Harmonic Analysis on SL(2,C) and Projectively Adapted Pattern Representation

Journal of Fourier Analysis and Applications

Volumn 4, Issue 1, 1998, Pages

  Turski, Jacek ^a  

^a UNIVERSITY OF HOUSTON DOWNTOWN   (United States)

Author keywords

Fourier analysis; Harmonic analysis on SL(2, C); Irreducible representations of the group SL(2, C); Projectively adapted pattern representation; Projectively invariant classification of patterns

Indexed keywords

EID: 1842766334     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Barrett, E.B., Payton, P.M., Brill, M.H., and Haag, N.N. (1990). Invariants Under Image Perspective Transformations: Theory and Examples, Intl. J. Imagining Systems Technol., 2, 296-314.
2. Barrett, E.B., Payton, P.M., Haag, N.N., and Brill, M.H. (1991). General Methods for Determining Projective Invariants in Imagery, CVGIP: Image Understanding, 53, 46-65.
3. Berger, M. (1987). Geometry I, Springer-Verlag.
4. Choquet-Bruhat, Y. and DeWitt-Morette, C. (1977). Analysis, Manifolds and Physics, 2nd ed., North-Holland.
5. Clausen, M. and Baum, U. (1993). Fast Fourier Transforms for Symmetric Groups: Theory and Implementation, Math. Computation, 61, 833-847.
6. Diaconis, P. (1989). A Generalization of Spectral Analysis with Applications to Ranked Data, Annal. Stat., 17, 949-979.
7. Diaconis, P. and Rockmore, D. (1990). Efficient Computation of the Fourier Transform on Finite Groups, J. Am. Math. Soc., 3, 297-330.
8. Driscoll, J.R. and Healy, D.M. (1994). Computing Fourier Transforms and Convolutions on the 2-Sphere, Adv. Appl. Math., 15, 202-250.
9. Dym, H. and McKean, H.P. (1972). Fourier Series and Integrals, Academic Press.
10. Gel'fand, I.M., Graev, M.I., and Vilenkin, N.Ya. (1966). Generalized Functions Vol. 5: Integral Geometry and Representation Theory, Academic Press.
11. Gross, K.I. (1977). On the Evolution of Noncommutative Harmonic Analysis, Am. Math. Monthly, 85, 525-548.
12. Gurarie, D. (1993). Symmetries and Laplacians: Introduction to Harmonic Analysis, Group Representations and Applications, in Mathematics Studies, Vol. 174, North-Holland.
13. Knapp, A.W. (1986). Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, Princeton, NJ.
14. Lewis, R. (1990). Practical Digital Image Processing, Ellis Harwood Series in Digital and Signal Processing, D.R. Sloggett, Ed., Ellis Harwood Limited.
15. Mackey, C.W. (1978). Harmonic Analysis as the Exploitation of Symmetry - A Historical Survey, Proc. Conf. on History of Analysis, Rice University, 1977, R.J. Stanton and R.O. Wells, Jr., Eds., 64(2-3), 73-228.
16. Mundy, J.L. and Zisserman, A., Eds., (1992). Geometric Invariance in Computer Vision, Appendix: Projective Geometry for Machine Vision, MIT Press.
17. Mundy, J.L. and Zisserman, A. Eds., (1993). Applications of Invariance in Computer Vision II, Proc. Second European-US Workshop on Invariance, ESPRIT ARPA/NSF.
18. Shapiro, L.S. (1995). Affine Analysis of Image Sequences, Cambridge University Press.
19. Singer, I.M. and Thorpe, J.A. (1967). Lectures Notes on Elementary Topology and Geometry, Scott, Foresman and Company, Dallas, TX.
20. Taylor, M.E. (1986). Noncommutative Harmonic Analysis, Mathematical Surveys and Monographs, Number 22, American Mathematical Society, Providence, RI.
21. Terras, A. (1985). Harmonic Analysis on Symmetries Spaces and Applications I, Springer-Verlag.
22. Wallach, N.R. (1973). Harmonic Analysis on Homogeneous Spaces, Pure and Applied Mathematics Vol. 19, Marcel Dekker.