This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Using Dynamic Programming for Solving Variational Problems in Vision
September 1990 (vol. 12 no. 9)
pp. 855-867

Early image understanding seeks to derive analytic representations from image intensities. The authors present steps towards this goal by considering the inference of surfaces from three-dimensional images. Only smooth surfaces are considered and the focus is on the coupled problems of inferring the trace points (the points through which the surface passes) and estimating the associated differential structure given by the principal curvature and direction fields over the estimated smooth surfaces. Computation of these fields is based on determining an atlas of local charts or parameterizations at estimated surface points. Algorithm robustness and the stability of results are essential for analyzing real images; to this end, the authors present a functional minimization algorithm utilizing overlapping local charts to refine surface points and curvature estimates, and develop an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties. Examples of the recovery of local structure are presented for synthetic images degraded by noise and for clinical magnetic resonance images.

[1] A. A. Amini, S. Tehrani, and T. E. Weymouth, "Using dynamic programming for minimizing the energy of active contours in the presence of hard constraints," inProc. Second Int. Conf. Computer Vision, Tarpon Springs, FL, Dec. 1988, pp. 95-99.
[2] A. Amini, "Using dynamic programming for solving variational problems in vision: Applications involving deformble models for contours and surfaces," Ph.D. dissertation, Dep. Elec. Eng. Comput. Sci., The Univ. Michigan, Ann Arbor, 1990.
[3] A. Amini, T. Weymouth, and B. Schuack, "Surface weaving with deformable signals," submitted to the Third Int. Conf. Computer Vision, Osaka, Japan, 1990.
[4] R. Bellman,Dynamic Programming. Princeton, NJ: Princeton University Press, 1957.
[5] R. Bellman,Adaptive Control Processes: A Guided Tour. Princeton, NJ: Princeton University Press, 1961.
[6] R. Bellman,Dynamic Programming. Princeton, NJ: Princeton University Press, 1957.
[7] M. Bertero, T. A. Poggio, and V. Torre, "Ill-posed problems in early vision,"Proc. IEEE, vol. 76, pp. 869-889, Aug. 1988.
[8] A. Blake and A. Zisserman,Visual Reconstruction. Cambridge, MA: MIT Press, 1987.
[9] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[10] R. Courant and D. Hilbert,Methods of Mathematical Physics, vol. I. London: Interscience, 1953.
[11] S. Dreyfus,Dynamic Programming and the Calculus of Variations. New York: Academic, 1965.
[12] S. Dreyfus, "The main results of optimal control theory made simple,"Population Dynamics, 1972.
[13] S. E. Dreyfus and A. M. Law,The Art and Theory of Dynamic Programming. New York: Academic, 1977.
[14] M. Furst and P. Caines, "Edge detection with image enhancement via dynamic programming,"Comput. Vision, Graphics, Image Processing, vol. 33, pp. 263-279, 1986.
[15] E. B. Gamble and T. Poggio, "Visual integration and detection of discontinuities: The key role of intensity edges," Artificial Intell. Lab., Massachusetts Inst. Technol., AI Memo 970, Oct. 1987.
[16] S. Geman and D. Geman, "Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 6, pp. 721-741, Nov. 1984.
[17] M. A. Gennert and A. L. Yuille, "Determining the optimal weights in multiple objective function optimization," inProc. Second Int. Conf. Comput. Vision, Dec. 1988, pp. 87-89.
[18] W. E. L. Grimson,From Images to Surfaces. Cambridge, MA: MIT Press.
[19] F. Hildebrand,Methods of Applied Mathematics. Englewood Cliffs, NJ: Prentice-Hall, 1965.
[20] B. K. P. Horn, "Image intensity understanding,"Artificial Intell., vol. 8, no. 2, pp. 201-231, 1977.
[21] B. K. P. Horn and B. Schunck, "Determining optical flow,"Artificial Intell., vol. 17, nos. 1-3, pp. 185-203, 1981.
[22] B. K. P. Horn,Robot Vision. Cambridge, MA: M.I.T. Press, 1986.
[23] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models,"Int. J. Comput. Vision, vol. 1, no. 4, pp. 321-331, 1988.
[24] J. Marroquin, S. Mitter, and T. Poggio, "Probabilistic solution of ill-posed problems in computational vision,"J. Amer. Statist. Assoc., vol. 82, no. 397, pp. 76-89, 1987.
[25] D. Mumford and J. Shah, "Boundary detection by minimizing functionals, I," inProc. IEEE Conf. Computer Vision and Pattern Recognition, San Francisco, CA, June 1985, pp. 22-26.
[26] Y. Ohta and T. Kanade, "Stereo by intra- and inter-scanline search using dynamic programming,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, pp. 139-154, 1985.
[27] T. Poggio and V. Torre, "Ill-posed problems and regularization analysis in early vision," inProc. AARPA Image Understanding Workshop, New orleams, LA, 1984, pp. 257-263.
[28] W. Press, B. Flannery, S. Teukolsky, and W. Vetterling,Numeric Recipes in C-The Art of Scientific Computing.Cambridge, UR: Cambridge University Press, 1988.
[29] A. Sage and C. White,Optimum Systems Control. Englewood Cliffs, NJ: Prentice-Hall, 1977.
[30] B. Shahraray and D. Anderson, "Optimal estimation of contour properties by cross-validated regularization,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 6, pp. 600-610, June 1989.
[31] T. Simchony, R. Chellappa, and Z. Lichtenstein, "Pyramid implementation of optimal step conjugate search algorithms for some computer vision problems,"Proc. Second Int. Conf. Computer Vision (ICCV'88), Tampa, FL, Dec. 1988. Washington, DC: IEEE Computer Society Press, 1988, pp. 580-590.
[32] D. Terzopoulos, "Regularization of inverse visual problems involving discontinuities,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 4, pp. 413-424, July 1986.
[33] D. Terzopoulos, "Computation of visible-surface representations,"IEEE Trans. Pattern Anal. Machine Intell., vol. 10, no. 4, pp. 417-438, July 1988.
[34] A. Tikhonov and V. Arsenin,Solution of lll-posed Problems, Washington, DC: Winston, 1977.
[35] G. Wahba and S. Wold, "Periodic splines for spectral density estimation: The use of cross validation for determining the degree of smoothing,"Commun. Statist., vol. 4, no. 2, pp. 125-141, 1975.
[36] G. Wahba and J. Wendelberger, "Some new mathematical methods for variational objective analysis using splines and cross validation,"Monthly Weather Rev., vol. 108, pp. 1122-1143, 1980.
[37] H. Yamada, C. Merritt, and T. Kasvand, "Recognition of kidney glomerulus by dynamic programming matching method,"IEEE Trans. Pattern Anal. Machine Intell., vol. 10, no. 5, pp. 731-737, Sept. 1988.
[38] A.L. Yuille, "Energy Functions for Early Vision and Analog Networks,"Artificial Intelligence Lab. Memo No. 987, MIT, Cambridge, Mass., 1987.

Index Terms:
machine vision; dynamic programming; variational problems; energy-minimizing active contours; optimization; discrete multistage decision process; computational costs; computer vision; dynamic programming; picture processing; variational techniques
Citation:
A.A. Amini, T.E. Weymouth, R.C. Jain, "Using Dynamic Programming for Solving Variational Problems in Vision," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 9, pp. 855-867, Sept. 1990, doi:10.1109/34.57681
Usage of this product signifies your acceptance of the Terms of Use.