Coping with Discontinuities in Computer Vision: Their Detection, Classification, and Measurement

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 12, Issue 4, 1990, Pages 321-344

  Lee, David ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE PROCESSING--IMAGE ANALYSIS; PATTERN RECOGNITION; SIGNAL FILTERING AND PREDICTION;

COMPUTER VISION; DISCONTINUITY DETECTION; EDGE DETECTION; OPTIMAL DETECTOR; PATTERN MATCHING; STOCHASTIC PROCESS;

VISION;

EID: 0025414203     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.50620     Document Type: Article

References (40)

1. J. s. Bendat, Principles and Applications of Random Noise Theory. New York: Wiley, 1958.
2. F. Bergholm, “Edge focusing,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 726–741, 1987.
3. T. A. Burton, Volterra Integral and Differential Equations. New York: Academic, 1983.
4. A. Blake and A. Zisserman, “Some properties of weak continuity constraints and the GNC algorithm,” in Proc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, Miami Beach, FL, 1986, pp. 656–661.
5. —, “Invariant surface reconstruction using weak continuity constraints,” in Proc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, Miami Beach, FL, 1986, pp. 62–67.
6. A. Boie and I. J. Cox, “Two dimensional edge recognition using matched and Wiener filters for machine vision,” in Proc. First Int. Conf. Computer Vision, London, 1987, pp. 450–456.
7. J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679–698, 1987.
8. K. R. Castleman, Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1979.
9. L. S. Davis, “A survey of edge detection techniques,” Comput. Graphics Image Processing, vol. 4, no. 3, pp. 248–270, 1975.
10. C. de Boor, A Practical Guide to Splines. New York: Springer-Verlag, 1978.
11. H. A. Gamber, “Choice of an optimal shape parameter when smoothing noisy data,” Commun. Stat.—Theory and Methods, vol. A8, no. 14, pp. 1425–1435, 1979.
12. I. M. Gelfand and G. E. Shilov, Generalized Functions. New York: Academic, 1964.
13. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721–741, 1984.
14. W. E. L. Grimson, From Images to Surfaces: a Computational Study of the Human Early Visual System. Cambridge, MA: MIT Press, 1981.
15. —, “Recognition of object families using parameterized models,” in Proc. First Int. Conf. Computer Vision, London, 1987, pp. 93–101.
16. W. E. L. Grimson and T. Pavlidis, “Discontinuity detection for visual surface reconstruction,” Comput. Vision, Graphics, Image Processing, vol. 30, pp. 316–330, 1985.
17. E. Grosse, “A catalog of algorithms for approximation,” in Algorithms for Approximation II, J. Mason, Ed. London: Chapman & Hall, 1989.
18. D. Lee, “Discontinuity detection, classification, and measurement,” SIAM J. Sci. Stat. Comput., to be published.
19. D. Lee and T. Pavlidis, “One-dimensional regularization with discontinuities,” IEEE Trans. Pattern Anal. Machine Intell., vol. 10, pp. 822–829, 1988.
20. D. Lee, T. Pavlidis, and K. Huang, “Edge detection through residual analysis,” in Proc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, Ann Arbor, MI, 1988, pp. 215–222.
21. D. Marr, Vision. San Francisco, CA: Freeman, 1982.
22. D. Marr and E. C. Hildreth, “Theory of edge detection,” Proc. Roy. Soc. London, vol. B 207, pp. 187–217, 1980.
23. J. L. Marroquin, S. Mitter, and T. Poggio, “Probabilistic solution of ill-posed problems in computational vision,” J. Amer. Stat. Assoc., vol. 82, pp. 76–89, 1987.
24. D. Mumford and J. Shah, “Boundary detection by minimizing functionals,” in Proc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, San Francisco, CA, 1985, pp. 22–26.
25. V. S. Nalwa and T. O. Binford, “On detecting edges,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 699–714, 1986.
26. A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York: McGraw-Hill, 1984.
27. T. Pavlidis, Structural Pattern Recognition. New York: Springer-Verlag, 1977.
28. T. Poggio, H. Voorhees, and A. Yuille, “A regularized solution of edge detection,” M.I.T. A.I. Memo 833, May 1985.
29. M. J. D. Powell, “Curve fitting by splines in one variable,” in Numerical Approximation to Functions and Data, J. G. Hayes, Ed. London: Athlone, 1970, pp. 65–83.
30. L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
31. A. Rosenfeld and M. Thurston, “Edge and curve detection for visual scene analysis,” IEEE Trans. Comput., vol. C-20, no. 5, pp. 562–567, 1971.
32. J. H. Shiau, “Smoothing spline estimation of functions with discontinuities,” Ph.D. dissertation, Dep. Stat., Univ. Wisconsin, Madison, 1985.
33. D. Terzopoulos, “Regularization of inverse visual problems involving discontinuities,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 413–424, 1986.
34. E. C. Titchmarsh, The Theory of Functions. Oxford, England: Oxford University Press, 1952.
35. V. Torre and T. A. Poggio, “On edge detection,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147–163, 1986.
36. J. E. Traub and H. Wozniakowski, A General Theory of Optimal Algorithms. New York: Academic, 1980.
37. V. Volterra, Theory of Functionals and of Integral and Integro-Dif-ferential Equations. New York: Dover, 1959.
38. G. Wahba, “Cross-validated spline methods for the estimation of multivariate functions from data on functionals,” in Statistics: An Appraisal, Proc. 50th Anniv. Conf, Iowa State Stat. Lab., H. A. David and H. T. David, Eds., 1984.
39. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series. New York: Wiley, 1949.
40. G. Wahba and J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross-validation,” Monthly Weather Rev., vol. 108, pp. 36–57, 1980.