", which allows, when transmitting the coefficients, to transmit the most significant bits of each coefficient first. This satisfies the progressivity requirements of the coding technique.

For a more detailed description of zero-tree techniques, reference may be made to Jerome M. Shapiro's articles, Embedded Image Coding.

Using Zerotrees of Wavelet Coefficients (IEEE Trans., Sig., Proc 41 (12), Dec.1993) and A. Said, W. A. Pearlman, "A New, Fast, and Efficient Image.

Coded Based on Partitioning in Hierarchical Trees "(IEEE Trans.

System. For Video Tech., 6 (3), June 1996).

As explained in this last article by A. Said and WA Pearlman, the "zero-tree" coding / decoding algorithm, also called SPIHT algorithm (for "Set Partitioning in Hierarchical Trees") makes it possible to obtain a global binary representation. of the set of wavelet coefficients, which contains sort bits and bits from the binary representation of the coefficients. Applied to the coding of two-dimensional wavelet images, this SPIHT algorithm, during decoding, reconstructs the hierarchy of the pixels of the image and distributes the bits as they are extracted from the bitstream.

The SPIHT algorithm, originally developed for two-dimensional image coding, has recently been applied to second-generation wavelet coefficients as described in the "Progressive" publications.

Geometry Compression "(SIGGRAPH 2000 proceedings) by A. Khodakovsky, P. Schröder and W. Sweldens, and" Hierarchical Coding of 3D Models with Subdivision

Surfaces "(IEEE ICIP 2000 Proceedings) by F. Moran and N. Garcia.

Thus, for second generation wavelets, a bit stream having the same type of format as for conventional wavelets used for the coding of two-dimensional images is obtained. 3. Disadvantages of prior art As initially presented in the framework of conventional wavelet coding of 2D images, by A. Said and WA Pearlman in the article cited above, the SPIHT algorithm requires keeping in memory a table of the size of the image to be reconstructed, that is to say containing as many elements as coefficients of wavelets. The inventors of the present patent application have established that its adaptation to the second generation wavelets retained this requirement; thus, in the case of partial or adaptive transmission of the data, the decoding of some wavelet coefficients requires storage in memory of the entire hierarchy of the mesh associated with the 3D object or the multimedia scene that is to be reconstructed.

The SPIHT algorithm, applied to 3D objects coded by wavelet second generation, therefore has severe limitations in the case where it is desired to perform adaptive decoding of the transmitted object.

However, such adaptive decoding proves particularly interesting for many applications, such as, for example, adaptive "streaming" of geographic terrain (in French "streaming"). In such an application, a user interactively visits a virtual geographical area, transmitted by a server over a communication network, such as the Internet for example. Depending on the area visited by the user, the server transmits to the display terminal only the data that may be seen by the latter. The relevance of the data is determined in particular according to the point of view of the user, his position in the virtual scene, or a specific request sent by the latter to the server, ...

A first disadvantage of the SPIHT algorithm of the prior art, as part of the coding of 3D objects by second-generation wavelets, therefore lies in the need to keep in memory the whole hierarchy of the "zero tree". . Indeed, a partial decoding of the bitstream requires creating in memory the whole of the hierarchical structure, even though part of this structure is intended to contain only zeros, only part of the scene encoded in the bit stream being visible to, or of interest to, the user. Another disadvantage of the SPIHT algorithm of the prior art, in the context of the coding of 3D objects by second generation wavelets, is of algorithmic order.

Indeed, during an adaptive transmission, the two phases of the reconstruction of a scene or a 3D object, from a bit stream (or "bitstream"), to obtain a 3D mesh, are as follows : "zero-tree" decoding, which, from the bit stream of data, produces wavelet coefficients; and the inverse wavelet transform, which, from the wavelet coefficients extracted from the bit stream, produces a 3D mesh.

In a conventional manner, and as illustrated in FIG. 1, the wavelet coefficients 15, after "zero-tree" decoding, are stored in a cache 10, accompanied by a location information, expressed for example in the form of barycentric coordinates. (F, A, B, C), where F is a facet of the basic mesh on which is the vertex indexing the wavelet coefficient, and where A, B and C are barycentric coordinates of the vertex on the facet F. This location information enables the reconstruction process 11 to integrate the corresponding wavelet coefficient into the 3D representation 12 independently. A disadvantage of the SPIHT technique of the prior art for objects

3D is therefore that the reconstruction process 11 is dependent on the stopping of the decoding process 13. In other words, it is not possible to carry out an adaptive reconstruction of the only portion of the 3D object likely to interest the user as the entire bit stream 14 has not been decoded 13. Such a SPIHT technique does not allow particular adaptive visualization in real time objects or 3D scenes.

4. Objectives of the invention

The invention particularly aims to overcome these disadvantages of the prior art. More specifically, an object of the invention is to provide a decoding technique of a data stream representative of a 3D object that allows reconstruction of the 3D object faster than according to the prior art, in particular the SPIHT algorithm. . An objective of the invention is in particular to propose such a decoding technique that allows an adaptive visualization in real time of a 3D object.

Another object of the invention is to provide such a decoding technique that allows space saving in memory size compared to prior techniques. More precisely, an object of the invention is to propose such a decoding technique that does not require storing in an intermediate structure the entirety of the decoded data before the beginning of the reconstruction phase of the representation of the 3D object.

The invention also aims to provide such a decoding technique that allows a partial reconstruction of the 3D object, according to the wishes of a user.

