skip to main content
article

Surface compression with geometric bandelets

Published:01 July 2005Publication History
Skip Abstract Section

Abstract

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.

Skip Supplemental Material Section

Supplemental Material

pps025.mp4

mp4

38.5 MB

References

  1. Agarwal, P. K., and Suri, S. 1998. Surface approximation and geometric partitions. SIAM Journal on Computing 27, 4 (Aug.), 1016--1035. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Agarwal, S., Ramamoorthi, R., Belongie, S., and Jensen, H. W. 2003. Structured importance sampling of environment maps. ACM Trans. Graph. 22, 3, 605--612. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Alliez, P., and Gotsman, C. 2005. Recent Advances in Compression of 3D Meshes. Springer-Verlag. 3--26.Google ScholarGoogle Scholar
  4. Alliez, P., Cohen-Steiner, D., Devillers, O., Levy, B., and Desbrun, M. 2003. Anisotropic polygonal remeshing. ACM Transactions on Graphics. Special issue for SIGGRAPH conference, 485--493. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Alpert, B. 1992. Wavelets and Other Bases for Fast Numerical Linear Algebra. C. K. Chui, editor, Academic Press. New York.Google ScholarGoogle Scholar
  6. Biermann, H., Zorin, D., and Levin, A. 2000. Piecewise smooth subdivision surfaces with normal control. In Proc. of SIGGRAPH 2000, Computer Graphics Proceedings, Annual Conference Series, 113--120. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Candès, E., and Donoho, D. 1999. Curvelets: A surprisingly effective nonadaptive representation of objects with edges. Vanderbilt University Press.Google ScholarGoogle Scholar
  8. Cignoni, P., Rocchini, C., and Scopigno, R. 1998. Metro: Measuring error on simplified surfaces. Computer Graphics Forum 17, 2 (June), 167--174.Google ScholarGoogle ScholarCross RefCross Ref
  9. Cohen-Steiner, D., Alliez, P., and Desbrun, M. 2004. Variational shape approximation. ACM Transactions on Graphics. Special issue for SIGGRAPH conference, 905--914. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Dahmen, W., and Schneider, R. 2000. Wavelets on manifolds I: Construction and domain decomposition. SIAM Journal on Mathematical Analysis 31, 1 (Jan.), 184--230.Google ScholarGoogle Scholar
  11. Dana, K. J., Van Ginneken, B., Nayar, N., and Koenderink, J. J. 1999. Reflectance and texture of real-world surfaces. In ACM Transactions on Graphics, vol. 18, 1--34. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Daubechies, I., Runborg, O., and Sweldens, W. 2004. Normal multiresolution approximation of curves. Constructive Approximation 20, 3, 399--463.Google ScholarGoogle ScholarCross RefCross Ref
  13. DeRose, T., Kass, M., and Truong, T. 1998. Subdivision surfaces in character animation. In Proc. of SIGGRAPH 98, Computer Graphics Proceedings, Annual Conference Series, 85--94. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Do, M. N., and Vetterli, M. 2005. The contourlet transform: an efficient directional multiresolution image representation. IEEE Transactions Image on Processing, To appear. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., and Stuetzle, W. 1995. Multiresolution Analysis of Arbitrary Meshes. Computer Graphics 29, Annual Conference Series, 173--182. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Farin, G. 1993. Curves and Surfaces for Computer Aided Geometric Design, 3. ed. Academic Press, Boston. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Garland, M., and Heckbert, P. 1997. Surface simplification using quadric error metrics. Proc. of SIGGRAPH 1997, 209--215. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Gu, X., Gortler, S., and Hoppe, H. 2002. Geometry Images. Proc. of SIGGRAPH 2002, 355--361. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Guskov, I., Vidimce, K., Sweldens, W., and Schröder, P. 2000. Normal meshes. In Proc. of SIGGRAPH 2000, Computer Graphics Proceedings, Annual Conference Series, 95--102. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Hertzmann, A., and Zorin, D. 2000. Illustrating smooth surfaces. In SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., 517--526. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Hoppe, H., and Praun, E. 2003. Shape compression using spherical geometry images. Multiresolution in Geometric Modelling.Google ScholarGoogle Scholar
