Advertisement

Recent Advances in Compression of 3D Meshes

  • Pierre Alliez
  • Craig Gotsman
Part of the Mathematics and Visualization book series (MATHVISUAL)

Summary

3D meshes are widely used in graphical and simulation applications for approximating 3D objects. When representing complex shapes in raw data format, meshes consume a large amount of space. Applications calling for compact storage and fast transmission of 3D meshes have motivated the multitude of algorithms developed to compress these datasets efficiently. In this paper we survey recent developments in compression of 3D surface meshes. We survey the main ideas and intuition behind techniques for single-rate and progressive mesh coding. Where possible, we discuss the theoretical results obtained for asymptotic behaviour or optimality of the approach. We also list some open questions and directions for future research.

Keywords

Subdivision Scheme Triangle Mesh Polygon Mesh Vertex Position Original Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Alliez, D. Cohen-Steiner, O. Devillers, B. Levy, and M. Desbrun. Anisotropic Polygonal Remeshing. In Proc. ACM SIGGRAPH, 2003.Google Scholar
  2. 2.
    P. Alliez and M. Desbrun. Progressive Encoding for Lossless Transmission of 3D Meshes. In Proc. ACM SIGGRAPH, pages 198–205, 2001.Google Scholar
  3. 3.
    P. Alliez and M. Desbrun. Valence-Driven Connectivity Encoding of 3D Meshes. In Eurographics Conference Proceedings, pages 480–489, 2001.Google Scholar
  4. 4.
    M. Attene, B. Falcidieno, M. Spagnuolo, and J. Rossignac. SwingWrapper: Retiling Triangle Meshes for Better EdgeBreaker Compression. ACM Transactions on Graphics, 22(4):982–996, 2003.CrossRefGoogle Scholar
  5. 5.
    M. Ben-Chen and C. Gotsman. On the Optimality of the Laplacian Spectral Basis for Mesh Geometry Coding. ACM Transactions on Graphics. to appear.Google Scholar
  6. 6.
    A. Bogomjakov and C. Gotsman. Universal Rendering Sequences for Transparent Vertex Caching of Progressive Meshes. Computer Graphics Forum, 21(2):137–148, 2002.CrossRefGoogle Scholar
  7. 7.
    R.C-N. Chuang, A. Garg, X. He, M-Y. Kao, and H-I Lu. Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses. In ICALP: Annual International Colloquium on Automata, Languages and Programming, pages 118–129, 1998.Google Scholar
  8. 8.
    D. Cohen-Or, D. Levin, and O. Remez. Progressive Compression of Arbitrary Triangular Meshes. In IEEE Visualization Conference Proceedings, pages 67–72, 1999.Google Scholar
  9. 9.
    R. Cohen D. Cohen-Or and T. Ironi. Multi-way Geometry Encoding, 2002. Technical report.Google Scholar
  10. 10.
    M. Deering. Geometry Compression. Proc. ACM SIGGRAPH, pages 13–20, 1995.Google Scholar
  11. 11.
    O. Devillers and P-M. Gandoin. Geometric Compression for Interactive Transmission. IEEE Visualization Conference Proceedings, pages 319–326, 2000.Google Scholar
  12. 12.
    P.-M. Gandoin and O. Devillers. Progressive Lossless Compression of Arbitrary Simplicial Complexes. ACM Transactions on Graphics, 21:372–379, 2002. Proc. ACM SIGGRAPH.CrossRefGoogle Scholar
  13. 13.
    C. Gotsman. On the Optimality of Valence-Based Connectivity Coding. Computer Graphics Forum, 22(1):99–102, 2003.CrossRefGoogle Scholar
  14. 14.
    C. Gotsman, S. Gumhold, and L. Kobbelt. Simplification and Compression of 3D Meshes, 2002. In Tutorials on Multiresolution in Geometric Modelling (Munich Summer School Lecture Notes), A. Iske, E. Quak, M. Floater (Eds.), Springer, 2002.Google Scholar
  15. 15.
    X. Gu, S. Gortler, and H. Hoppe. Geometry Images. In Proc. ACM SIGGRAPH, pages 355–361, 2002.Google Scholar
  16. 16.
    S. Gumhold. Improved Cut-Border Machine for Triangle Mesh Compression. Erlangen Workshop'99 on Vision, Modeling and Visualization, 1999.Google Scholar
  17. 17.
    S. Gumhold. New Bounds on the Encoding of Planar Triangulations. Technical Report WSI-2000-1, Univ. of Tübingen, 2000.Google Scholar
  18. 18.
    S. Gumhold and W. Strasser. Real Time Compression of Triangle Mesh Connectivity. In Proc. ACM SIGGRAPH, pages 133–140, 1998.Google Scholar