Another object of the invention is to propose such a decoding technique that makes it possible to decode a bit stream of wavelet coefficients by a process independent of the reconstruction of the representation of the 3D object or the associated multimedia scene.

5. Essential characteristics of the invention

These objectives, as well as others that will appear later, are achieved by means of a method of decoding a data stream representative of an object having at least three dimensions, said object being associated with a mesh base consisting of a set of facets defined by a set of vertices and edges, and coefficients in a wavelet basis corresponding to local modifications of said basic mesh, called wavelet coefficients, each coefficient of wavelet being indexed by a vertex of said base mesh, said data stream comprising at least some of said wavelet coefficients. According to the invention, for at least some wavelet coefficients of said data stream, such a method implements the following steps: determining an orientation of an edge carrying said vertex indexing said wavelet coefficient, called the orientation of said wavelet coefficient; determining, according to said orientation, location information in said base mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, so as to extract from said data stream at least some of said wavelet coefficients, each associated with location information.

Thus, the invention is based on a completely new and inventive approach to the decoding of a bit stream containing wavelet coefficients, allowing the reconstruction of a 3D object or a multimedia scene. Indeed, the invention proposes, as the decoding of the bitstream, to determine, for each wavelet coefficient, location information of its descendants, or son. In this way, these coefficients can be directly used during the reconstruction of the 3D object. It is therefore no longer necessary to have decoded the entire bit stream to be able to have the location information associated with each of the wavelet coefficients, and thus to begin the reconstruction of the representation of the 3D object, by applying the wavelet coefficients decoded at the basic mesh.

The location information associated with the wavelet coefficients and their descendants is thus calculated during the decoding, as a function of the orientation of the edge of the base mesh that carries the vertex indexing the wavelet coefficient. In other words, we determine the orientation of a parent wavelet coefficient, and we deduce what is the calculation rule to be applied to determine the location information of one of his descendants, as more in detail later in this document. Since such decoding makes it possible to directly access the wavelet coefficients of the bit stream, associated with information making it possible to locate them in the basic mesh, the invention makes it possible to carry out an adaptive reconstruction in real time of the object. 3D thus coded. In addition, unlike the techniques of the prior art, it is no longer necessary, according to the invention, to have a large intermediate structure in which to store the entire coding hierarchy of the 3D object. It is sufficient to decode only the portions of interest of the bit stream, and to store in cache the only decoded wavelet coefficients, associated with location information, for the reconstruction of the 3D object.

Preferably, for said at least one descendant, if said location information expressed in an affine base does not satisfy at least one predetermined criterion, said method implements a step of modifying said affine base, so that said information of localization expressed in said modified affine base satisfies said at least one criterion.

According to an advantageous characteristic of the invention, such a decoding method also comprises, for said at least one descendant, a subsequent step of reducing said location information.

Such a reduction step makes it possible, on the one hand, to have uniqueness of the location information of a wavelet coefficient at the output of the decoding method and, on the other hand, to reduce as much as possible the memory space occupied by this location information. Advantageously, said wavelet coefficients are coded according to a zero-tree type technique, in said bit stream.

As indicated previously in this document, such a zero-tree type technique makes it possible to achieve satisfactory results in terms of compression of the coefficients to be transmitted. Preferably, for a wavelet coefficient of index n, said location information comprises four parameters (F (n), A (n), B (n), C (n)), where F (n) is a facet of said base mesh on which is said vertex indexing said coefficient of wavelets, and wherein A (n), B (n) and C (n) are integer multiples of barycentric coordinates of said vertex on said facet F (n).

The affine base in which the location information is expressed thus corresponds to the facet of the mesh in which the barycentric coordinates of the vertex indexing the wavelet coefficient are expressed.

According to an advantageous characteristic of the invention, such a decoding method comprises a preliminary step of initialization of said location information, during which said parameters (F (n), A (n), B (n) , C (n)) the value zero.

Advantageously, said orientation of said wavelet coefficient of index n is given by the formula: Orientation = (! (A (n)% 2)) + 2 * (! (B (n)% 2)) + 3 * (! (C (n)% 2)) where% is the operator of the rest of the Euclidean division,! is the Boolean negation operator, and where A (n), B (n) and C (n) are the barycentric coordinates (or multiples of these coordinates) of the wavelet coefficient of index n in the facet F ( n) the mesh. Preferably, said location information of said descendants of said wavelet coefficient is determined according to the following formulas (where the index n denotes the father wavelet coefficient and m, its descendant): for a first descendant of said wavelet coefficient: the orientation of said wavelet coefficient is 1: F (n) = F (m)

A (n) = 2 * A (m) B (n) = 2 * B (m) + 1 C (n) = 2 * C (m) -1; if the orientation of said wavelet coefficient is 2: F (n) = F (m) A (n) = 2 * A (m) -l

B (n) = 2 * B (m)

C (n) = 2 * C (m) + 1; if the orientation of said wavelet coefficient is 3: F (n) = F (m)

A (n) = 2 * A (m) + l

B (n) = 2 * B (m) -l

C (n) = 2 * C (m); for a second descendant of said wavelet coefficient: if the orientation of said wavelet coefficient is 1:

F (n) = F (m)

A (n) = 2 * A (m)

B (n) = 2 * B (m) -l

C (n) = 2 * C (m) + l; if the orientation of said wavelet coefficient is 2:

F (n) = F (m)

A (n) = 2 * A (m) + l

B (n) = 2 * B (m)

