“Progressive compression for lossless transmission of triangle meshes” by Alliez and Desbrun

Lossless transmission of 3D meshes is a very challenging and timely problem for many applications, ranging from collaborative design to engineering. Additionally, frequent delays in transmissions call for progressive transmission in order for the end user to receive useful successive refinements of the final mesh. In this paper, we present a novel, fully progressive encoding approach for lossless transmission of triangle meshes with a very fine granularity. A new valence-driven decimating conquest, combined with patch tiling and an original strategic retriangulation is used to maintain the regularity of valence. We demonstrate that this technique leads to good mesh quality, near-optimal connectivity encoding, and therefore a good rate-distortion ratio throughout the transmission. We also improve upon previous lossless geometry encoding by decorrelating the normal and tangential components of the surface. For typical meshes, our method compresses connectivity down to less than 3.7 bits per vertex, 40% better in average than the best methods previously reported [5, 18]; we further reduce the usual geometry bit rates by 20% in average by exploiting the smoothness of meshes. Concretely, our technique can reduce an ascii VRML 3D model down to 1.7% of its size for a 10-bit quantization (2.3% for a 12-bit quantization) while providing a very progressive reconstruction.

1. P. Alliez and M. Desbrun. Valence-Driven Connectivity Encoding of 3D Meshes. In Eurographics Conference Proceedings, 2001.
2. R. Bar-Yehuda and C. Gotsman. Time/space Tradeoffs for Polygon Mesh Rendering. ACM Transactions on Graphics, 15(2):141-152, 1996.
3. J-D. Boissonnat and F. Cazals. Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions. In ACM Symposium on Computational Geometry, 2000.
4. P. Cignoni, C. Rocchini, and R. Scopigno. Metro: Measuring Error on Simplified Surfaces. Computer Graphics Forum, 17(2):167-174, 1998.
5. D. Cohen-Or, D. Levin, and O. Remez. Progressive Compression of Arbitrary Triangular Meshes. In IEEE Visualization 99 Conference Proceedings, pages 67-72, 1999.
6. M. Deering. Geometry Compression. In ACM SIGGRAPH 95 Conference Pro-ceedings, pages 13-20, 1995.
7. M. Denny and C. Sohler. Encoding a Triangulation as a Permutation of its Point Set. 9th Canadian Conference on Computational Geometry, pages 39-43, 1997.
8. O. Devillers and P-M. Gandoin. Geometric Compression for Interactive Transmission. In IEEE Visualization 00 Conference Proceedings, pages 319-326, 2000.
9. M. Garland and P. Heckbert. Simplifying Surfaces with Color and Texture using Quadric Error Metrics. In IEEE Visualization 98 Conference Proceedings, pages 263-269, 1998.
10. S. Gumhold and W. Strasser. Real Time Compression of Triangle Mesh Connectivity. In ACM SIGGRAPH 98 Conference Proceedings, pages 133-140, 1998.
11. H. Hoppe. Progressive meshes. In ACMSIGGRAPH 96 Conference Proceedings, pages 99-108, 1996.
12. H. Hoppe. New Quadric Metric for Simpliying Meshes with Apperance Attributes. In IEEE Visualization 99 Conference Proceedings, pages 59-66, 1999.
13. A. Khodakovsky, P. Schroder, and W. Sweldens. Progressive Geometry Compression. In ACM SIGGRAPH 00 Conference Proceedings, pages 271-278, 2000.
14. D. King and J. Rossignac. Guaranteed 3.67v bit Encoding of Planar Triangle Graphs. In Proceedings of the 11th Canadian Conference on Computational Geometry, pages 146-149, 1999.
15. D. King and J. Rossignac. Optimal Bit Allocation in 3D Compression. Journal of Computational Geometry, Theory and Applications, 14:91-118, 1999.
16. L. Kobbelt. p3-Subdivision. In ACM SIGGRAPH 00 Conference Proceedings, pages 103-112, 2000.
17. P. Lindstrom and G. Turk. Fast and Memory Efficient Polygonal Simplification. In IEEE Visualization 98 Conference Proceedings, pages 279-286, 1998.
18. R. Pajarola and J. Rossignac. Compressed Progressive Meshes. IEEE Transactions on Visualization and Computer Graphics, 6(1):79-93, 2000.
19. R. Pajarola and J. Rossignac. Squeeze: Fast and Progressive Decompression of Triangle Meshes. In Proceedings of the Computer Graphics International Conference, 2000.
20. J. Rossignac. EdgeBreaker : Connectivity Compression for Triangle Meshes. IEEE Transactions on Visualization and Computer Graphics, pages 47-61, 1999.
21. J. Rossignac and A. Szymczak. WrapZip Decompression of the Connectivity of Triangle Meshes Compressed with Edgebreaker. Journal of Computational Geometry, Theory and Applications, 14:119-135, november 1999.
22. M. Schindler. A Fast Renormalization for Arithmetic Coding. In Proceedings of IEEE Data Compression Conference, Snowbird, UT, page 572, 1998. http://www.compressconsult.com/rangecoder/.
23. J. Snoeyink and M. van Kerveld. Good Orders for Incremental (Re)construction. 13th annual ACM Symposium on Comp. Geometry, pages 400-402, 1997.
24. A. Szymczak, D. King, and J. Rossignac. An Edgebreaker-based Efficient Compression Scheme for Regular Meshes, 2000. To appear in a special issue of Journal of Computational Geometry: Theory and Applications.
25. G. Taubin, A. Gueziec, W. Horn, and F. Lazarus. Progressive Forest Split Compression. In ACM SIGGRAPH 98 Conference Proceedings, pages 123-132, 1998.
26. G. Taubin, W. Horn, J. Rossignac, and F. Lazarus. Geometry Coding and VRML. In Proceedings of the IEEE, Special issue on Multimedia Signal Processing, volume 86(6), pages 1228-1243, june 1998.
27. G. Taubin and J. Rossignac. 3D Geometry Compression, 1999-2000. ACM SIGGRAPH Conference course notes.
28. C. Touma and C. Gotsman. Triangle Mesh Compression. In Graphics Interface 98 Conference Proceedings, pages 26-34, 1998.
29. I.H. Witten, R.M. Neal, and J.G. Cleary. Arithmetic Coding for Data Compression. Communications of the ACM, 30(6), june 1987.