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Interpolation Using Wavelet Bases
April 1994 (vol. 16 no. 4)
pp. 410-414
Efficient solutions to regularization problems can be obtained using orthogonal wavelet bases for preconditioning. Good approximate solutions can be obtained in only two or three iterations, with each iteration requiring only O(n) operations and O(n) storage locations. Two- and three-dimensional examples are shown using both synthetic and real range data.
[1] 410B. Albert, G. Beylkin, R. Coifman, and V. Rokhlin, "Wavelets for the fast solution of second-kind integral equations," Yale Univ., New Haven, CT, Res. Rep. DCS. RR-837, Dec. 1990.[2] A. Blake and A. Zisserman,Visual Reconstruction. Cambridge, MA: MIT Press, 1987.[3] T. Boult and J. Kender, "Visual surface reconstruction using sparse depth data," inProc. IEEE Conf. Computer Vision and Pattern Recognition '86, Miami Beach, FL, pp. 68-76, 1986.[4] M. Bove, "Discrete Fourier transform based depth-from-focus," inProc. Optical Society of America Image Understanding and Machine Vision Conf., Falmouth, MA, June 12-14, pp. 118-121.[5] I. Daubechies, "Orthonormal bases of compactly supported wavelets,"Commun. Pure and Applied Math., vol. 41, pp. 909-996, 1988.[6] W. E. L. Grimson, "An implementation of a computational theory of visual surface interpolation.,"Comput. Vision, Graphics, and Image Processing. vol. 22, pp. 39-69, 1983.[7] S. G. Mallat, "A theory for multiresolution signal decomposition: the wavelet representation,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 7, pp. 674-693, 1987.[8] A. P. Pentland, "A new sense for depth of field,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, no. 4, pp. 523-531, July 1987.[9] A. P. Pentland, "Physically-based dynamical models for image processing and recognition,"Mustererkennung 1990, Informatik-Fachberiche 254, pp. 171-193, R. E. Grosskopf, Ed. Berlin: Springer-Verlag.[10] A. P. Pentland, "Cue integration and surface completion,"Invest. Opthal. and Visual Science, vol. 32, no. 4, p. 1197, Mar. 1991.[11] A. P. Pentland, "Fast solutions to physical equilibrium and interpolation problems,"The Visual Comput., vol. 8, no. 5-6, pp. 303-314, June 1992.[12] A. P. Pentland, "Surface interpolation networks,"Neural Computation, to appear.[13] T. Poggio, V. Torre, and C. Koch, "Computational vision and regularization theory,"Nature, vol. 317, pp. 314-319, 1985.[14] S. Sclaroff, "C implementation of wavelet-based regularization," available by anonymous FTP from whitechapel.media.mit.edu.[15] E. P. Simoncelli and E. H. Adelson, "Non-separable extensions of quadrature mirror filters to multiple dimensions,"Proc. IEEE, vol. 78, no. 4, pp. 652-664, 1990.[16] G. Strang,Linear Algebra and its Applications, 3rd ed. Cambridge, MA: Wellesley-Cambridge.[17] R. Szeliski, "Fast surface interpolation using hierarchical basis functions,"IEEE Trans. Pattern Anal. Machine Intell., vol. 12, no. 6, pp. 513-528, 1990.[18] D. Terzopoulos, "The computation of visible surface representations,"IEEE Trans. Pattern Anal. Machine Intell., vol. 10, no. 4, pp. 417-439, 1988.[19] H. Wilson and G. Gelb, "Modified line-element theory for spatial-frequency and width discrimination,"J. Opt. Soc. Amer. A, vol. 1, no. 1, pp. 124-131, Jan. 1984.[20] T. Broida and R. Chellappa, "Estimation of object motion parameters from noisy images,"IEEE Trans. Pattern Anal. Machine Intell, vol. PAMI-8, no. 1, Jan. 1986.[21] O. D. Faugeras, N. Ayache, B. Faverjon, and F. Lutsman, "Building visual maps by combining noisy stereo measurements," inProc. IEEE Conf. Robotics Automat.pp. 1433-1438, 1987.
Index Terms:
wavelet transforms; interpolation; iterative methods; image processing; orthogonal wavelet bases; preconditioning; approximate solutions; iterative methods; range data; regularization; surface interpolation; wavelet transforms
Citation:
A.P. Pentland, "Interpolation Using Wavelet Bases," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 4, pp. 410-414, Apr. 1994, doi:10.1109/34.277594