C (n) = 2 * C (m) -1; if the orientation of said wavelet coefficient is 3:

F (n) = F (m)

A (n) = 2 * A (m) -l

B (n) = 2 * B (m) + l

C (n) = 2 * C (m); for a third descendant of said wavelet coefficient: if the orientation of said wavelet coefficient is 1:

F (n) = F (m)

A (n) = 2 * A (m) 2

B (n) = 2 * B (m) -1 C (n) = 2 * C (m) -1; if the orientation of said wavelet coefficient is 2:

F (n) = F (m)

A (n) = 2 * A (m) -l

B (n) = 2 * B (m) + 2 C (n) = 2 * C (m) -1 if the orientation of said wavelet coefficient is 3:

F (n) = F (m)

A (n) = 2 * A (m) -l

B (n) = 2 * B (m) -l C (n) = 2 * C (m) +2 for a fourth descendant of said wavelet coefficient, if it exists: if the orientation of said wavelet coefficient is 1:

F (n) = F (m)

A (n) = 2 * A (m) -2 B (n) = 2 * B (m) + 1

C (n) = 2 * C (m) + 1; if the orientation of said wavelet coefficient is 2:

F (n) = F (m)

A (n) = 2 * A (m) + 1 B (n) = 2 * B (m) -2

C (n) = 2 * C (m) + l; if the orientation of said wavelet coefficient is 3:

F (n) = F (m)

A (n) = 2 * A (m) + 1 B (n) = 2 * B (m) + 1

C (n) = 2 * C (m) -2; where m denotes the index of said wavelet coefficient and n denotes the index of said descendant.

According to an advantageous characteristic of the invention, said location information does not satisfy said at least one predetermined criterion if said vertex indexing said wavelet coefficient is located on an edge of said basic mesh.

Thus, said location information does not satisfy said at least one predetermined criterion if at least one of the parameters A (n), B (n) and C (n) of said wavelet coefficient is negative. Indeed, when a vertex is located on an edge of the mesh, at least one of its barycentric coordinates is negative.

Preferably, during said step of reducing said location information, said parameters A (n), B (n) and C (n) are divided by two, as long as said parameters A (n), B (n) and C (n) are all peers.

In this way, the smallest integer multiples of the barycentric coordinates of the wavelet coefficient of index n are determined.

Advantageously, such a decoding method also comprises, for each of said wavelet coefficients extracted from said data stream, a subsequent step of storage in a cache of said wavelet coefficient and said associated reduced location information, so as to what said stored wavelet coefficients may be used during a step of reconstructing said at least three-dimensional object implementing an inverse wavelet transform.

Thus, as soon as they are decoded, the wavelet coefficients associated with information for locating them in the basic mesh are stored directly in the cache. One can proceed, from the information of this cache, to the adaptive reconstruction and in real time of a representation of the 3D object or the multimedia scene considered, without it being necessary to have previously decoded the the entire binary train.

Preferably, such a decoding method is implemented in the context of an algorithm for sorting the wavelet coefficients of said data stream of SPIHT type ("Set Partitioning In Hierarchical Trees", in French "partitioning of sets in hierarchical trees ").

The invention also relates to a device for decoding a data stream representative of an object having at least three dimensions, said object being associated with a basic mesh consisting of a set of facets defined by a set vertices and edges, and coefficients in a wavelet basis corresponding to local modifications of said basic mesh, said wavelet coefficients, each wavelet coefficient being indexed by a vertex of said basic mesh, said train of data comprising at least some of said wavelet coefficients.

According to the invention, for at least some wavelet coefficients of said data stream, such a decoding device implements the following means: means for determining an orientation of an edge carrying said vertex indexing said coefficient of wavelets, referred to as the orientation of said wavelet coefficient; means for determining, according to said orientation, location information in said basic mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, so as to extract said data stream at least some of said wavelet coefficients, each associated with location information.

The invention also relates to a terminal for restoring an object to at least three dimensions, said object being associated with a basic mesh consisting of a set of facets defined by a set of vertices and edges, and coefficients in a wavelet basis corresponding to local modifications of said basic mesh, called wavelet coefficients, each wavelet coefficient being indexed by a vertex of said basic mesh, said terminal comprising means for receiving a data stream representative of said object comprising at least some of said wavelet coefficients. According to the invention, for at least some wavelet coefficients of said data stream, such a restitution terminal implements the following means: means for determining an orientation of an edge carrying said vertex indexing said coefficient of wavelets, referred to as the orientation of said wavelet coefficient; means for determining, according to said orientation, a location information in said base mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, and in that said terminal includes means for cache storage of said wavelet coefficients , each associated with location information, and means for reconstructing said at least three-dimensional object implementing an inverse wavelet transform.

The invention further relates to a computer program product comprising program code instructions recorded on a medium usable in a computer, and for decoding a data stream representative of an object having at least three dimensions, said object being associated with a basic mesh consisting of a set of facets defined by a set of vertices and edges, and coefficients in a wavelet basis corresponding to local modifications of said basic mesh, called wavelet coefficients each wavelet coefficient being indexed by a vertex of said base mesh, said data stream comprising at least some of said wavelet coefficients.

