Surface compression with geometric bandelets

This paper describes the construction of second generation bandelet bases and their application to 3D geometry compression. This new coding scheme is orthogonal and the corresponding basis functions are regular. In our method, surfaces are decomposed in a bandelet basis with a fast bandeletization algorithm that removes the geometric redundancy of orthogonal wavelet coefficients. The resulting transform coding scheme has an error decay that is asymptotically optimal for geometrically regular surfaces. We then use these bandelet bases to perform geometry image and normal map compression. Numerical tests show that for complex surfaces bandelets bring an improvement of 1.5dB to 2dB over state of the art compression schemes.

[1]  Aaron Hertzmann,et al.  Illustrating smooth surfaces , 2000, SIGGRAPH.

[2]  Thomas Malzbender,et al.  A Survey of Methods for Volumetric Scene Reconstruction from Photographs , 2001, VG.

[3]  Stephen Lin,et al.  View-dependent displacement mapping , 2003, ACM Trans. Graph..

[4]  Yihong Du,et al.  Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations , 1999, SIAM J. Math. Anal..

[5]  Stéphane Mallat,et al.  Bandelet Image Approximation and Compression , 2005, Multiscale Model. Simul..

[6]  Hugues Hoppe,et al.  Shape Compression using Spherical Geometry Images , 2005, Advances in Multiresolution for Geometric Modelling.

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

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

[9]  Tony DeRose,et al.  Piecewise smooth surface reconstruction , 1994, SIGGRAPH.

[10]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[11]  Paolo Cignoni,et al.  Metro: Measuring Error on Simplified Surfaces , 1998, Comput. Graph. Forum.

[12]  Andrei Khodakovsky,et al.  Compression of Normal Meshes , 2004 .

[13]  Justin K. Romberg,et al.  Wavelet-domain approximation and compression of piecewise smooth images , 2006, IEEE Transactions on Image Processing.

[14]  Mark S. Peercy,et al.  Efficient bump mapping hardware , 1997, SIGGRAPH.

[15]  I. Daubechies,et al.  Normal Multiresolution Approximation of Curves , 2004 .

[16]  B. Alpert.  Wavelets and other bases for fast numerical linear algebra , 1993 .

[17]  Mathieu Desbrun,et al.  Variational shape approximation , 2004, SIGGRAPH 2004.

[18]  H. Seidel,et al.  Ridge-valley lines on meshes via implicit surface fitting , 2004, SIGGRAPH 2004.

[19]  Wolfgang Dahmen,et al.  Wavelets on Manifolds I: Construction and Domain Decomposition , 1999, SIAM J. Math. Anal..

[20]  Pierre Alliez,et al.  Anisotropic polygonal remeshing , 2003, ACM Trans. Graph..

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

[22]  Greg Turk,et al.  Fast and memory efficient polygonal simplification , 1998 .

[23]  S. Mallat.  VI – Wavelet zoom , 1999 .

[24]  Shree K. Nayar,et al.  Reflectance and texture of real-world surfaces , 1999, TOGS.

[25]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[26]  Henning Biermann,et al.  Piecewise smooth subdivision surfaces with normal control , 2000, SIGGRAPH.

[27]  Subhash Suri,et al.  Surface approximation and geometric partitions , 1994, SODA '94.

[28]  Marc Levoy,et al.  The digital Michelangelo project: 3D scanning of large statues , 2000, SIGGRAPH.

[29]  Stéphane Mallat,et al.  Sparse geometric image representations with bandelets , 2005, IEEE Transactions on Image Processing.

[30]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[31]  Serge J. Belongie,et al.  Structured importance sampling of environment maps , 2003, ACM Trans. Graph..

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

[33]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[34]  T. Igarashi,et al.  Volumetric illustration: designing 3D models with internal textures , 2004, SIGGRAPH 2004.

[35]  Tony DeRose,et al.  Subdivision surfaces in character animation , 1998, SIGGRAPH.

[36]  Albert Cohen,et al.  Nonlinear Subdivision Schemes: Applications to Image Processing , 2002, Tutorials on Multiresolution in Geometric Modelling.

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

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

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

[40]  S. Mallat.  A wavelet tour of signal processing , 1998 .