Projective Fourier analysis for patterns

Pattern Recognition - Tập 33 - Trang 2033-2043 - 2000
Jacek Turski1
1Department of Computer and Mathematical Sciences, University of Houston-Downtown, One Main Street, Houston, TX 77002, USA

Tài liệu tham khảo

Blatt, 1994, The canonical coordinates method for pattern recognition — II. Isomorphism with affine transformations, Pattern Recognition, 27, 99, 10.1016/0031-3203(94)90020-5 Cealli, 1988, On the minimum number of templates required for shift, rotation and size invariant pattern recognition, Pattern Recognition, 21, 205, 10.1016/0031-3203(88)90055-6 Ferraro, 1988, Relationship between integral transform invariances and Lie group theory, J. Opt. Soc. Amer., A5, 738, 10.1364/JOSAA.5.000738 Gauthier, 1991, Motions and pattern analysis: harmonic analysis on groups and their homogeneous spaces, IEEE Trans. Systems Man Cybernet., 21, 149, 10.1109/21.101146 Giulianini, 1992, Transformational properties of integral transforms of images, J. Opt. Soc. Amer., A9, 494, 10.1364/JOSAA.9.000494 Ghorbel, 1994, A complete invariant description for gray-level images by the harmonic analysis approach, Pattern Recognition Lett., 15, 1043, 10.1016/0167-8655(94)90037-X Rubinstein, 1991, Recognition of distorted patterns by invariant kernels, Pattern Recognition, 24, 959, 10.1016/0031-3203(91)90093-K Segman, 1992, The canonical coordinates method for pattern recognition: theoretical and computational considerations, IEEE Trans. Pattern Analysis Mach. Intell., 14, 1171, 10.1109/34.177382 Tanaka, 1993, On the representation of the projected motion group in 2+1D, Pattern Recognition Lett., 14, 671, 10.1016/0167-8655(93)90053-G D. Mumford, Mathematical theories of shape: do they model perception? in: B.C. Vemuri, (Ed.), SPIE Vol. 1570 Geometric Methods in Computer Vision, 1991, pp. 2–10. Turski, 1998, Harmonic analysis on SL(2, C) and projectively adapted pattern representation, J. Fourier Anal. Appl., 4, 67, 10.1007/BF02475928 J. Turski, Projective Fourier analysis in computer vision: theory and computer simulations, in: Malter et al. (Eds.), SPIE Vol. 3168 Vision Geometry VI, 1997, pp. 124–135. J. Turski, Projective Fourier analysis for computational vision of planar objects, submitted for publication. Gross, 1977, On the evolution of noncommutative harmonic analysis, Amer. Math. Monthly, 85, 525, 10.2307/2320861 J. Turski, Projective harmonic analysis and rendering perspective distortions of patterns, Presented at the 4th International Conference Curves and Surfaces, Saint-Malo, France, July 1–7, 1999. A.W. Knapp, Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton Univ. Press, Princeton, 1986. I.M. Gel'fand, M.I. Graev, N.Ja. Vilenkin, Generalized Functions Vol. 5: Integral Geometry and Representations Theory, Academic Press, New York, 1966. E.M. Stein, G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, 1971. Driscoll, 1994, Computing Fourier transforms and convolutions on the 2-sphere, Adv. Appl. Math., 15, 202, 10.1006/aama.1994.1008 T. Needham, Visual Complex Analysis, Clarendon Press, Oxford, 1997. J.L. Mundy, A. Zisserman, Appendix — Projective geometry for machine vision, in: J.L. Mundy, A. Zisserman (Eds.), Geometric Invariance in Computer Vision, 1992, pp. 463–519. Dutt, 1995, Fast Fourier transforms for nonequispaced data, II, Appl. Comp. Harmon. Anal., 2, 85, 10.1006/acha.1995.1007 Feichtinger, 1995, Efficient numerical methods in non-uniform sampling theory, Numer. Math., 69, 423, 10.1007/s002110050101 Mohlenkamp, 1999, A fast transform for spherical harmonics, J. Fourier Anal. Appl., 5, 159, 10.1007/BF01261607