California Institute of Technology

Lucent Technologies Inc.

Alcatel Lucent

Princeton University

Interval Research Corporation

Peter Schröder

Wim Sweldens

Igor V Guskov

Andrei Khodakovsky

Krasimir D Kolarov

William C Lynch

An irregular connectivity mesh representative of a surface having an arbitrary topology is processed using a non-uniform relaxation procedure. The non-uniform relaxation procedure minimizes differences between vectors normal to faces of pairs of triangles having a common edge and located within a designated neighborhood of a given vertex. The relaxation procedure may be used to construct subdivision and pyramid algorithms for performing processing operations such as upsampling, downsampling and filtering on irregular connectivity meshes. The signal processing algorithms may be utilized in applications such as smoothing, enhancement, editing, texture mapping and compression.

Non-uniform relaxation procedure for multiresolution mesh processing

A method of forming a hybrid mesh representation of an object surface is provided, along with the hybrid mesh representation and data structures corresponding to various polygons in the hybrid mesh representation. The hybrid mesh representation comprises a base mesh and one or more higher level meshes. At least one of the higher level meshes representing a patch is an irregular mesh. The method of forming the hybrid mesh representation comprises the steps of forming a base mesh, and then forming one or more higher level meshes from the base mesh through one or more regular refinement operations in combination with at least one irregular operation.

Hybrid meshes

A technique for compression and expansion of a function defined upon an M-dimensional manifold embedded in N-dimensional space uses a second generation wavelet transform and a modified zerotree bit-encoding scheme. Typically, a function is defined upon a two-dimensional manifold embedded in three-dimensional space, such as a sphere. A geometric base is chosen as a coarse initial model of the manifold. Second generation wavelets for the function are calculated using a triangular subdivision scheme in order to subdivide the geometric base in order to produce a refined triangular mesh. The wavelet coefficients are defined at the vertices of the triangles in the triangular mesh. A tree structure is created in which each node of the tree structure represents an associated triangle of the triangular mesh. Each triangle in the mesh is recursively subdivided into four subtriangles and each associated node in the tree structure also has four children, which correspond to the four subtriangles. Each wavelet coefficient defined at a particular vertex in the triangular mesh is uniquely assigned to a single one of the triangles at a next higher level of subdivision, such that each triangle at the next higher level of subdivision has from zero to three assigned wavelet coefficients. Using a modified zerotree encoding scheme, values of the wavelet coefficients are processed bit plane by bit plane, outputting bits indicative of significant nodes and their descendants. Sign bits and data bits are also output. An expansion technique inputs bits according to the modified zerotree scheme into the tree structure in order to define wavelet coefficients. An inverse second generation wavelet transform is used to synthesize the original function from the wavelet coefficients.

Wavelet-based data compression

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Peter Schröder