Fingerprints theorems for zero crossings

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 2, Issue 5, 1985, Pages 683-692

  Yuille, A L ^a   Poggio, T ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84975551810     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.2.000683     Document Type: Article

References (29)

1. D. Marr, Vision, A Computational Investigation into the Human Representation and Processing of Visual Information (Freeman, San Francisco, Calif., 1982).
2. B. F. Logan, " Information in the zero crossings of bandpass signals, " Bell Syst. Tech. J. 56, 487-510 (1977).
3. T. Poggio, H. K. Nishihara, and K. R. K. Nielsen, " Zero-crossings and spatiotemporal interpolation in vision: aliasing and electrical coupling between sensors, " Artificial Intelligence Memo 675 (Massachusetts Institute of Technology, Cambridge, Mass., May 1982).
4. D. Marr, T. Poggio, and S. Ullman, " Bandpass channels, zero-crossings and early visual information processing, " J. Opt. Soc. Am. 70, 868-870 (1979).
5. W. E. L. Grimson, From Images to Surfaces (MIT Press, Cambridge, Mass., 1981).
6. D. Marr and E. Hildreth, " Theory of edge detection, " Proc. R. Soc. London Ser. B, 207, 187-217 (1980).
7. J. L. Crowley, " A representation for visual information, " Rep. No. CMU-RI-TR-82-7 (Robotics Institute, Carnegie-Mellon University, Pittsburgh, Pa., 1982).
8. A. Rosenfeld, " Quadtrees and pyramids: hyerarchical representation of images, " Tech. Rep. 1171 (University of Maryland, College Park, Md., 1982).
9. F. W. Campbell and J. G. Robson, " Applications of Fourier analysis to the visibility of gratings, " J. Physiol. (London) 197, 551-556 (1968).
10. C. Enroth-Cugell and J. G. Robson, " The contrast sensitivity of retinal ganglion cells of the cat, " J. Physiol. London 187, 517-552 (1966).
11. A. Witkin, " Scale-space filtering, " presented at the International Joint Conference on Artificial Intelligence, Karlsruhe, Federal Republic of Germany, 1983.
12. J. L. Stansfield, " Conclusions from the commodity expert project, " Artificial Intelligence Memo 601 (Massachusetts Institute of Technology, Cambridge, Mass., 1980).
13. J. Babaud, A. Witkin, and R. Duda, " Uniqueness of the Gaussian kernel for scale-space filtering, " Fairchild Tech. Rep. 645, Flair 22 (Fairchild Artificial Intelligence Laboratory, Palo Alto, Calif., 1983).
14. A. L. Yuille and T. Poggio, " Scaling theorems for zero-crossings, " Artificial Intelligence Memo 722 (Massachusetts Institute of Technology, Cambridge, Mass., June 1983).
15. A. L. Yuille and T. Poggio, " Fingerprints theorems for zero-crossings, " Artificial Intelligence Memo 730 (Massachusetts Institute of Technology, Cambridge, Mass., October 1983).
16. J. Koenderink, University of Utrecht, Utrecht, The Netherlands (personal communication, 1984).
17. H. K. Nishihara, " Intensity, visible-surface, and volumetric representations, " Art. Intell. 17, 265-284 (1981).
18. Clearly, the scale-map fingerprint cannot always be a more compact description of the signal than the signal itself, unless the signal is redundant in precisely the way that the fingerprint representation can exploit. We expect this to be the case for images, if an appropriate differential operator is used, because images are not a purely random array of numbers. Usually images consist of rather homogeneous regions that do not change much over significant scale intervals.
19. H. Asada and M. Brady, " The curvature primal sketch, " Artificial Intelligence Memo 758 (Massachusetts Institute of Technology, Cambridge, Mass., 1984).
20. A. L. Yuille and T. Poggio, " Fingerprints and the psychophysics of gratings, " Artificial Intelligence Memo 751 (Massachusetts Institute of Technology, Cambridge, Mass., 1984).
21. A. L. Yuille and T. Poggio, " Fingerprints theorems, " presented at the Conference on Artificial Intelligence, Austin, Texas, 1984.
22. S. W. Zucker and R. A. Hummel, " Receptive fields and the reconstruction of visual information, " Tech. Rep. 83-17 (Courant Institute, New York, N. Y., 1983).
23. 20 In this case the matrices in Eqs. (3. 3. 1) and (3. 3. 2) take simple forms.
24. A. Albert, Regression and the Moore-Penrose Pseudoinverse (Academic, New York, 1982).
25. W. E. L. Grimson, " Surface consistency constants in vision, " Comput. Vision Graph. Inf. Process, 24, 28-51 (1983).
26. A. L. Yuille, " Zero-crossings and lines of curvature, " Artificial Intelligence Memo 718 (Massachusetts Institute of Technology, Cambridge, Mass., 1983).
27. R. A. Hummel, Courant Institute, New York, N. Y. (personal communication).
28. A. L. Yuille and T. Poggio, " Fingerprints and their slope, " Artificial Intelligence Memo 752 (Massachusetts Institute of Technology, Cambridge, Mass., 1984).
29. D. Marr, " Early processing of visual information, " Phil. Trans. R. Soc. London Ser. B 275, 483-524 (1976).