This Article 
 Bibliographic References 
 Add to: 
Edge Detection and Surface Reconstruction Using Refined Regularization
May 1993 (vol. 15 no. 5)
pp. 492-499

An edge detection and surface reconstruction algorithm in which the smoothness is controlled spatially over the image space is presented. The values of parameters in the model are adaptively determined by an iterative refinement process; hence, the image-dependent parameters such as the optimum value of the regularization parameter or the filter size are eliminated. The algorithm starts with an oversmoothed regularized solution and iteratively refines the surface around discontinuities by using the structure exhibited in the error signal. The spatial control of smoothness is shown to resolve the conflict between detection and localization criteria of edge detection by smoothing the noise in continuous regions while preserving discontinuities. The performance of the algorithm is quantitatively and qualitatively evaluated on real and synthetic images, and it is compared with those of Marr-Hildreth and Canny edge detectors.

[1] M. Bertero, T. A. Poggio, and V. Torre, "Ill-posed problems in early vision,"Proc. IEEE, vol. 76, pp. 869-889, Aug. 1988.
[2] D. Marr and E. Hildreth, "Theory of edge detection," inProc. Roy. Soc.(London)Ser. B, vol. 207, 1980, pp. 187-217.
[3] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[4] R. M. Haralick, "The digital step edge from zero-crossings of second directional derivatives,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 1, pp. 58-68, 1984.
[5] A. Blake and A. Zisserman,Visual Reconstruction. Cambridge, MA: MIT Press, 1987.
[6] D. Terzopoulos, "The computation of visual surface representations,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-10, no. 4, pp. 417-438, 1988.
[7] D. Geiger and T. Poggio, "An optimal scale for edge detection," Tech. Rep., MIT AI Lab., AI Memo 1078, 1988.
[8] G. Wahba, "Practical approximate solutions to linear operator equations when the data are noisy,"SIAM J. Numer. Anal., vol. 14, no. 4, pp. 651-667, 1977.
[9] M. Gökmen, "Edge detection using regularization theory," Ph.D. dissertation, Dept. of Elec. Eng., Univ. of Pittsburgh, Pittsburgh, PA, 1990.
[10] S. Geman, and D. Geman, "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 6, pp. 721-741, 1984.
[11] J. Shah, "Segmentation by nonlinear diffusion," inProc. IEEE Conf. Comput. Vision Patt. Recogn.(Maui, HI), June 1991, pp. 202-207.
[12] M. Gökmen and C. C. Li, "Edge detection with iteratively refined regularization," inProc. 10th Int. Conf. Patt. Recogn.(Atlantic City, NJ), June 1990, pp. 690-693.
[13] M. Gökmen and C. C. Li, "Edge detection using refined regularization," inProc. IEEE Conf. Comput. Vision Patt. Recogn.(Maui, HI), June 1991, pp. 215-221.
[14] A. N. Tikhonov and V. Y. Arsenin,Solution of Ill-posed Problems. Washington, DC: Winston, 1977.
[15] A. N. Tikhonov, "Regularization of incorrectly posed problems,"Sov. Math. Dokl., vol. 4, pp. 1624-1627, 1963.
[16] D. Mumford and J. Shah, "Boundary detection by minimizing functionals," inProc. IEEE Conf. Comput. Vision Patt. Recogn.(San Francisco, CA), June 1985, pp. 22-26.
[17] W. E. L. Grimson and T. Pavlidis, "Discontinuity detection for visual surface reconstruction,"Comput. Vision Graphics Image Processing, vol. 30, pp. 316-330, 1985.
[18] D. Lee and T. Pavlidis, "One-dimensional regularization with discontinuities,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, pp. 822-829, 1988.
[19] J. 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.
[20] P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion,"IEEE Trans. Patt. Anal. Machine Intell., vol. 12, no. 7, pp. 629-639, 1990.

Index Terms:
filtering; surface reconstruction; refined regularization; edge detection; image space; iterative refinement process; smoothness; localization criteria; edge detection; filtering and prediction theory; image reconstruction; iterative methods
M. Gökmen, C.C. Li, "Edge Detection and Surface Reconstruction Using Refined Regularization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 5, pp. 492-499, May 1993, doi:10.1109/34.211469
Usage of this product signifies your acceptance of the Terms of Use.