Karhunen-Loève decomposition in the presence of symmetry - Part I

IEEE Transactions on Image Processing

Volumn 8, Issue 9, 1999, Pages 1183-1190

  Lahme, Brigitte ^a   Miranda, Rick ^b  

^a University of Arizona   (United States)

^b Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

Data compression; Dimension reduction; Finite groups; Karhunen Lo ve decomposition; Lie groups; Representation theory; Symmetry

Indexed keywords

EID: 0010790771     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.784431     Document Type: Article

References (19)

1. R. B. Ash and M. F. Gardner, Topics in Stochastic Processes. New York: Academic, 1975.
2. M. J. Atallah, "On symmetry detection," IEEE Trans. Comput., vol. C-35, pp. 663-666, 1985.
3. P. G. Ciarlet, Introduction to Numerical Linear Algebra and Optimization. Cambridge, U.K.: Cambridge Univ. Press, 1982.
4. C. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras. New York: Wiley 1962.
5. W. Fulton and J. Harris, Representation Theory. Berlin, Germany: Springer-Verlag, 1991.
6. I. Hargittai, Quasicrystals, Networks, and Molecules of Fivefold Symmetry. New York: VCH, 1990.
7. H. J. A. M. Heijmans and A. V. Tuzikov, "Similarity and symmetry measures for convex shapes using Minkowski addition," IEEE Trans. Pattern Anal. Machine Intell., vol. 20, pp. 980-992, 1998.
8. M. Kirby and L. Sirovich, "Applications of the Karhunen-Loève procedure for the characterization of human faces," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 103-108, 1990.
9. N. Kiryati and Y. Gofman, "Detecting symmetry in grey level images: The global optimization approach," Int. J. Comput. Vis., vol. 29, pp. 29-45, 1998.
10. A. L. Loeb, Color and Symmetry. New York: Wiley, 1971.
11. J. Maddox, "Toward fivefold symmetry?," Nature, vol. 313, pp. 263-264, 1985.
12. J. P. Serre, Linear Representations of Finite Groups. Berlin, Germany: Springer-Verlag, 1977,
13. L. Sirovich, "Turbulence and the dynamics of coherent structures - I: Coherent Structures," Quart. Appl. Math., vol. XLV, no. 3, pp. 561-571, 1987.
14. N. Smaoui and D. Armbruster, "Symmetry and the Karhunen Loève analysis," SIAM J, Sci. Comput., vol. 18, pp. 1526-1532, 1997.
15. I. Stewart and M. Golubitsky, Fearful Symmetry. Oxford, U.K.: Blackwell, 1992.
16. S. Strogatz and I. Stewart, "Coupled oscillators and biological synchronization," Sci. Amer., pp. 102-109, Dec. 1993.
17. L. Van Gool, T. Moons, D Ungureanu, and E. Pauwels, "Symmetry from shape and shape from symmetry," Int. J. Robot. Res., vol. 14, pp. 407-424, 1995.
18. E. Vinberg, Linear Representations of Groups. Basel, Switzerland: Birkhäuser Verlag, 1989.
19. E. P. Wigner, Group Theory and Its Applications to Quantum Mechanics. New York: Academic, 1959.