  19. 19.
    I. Guskov, K. Vidimce, W. Sweldens, and P. Schröder. Normal Meshes. In Proc. ACM SIGGRAPH, pages 95–102, 2000.Google Scholar
  20. 20.
    Henry Helson. Harmonic Analysis. Wadsworth & Brooks/Cole, 1991.Google Scholar
  21. 21.
    J. Ho, K-C. Lee, and D. Kriegman. Compressing Large Polygonal Models. In IEEE Visualization Conference Proceedings, pages 357–362, 2001.Google Scholar
  22. 22.
    H. Hoppe. Progressive meshes. In Proc. ACM SIGGRAPH, pages 99–108, 1996.Google Scholar
  23. 23.
    M. Isenburg. Compressing Polygon Mesh Connectivity with Degree Duality Prediction. In Graphics Interface Conference Proc., pages 161–170, 2002.Google Scholar
  24. 24.
    M. Isenburg and P. Alliez. Compressing Hexahedral Volume Meshes. In Pacific Graphics Conference Proceedings, pages 284–293, 2002.Google Scholar
  25. 25.
    M. Isenburg and P. Alliez. Compressing Polygon Mesh Geometry with Parallelogram Prediction. In IEEE Visualization Conference Proceedings, pages 141–146, 2002.Google Scholar
  26. 26.
    M. Isenburg, P. Alliez, and J. Snoeyink. A Benchmark Coder for Polygon Mesh Compression, 2002. http://www.cs.unc.edu/~isenburg/pmc/.Google Scholar
  27. 27.
    M. Isenburg and S. Gumhold. Out-of-Core Compression for Gigantic Polygon Meshes. In ACM Transactions on Graphics (Proc. ACM SIGGRAPH), 22(3):935–942, 2003.CrossRefGoogle Scholar
  28. 28.
    M. Isenburg and J. Snoeyink. Mesh Collapse Compression. In Proc. of SIBGRAPI'99, Campinas, Brazil, pages 27–28, 1999.Google Scholar
  29. 29.
    M. Isenburg and J. Snoeyink. Face Fixer: Compressing Polygon Meshes With Properties. In Proc. ACM SIGGRAPH, pages 263–270, 2000.Google Scholar
  30. 30.
    M. Isenburg and J. Snoeyink. Spirale Reversi: Reverse Decoding of the Edgebreaker Encoding. In Proc. 12th Canadian Conference on Computational Geometry, pages 247–256, 2000.Google Scholar
  31. 31.
    M. Isenburg and J. Snoeyink. Binary Compression Rates for ASCII Formats. In Proc. Web3D Symposium, pages 173–178, 2003.Google Scholar
  32. 32.
    Z. Karni, A. Bogomjakov, and C. Gotsman. Efficient Compression and Rendering of Multi-Resolution Meshes. In IEEE Visualization Conference Proceedings, 2002.Google Scholar
  33. 33.
    Z. Karni and C. Gotsman. Spectral Compression of Mesh Geometry. In Proc. ACM SIGGRAPH, pages 279–286, 2000.Google Scholar
  34. 34.
    Keeler and Westbrook. Short Encodings of Planar Graphs and Maps. Discrete Appl. Math., 58:239–252, 1995.MathSciNetCrossRefGoogle Scholar
  35. 35.
    A. Khodakovsky, P. Alliez, M. Desbrun, and P. Schröder. Near-Optimal Connectivity Encoding of 2-Manifold Polygon Meshes. Graphical Models, special issue, 2002.Google Scholar
  36. 36.
    A. Khodakovsky and I. Guskov. Compression of Normal Meshes. In Proc. ACM SIGGRAPH. Springer-Verlag, 2003.Google Scholar
  37. 37.
    A. Khodakovsky, N. Litke, and P. Schröder. Globally Smooth Parameterizations with Low Distortion. In ACM Transactions on Graphics (Proc. ACM SIGGRAPH), 22(3):350–357, 2003.CrossRefGoogle Scholar
  38. 38.
    A. Khodakovsky, P. Schröder, and W. Sweldens. Progressive Geometry Compression. Proc. ACM SIGGRAPH, pages 271–278, 2000.Google Scholar
  39. 39.
    D. King and J. Rossignac. Guaranteed 3.67V bit Encoding of Planar Triangle Graphs. In 11th Canadian Conference on Computational Geometry, pages 146–149, 1999.Google Scholar
  40. 40.
    D. King, J. Rossignac, and A. Szmczak. Compression for Irregular Quadrilateral Meshes. Technical Report TR-99-36, GVU, Georgia Tech, 1999.Google Scholar
  41. 41.
    D. Knuth. Exhaustive Generation, 2003. volume 4 of The Art of Computer Programming, in preparation, available electronically, http://www.cs.stanford.edu/~knuth.Google Scholar
  42. 42.
    B. Kronrod and C. Gotsman. Efficient Coding of Non-Triangular Mesh Connectivity. Graphical Models, 63(263–275), 2001.CrossRefGoogle Scholar
  43. 43.
    B. Kronrod and C. Gotsman. Optimized Compression of Triangle Mesh Geometry Using Prediction Trees. Proc. 1st International Symposium on 3D Data Processing, Visualization and Transmission, pages 602–608, 2002.Google Scholar