According to the invention, such a computer program product comprises computer readable programming means for performing, for at least some wavelet coefficients of said data stream: a step of determining an orientation of an edge carrying said vertex indexing said wavelet coefficient, referred to as the orientation of said wavelet coefficient; a step of determining, according to said orientation, location information in said base mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, so as to extract from said train at least some of said wavelet coefficients, each associated with location information. 6. List of figures Other features and advantages of the invention will appear more clearly on reading the following description of a preferred embodiment, given as a simple illustrative and nonlimiting example, and the appended drawings, among which: FIG. 1, already described in relation with the prior art, presents a block diagram of the process of decoding a bit stream and reconstructing the 3D representation of the associated object; FIG. 2 illustrates, according to the prior art, the hierarchical structure of an image in the context of the SPIHT algorithm for the coding of two-dimensional images; FIG. 3 describes, according to the invention, the hierarchical structure of a mesh in the context of the application of the SPIHT algorithm to the coding of semi-regular meshes (associated with 3D objects); FIG. 4 presents a flowchart of the SPIHT algorithm of the prior art; FIG. 5 illustrates the different steps implemented in the method of decoding a bit stream according to the invention; Figure 6 illustrates the notion of orientation, as defined and used throughout this document. 7. Description of an embodiment of the invention

The general principle of the invention is based on the direct determination, during the decoding of a bit stream, of the location information associated with a wavelet coefficient and its descendants, as a function of the orientation, in the basic mesh. , of the edge with which the father coefficient is associated. In order to better understand this principle, we first recall, in relation with FIGS. 2 and 4, the technique of the SPIHT algorithm, presented by A. Said and WA Pearlman in "A New, Fast, and Efficient Coded Image". Based on Set Partitioning in Hierarchical Trees "for the coding of 2D images. Figure 2 shows the hierarchical structure of a two-dimensional image used in the SPIHT algorithm of the prior art. A tree structure, or tree, defines the spatial relationships in the hierarchical pyramid associated with the image. Figure 2 shows such a tree in the case of a pyramid constructed by recursively dividing the 2D image into 4 subbands. Each node of the tree corresponds to a pixel of the image and is identified by the coordinates of the pixel in the image. His direct descendants correspond to pixels of the same spatial position in the next level of sophistication of the pyramid. The tree is defined in such a way that each node has either no descendants or four descendants, which always form a group of adjacent 2x2 pixels. In Figure 2, the arrows are oriented from the parent node to its four sons. The pixels of the highest level of the pyramid form the roots of the tree, and are also grouped into sets of 2x2 adjacent pixels.

Thus, the pixel referenced 201 of the level of subdivision 20 of the image has four son pixels referenced 211 to 214 in the next level of subdivision 21. The son referenced 212 itself has four descendants referenced 221 to 224 in the level of next subdivision of the hierarchical pyramid.

FIG. 4 presents a flow diagram of the SPIHT decoding algorithm of the bit stream (or "bitstream"), making it possible, for a 2D image, to pass from the bitstream to a set of wavelet coefficients. The detailed algorithm can be found in the article by A. Said and WA Pearlman in "A New, Fast, and Efficient Image Coded Based on Partitioning in Hierarchical Trees" (IEEE Trans. 6 (3), June 1996).

The principle of this algorithm is based on the use and management of three ordered lists, in which the relevance information relating to each pixel of the image is stored; these three lists are: the list LIS 41 of non-significant sets (List of Insignificant Sets); the LIP 40 list of non-significant pixels (List of Insignificant Pixels); the LSP 42 list of significant pixels (List of Significant Pixels). At initialization, the LSP 42 is initialized to the empty list, the LIS 41 and the LIP 40 are initialized to all the roots of the hierarchy of FIG. 2.

At a given subdivision level, the LIP list 40 is then scanned for all the pixels that are not significant for rendering the image, and 401 is determined if, taking into account the relevance threshold associated with this level of subdivision, the coefficient d wavelet associated with one of these pixels must now be considered relevant. In the negative 402, this pixel is left in the LIP 40 list.

In the affirmative 403, the value of the wavelet coefficient is sent, and the pixel is moved in the list LSP 42.

The same is true for the LIS 41 list of sets of non-significant pixels. When the wavelet coefficient associated with a pixel is considered relevant, its direct descendants are searched in the hierarchy to determine whether or not they are equally relevant, and therefore decide whether to move 413, 412 in the hierarchy. LSP 42 or LIP 40 list.

The set of wavelet coefficients associated with the pixels of the LSP list 42 are extracted, and sent 420 in the form of refinement bits, to be used during the reconstruction of the image.

The present invention is in the context of the application of this SPIHT algorithm to 3D objects encoded by meshes and wavelets of second generation (it is recalled that a wavelet is called "second generation" if it is a wavelet allowing the coding of semi-regular meshes, as opposed to the classical wavelets which encode the pixels of a 2D image).

Figure 3 illustrates the hierarchical structure used in this framework for meshing. Each wavelet coefficient is associated bijectively with an edge of the base mesh, and is indexed by the vertex forming the middle of this edge. In the basic mesh, the middle of each edge is therefore associated with a wavelet coefficient, which is the root of a subtree. Each edge of the base mesh is the parent of four edges of the same orientation (i.e. parallel to it) in the directly adjacent refined mesh in the hierarchical subdivision order.

Thus, in FIG. 3, the wavelet coefficient associated with the vertex C, middle of [IJ], has four descendants, or sons, which are respectively associated with the following vertices:

C ₀ , middle of [CJ]; C ₁ , middle of [IC]; C ₂ , middle of [MN]; - C ₃ , middle of [GH].

