Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; 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
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T9/00—Image coding
  • G06T9/001—Model-based coding, e.g. wire frame

Definitions

• the field of the invention is that of coding images or image elements. More specifically, the invention relates to the adaptive representation and coding of scenes (or objects of a scene) in three dimensions (3D) represented by meshes.
• the invention finds applications in all fields where it is desirable to reduce the amount of information necessary to efficiently represent a digital image, to store it and / or transmit it.
• the invention can be used for transmitting images via the network
• the invention can, in this case, be a primitive of a data transmission language such as VRML.
• Other possible applications include the storage of animated data on CD-ROM (or equivalent data carrier), multi-user applications, digital television, etc.
• the invention proposes an improvement to the so-called "wavelet” methods, which make it possible to represent a mesh as a succession of details added to a basic mesh.
• wavelet a technique that makes 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. Lounsberry, T. DeRose and J. Warren, "Multiresolution analysis for surfaces or arbitrary topological type" (ACM Transaction on Graphics, Vol.16, No. 1, pp. 34-73).
• a mesh is therefore represented by a series of coefficients which correspond to the coordinates in a wavelet base of a parametrization of said mesh by a simple polyhedron.
• the corresponding mathematical principles are recalled in the appendix (this appendix is part of this description).
• each of its faces is the root of a tree whose the threads of each node are the four faces obtained after canonical subdivision.
• the wavelet coefficients are indexed by their barycentric coordinates on a face of M 0 .
• the principle is to start from the vertex indexing the wavelet coefficient considered and to make complete, by subdivision, its neighbors, then the neighbors of its neighbors, recursively until all the vertices considered are complete. This rule comes from the observation that this algorithm is sufficient to ensure a subdivision adapted to the modifications brought by the wavelet coefficient considered.
• an objective of the invention is to provide a method of coding a representative mesh of an object in three dimensions, which produces a limited number of facets, compared to the known technique, for a level of quality of identical or similar restitution.
• Another objective of the invention is to provide such a coding method, the complexity of which (in particular in terms of the number of operations carried out and the memory capacity required) is less, or at the very least, of the same order of magnitude. , to known techniques.
• the invention also aims to provide such a coding method, making it possible to have several levels of quality of restitution of the object, according to various criteria (processing capacity of the terminal, capacity of the storage means available, bit rate transmission, user needs ).
• Yet another objective of the invention is to provide such a coding method, allowing a progressive reconstruction of the object.
• the invention also aims, of course, to provide a method of reconstructing an object coded according to this coding method.
• a method of coding a source mesh (M) representative of a three-dimensional object in which one determines a simple mesh (M 0 ) having a reduced number of faces each defined by vertices and edges, then coefficients in a wavelet base of a function (f) of which said source mesh is the image defined on said simple mesh (M 0 ), so as to provide a decomposition of said source mesh (M) into successive refined meshes (or sub-meshes) (M,), according to a predetermined criterion.
• each of the faces of one of said meshes (M.) is subdivided into a limited number of facets to form the upper level mesh (M, +1 ), the subdivisions of said face corresponding only to those necessary for respect an affinity condition of said function (f) on said face.
• the inventor has observed that taking into account a wavelet coefficient must be accompanied by a local subdivision in the vicinity of the vertex indexing the wavelet in question, so that the latter is refined in pieces on each facet . Since the wavelets are sums of functions ⁇ J , it suffices to know how to localize the support of such a function and to locally subdivide the facets which contain them until this function is refined on each resulting facet.
• said source mesh (M) is broken down into a set of trees, each of said trees representing one face of said simple mesh (M Q ) and comprising nodes each representing one face of a mesh
• each of said trees is the smallest such that, when a given face is subdivided into four facets, the corresponding node comprises four wires representing said four facets.
• the method of the invention allows access to several levels of coding quality, corresponding to each of said successive meshes.
• said successive meshes are obtained by the implementation of a recursive algorithm.
• the method is thus particularly simple to implement.
• said recursive algorithm comprises the following steps:
• step (b) we subdivide the face F; the processing is resumed in step (b), for the four wires of the face F successively.
• the invention also relates to a method for reconstructing a source mesh (M) representative of a three-dimensional object and coded according to the coding method described above.
• such a reconstruction method ensures the progressive reconstruction of said object, from the simple mesh (M 0 ) then using successive meshes (M ; ).
• this reconstruction method allows access to several levels of coding quality, corresponding to each of said successive meshes.
• the invention advantageously applies to many fields, and can in particular apply to at least one of the following fields: display of mesh objects in three dimensions on a screen; progressive display of mesh objects in three dimensions on a screen, said wavelet coefficients being taken into account as they arrive; display of mesh objects in three dimensions on a screen with at least two levels of detail, a level of detail corresponding to one of said successive meshes (M j ); display of different parts of a mesh object with at least two different levels of detail; compression of a mesh of a mesh object.
• FIG. 1 is a simplified general block diagram of the coding method according to the invention
• FIG. 4 is a more detailed block diagram, taking up and detailing the localization and subdivision steps of FIG. 3.
• the coding method of a mesh according to the invention therefore aims, in particular, to operate the minimum number of subdivisions necessary while remaining of the same algorithmic complexity as the known technique.
• the barycentric coordinates of these two vertices are characterized by the following criterion:
• a localization step 32 is carried out, in which the elements to be treated are brought back to the base. adequate refining, then a subdivision step (33) of each face considered.
• Localization 32 consists of, ⁇ J written as a weighted sum
• scale functions at level j + 1 determine the faces and barycentric coordinates of the points of M 0 (or vertices of M) indexing these scale functions. Then, for each triplet of coordinates ( ⁇ , ⁇ , ⁇ ) associated with a face F
• a surface S in space can be represented as the image of an injective continuous function defined on a polyhedron Mo of the same topological type and with values in R 3 .
• the surface is parametrized by the polyhedron, and we call parametrization the said function.
• This function is a triplet of functions with values in R, which can each be developed in a base of the space C ° (M 0 ) of continuous functions on the polyhedron with values in R.
• C ⁇ and d are in R 3 , and are called wavelet coefficients.
• the wavelets are chosen so that their support allows a determination of the wavelet coefficients at 0 (n), where n is the number of vertices of the mesh M: for fixed integer, if we denote by D k, i the set of indices of the vertices of a mesh M j which are less than k edges away from the vertex i, the wavelet ⁇ ⁇ is given by
• ⁇ i ⁇ i +1 + ⁇ ai ⁇ i, ieD k ⁇ t so that ⁇ ⁇ has support in D k + ⁇ , i-

