Stochastic motion and the level set method in computer vision: Stochastic active contours

International Journal of Computer Vision

Volumn 69, Issue 1, 2006, Pages 7-25

  Juan, Olivier ^a   Keriven, Renaud ^a,b   Postelnicu, Gheorghe ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITÉ PARIS EST   (France)

Author keywords

Active contours; Level sets; Segmentation; Shape optimization; Stochastic optimization; Stochastic partial differential equations

Indexed keywords

ACTIVE CONTOURS; LEVEL SETS; SHAPE OPTIMIZATION; STOCHASTIC OPTIMIZATION; STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS;

APPROXIMATION THEORY; IMAGE SEGMENTATION; MOTION ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS; RANDOM PROCESSES;

COMPUTER VISION;

EID: 33646879813     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-006-6849-5     Document Type: Article

References (40)

1. Ballerini, L. 1999. Genetic snakes for image segmentation. In Evolutionary Image Analysis, Signal Processing and Telecommunication, vol. 1596 of Lecture Notes in Computer Science, Springer, pp. 59-73.
2. Ben-Arous, G., Tannenbaum, A., and Zeitouni, O. 2002. Stochastic approximations to curve shortening flows via particle systems. Technical report, Technion Institute.
3. Bezdek, J.C. 1981. Pattern Recognition with Fuzzy Objective Function Algorithms, Kluwer Academic Publishers.
4. Buckdahn, R. and Ma, J. 2001. Stochastic viscosity solutions for nonlinear stochastic partial differential equations. Stochastic Processes and their Applications, 93:181-228.
5. Cances, E., Keriven, R., Lodier, F., and Savin, A. 2004. How electrons guard the space: Shape optimization with probability distribution criteria. Theoret. Chem. Acc.
6. Caselles, V., Kimmel, R., and Sapiro, G. 1997. Geodesic active contours. The International Journal of Computer Vision, 22(1): 61-79.
7. deGruijter, J. and McBratney, A. 1988. A modified fuzzy k means for predictive classification. In Bock, H.H.(ed), Classification and Related Methods of Data Analysis, Elsevier Science, Amsterdam., pp. 97-104.
8. Dempster, A.P., Laird, N.M., and Rubin, D.B. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39:1-38.
9. Faugeras, O. and Keriven, R. 1998. Variational principles, Surface Evolution, PDE's, level set methods and the Stereo Problem. IEEE Transactions on Image Processing, 7(3):336-344.
10. Gard, T. 1988. Introduction to Stochastic Differential Equations. Marcel Dekker, New York and Basel.
11. Jiang, G.S. and Peng, D. 2000. Weighted ENO schemes for hamilton-jacobi equations. SIAM Journal of Scientific Computing, 21(6):2126-2143.
12. Juan, O., Keriven, R., and Postelnicu, G. 2004. Stochastic motion and the level set method in computer vision: Stochastic active contours. Technical Report 04-01, CERTIS.
13. Karatzas, I. and Shreve, S. 1991. Brownian Motion and Stochastic Calculus, Springer-Verlag, New York.
14. Katsoulakis, M. and Kho, A. 2001. Stochastic curvature flows: Asymptotic derivation, level set formulation and numerical experiments. Journal of Interfaces and Free Boundaries, 3:265-290.
15. Kirkpatrick, S., Gelatt, C.J., and Vecchi, M. 1983. Optimization by Simulated Annealing. Science, 220(4598).
16. Kunita, H. 1990. Stochastic Flows and Stochastic Differential Equations, Cambridge University Press.
17. Lions, P. and Souganidis, P. 1998a. Fully nonlinear stochastic partial differential equations. C.R. Acad. Sci. Paris Ser. I Math, 326:1085-1092.
18. Lions, P. and Souganidis, P. 1998b. Fully nonlinear stochastic partial differential equations: Nonsmooth equations and applications. C.R. Acad. Sci. Paris Ser. I Math, 327:735-741.
19. Lions, P. and Souganidis, P. 1999. Equations aux derivees partielles stochastiques non lineaires et solutions de viscosite. Seminaire X-EDP (Unpublished Lecture).
20. Lions, P. and Souganidis, P. 2000a. Fully nonlinear stochastic partial differential equations with semilinear stochastic dependence. C.R. Acad. Sci. Paris Ser. I Math, 331:617-624.
21. Lions, P. and Souganidis, P. 2000b. Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations. C.R. Acad. Sci. Paris Ser. I Math, 331:783-790.
22. MacQueen, J. 1967. Some methods for classification and analysis of multivariate. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 281-297.
23. McLachlan, G. and David, P. 2000. Finite Mixture Models, Wiley, New York.
24. McLachlan, G. and Krishnan, T. 1997. The EM Algorithm and Extensions, Wiley, New York.
25. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and T.E. 1953. Equation of state calculations by fast computing machines. J. Chem. Phys., 21(6):1087-1092.
26. Osher, S. and Sethian, J. 1988. Fronts propagating with curvature dependent speed: Algorithms based on the hamilton-jacobi formulation. Journal of Computational Physics, 79:12-49.
27. Paragios, N. and Deriche, R. 2002. Geodesic active regions and level set methods for supervised texture segmentation. The International Journal of Computer Vision, 46(3):223.
28. Rissanen, J. 1989. Stochastic Complexity in Statistical Inquiry, World Scientific Publishing Company.
29. Rousson, M. and Deriche, R. 2002. A variational framework for active and adaptative segmentation of vector valued images. In Proc. IEEE Workshop on Motion and Video Computing, Orlando, Florida, pp. 56-62.
30. Storvik, G. 1994. A bayesian approach to dynamic contours through stochastic sampling and simulated annealing. IEEE Trans. Pattern Analysis and Machine Intelligence, 16(10):976-986.
31. Ueda, N., Nakano, R., Ghahramani, Z., and Hinton, G.E. 2000. SMEM algorithm for mixture models. Neural Computation, 12(9):2109-2128.
32. Unal, G., Krim, H., and Yezzi, A. 2002. Stochastic differential equations and geometric flows. IEEE Transactions in Image Processing, 11(12):1405-1416.
33. Unal, G., Nain, D., Ben-Arous, G., Shimkin, N., Tannenbaum, A., and Zeitouni, O. 2003. Algorithms for stochastic approximations of curvature flows. In IEEE International Conference on Image Processing.
34. Vese, L. and Chan, T. 2002. A multiphase level set framework for image segmentation using the mumford and shah model. International Journal of Computer Vision, 50(3):271-293.
35. Wallace, C. and Boulton, D. 1968. An information measure for classification. Computer Journal, 11(2):185-194.
36. Walsh, J. 1994. An introduction to stochastic partial differential equations. In Ecole d'Été de Probabilités de Saint-Flour, vol. XIV-1180 of Lecture Notes in Math. Springer.
37. Yip, N. 1998. Stochastic motion by mean curvature. Arch. Rational Mech. Anal., 144:331-355.
38. Yip, N. 2002. Stochastic curvature driven flows. In G. Da Prato and L. Tubaro (eds.), Stochastic Partial Differential Equations and Applications, vol. 227 of Lecture Notes in Pure and Applied. Mathematics. Springer, pp. 443-460.
39. Yip, N. and Souganidis, P. 2004. Uniqueness of motion by mean curvature perturbed by stochastic noise. Annales de l'Institut Henri Poincare - analyse non lineaire, (21):1-23.
40. Zhang, B. and Hsu, M. 1999. K-Harmonic Means - A Data Clustering Algorithm.