Fast Surface Interpolation Using Multiresolution Wavelet Transform

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 16, Issue 7, 1994, Pages 673-688

  Yaou, Ming Haw ^a   Chang, Wen Thong ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

basis transfer scheme; discretization; preconditioning; regularization; Surface interpolation; wavelet transform

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FREQUENCY DOMAIN ANALYSIS; INTERPOLATION; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; SURFACES;

BASIS TRANSFER SCHEME; DISCRETIZATION; LINEAR EQUATION; MULTIRESOLUTION WAVELET TRANSFORM; PRECONDITIONING; REGULARIZATION; SURFACE INTERPOLATION;

COMPUTER VISION;

EID: 0028467706     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.297948     Document Type: Article

References (40)

1. A. Aldroubi, M. Unser, and M. Eden, “Discrete spline filters for multiresolutions and wavelet of l2,” BEIP/National Center for Res. Resources, Rep. No. 21/91, 1991.
2. O. Axelsson and V. A. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation. Orlando, FL: Academic, 1984.
3. A. Brandt, “Multilevel adaptive solutions to boundary-value problems,” Math. Computat., vol. 31, pp. 333–390, 1977.
4. M. T. Chiaradia, A. Distante, and E. Stella, “Three-dimensional surface reconstruction integrating shading and sparse stereo data,” Optic Eng., vol. 28, no. 9, pp. 935–942, 1989.
5. C. K. Chui, An Introduction to Wavelets. Boston, MA: Academic Press, Boston, 1992.
6. “On compactly supported spline wavelets and a duality principle,” Trans. Amer. Math. Soc., vol. 330, no. 2, pp. 903–915, 1992.
7. A. Cohen, I. Daubechies, and J.C. Feauveau, “Biorthogonal bases of compactly supported wavelets,” Commun. Pure Appl. Math., to appear.
8. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math., vol. XLI, pp. 909–996, 1988.
9. R. D. Eastman and A. M. Waxman, “Using disparity functionals for stereo correspondence and surface reconstruction,” Comput. Vision Graphics Image Processing, vol. 39, pp. 73–101, 1987.
10. W. E. L. Grimson, “An implementation of a computational theory of visual surface interpolation,” Comput. Vision Graphics Image Processing, vol. 22, pp. 39–69, 1983.
11. “Computational experiment with a feature based stereo algorithm,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, no. 1, pp. 17–34, 1985.
12. C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. Boston, MA: Pitman, 1984.
13. W. Hackbusch, MultiGrid Methods and Applications. New York: Springer-Verlag, 1985.
14. W. Hackbusch and U. Trottenberg, Eds., Multigrid Methods. New York: Springer-Verlag, 1982.
15. L. A. Hageman and D. M. Young, Applied Iterative Methods. New York: Academic Press, 1981.
16. W. Hoff and N. Ahuja, “Surfaces from stereo: Integrating feature matching, disparity estimation, and contour detection,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAM1-11, no. 2, pp. 121–136, 1989.
17. H. C. Hsieh and W. T. Chang, “Computation network for visible surface reconstruction,” in Proc. SPIE Conf. Visual Commun. Image Processing, Lausanne, Switzerland, 1990, pp. 1504–1515.
18. W. T. Chang, H. C. Hsieh, and W. Hsing Lai, “Second order smoothness measure in curve fitting,” in Proc. Telecommun. Symp., Hsinchu, ROC, 1990, pp. 550–555.
19. H. C. Hsieh and W. T. Chang, “Analog computation structure for surface reconstruction,” J. Visual Commun. Image Represent., vol. 2, no. 4, pp. 381–394, 1991.
20. “Multilayer computation structure for surface reconstruction,” IEEE Trans. Image Processing, submitted.
21. S. Jaffard, “Wavelet methods for fast resolution of elliptic problems,” SIAM J. Numerical Anal., vol. 29, no. 4, pp. 965–986, 1992.
22. D. R. Kincaid and L. J. Hayes, Iterative Methods for Large Linear Systems. New York: Academic Press, 1990.
23. P. Lancaster and K. Salkauskas, Curve and Surface Fitting. New York: Academic Press, 1986.
24. M. M. Lavrentev, V. G. Romanov, and S. P. Shishatskii, “III-posed problems of mathematical physics and analysis,” Amer. Math., Providence, RI, 1986.
25. G. G. Lorentz, C. K. Chui, and L. L. Schumaker, Eds., Approximation Theory. New York: Academic Press, 1976.
26. S. G. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-II, no. 7, pp. 647–693, 1989.
27. “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Signal Processing, vol. 37, no. 12, pp. 2091–2110, 1989.
28. D. Man, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. San Francisco, CA: Freeman, 1982.
29. A. P. Pentland, “Surface interpolation networks,” Neural Computat., vol. 5, no. 3, pp. 430-442, 1993.
30. “Interpolation using wavelet bases,” IEEE Trans. Pattern Anal. Machine Intell., vol. 16, no. 4, pp. 410–414, Apr. 1994.
31. P. R. Prenter, Spline and Variational Methods. New York: John Wiley, 1975.
32. K. Rektorys, Variational Methods in Mathematics, Science, and Engineering, second ed. Dordrecht, The Netherlands: Reidel, 1980.
33. M. B. Ruskai, R. Coifman, Y. Meyer, et al., Wavelets and Their Applications. Boston, MA: John and Bartlett, 1992.
34. R. Szeliski, “Fast surface interpolation usin g hierarchical basis functions,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-12, no. 6, pp. 513–528, 1990.
35. D. Terzopoulos, “Multilevel computational processes for visual surface reconstruction,” Comput. Vision Graphics Image Processing, vol. 24, pp. 52–96, 1983.
36. “Regularization of inverse visual problems involving discontinuities,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 4, pp. 413–424, 1986.
37. “Image analysis using multigrid relaxation methods,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 2, pp. 129–139. 1986.
38. “The computation of visible-surface representations,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-10, no. 4, pp. 417–438, 1988.
39. H. Yserentant, “On the multilevel splitting of finite element space,” Numerische Mathimatik, vol. 49, pp. 379–412, 1986.
40. D. M. Young, Iterative Solution of Large Linear Systems. New York: Academic Press, 1971.