“Interactive and anisotropic geometry processing using the screened Poisson equation” by Kazhdan and Chuang

  • ©Michael Kazhdan and Ming Chuang

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Title:

    Interactive and anisotropic geometry processing using the screened Poisson equation

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Abstract:


    We present a general framework for performing geometry filtering through the solution of a screened Poisson equation. We show that this framework can be efficiently adapted to a changing Riemannian metric to support curvature-aware filtering and describe a parallel and streaming multigrid implementation for solving the system. We demonstrate the practicality of our approach by developing an interactive system for mesh editing that allows for exploration of a large family of curvature-guided, anisotropic filters.

References:


    1. Aksoylu, B., Khodakovsky, A., and Schröder, P. 2003. Multilevel solvers for unstructured surface meshes. SIAM Journal of Scientific Computing 26. Google Scholar
    2. Bajaj, C. L., Xu, G. L., Bajaj, R. L., and T, G. X. 2002. Anisotropic diffusion of subdivision surfaces and functions on surfaces. ACM Transactions on Graphics 22, 4–32. Google ScholarDigital Library
    3. Bhat, P., Curless, B., Cohen, M., and Zitnick, L. 2008. Fourier analysis of the 2D screened Poisson equation for gradient domain problems. In Proceedings of the 10th European Conference on Computer Vision, 114–128. Google Scholar
    4. Bhat, P., Zitnick, L., Cohen, M., and Curless, B. 2010. Gradientshop: A gradient-domain optimization framework for image and video filtering. ACM Transactions on Graphics 29, 10:1–10:14. Google ScholarDigital Library
    5. Burt, P., and Adelson, E. 1983. The Laplacian pyramid as a compact image code. IEEE Transactions on Communication 31, 532–540.Google ScholarCross Ref
    6. Chuang, M., Luo, L., Brown, B., Rusinkiewicz, S., and Kazhdan, M. 2009. Estimating the Laplace-Beltrami operator by restricting 3D functions. Computer Graphics Forum (Symposium on Geometry Processing), 1475–1484. Google Scholar
    7. Clarenz, U., Diewald, U., and Rumpf, M. 2000. Anisotropic geometric diffusion in surface processing. Visualization Conference, IEEE 0, 70. Google ScholarDigital Library
    8. Cowper, C. 1973. Gaussian quadrature formulas for triangles. International Journal of Numerical Methods in Engineering 7, 405–408.Google ScholarCross Ref
    9. Desbrun, M., Meyer, M., Schröder, P., and Barr, A. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In ACM SIGGRAPH Conference Proceedings, 317–324. Google Scholar
    10. Douglas, C., Hu, J., Kowarschik, M., Rüde, U., and Weiss, C. 2000. Cache optimization for structured and unstructured grid multigrid. Electronic Transactions on Numerical Analysis 10, 21–40.Google Scholar
    11. Eckstein, I., Pons, J.-P., Tong, Y., Kuo, C., and Desbrun, M. 2007. Generalized surface flows for mesh processing. In Symposium on Geometry Processing, 183–192. Google ScholarDigital Library
    12. Guskov, I., Sweldens, W., and Schröder, P. 1999. Multiresolution signal processing for meshes. In ACM SIGGRAPH Conference Proceedings, 325–334. Google Scholar
    13. Kazhdan, M., and Hoppe, H. 2008. Streaming multigrid for gradient-domain operations on large images. ACM Transactions on Graphics (SIGGRAPH ’08) 27. Google Scholar
    14. Kobbelt, L., Campagna, S., Vorsatz, J., and Seidel, H. 1998. Interactive multi-resolution modeling on arbitrary meshes. In ACM SIGGRAPH Conference Proceedings, 105–114. Google Scholar
    15. McCann, J., and Pollard, N. 2008. Real-time gradient-domain painting. ACM Transactions on Graphics (SIGGRAPH ’08) 27. Google Scholar
    16. Meyer, M., Desbrun, M., Schröder, P., and Barr, A. 2002. Discrete differential-geometry operators for triangulated 2-manifolds. Visualization and Mathematics 3, 34–57.Google Scholar
    17. Ohtake, Y., Belyaev, A., and Bogaevski, I. 2000. Polyhedral surface smoothing with simultaneous mesh regularization. In Proceedings of the Geometric Modeling and Processing (GMP ’00), 229–237. Google ScholarDigital Library
    18. Pfeifer, C. 1963. Data flow and storage allocation for the PDQ-5 program on the Philco-2000. Communications of the ACM 6, 365–366.Google Scholar
    19. Pinkall, U., and Polthier, K. 1993. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2, 15–36.Google ScholarCross Ref
    20. Shi, L., Yu, Y., Bell, N., and Feng, W. 2006. A fast multigrid algorithm for mesh deformation. ACM Transactions on Graphics (SIGGRAPH ’06) 25, 1108–1117. Google Scholar
    21. Smith, B., Bjorstad, P., and Gropp, W. 1996. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press. Google ScholarDigital Library
    22. Tasdizen, T., Whitaker, R., Burchard, P., and Osher, S. 2002. Geometric surface smoothing via anisotropic diffusion of normals. In VIS ’02: Proceedings of the conference on Visualization ’02, IEEE Computer Society, Washington, DC, USA, 125–132. Google ScholarDigital Library
    23. Taubin, G. 1995. A signal processing approach to fair surface design. In ACM SIGGRAPH Conference Proceedings, 351–358. Google Scholar
    24. Trimesh 2.9, 2009. www.cs.princeton.edu/gfx/proj/trimesh2/.Google Scholar
    25. Vallet, B., and Lévy, B. 2008. Spectral geometry processing with manifold harmonics. Computer Graphics Forum (Proceedings Eurographics) 27, 251–160.Google ScholarCross Ref
    26. Weber, O., Devir, Y., Bronstein, A., Bronstein, M., and Kimmel, R. 2008. Parallel algorithms for approximation of distance maps on parametric surfaces. ACM Transactions on Graphics 27. Google Scholar
    27. Witkin, A. 1983. Scale-space filtering. In International Joint Conference on Artificial Intelligence, 1019–1022. Google Scholar
    28. Zhou, K., Gong, M., Huang, X., and Guo, B. 2010. Data-parallel octrees for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics. Google Scholar


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