In a particular embodiment of the invention, which will be limited throughout the rest of this document, a wavelet coefficient of index n in the coefficient table is identified, in such a hierarchical mesh, by four parameters, given by four functions F (n), A (n), B (n) and C (n). The first function indicates a facet of the base mesh on which is the vertex indexing the coefficient. The other three coefficients A (n), B (n) and C (n) are the smallest integer multiples of the barycentric coordinates of this vertex on the facet F (n). We choose indeed to work with whole coordinates, for the sake of simplification, and we therefore do not always manipulate the barycentric coordinates, which can be decimal numbers. By misuse of language, one will speak indifferently in the continuation of this document of barycentric coordinates or smaller integer multiples of these coordinates.

The basic mesh is a mesh having few facets and which is intended to be refined according to the information carried by the coefficients of wavelets.

In order to be able to apply the SPIHT algorithm to the second generation wavelet-coded 3D objects, it is necessary to replace the hierarchy of FIG. 2 by that of FIG. 3, and to replace the notion of pixel by that of wavelet coefficient, or of the mesh indexing this coefficient. This is the context of the present invention. In order to avoid the disadvantages of the SPIHT algorithm adapted to the coding of 3D objects mentioned at the beginning of this document (slow and non-adaptive reconstruction, related to the need to store the entire hierarchy of the object 3D in a cache before being able to begin the reconstruction), the invention consists in modifying this algorithm so that each time that a test is made on the descendants of a coefficient of wavelets, one proceeds in the manner next: if at least one of the descendants does not exist in the cache 10 of FIG. 1, it is created in memory and it is assigned location information in the base mesh, which is determined according to the algorithm presented below in connection with FIG.

These coefficients can thus be directly used during the 3D reconstruction. Indeed, as soon as these wavelet coefficients are extracted from the bitstream and decoded, they are directly registered in the cache 10, so that they are directly usable for the reconstruction 11 of the 3D object 12. Thanks to the using a "zero-tree" coding technique, only part of the bitstream 14 corresponding to the visually relevant areas of the 3D object 12 can be decoded from a user's point of view. In particular, the client user can ask a server to send him only the bits of bitstream 14 corresponding to the subtrees, or "zero-tree", whose root is a visible edge of the mesh zone which interested. Such a technique is for example described in international patent application published under the number WO 03/009234 entitled "Wavelet coding method of an at least two-dimensional meshed object allowing adaptive transmission of wavelet coefficients, signal, system and corresponding devices "on behalf of the same applicants as the present patent application.

The cache 10 then contains only the wavelet coefficients 15 relevant for the reconstruction 11.

It is therefore no longer necessary to wait for all the bitstream 14 to be decoded 13 to begin the reconstruction phase 11, so that it is possible to envisage real-time applications. In the embodiment of the invention described hereinafter, the location information associated with the wavelet coefficients takes the form of the quadruplet

(F, A, B, C), where F is the face of the mesh on which the coefficient is, and

(A ₅ B ₅ C) are the smallest integer multiples of its barycentric coordinates on this face.

The invention consists, during the decoding of the bit stream, in performing tests on the progeny of the wavelet coefficients, in order to locate the entire hierarchy as a function of the quadruplets (F, A, B, C) of the descendants. It thus makes it possible to perform the maintenance of the cache 10, and the association of the wavelet coefficients with their barycentric coordinates. In other words, the invention makes it possible to directly manage the hierarchy of wavelet coefficients in a cache used for the reconstruction.

The different steps of the decoding algorithm of the invention are now presented in greater detail in connection with FIG. At the input of this algorithm, we receive portions of a bit stream, which contains at least the zero-tree encoded wavelet coefficients associated with a multimedia scene or a 3D object (for example a relief of field, or a 3D avatar evolving in a virtual environment). The steps of FIG. 5 are repeated for each of the subtrees or "zero-trees" that one wishes to decode. For example, we first look at a first subtree, whose root is a parent node of the basic mesh, index m.

In a first initialization step referenced 50, the new coordinates F (n), A (n), B (n) and C (n) are initialized to 0, where n is the index of the descendant of the node m. whose coordinates are to be determined. In a second referenced orientation step 51, the orientation of the wavelet coefficient indexed by the node of index m is determined according to the formula:

Orientation = (! (A (m)% 2)) + 2 * (! (B (m)% 2)) + 3 * (! (C (m)% 2)) where% is the operator of the remainder of Euclidean division and! the Boolean negation operator. It is recalled that the notion of orientation, as used and defined throughout this document, is a function of the orientation of the edge of the mesh whose middle is the vertex indexing the coefficient of wavelets considered . Referring to Figure 6, which illustrates a basic mesh, the orientation of an edge is described by the order of the KJI vertices of the base mesh. As illustrated in this figure, the mesh comprises three types of distinct edges: the edges referenced 60, which are parallel to (KJ), and whose orientation is 1; the referenced edges 61, which are parallel to (JI), and whose orientation is 2; the edges referenced 62, which are parallel to (KI), and whose orientation is 3.

After determining the orientation of the wavelet coefficient C of index m, the coordinates of the wires C ₀ , C ₁ , C ₂ and C ₃ of this coefficient are calculated in the hierarchical structure of FIG.

