Duality of log-polar image representations in the space and spatial-frequency domains

IEEE Transactions on Signal Processing

Volumn 47, Issue 9, 1999, Pages 2469-2479

  Tabernero, Antonio ^a,b   Portilla, Javier ^a,b   Navarro, Rafael ^a,b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b INSTITUTO DE ÓPTICA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER TRANSFORMS; FREQUENCY DOMAIN ANALYSIS; LOW PASS FILTERS; MATHEMATICAL OPERATORS; SPECTRUM ANALYSIS; WAVELET TRANSFORMS;

LOG-POLAR MAPPING; SCALING-ROTATING VARIANT FILTERING (SRVF);

SIGNAL FILTERING AND PREDICTION;

EID: 0032689866     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.782190     Document Type: Article

References (28)

1. C. Braccini, G. Gambardella, and G. Sandini, A signal theory approach to the space and frequency variant filtering performed by the human visual system, Signal Process., vol. 3, pp. 231-240, 1981.
2. C.A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrikson, Human photoreceptor topography, J. Comput. Neurol., vol. 292, pp. 497-523, 1990.
3. D.C. van Essen, W. T. Newsome, and J. H. R. Maunsell, The visual field representation in striate cortex of the macaque monkey, Vision Res., vol. 24, pp. 429-448, 1984.
4. D.G. Green, Regional variations in the visual acuity for interference fringes on the retina, J. Physiol., vol. 207, pp. 351-356, 1970.
5. P. Kortum and W. Geisler, Implementation of a foveated image coding system for image bandwidth reduction, Proc. SPIE, vol. 2657, pp. 350-360, 1996.
6. H. Yamamoto, Y. Yeshurun, and M.D. Levine, An active foveated vision system: attention mechanisms and scan path convergence measures, Comput. Vision Image Understanding, vol. 63, pp. 50-65, 1996.
7. W. Geisler and J.S. Perry, A real-time foveated multiresolution system for low-bandwidth video communication, Proc. SPIE, vol. 3299, pp. 294-305, 1998.
8. D.L. Jones and T. W. Parks, A high-resolution data-adaptative time-frequency representation, IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 2127-2135, 1990.
9. S.G. Mallat, A theory for multiresolution signal decomposition: The wavelet transform, IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674-693, 1989.
10. I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.
11. G. Cristobal and L. Cohen, Scale in images, SPIE Proc. Adv. Signal Process., vol. 2846, pp. 251-261, 1996.
12. D.A. Pollen and S. F. Ronner, Visual cortical neurons as localized spatial filters, IEEE Trans. Syst., Man, Cybern., vol. 13, pp. 907-916, 1983.
13. J.G. Daugman, Spatial visual channels in the Fourier plane, Vision Res., vol. 24, pp. 891-910, 1984.
14. D.J. Field, Relation between the statistics of natural images and the response properties of cortical cells, J. Opt. Soc. Amer. A, vol. 4, pp. 2379-2394, 1987.
15. L. Cohen, The scale representation, IEEE Trans. Signal Processing, vol. 41, pp. 3275-3293, 1993.
16. W. Beil, Steerable filters and invariance theory, Patt. Recogn. Lett., 15, pp. 453-460, 1994.
17. H. Greenspan, S. Belongie, R. Gooodman, P. Perona, S. Rakshit, and C.H. Andersen, Overcomplete steerable pyramid filters and rotation invariance, in Proc. IEEE Conf. Comput. Vis. Patt. Recogn., Seattle, WA, 1994, pp. 222-228.
18. A. Tabernero, J. Portilla, and R. Navarro. Duality between the local spectrum of a signal and its inverse Fourier transform, the local signal, Instituto de Óptica (CSIC), Tech. Rep. 53.
19. C. Gasquet and P. Witomski, Analyze de Fourier et Applications. Paris, France: Masson, 1990.
20. J.B. Allen and L. R. Rabiner, A unified approach to short-time Fourier analysis and synthesis, Proc. IEEE, vol. 65, pp. 1558-1564, 1977.
21. M. Michaelis and G. Sommer, A Lie group-approach to steerable filters, Pattern Recognit. Lett., vol. 16, pp. 1165-1174, 1995.
22. W.T. Freeman and E. H. Adelson, The design and use of steerable filters, IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 891-906, 1991.
23. E.P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. Heeger, Shiftable multiscale transforms, IEEE Trans. Inform. Theory, vol. 38, pp. 587-607, 1992.
24. P. Perona, Deformable kernels for early vision, IEEE Trans. Pattern Anal. Machine. Intell., vol. 17, pp. 488-499, 1995.
25. P.C. Teo and Y. Hel-Or, A computational group theory approach to steerable functions, Stanford Univ., Stanford, CA, Tech. Rep. STAN-CS-TN-96-33, Apr. 1996.
26. J. Portilla, R. Navarro, and A. Tabernero, Optimizing parametric deformable kernels, in Proc. IEEE Int. Symp. Time-Scale Time-Freq. Anal., Pittsburgh, PA, Oct. 1998.
27. J. Portilla and R. Navarro, Efficient method for space-variant lowpass filtering, in Proc. SNRFAI, Barcelona, Spain, 1997, pp. 287-292.
28. A.B. Watson, Detection and recognition of simple spatial forms, in Physical and Biological Processing of Images, A. C. Sleight, Ed. Berlin, Germany: Springer-Verlag, 1982, pp. 100-114.