  44. 44.
    A. W. F. Lee, W. Sweldens, P. Schröder, L. Cowsar, and D. Dobkin. MAPS: Multiresolution adaptive parameterization of surfaces. Computer Graphics, 32(Annual Conference Series):95–104, August 1998.Google Scholar
  45. 45.
    E. Lee and H. Ko. Vertex Data Compression For Triangular Meshes. In Proc. Pacific Graphics, pages 225–234, 2000.Google Scholar
  46. 46.
    H. Lee, P. Alliez, and M. Desbrun. Angle-Analyzer: A Triangle-Quad Mesh Codec. In Eurographics Conference Proceedings, pages 383–392, 2002.Google Scholar
  47. 47.
    M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, and D. Fulk. The Digital Michelangelo Project. In Proc. ACM SIGGRAPH, pages 131–144, 2000.Google Scholar
  48. 48.
    J. Li and C.-C. Jay Kuo. Mesh Connectivity Coding by the Dual Graph Approach, July 1998. MPEG98 Contribution Document No. M3530, Dublin, Ireland.Google Scholar
  49. 49.
    R. Pajarola and J. Rossignac. Compressed Progressive Meshes. IEEE Transactions on Visualization and Computer Graphics, 6(1):79–93, 2000.CrossRefGoogle Scholar
  50. 50.
    F. Payan and M. Antonini. 3D Mesh Wavelet Coding Using Efficient Modelbased Bit Allocation. In Proc. 1st Int. Symposium on 3D Data Processing Visualization and Transmission, pages 391–394, 2002.Google Scholar
  51. 51.
    D. Poulalhon and G. Schaeffer. Optimal Coding and Sampling of Triangulations, 2003. 30th international colloquium on automata, languages and programming (ICALP'03).Google Scholar
  52. 52.
    J. Rossignac. Edgebreaker: Connectivity Compression for Triangle Meshes. IEEE Transactions on Visualization and Computer Graphics, 1999.Google Scholar
  53. 53.
    P. Sander, S. Gortler, J. Snyder, and H. Hoppe. Signal-Specialized Parametrization. In Eurographics Workshop on Rendering 2002, 2002.Google Scholar
  54. 54.
    P. Sander, Z. Wood, S. Gortler, J. Snyder, and H. Hoppe. Multi-Chart Geometry Images. In Proc. Eurographics Symposium on Geometry Processing, 2003.Google Scholar
  55. 55.
    J.M. Shapiro. Embedded Image Coding Using Zerotrees of Wavelet Coefficients. IEEE Transactions on Signal Processing, 41(12):3445–3462, 1993.MATHCrossRefGoogle Scholar
  56. 56.
    D. Shikhare, S. Bhakar, and S.P. Mudur. Compression of Large 3D Engineering Models using Automatic Discovery of Repeating Geometric Features. In proceedings of 6th International Fall Workshop on Vision, Modeling and Visualization, 2001.Google Scholar
  57. 57.
    O. Sorkine, D. Cohen-Or, and S. Toldeo. High-Pass Quantization for Mesh Encoding. In Proc. of Eurographics Symposium on Geometry Processing, 2003.Google Scholar
  58. 58.
    V. Surazhsky and C. Gotsman. Explicit Surface Remeshing. In Proc. Eurographics Symposium on Geometry Processing, pages 20–30, 2003.Google Scholar
  59. 59.
    A. Szymczak, D. King, and J. Rossignac. An Edgebreaker-Based Efficient Compression Scheme for Regular Meshes. Computational Geometry, 20(1–2):53–68, 2001.MathSciNetCrossRefGoogle Scholar
  60. 60.
    A. Szymczak, J. Rossignac, and D. King. Piecewise Regular Meshes: Construction and Compression. Graphical Models, 64(3–4):183–198, 2003.Google Scholar
  61. 61.
    G. Taubin, W. Horn, J. Rossignac, and F. Lazarus. Geometry Coding and VRML. In Proc. IEEE, volume 86(6), pages 1228–1243, June 1998.CrossRefGoogle Scholar
  62. 62.
    C. Touma and C. Gotsman. Triangle Mesh Compression. Graphics Interface 98 Conference Proceedings, pages 26–34, 1998.Google Scholar
  63. 63.
    G. Turan. Succinct Representations of Graphs. Discrete Applied Mathematics, 8:289–294, 1984.MATHMathSciNetCrossRefGoogle Scholar
  64. 64.
    W. Tutte. A Census of Planar Maps. Canadian Journal of Mathematics, 15:249–271, 1963.MATHMathSciNetGoogle Scholar
  65. 65.
    Viewpoint. Premier Catalog (2000 Edition) www.viewpoint.com. Viewpoint editor, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Pierre Alliez
    • 1
  • Craig Gotsman
    • 2
  1. 1.INRIA, Sophia-AntipolisFrance
  2. 2.TechnionHaifaIsrael

Personalised recommendations