The coordinates of the first son C ₀ are calculated according to the formulas:

F (n) = F (m)

A (n) = 2 * A (m)

B (n) = 2 * B (m) +1 C (n) = 2 * C (m) -1, if the orientation of the coefficient C is 1,

F (n) = F (m)

A (n) = 2 * A (m) -1

B (n) = 2 * B (m)

C (n) = 2 * C (m) +1, if the orientation of the coefficient C is 2, - F (n) = F (m)

A (n) = 2 * A (m) 1

B (n) = 2 * B (m) -1

C (n) = 2 * C (m), if the orientation of the coefficient C is 3.

The coordinates of the second son C ₁ are calculated according to the formulas: F (n) = F (m) A (n) = 2 * A (m)

B (n) = 2 * B (m) -1

C (n) = 2 * C (m) +1, if the orientation of the coefficient C is 1,

F (n) = F (m) A (n) = 2 * A (m) +1

B (n) = 2 * B (m)

C (n) = 2 * C (m) -1, if the orientation of the coefficient C is 2,

F (n) = F (m)

A (n) = 2 * A (m) -1 B (n) = 2 * B (m) +1

C (n) = 2 * C (m), if the orientation of the coefficient C is 3.

The coordinates of the third son C ₂ are calculated according to the formulas:

F (n) = F (m)

A (n) = 2 * A (m) + 2 B (n) = 2 * B (m) -1

C (n) = 2 * C (m) -1, if the orientation of the coefficient C is 1,

F (n) = F (m)

A (n) = 2 * A (m) -1

B (n) = 2 * B (m) + 2 C (n) = 2 * C (m) -1, if the orientation of the coefficient C is 2,

F (n) = F (m)

A (n) = 2 * A (m) -1

B (n) = 2 * B (m) -1

C (n) = 2 * C (m) +2, if the orientation of the coefficient C is 3. The coordinates of the fourth son C ₃ , if it exists, are calculated according to the formulas:

F (n) = F (m)

A (n) = 2 * A (m) -2

B (n) = 2 * B (m) +1 C (n) = 2 * C (m) +1, if the orientation of the coefficient C is 1, F (n) = F (m) A (n) = 2 * A (m) +1 B (n) = 2 * B (m) -2

A (n) = 2 * A (m) +1 B (n) = 2 * B (m) +1

C (n) = 2 * C (m) -2, if the orientation of the coefficient C is 3.

It is indeed possible that a wavelet coefficient has less than four descendants, for example if it is located on one edge of the mesh. It can be determined that one is on an edge of the mesh if the parent edge of level 0 is traversed only once in the basic mesh.

Referring to FIG. 6, the first son C ₀ of the wavelet coefficient C of level j is indexed by the level vertex (j + 1) which has the mother edge [aC], where C is the middle of the ridge [ab]. The second son C ₁ of C is indexed by the level vertex (j + 1) which has the mother edge [bC].

In addition, C belongs to at least 6 level faces (J ⁺ I) ₅ , two of which have for their only intersection with the mother vertex [ab] the vertex C. These two faces have two potentially mother edges which do not contain C The third son C ₂ is such that abC ₂ is oriented in the same direction as KJI. The fourth son C ₃ is such that abC ₃ is oriented in the other direction.

After determination of the barycentric coordinates (to a multiple) of the descendants of the wavelet coefficient of index m, the sign of these coordinates is tested. If A (n) <0 or B (n) <0 or C (n) <0, we must proceed to an affine base change 53, to express them on a facet of the mesh where these barycentric coordinates will be non-negative. We proceed according to the following algorithm:

For each face F 'close to F (n) on the base mesh and as long as A (n) <0 or B (n) <0 or C (n) <0 Calculate F' (n), A '(n) ), B '(n) and C' (n) as described in the following If A '(n)> 0 and B'(n)> 0 and C (n)> 0 {

F (n) = F (n)

C (n) = C '(n)

}} The computation of F '(n), A' (n), B '(n) and C' (n) is realized in the following way: Let FOa [O], FOa [I] and F0a [2] the vertices of F (n) and let FOb [O], FOb [I] and F0b [2] be the vertices of F. F '(n) = F If A (n) + B (n) + C (n) == 1 {ind1 = 2 * (A (n) == 1) + 3 * (B (n) == 1) + 4 * (C (n) == 1) -2 ind2 = (F0a [ind1] == F0b [0]) + 2 * (F0a [ind1] == F0b [1]) + 3 * (F0a [ind1] == F0b [2]) if ind2 == 1

AXn) = I BXn) = O CXn) = O if ind2 == 2

AXn) = O BXn) = I CXn) = O if ind2 == 3 AXn) = O

BXn) = O CXn) = I} else {if (F0a [0] == F0b [0] and F0a [1] == F0b [2]) {Aχn) = A (n) BW≈Cfn) C ^I (n) = B (n)

} if F0a [0] == F0b [1] and F0a [1] == F0b [0] {5 A '(n) = B (n);

B ^I (n) = A (n); C '(n) = C (n);

} if F0a [0] == F0b [2] and F0a [1] == F0b [1] {10 A '(n) = C (n);

B ^I (n) = B (n); C ^I (n) = A (n);

} if F0a [1] == F0b [0] and F0a [2] == F0b [2] {15 A '(n) = B (n);

B ^I (n) = A (n); C '(n) = C (n);

} if F0a [1] == F0b [2] and F0a [2] == F0b [1] {20 A '(n) = A (n);

BW≈Cfn); C ^I (n) = B (n);

} if F0a [1] == F0b [1] and F0a [2] == F0b [0] {25 A '(n) = C (n);

B ^I (n) = B (n); C ^I (n) = A (n);

} if F0a [0] == F0b [0] and F0a [2] == F0b [1] {30 A '(n) = A (n); BW≈Cfn); C ^I (n) = B (n);

} if F0a [0] == F0b [2] and F0a [2] == F0b [0] {A (n) = C (n);

B ^I (n) = B (n); C ^I (n) = A (n);

} if F0a [0] == F0b [1] and F0a [2] == F0b [2] {A '(n) = B (n);

B ^I (n) = A (n);

C '(n) = C (n); }

Thus, the objective of this affine base change step 53 is to find a face F of the mesh in which all the associated barycentric coordinates A, B and C are positive or zero. Each affine base being associated with one face of the mesh, an affine base change therefore amounts to effecting a face change. By this change, we try to express the coordinates of a point of the mesh according to the vertices of another face to which it belongs, so that all these coordinates are positive or zero.

