Geometric surface processing via normal maps

ACM Transactions on Graphics

Volumn 22, Issue 4, 2003, Pages 1012-1033

  Tasdizen, Tolga ^a,c   Whitaker, Ross ^a,c   Burchard, Paul ^b   Osher, Stanley ^b  

^a UNIVERSITY OF UTAH   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Department of Electrical and Computer Engineering   (United States)

Author keywords

Anisotropic diffusion; Geometric surface processing; High boost filtering; Level sets; Surface fairing

Indexed keywords

ANISOTROPIC DIFFUSION; GEOMETRIC SURFACE PROCESSING; HIGH-BOOST FILTERING; LEVEL SETS; SURFACE FAIRING;

COMPUTATION THEORY; EDGE DETECTION; IMAGE RECONSTRUCTION; PARTIAL DIFFERENTIAL EQUATIONS;

COMPUTATIONAL GEOMETRY;

EID: 1042274728     PISSN: 07300301     EISSN: 07300301     Source Type: Conference Proceeding    
DOI: 10.1145/944020.944024     Document Type: Article

References (40)

1. ADALSTEINSON, D. AND SETHIAN, J. A. 1995. A fast level set method for propogating interfaces. J. Computat. Phys. 118, 269-277.
2. ALEXA, M. 2002. Wiener filtering of meshes. In Proceedings of the Shape Modeling International. 51-57.
3. BALLESTER, C., BERTALMIO, M., CASELLES, V., SAPIRO, G., AND VERDERA, J. 2001. Filling-in by joint interpolation of vector fields and gray levels. IEEE Trans. Image Process. 10, 8 (Aug.), 1200-1211.
4. BERTALMIO, M., CHENG, L.-T., OSHER, S., AND SAPIRO, G. 2001. Variational problems and partial differential equations on implicit surfaces. J. Computat. Phys. 174, 759-780.
5. BURCHARD, P. 2002. Total variation geometry 1: Concepts and motivation. Tech. rep. UCLA CAM-02-01. University of California, Los Angeles, Los Angeles, CA.
6. CHOPP, D. L. AND SETHIAN, J. A. 1999. Motion by intrinsic laplacian of curvature. Interfaces Free Bound. 1, 1-18.
7. CLARENZ, U., DIEWALD, U., AND RUMPF, M. 2000. Anisotropic geometric diffusion in surface processing. In Proceedings of IEEE Visualization. 397-405.
8. CURLESS, B. AND LEVOY, M. 1996. A volumetric method for building complex models from range images. In Proceedings of SIGGRAPH'96. 303-312.
9. DESBRUN, M., MEYER, M., SCHRÖDER, M., AND BARR, A. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proceedings of SIGGRAPH'99. 317-324.
10. DESBRUN, M., MEYER, M., SCHRÖDER, P., AND BARR, A. H. 2000. Anisotropic feature-preserving denoising of height fields and bivariate data. In Proceedings of Graphics Interface. 145-152.
11. DOCARMO, M. P. 1976. Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ.
12. EBERLY, D. 1996. Ridges in Image and Data Analysis. Kluwer Academic Publishers, Norwell, MA.
13. GONZALEZ, R. C. AND WOODS, R. E. 1992. Digital Image Processing. Addison-Wesley Publishing Company, Reading, MA.
14. GUSKOV, I., SWELDENS,W, AND SCHRÖDER, P. 1999. Multiresolution signal processing for meshes. In Proceedings of SIGGRAPH'99. 325-334.
15. HALSTEAD, M., KASS, M., AND DEROSE, T. 1993. Efficient, fair interpolation using catmull-clark surface. In Proceedings of SIGGRAPH'93. 35-44.
16. KOBBELT, L., CAMPAGNA, S., VORSATZ, J., AND SEIDEL, H.-P. 1998. Interactive multi-resolution modeling on arbitrary meshes. In Proceedings of SIGGRAPH'98. 105-114.
17. LORENSON, W. AND CLINE, H. 1987. Marching cubes: A high resolution 3d surface reconstruction algorithm. In Proceedings of SIGGRAPH'87. 163-169.