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• Engineering & Computer Science (AREA)
• Physics & Mathematics (AREA)
• Theoretical Computer Science (AREA)
• General Physics & Mathematics (AREA)
• Geometry (AREA)
• Computer Graphics (AREA)
• Multimedia (AREA)
• Software Systems (AREA)
• Processing Or Creating Images (AREA)
• Compression Or Coding Systems Of Tv Signals (AREA)
• Image Processing (AREA)
• Image Generation (AREA)
• Compression, Expansion, Code Conversion, And Decoders (AREA)

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• 1998
  • 1998-08-03 FR FR9810097A patent/FR2781908B1/fr not_active Expired - Fee Related
• 1999
  • 1999-08-03 CA CA002337360A patent/CA2337360C/en not_active Expired - Lifetime
  • 1999-08-03 EP EP99936681A patent/EP1101200B1/fr not_active Expired - Lifetime
  • 1999-08-03 JP JP2000564166A patent/JP4216477B2/ja not_active Expired - Fee Related
  • 1999-08-03 US US09/743,972 patent/US6931155B1/en not_active Expired - Fee Related
  • 1999-08-03 DE DE69907917T patent/DE69907917T2/de not_active Expired - Lifetime
  • 1999-08-03 WO PCT/FR1999/001924 patent/WO2000008604A1/fr not_active Ceased

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