Finally, during a referenced step 54 for reducing the coordinates, the following operation is carried out as long as A (n), B (n) and C (n) are all even: A (n): = A ( n) / 2

B (n): = B (n) / 2

C (n): = C (n) / 2

In other words, if we denote by α, β and γ the true barycentric coordinates of a vertex of the mesh, we have, by definition: α + β + γ = 1. According to the invention, we work during decoding with components, which one could be termed extended barycentric coordinates A (n), B (n) and C (n), which are such that: A (n) + B (n) + C (n) = 2 \ where j is a positive integer. Thus, we have:

A (n) = 2 ^f α

B (n) = 2'β C (n) = 2'γ, which makes it possible to manipulate the coordinates in the form of integer values without losing in precision.

During the reduction step 54 of the coordinates, it is verified that A (n), B (n) and C (n) are indeed the smallest integer multiples of the barycentric coordinates α, β and γ, which makes it possible to on the one hand, to have uniqueness of the output solution 55 of the algorithm of FIG. 5, and on the other hand, to reduce as much as possible the memory space occupied by these coordinates (for example in the cache 10 ).

The algorithm of FIG. 5 can be reiterated for each of the subtrees of the bitstream that it is desired to decode. It makes it possible to follow the coordinates of the wavelet coefficients and their descendants during the course of the SPIHT type algorithm of FIG. 4, so as to minimize the memory space used and the management of the processes using a single memory cache .

The invention is particularly applicable to the decoding of binary trains representative of terrain reliefs, as part of the transmission and reconstruction of large virtual environments. It is recalled that, in this context, various topographic surveys are carried out, which make it possible to construct the basic mesh, and aerial photographs are used to determine the texture to be associated with this basic mesh, with a view to determining the coefficients of gravity. wavelet.

Claims

A method of decoding a data stream representative of an object of at least three dimensions, said object being associated with a base mesh consisting of a set of facets defined by a set of vertices and edges, and coefficients in a wavelet basis corresponding to local modifications of said basic mesh, said wavelet coefficients, each wavelet coefficient being indexed by a vertex of said basic mesh, said data stream comprising at least some of said coefficients wavelet pattern, characterized in that, for at least some wavelet coefficients of said data stream, said method implements the following steps: determining an orientation of an edge carrying said vertex indexing said wavelet coefficient, called the orientation of said wavelet coefficient; determination, according to said orientation, of location information in said basic mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, so as to extract from said train of data at least some of said wavelet coefficients, each associated with location information.

2. Decoding method according to claim 1, characterized in that, for said at least one descendant, if said location information expressed in an affine base does not satisfy at least one predetermined criterion, said method implements a modification step of said affine base, so that said location information expressed in said modified affine base satisfies said at least one criterion.

3. decoding method according to any one of claims 1 and 2, characterized in that it also comprises, for said at least one descendant, a subsequent step of reducing said location information.

4. Decoding method according to any one of claims 1 to 3, characterized in that said wavelet coefficients are encoded according to a zero-tree technique, in said bit stream.

5. Decoding method according to any one of claims 1 to 4, characterized in that, for a wavelet coefficient of index n, said location information comprises four parameters F (n), A (n), B (n), C (n), where F (n) is a facet of said base mesh on which is said vertex indexing said wavelet coefficient, and where A (n), B (n) and C (n) are integer multiples of barycentric coordinates of said vertex on said facet F (n).

6. Decoding method according to claim 5, characterized in that it comprises a preliminary step of initialization of said location information, during which said parameters F (n), A (n), B (n) are assigned to ), C (n) the value zero.

7. decoding method according to any one of claims 5 and 6, characterized in that said orientation of said wavelet coefficient index n is given by the formula:

Orientation = (! (A (n)% 2)) + 2 * (! (B (n)% 2)) + 3 * (! (C (n)% 2)) where% is the operator of the remainder of Euclidean division and! is the Boolean negation operator.