18. LORIGO, L., FAUGERAS, O., GRIMSON, E., KERIVEN, R., KIKINIS, R., NABAVI, A., AND WESTIN, C.-F. 2000. Co-dimension 2 geodesic active contours for the segmentation of tubular strucures. In Proceedings of Computer Vision and Pattern Recognition. 1441-1451.
19. MALLADI, R., SETHIAN, J. A., AND VEMURI, B. C. 1995. Shape modeling with front propagation: A level set approach. IEEE Trans. Patt. Analy. Machine Intell. 17, 2, 158-175.
20. MORETON, H. P. AND SÉQUIN, C. H. 1992. Functional optimization for fair surface design. In Proceedings of SIGGRAPH'92. 167-176.
21. OHTAKE, Y., BELYAEV, A. G., AND BOGAEVSKI, I. A. 2000. Polyhedral surface smoothing with simultaneous mesh regularization. In Proceedings of Geometric Modeling and Processing. 229-137.
22. OSHER, S. AND SETHIAN, J. A. 1988. Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulation. J. Computat. Phys. 79, 12-19.
23. PENG, D., MERRIMAN, B., OSHER, S., ZHAO, H.-K., AND KANG, M. 1999. A PDE based fast local level set method. J. Computat. Phys. 155, 410-438.
24. PERONA, P. 1998. Orientation diffusion. IEEE Trans. Image Processing 7, 3, 457-467.
25. PERONA, P. AND MALIK, J. 1990. Scale space and edge detection using anisotropic diffusion. IEEE Trans. Patt. Analy. Machine Intell. 12, 7 (July), 629-639.
26. POLDEN, A. 1997. Compact surfaces of least total curvature. Tech. rep., University of Tubingen, Tubingen, Germany.
27. RUDIN, L., OSHER, S., AND FATEMI, C. 1992. Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268.
28. SAPIRO, G. 2001. Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, Cambridge, U.K. See Chapter on "Geometric Curve and Surface Evolution."
29. 1 boundary conditions. In Geometric Modeling and Processing Proceedings. 251-261.
30. SCHNEIDER, R. AND KOBBELT, L. 2001. Geometric fairing of irregular meshes for free-form surface design. Comput. Aid. Geom. Des. 18, 359-379.
31. SETHIAN, J. A. 1999. Level Set Methods and Fast Marching Methods Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, Cambridge, U.K.
32. TANG, B., SAPIRO, G., AND CASELLES, V. 2000. Diffusion of general data on non-flat manifolds via harmonic maps theory: The direction diffusion case. Int. J. Comput. Vis. 36, 2, 149-161.
33. TASDIZEN, T, WHITAKER, R., BURCHARD, P., AND OSHER, S. 2002. Geometric surface smoothing via anisotropic diffusion of normals. In Proceedings of IEEE Visualization. 125-132.
34. TAUBIN, G. 1995. A signal processing approach to fair surface design. In Proceedings of SIGGRAPH'95. 351-358.
35. TAUBIN, G. 2001. Linear anisotropic mesh filtering. Tech. rep. RC22213. IBM Research Division, Yorktown Heights, NY.
36. TAUBIN, G., ZHANG, T., AND GOLUB, G. 1996. Optimal surface smoothing as filter design. In Proceedings of the European Conference on Computer Vision. Vol. 1. 283-292.
37. WELCH, W. AND WITKIN, A. 1992. Variational surface modeling. In Proceedings of SIGGRAPH'92. 157-166.
38. WELCH, W. AND WITKIN, A. 1994. Free-form shape design using triangulated surfaces. In Proceedings of SIGGRAPH'94. 247-256.
39. WHITAKER, R. T. 1994. Volumetric deformable models: Active blobs. In Visualization in Biomedical Computing, R. A. Robb, Ed. SPIE Press, Bellingham, WA. 122-134.
40. WHITAKER, R. T. 1998. A level-set approach to 3D reconstruction from range data. Int. J. Comput. Vis. 29, 3, 203-231.