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.
Supplemental Material
- Agarwal, P. K., and Suri, S. 1998. Surface approximation and geometric partitions. SIAM Journal on Computing 27, 4 (Aug.), 1016--1035. Google ScholarDigital Library
- 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
- Alliez, P., and Gotsman, C. 2005. Recent Advances in Compression of 3D Meshes. Springer-Verlag. 3--26.Google Scholar
- 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
- Alpert, B. 1992. Wavelets and Other Bases for Fast Numerical Linear Algebra. C. K. Chui, editor, Academic Press. New York.Google Scholar
- 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
- Candès, E., and Donoho, D. 1999. Curvelets: A surprisingly effective nonadaptive representation of objects with edges. Vanderbilt University Press.Google Scholar
- 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
- 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
- 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
- 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
- Daubechies, I., Runborg, O., and Sweldens, W. 2004. Normal multiresolution approximation of curves. Constructive Approximation 20, 3, 399--463.Google ScholarCross Ref
- 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
- 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
- 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
- Farin, G. 1993. Curves and Surfaces for Computer Aided Geometric Design, 3. ed. Academic Press, Boston. Google ScholarDigital Library
- Garland, M., and Heckbert, P. 1997. Surface simplification using quadric error metrics. Proc. of SIGGRAPH 1997, 209--215. Google ScholarDigital Library
- Gu, X., Gortler, S., and Hoppe, H. 2002. Geometry Images. Proc. of SIGGRAPH 2002, 355--361. Google ScholarDigital Library
- 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
- 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
- Hoppe, H., and Praun, E. 2003. Shape compression using spherical geometry images. Multiresolution in Geometric Modelling.Google Scholar
- 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
- Hoppe, H. 1996. Progressive meshes. Proc. of SIGGRAPH 1996, 99--108. Google ScholarDigital Library
- Khodakovsky, A., and Guskov, I. 2003. Compression of Normal Meshes. Springer-Verlag, In Geometric Modeling for Scientific Visualization.Google Scholar
- 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
- Le Pennec, E., and Mallat, S. 2005. Bandelet Image Approximation and Compression. SIAM Multiscale Modeling and Simulation, to appear.Google Scholar
- 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
- Lindstrom, P., and Turk, G. 1998. Fast and memory efficient polygonal simplification. Proc. IEEE Visualization '98 (Oct.), 279--286. Google ScholarDigital Library
- Mallat, S. 1998. A Wavelet Tour of Signal Processing. Academic Press, San Diego. Google ScholarDigital Library
- 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
- 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
- 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
- Peercy, M., Airey, J., and Cabral, B. 1997. Efficient bump mapping hardware. In Proc. of SIGGRAPH 1997, 303--306. Google ScholarDigital Library
- Peyré, G., and Mallat, S., 2005. Bandelets toolbox, available on Matlab Central. http://www.mathworks.com/matlabcentral/.Google Scholar
- Peyré, G., and Mallat, S. 2005. Image approximation with geometric bandelets. In Preprint CMAP.Google Scholar
- 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
- Schröder, P., and Sweldens, W. 1995. Spherical Wavelets: Efficiently Representing Functions on the Sphere. In Proc. of SIGGRAPH 95, 161--172. Google ScholarDigital Library
- 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
- 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
- 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
Index Terms
- Surface compression with geometric bandelets
Recommendations
Surface compression with geometric bandelets
SIGGRAPH '05: ACM SIGGRAPH 2005 PapersThis 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 ...
Sparse geometric image representations with bandelets
This paper introduces a new class of bases, called bandelet bases, which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow. This geometric flow indicates directions in which the image gray levels have ...
A Novel Image Compression Algorithm Using Ridgelet Transformation with Modified EBCOT
ISECS '09: Proceedings of the 2009 Second International Symposium on Electronic Commerce and Security - Volume 02JPEG2000 is the image compression standard which includes three core techniques: wavelet lifting scheme and EBCOT and MQ arithmetic coder. The EBCOT algorithm uses a Wavelet transform to generate the subband samples, which are quantized and coded. ...
Comments