8. decoding method according to any one of claims 5 to 7, characterized in that said location information of said descendants of said wavelet coefficient is determined according to the following formulas: for a first descendant of said coefficient of wavelets: if orientation of said wavelet coefficient is 1:

F (n) = F (m) A (n) = 2 * A (m)

B (n) = 2 * B (m) + l

C (n) = 2 * C (m) -1; if the orientation of said wavelet coefficient is 2:

F (n) = F (m) A (n) = 2 * A (m) -1 B (n) = 2 * B (m)

C (n) = 2 * C (m) + 1; if the orientation of said wavelet coefficient is 3:

F (n) = F (m) A (n) = 2 * A (m) + 1

B (n) = 2 * B (m) -l

C (n) = 2 * C (m); for a second descendant of said wavelet coefficient: if the orientation of said wavelet coefficient is 1: F (n) = F (m)

A (n) = 2 * A (m)

B (n) = 2 * B (m) -l

C (n) = 2 * C (m) + l; if the orientation of said wavelet coefficient is 2: F (n) = F (m)

A (n) = 2 * A (m) + l

B (n) = 2 * B (m)

C (n) = 2 * C (m) -1; if the orientation of said wavelet coefficient is 3: F (n) = F (m)

A (n) = 2 * A (m) -l

B (n) = 2 * B (m) + l

F (n) = F (m)

A (n) = 2 * A (m) 2

B (n) = 2 * B (m) -l

C (n) = 2 * C (m) -l; if the orientation of said wavelet coefficient is 2: F (n) = F (m)

A (n) = 2 * A (m) -l

B (n) = 2 * B (m) 2

C (n) = 2 * C (m) -1 - if the orientation of said wavelet coefficient is 3:

F (n) = F (m)

A (n) = 2 * A (m) -l

B (n) = 2 * B (m) -l

C (n) = 2 * C (m) +2 - for a fourth descendant of said wavelet coefficient, if it exists: if the orientation of said wavelet coefficient is 1:

F (n) = F (m)

A (n) = 2 * A (m) -2

B (n) = 2 * B (m) + 1 C (n) = 2 * C (m) + 1; if the orientation of said wavelet coefficient is 2:

F (n) = F (m)

A (n) = 2 * A (m) + l

B (n) = 2 * B (m) -2 C (n) = 2 * C (m) + 1; if the orientation of said wavelet coefficient is 3:

F (n) = F (m)

A (n) = 2 * A (m) + l

B (n) = 2 * B (m) + 1 C (n) = 2 * C (m) -2; where m denotes the index of said wavelet coefficient and n denotes the index of said descendant.

9. decoding method according to any one of claims 1 to 8, characterized in that said location information does not satisfy said at least one predetermined criterion if said vertex indexing said coefficient wavelet is located on an edge of said basic mesh.

10. Decoding method according to claim 9, characterized in that said location information does not satisfy said at least one predetermined criterion if at least one of the parameters A (n), B (n) and C (n) of said wavelet coefficient is negative.

11. Decoding method according to any one of claims 3 and 5 to 10, characterized in that, during said step of reducing said location information, said parameters A (n), B (n) and C are divided (n) in pairs, as long as said parameters A (n), B (n) and C (n) are all even.

12. decoding method according to any one of claims 1 to 11, characterized in that it also comprises, for each of said wavelet coefficients extracted from said data stream, a subsequent step of storage in a cache of said coefficient of wavelet and associated reduced location information so that said stored wavelet coefficients can be used in a step of reconstructing said at least three dimensional object implementing an inverse wavelet transform.

13. decoding method according to any one of claims 1 to 12, characterized in that it is implemented in the context of an algorithm for sorting the wavelet coefficients of said data stream type SPIHT ("Set Partitioning In Hierarchical Trees ", in French" partitioning sets in hierarchical trees ").

Apparatus for decoding a data stream representative of an object of at least three dimensions, said object being associated with a base mesh consisting of a set of facets defined by a set of vertices and edges, and coefficients in a wavelet basis corresponding to local modifications of said basic mesh, said wavelet coefficients, each wavelet coefficient being indexed by a vertex of said basic mesh, said data stream comprising at least some of said coefficients wavelet, characterized in that, for at least some wavelet coefficients of said data stream, said device implements the following means: means for determining an orientation of an edge carrying said vertex indexing said wavelet coefficient, called orienting said wavelet coefficient; means for determining, according to said orientation, location information in said basic mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, so as to extract said data stream at least some of said wavelet coefficients, each associated with location information.

15. Terminal for restoring an object to at least three dimensions, said object being associated with a basic mesh consisting of a set of facets defined by a set of vertices and edges, and coefficients in a base d wavelets corresponding to local modifications of said basic mesh, called wavelet coefficients, each wavelet coefficient being indexed by a vertex of said basic mesh, said terminal including means for receiving a data stream representative of said object comprising at least some of said wavelet coefficients, characterized in that, for at least some wavelet coefficients of said data stream, said terminal implements the following means: means for determining an orientation of an edge carrying said vertex indexing said wavelet coefficient, referred to as the orientation of said wavelet coefficient; means for determining, according to said orientation, location information in said basic mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, and that said terminal includes storage means in a cache said wavelet coefficients, each associated with location information, and means for reconstructing said at least three-dimensional object implementing an inverse wavelet transform.

16. A computer program product comprising program code instructions recorded on a medium usable in a computer, and for decoding a data stream representative of an object of at least three dimensions, said object being associated with a base mesh consisting of a set of facets defined by a set of vertices and edges, and coefficients in a wavelet basis corresponding to local modifications of said basic mesh, called wavelet coefficients, each coefficient of wavelet being indexed by a vertex of said basic mesh, said data stream comprising at least some of said wavelet coefficients, said computer program product including computer readable programming means for performing, for at least some of said coefficients of wavelets of said data stream: a step of determining an orientation of an edge carrying said vertex indexing said wavelet coefficient, referred to as the orientation of said wavelet coefficient; a step of determining, according to said orientation, location information in said base mesh of at least one descendant of said wavelet coefficient, distinct location rules being associated with each orientation, so as to extract from said train at least some of said wavelet coefficients, each associated with location information.