Zero-Crossings of a Wavelet Transform

IEEE Transactions on Information Theory

Volumn 37, Issue 4, 1991, Pages 1019-1033

  Mallat, Stephane ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Multiscale; pattern matching; signal representation; wavelet transform; zero crossings

Indexed keywords

MATHEMATICAL TECHNIQUES; MATHEMATICAL TRANSFORMATIONS; PATTERN RECOGNITION;

WAVELET TRANSFORMS; ZERO CROSSINGS;

COMPUTER PROGRAMMING;

EID: 0026187946     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.86995     Document Type: Article

References (23)

1. S. Curtis, S. Shitz, and V. Oppenheim, “Reconstruction of nonperiodic two-dimensional signals from zero-crossings,” IEEE Trans. Acoust. Speech Signal Processing, vol. 35, pp. 890–893, 1987.
2. I. Daubechies, “The wavelet transform: A method of time-frequency localization,” in Advance in Spectral Analysis, S. Haykin, Ed. New York: Prentice-Hall, 1990.
3. ——, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inform. Theory, vol. 36, no. 5, pp. 961–1005, Sept. 1990.
4. W. Grimson, “Computational experiments with a feature based stereo algorithm,” IEEE Trans. Pattern Anal. Machine Intell., vol. 7, pp. 17–34, Jan. 1985.
5. A. Grossmann and J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math., vol. 15, pp. 723–736, 1984.
6. R. Hummel and R. Moniot, “A network approach to reconstruction from zero-crossings,” in Proc. IEEE Workshop Computer Vision, Dec. 1987.
7. ——, “Reconstruction from zero-crossings in scale-space,” IEEE Trans. Acoust. Speech Signal Processing, vol. 37, no. 12, Dec. 1989.
8. J. Koenderink, “The structure of images,” in Biological Cybernetics. New York: Springer-Verlag, 1984.
9. B. Logan, “Information in the zero-crossings of band pass signals,” Bell Syst. Tech. J., vol. 56, p. 510, 1977.
10. S. Mallat, “Multiresolution approximation and wavelet orthonormal bases of L2,” Trans. Amer. Mathematical Soc., vol. 315, pp. 69–87, Sept. 1989.
11. ——, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 7, pp. 674–693, July 1989.
12. ——, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoust. Speech Signal Processing, vol. 37, no. 12, pp. 2091–2110, Dec. 1989.
13. S. Mallat and S. Zhong, “Complete signal representation with multiscale edges,” Comput. Sci. Tech. Rep. 483, New York Univ., Dec. 1989. To appear in IEEE Trans. Pattern Anal. Machine Intell.
14. D. Marr and E. Hildreth, “Theory of edge detection,” Proc. Roy. Soc. Lon., vol. 207, 1980, pp. 187–217.
15. D. Marr and T. Poggio, “A theory of human stereo vision,” Proc. Roy. Soc. Lon., vol. B204, 1979, pp. 301–328.
16. Y. Meyer, in Ondelettes et Operateurs. Paris: Hermann, 1988.
17. A. Rosenfeld and M. Thurston, “Edge and curve detection for visual scene analysis,” IEEE Trans. Comput., vol. C-20, pp. 562–569, 1971.
18. J. Sanz and T. Huang, “Theorem and experiments on image reconstruction from zero-crossings,” IBM, Res. Rep. RJ5460, Jan. 1987.
19. M. J. Smith and T. P. Barnwell, “Exact reconstruction techniques for tree-structured subband coders,” IEEE Trans. Acoust. Speech Signal Processing, vol. 34, June 1986.
20. A. Witkin, “Scale space filtering,” in Proc. Int. Joint Conf. Artificial Intell., 1983.
21. D. Youla and H. Webb, “Image restoration by the method of convex projections,” IEEE Trans. Med. Imaging, vol. 1, pp. 81–101, Oct. 1982.
22. A. Yuille and T. Poggio, “Scaling theorems for zero-crossings,” IEEE Trans. Pattern Anal. Machine Intell., vol. 8, Jan. 1986.
23. Y. Zeevi and D. Rotem, “Image reconstruction from zero-crossings,” IEEE Acoust. Speech Signal Processing, vol. 34, pp. 1269–1277, 1986.