Spherical diffusion for 3D surface smoothing

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 26, Issue 12, 2004, Pages 1650-1654

  Bülow, Thomas ^a  

^a PHILIPS RESEARCH LABORATORIES   (Germany)

Author keywords

Diffusion; Spherical harmonics; Surface smoothing

Indexed keywords

COMPUTER VISION; ESTIMATION; FEATURE EXTRACTION; FOURIER TRANSFORMS; IMAGE ANALYSIS; ITERATIVE METHODS; MATHEMATICAL OPERATORS; SURFACES; THEOREM PROVING; THREE DIMENSIONAL COMPUTER GRAPHICS;

DIFFUSION BASED APPROACH; NONLINEAR MODIFICATION; SPHERICAL HARMONICS; SURFACE SMOOTHING;

OBJECT RECOGNITION;

ARTICLE; AUDIOVISUAL EQUIPMENT; AUTOMATED PATTERN RECOGNITION; CEPHALOMETRY; HEAD; HUMAN;

CEPHALOMETRY; HEAD; HUMANS; MODELS, ANATOMIC; PATTERN RECOGNITION, AUTOMATED;

EID: 9244244242     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2004.129     Document Type: Article

References (35)

1. D.H. Ballard and C.M. Brown, Computer Vision. Prentice-Hall Inc., 1982.
2. A. Belyaev and Y. Ohtake, "A Comparison of Mesh Smoothing Methods," Proc. Israel-Korea Bi-Nat'l Conf. Geometric Modeling and Computer Graphics, pp. 83-87, 2003.
3. Ch. Brechbühler, G. Gerig, and O. Kübler, " Parametrization of Closed Surfaces for 3D Shape Description," Computer Vision and Image Understanding, vol. 61, no. 2, pp. 154-170, 1995.
4. T. Bülow, "Multi-Scale Image Processing on the Sphere," Proc 24th Symp. Pattern Recognition of the DAGM, L. van Gool, ed., 2002.
5. T. Bülow, "Reverse Diffusion for Smooth Buildup of Progressively Transmitted Geometry," Proc. EUROGRAPHICS, 2002.
6. T. Bülow, "Spherical Diffusion for 3D Surface Smoothing," Proc. First Int'l Symp. 3D Data Processing, Visualization, and Transmission, pp. 449-458, 2002.
7. T. Bülow and K. Daniilidis, "Surface Representations Using Spherical Harmonics and Gabor Wavelets on the Sphere," Technical Report MS-CIS-01-37, CIS Dept., Univ. of Pennsylvania, 2001.
8. G.S. Chirikjian and A.B. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis. CRC Press, 2001.
9. R. Courant and D. Hilbert, Methods of Mathematical Physics. New York: Interscience Publishers, 1953.
10. M. Desbrun, M. Meyer, P. Schröder, and A. Barr, "Implicit Fairing of Regular Meshes Using Diffusion and Curvature Flow," Proc. SIGGRAPH 1999.
11. J.R. Driscoll and D.M. Healy, "Computing Fourier Transforms and Convolutions on the 2-Sphere," Advances in Applied Math., vol. 15, pp. 202-250, 1994.
12. S. Ertürk and T.J. Dennis, "Efficient Representations of 3D Human Head Models," Proc. British Machine Vision Conf., pp. 329-339, 1999.
13. W. Freeden and M. Schreiner, "Non-Orthgonal Expansions on the Sphere," Math. Methods in the Applied Sciences, vol. 18, pp. 83-120, 1995.
14. B.K.P. Horn, "Extended Gaussian Images," Proc. IEEE, vol. 72, no. 12, pp. 1671-1686, 1984.
15. T. Iijima, "Basic Theory of Pattern Normalization (for the Case of a Typical (1D) Pattern)," Bull. Electrotechnical Laboratory, vol. 26, pp. 368-388, 1962.
16. T.R. Jones, F. Durand, and M. Desbrun, "Non-Iterative, Feature-Preserving Mesh Smoothing," Proc. SIGGRAPH, pp. 943-949, 2003.
17. S.B. Kang and K. Ikeuchi, "The Complex EGI: A New Representation for 3D Pose Determination," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 7, pp. 707-721, July 1993.
18. G. Kin and M. Sato, "Scale Space Filtering on Spherical Pattern," Proc. 11th Int'l Conf. Pattern Recognition, vol. C, pp. 638-641, 1992.
19. J.J. Koenderink, "The Structure of Images," Biological Cybernetics vol. 50, pp. 363-370, 1984.
20. J.J. Koenderink and A.J. van Doorn, "Dynamic Shape," Biological Cybernetics, vol. 53, pp. 383-396, 1986.
21. T. Lindeberg, "Scale-Space Theory: A Basic Tool for Analysing Structures at Different Scales," J. Applied Statistics, vol. 21, no. 2, pp. 225-270, 1994.
22. A. Matheny and D.B. Goldgof, "The Use of Three and Four-Dimensional Surface Harmonics for Rigid and Nonrigid Shape Recovery and Representation," IEEE Pattern Analysis and Machine Intelligence, vol. 17, no. 10, pp. 967-981, Oct. 1995.
23. F. Mokhtarina, N. Khalili, and P. Yuen, "Curvature Computation on Free-Form 3D Meshes at Multiple Scales," Computer Vision and Image Understanding, vol. 83, pp. 118-139, 2001.
24. S. Rosenberg, The Laplacian on a Riemannian Manifold. London Math. Soc., 1997.
25. R.B. Schudy and D.H. Ballard, "Towards an Anatomical Model of Heart Motion as Seen in 4-D Cardiac Ultrasound Data," Proc. Sixth Conf. Computer Applications in Radiology and Analysis of Radiological Images June 1979.
26. J. Sijbert and D. van Dyck, " Efficient Algorithm for the Computation of 3D Fourier Descriptors," Proc. First Int'l Symp. 3D Data Processing, Visualization, and Transmission, pp. 640-643, 2002.
27. K. Tanaka, M. Sano, N. Mukawa, and H. Kaneko, "3d Object Representation Using Spherical Harmonic Functions," Proc. Int'l Conf. Intelligent Robots and Systems, 1993.
28. T. Tasdizen, R. Whitaker, P. Burchard, and S. Osher, "Geometric Surface Smoothing via Anisotropic Diffusion of Normals," Proc. IEEE Visualization, pp. 125-132, 2002.
29. G. Taubin, "A Signal Processing Approach to Fair Surface Design," Proc. SIGGRAPH, 1995.
30. G. Taubin, "Geometric Signal Processing on Polygonal Meshes," Proc. EUROGRAPHICS, 2000.
31. B.L. van der Waerden, Group Theory and Quantum Mechanics. Springer Verlag, 1974.
32. J. Weickert, Anisotropic Diffusion in Image Processing. Stuttgart, Germany: ECMI Series, 1998.
33. J. Weickert, "Nonlinear Diffusion Filtering," Handbook on Computer Vision and Applications, B. Jähne et al., eds., vol. 2, pp. 423-450, Academic Press, 1999.
34. J. Weickert, S. Ishikawa, and A. Imiya, "On the History of Gaussian Scale-Space Axiomatics," Gaussian Scale-Space Theory, J. Sporring, ed., Dordrecht: Kluwer, 1997.
35. A.P. Witkin, "Scale-Space Filtering," Proc. Eighth Int'l Joint Conf. Artificial Intelligence, pp. 1019-1022, Aug. 1983.