  22. Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., and Stuetzle, W. 1994. Piecewise smooth surface reconstruction. In Proc. of SIGGRAPH 94, Computer Graphics Proceedings, Annual Conference Series, 295--302. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Hoppe, H. 1996. Progressive meshes. Proc. of SIGGRAPH 1996, 99--108. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Khodakovsky, A., and Guskov, I. 2003. Compression of Normal Meshes. Springer-Verlag, In Geometric Modeling for Scientific Visualization.Google ScholarGoogle Scholar
  25. Le Pennec, E., and Mallat, S. 2004. Sparse Geometrical Image Approximation with Bandelets. IEEE Transaction on Image Processing 14, 4, 423--438. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Le Pennec, E., and Mallat, S. 2005. Bandelet Image Approximation and Compression. SIAM Multiscale Modeling and Simulation, to appear.Google ScholarGoogle Scholar
  27. Levoy, M., Pulli, K., Curless, B., Rusinkiewicz, S., Koller, D., Pereira, L., Ginzton, M., Anderson, S., Davis, J., Ginsberg, J., Shade, J., and Fulk, D. 2000. The digital michelangelo project: 3D scanning of large statues. In Proc. of Siggraph 2000, 131--144. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Lindstrom, P., and Turk, G. 1998. Fast and memory efficient polygonal simplification. Proc. IEEE Visualization '98 (Oct.), 279--286. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Mallat, S. 1998. A Wavelet Tour of Signal Processing. Academic Press, San Diego. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Matei, B., and Cohen, A. 2002. Nonlinear Subdivison Schemes: Applications to Image processing, in Tutorials on Multiresolution in Geometric Modelling. Springer Verlag, 93--97.Google ScholarGoogle Scholar
  31. Ohtake, Y., Belyaev, A., and Seidel, S. 2004. Ridge-valley lines on meshes via implicit surface fitting. ACM Transactions on Graphics 23, 3 (Aug.), 609--612. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Owada, S., Nielsen, F., Okabe, M., and Igarashi, T. 2004. Volumetric illustration: Designing 3D models with internal textures. Proceedings of SIGGRAPH 2004, 322--328. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Peercy, M., Airey, J., and Cabral, B. 1997. Efficient bump mapping hardware. In Proc. of SIGGRAPH 1997, 303--306. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Peyré, G., and Mallat, S., 2005. Bandelets toolbox, available on Matlab Central. http://www.mathworks.com/matlabcentral/.Google ScholarGoogle Scholar
  35. Peyré, G., and Mallat, S. 2005. Image approximation with geometric bandelets. In Preprint CMAP.Google ScholarGoogle Scholar
  36. Sander, P., Wood, Z., Gortler, S., Snyder, J., and Hoppe, H. 2003. Multi-chart Geometry Images. Proc. Symposium on Geometry Processing 2003, 146--155. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Schröder, P., and Sweldens, W. 1995. Spherical Wavelets: Efficiently Representing Functions on the Sphere. In Proc. of SIGGRAPH 95, 161--172. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Slabaugh, G., Culbertson, B., Malzbender, T., and Schafer, S. 2001. A survey of methods for volumetric scene reconstruction from photographs. In Proc. of IEEE Eurographics Workshop, Springer-Verlag, Wien, 81--100. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Wakin, M., Romberg, J., Choi, H., and Baraniuk, R. 2005. Wavelet-domain Approximation and Compression of Piecewise Smooth Images. IEEE Transactions on Image Processing, To appear. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Wang, L., Wang, X., Tong, X., Lin, S., Hu, S., Guo, B., and Shum, H.-Y. 2003. View-dependent displacement mapping. ACM Trans. Graph. 22, 3, 334--339. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Surface compression with geometric bandelets

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image ACM Transactions on Graphics
        ACM Transactions on Graphics  Volume 24, Issue 3
        July 2005
        826 pages
        ISSN:0730-0301
        EISSN:1557-7368
        DOI:10.1145/1073204
        Issue’s Table of Contents

        Copyright © 2005 ACM

        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 July 2005
        Published in tog Volume 24, Issue 3

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • article

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader