“Surface compression with geometric bandelets” by Peyré and Mallat

  • ©Gabriel Peyré and Stéphane Mallat

Conference:


Type(s):


Title:

    Surface compression with geometric bandelets

Presenter(s)/Author(s):



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.

References:


    1. Agarwal, P. K., and Suri, S. 1998. Surface approximation and geometric partitions. SIAM Journal on Computing 27, 4 (Aug.), 1016–1035. Google ScholarDigital 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 ScholarDigital Library
    3. Alliez, P., and Gotsman, C. 2005. Recent Advances in Compression of 3D Meshes. Springer-Verlag. 3–26.Google 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 ScholarDigital Library
    5. Alpert, B. 1992. Wavelets and Other Bases for Fast Numerical Linear Algebra. C. K. Chui, editor, Academic Press. New York.Google 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 ScholarDigital Library
    7. Candès, E., and Donoho, D. 1999. Curvelets: A surprisingly effective nonadaptive representation of objects with edges. Vanderbilt University Press.Google 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 ScholarCross 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 ScholarDigital 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 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 ScholarDigital Library
    12. Daubechies, I., Runborg, O., and Sweldens, W. 2004. Normal multiresolution approximation of curves. Constructive Approximation 20, 3, 399–463.Google ScholarCross 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 ScholarDigital 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 ScholarDigital 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 ScholarDigital Library
    16. Farin, G. 1993. Curves and Surfaces for Computer Aided Geometric Design, 3. ed. Academic Press, Boston. Google ScholarDigital Library
    17. Garland, M., and Heckbert, P. 1997. Surface simplification using quadric error metrics. Proc. of SIGGRAPH 1997, 209–215. Google ScholarDigital Library
    18. Gu, X., Gortler, S., and Hoppe, H. 2002. Geometry Images. Proc. of SIGGRAPH 2002, 355–361. Google ScholarDigital 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 ScholarDigital 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 ScholarDigital Library
    21. Hoppe, H., and Praun, E. 2003. Shape compression using spherical geometry images. Multiresolution in Geometric Modelling.Google 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 ScholarDigital Library
    23. Hoppe, H. 1996. Progressive meshes. Proc. of SIGGRAPH 1996, 99–108. Google ScholarDigital Library
    24. Khodakovsky, A., and Guskov, I. 2003. Compression of Normal Meshes. Springer-Verlag, In Geometric Modeling for Scientific Visualization.Google 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 ScholarDigital Library
    26. Le Pennec, E., and Mallat, S. 2005. Bandelet Image Approximation and Compression. SIAM Multiscale Modeling and Simulation, to appear.Google 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 ScholarDigital Library
    28. Lindstrom, P., and Turk, G. 1998. Fast and memory efficient polygonal simplification. Proc. IEEE Visualization ’98 (Oct.), 279–286. Google ScholarDigital Library
    29. Mallat, S. 1998. A Wavelet Tour of Signal Processing. Academic Press, San Diego. Google ScholarDigital 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 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 ScholarDigital 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 ScholarDigital Library
    33. Peercy, M., Airey, J., and Cabral, B. 1997. Efficient bump mapping hardware. In Proc. of SIGGRAPH 1997, 303–306. Google ScholarDigital Library
    34. Peyré, G., and Mallat, S., 2005. Bandelets toolbox, available on Matlab Central. http://www.mathworks.com/matlabcentral/.Google Scholar
    35. Peyré, G., and Mallat, S. 2005. Image approximation with geometric bandelets. In Preprint CMAP.Google 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 ScholarDigital Library
    37. Schröder, P., and Sweldens, W. 1995. Spherical Wavelets: Efficiently Representing Functions on the Sphere. In Proc. of SIGGRAPH 95, 161–172. Google ScholarDigital 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 ScholarDigital 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 ScholarDigital 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 ScholarDigital Library


ACM Digital Library Publication:



Overview Page: