Shape Compression using Spherical Geometry Images

We recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genus-zero surface onto a regular 2D grid, a spherical geometry image. These geometry images offer several advantages for shape compression. First, simple extension rules extend the square image domain to cover the infinite plane, thereby providing a globally smooth surface parametrization. The 2D grid structure permits use of ordinary image wavelets, including higher-order wavelets with polynomial precision. The coarsest wavelets span the entire surface and thus encode the lowest frequencies of the shape. Finally, the compression and decompression algorithms operate on ordinary 2D arrays, and are thus ideally suited for hardware acceleration. In this paper, we detail two wavelet-based approaches for shape compression using spherical geometry images, and provide comparisons with previous compression schemes.

[1]  Leif Kobbelt,et al.  Simplification and Compression of 3D Meshes , 2002, Tutorials on Multiresolution in Geometric Modelling.

[2]  Hugues Hoppe,et al.  Spherical parametrization and remeshing , 2003, ACM Trans. Graph..

[3]  Andrei Khodakovsky,et al.  Progressive geometry compression , 2000, SIGGRAPH.

[4]  Andrei Khodakovsky,et al.  Globally smooth parameterizations with low distortion , 2003, ACM Trans. Graph..

[5]  Peter Schröder,et al.  Spherical wavelets: efficiently representing functions on the sphere , 1995, SIGGRAPH.

[6]  A. Khodakovsky Normal Mesh Compression , 2000 .

[7]  Wolfgang Straßer,et al.  Real time compression of triangle mesh connectivity , 1998, SIGGRAPH.

[8]  Sivan Toledo,et al.  High-Pass Quantization for Mesh Encoding , 2003, Symposium on Geometry Processing.

[9]  Pedro V. Sander,et al.  Multi-Chart Geometry Images , 2003, Symposium on Geometry Processing.

[10]  Peter Schröder,et al.  Normal meshes , 2000, SIGGRAPH.

[11]  Pierre Alliez,et al.  Valence‐Driven Connectivity Encoding for 3D Meshes , 2001, Comput. Graph. Forum.

[12]  Craig Gotsman,et al.  Triangle Mesh Compression , 1998, Graphics Interface.

[13]  Hugues Hoppe,et al.  Progressive meshes , 1996, SIGGRAPH.

[14]  Steven J. Gortler,et al.  Geometry images , 2002, SIGGRAPH.

[15]  Gabriel Taubin,et al.  Progressive forest split compression , 1998, SIGGRAPH.

[16]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..

[17]  Michael Deering,et al.  Geometry compression , 1995, SIGGRAPH.

[18]  Pierre Alliez,et al.  Progressive compression for lossless transmission of triangle meshes , 2001, SIGGRAPH.

[19]  Marco Attene,et al.  SwingWrapper: Retiling triangle meshes for better edgebreaker compression , 2003, TOGS.

[20]  Jaroslaw R. Rossignac,et al.  3D Mesh Compression , 2005, The Visualization Handbook.

[21]  Craig Gotsman,et al.  Spectral compression of mesh geometry , 2000, EuroCG.

[22]  Jarek Rossignac,et al.  Edgebreaker: Connectivity Compression for Triangle Meshes , 1999, IEEE Trans. Vis. Comput. Graph..

[23]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[24]  Ayellet Tal,et al.  Polyhedron realization for shape transformation , 1998, The Visual Computer.

[25]  Pierre Alliez,et al.  Recent advances in compression of 3D meshes , 2005, 2005 13th European Signal Processing Conference.

[26]  Pedro V. Sander,et al.  Geometry videos: a new representation for 3D animations , 2003, SCA '03.

[27]  Tony DeRose,et al.  Multiresolution analysis for surfaces of arbitrary topological type , 1997, TOGS.