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Optimal Generating Kernels for Image Pyramids by Piecewise Fitting
December 1992 (vol. 14 no. 12)
pp. 1190-1198

A novel class of generating kernels for image pyramids is introduced. When these kernels are convolved with intensity functions of images, continuous piecewise surfaces composed of polynomial tensor products are fitted to the intensity functions. The fittings are optimal in the sense that the mean square error between them and the original intensity functions is minimized. Two members of the class are introduced, and symmetry, normalization, unimodality, and equal contribution properties are proved. These kernels possess attractive properties such as small window size, fast inverse transformation, and minimum error. Experiments show that they compare favorably with existing ones in terms of mean square error.

[1] P. J. Burt, "Fast filter transforms for image processing,"Comput. Graphics Image Processing, vol. 16, pp. 20-51, 1981.
[2] P. J. Burt and E.H. Adelson, "The Laplacian pyramid as a compact image code,"IEEE Trans. Commun., vol. COM-31, pp. 532-540, Apr. 1983.
[3] V. Cantoni and S. Levialdi, Eds.,Pyramidal Systems for Computer Vision. Berlin: Springer-Verlag, 1986.
[4] S. Castan and J. Shen, "Fast filter transform theory and design for image processing," inProc. CVPR-85(San Francisco, CA), June 19-23, 1985, pp. 420-422.
[5] R. Chapman and T. S. Durrani, "Circularly symmetric filter design using 2-d prolate spheroidial sequences," inProc. ICASSP-84(San Diego), 1984, pp. 20.3.1-20.3.4.
[6] F. Chin, A. Choi, and Y. Luo, "Optimal generating kernels for image pyramids by Linear fitting," inProc. 1989 Int. Symp. Comput. Architecture Digital Signal Processing(Hong Kong), Oct. 11-14, 1989, pp. 612-617.
[7] P. E. Danielsson, "Rotation-invariant linear operators with directional response," inProc. 5th ICPR(Miami), 1980, pp. 1171-1176.
[8] W. W. Hager,Applied Numerical Linear Algebra. Englewood Cliffs, NJ: Prentice-Hall, 1988.
[9] Y. Luo, "A pyramid model driven 2-D object recognition system,"J. Commun. China, vol. 9, no. 2, pp. 43-50, Sept. 1988.
[10] Y. Luo, R. Chin, and C. Dyer, "2-D object recognition using hierarchical boundary segments," inIEEE Proc. CVPR-85(San Francisco, CA), June 19-23, 1985, pp. 426-428.
[11] D. Marr and E. Hildreth, "Theory of edge detection," inProc. R. Soc. London, vol. B 207, pp. 187-217, 1980.
[12] P. Meer, E. S. Baugher, and A. Rosenfeld, "Frequency domain analysis and synthesis of image pyramid generating kernels,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 512-522, 1987.
[13] A. V. Oppenheim and R. W. Schafer,Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
[14] A. Rosenfeld (Ed.),Multiresolution Image Processing and Analysis. New York: Springer-Verlag, 1984.
[15] G. E. Sotak and K. L. Boyer, "The Laplacian-of-Gaussian kernel: A formal analysis and design procedure for fast, accurate convolution and full-frame output,"Comput. Vision Graphics Image Processing, vol. 48, no. 2, pp. 147-189, 1989.
[16] S. L. Tanimoto and T. A. Pavlidis, A hierarchical data structure for picture processing,"Comput. Graphics Image Processing, vol. 4, pp. 104-119, 1975.
[17] R. Wilson and M. Spann, "Finite prolate spheroidal sequences and their applications I, II: image feature description and segmentation,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, pp. 193-203, 1988.

Index Terms:
optimal generating kernels; convolution; mean square error minimization; image pyramids; piecewise fitting; intensity functions; continuous piecewise surfaces; polynomial tensor products; symmetry; normalization; unimodality; equal contribution properties; small window size; fast inverse transformation; minimum error; image processing; least squares approximations; optimisation
Citation:
F. Chin, A. Choi, Y. Luo, "Optimal Generating Kernels for Image Pyramids by Piecewise Fitting," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 12, pp. 1190-1198, Dec. 1992, doi:10.1109/34.177384
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