Energy minimization based segmentation and denoising using a multilayer level set approach

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3757 LNCS, Issue , 2005, Pages 439-455

  Chung, Ginmo ^a   Vese, Luminita A ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; IMAGE ANALYSIS; PROBLEM SOLVING; SET THEORY;

CURVE EVOLUTION; LEVEL LINES; NESTED STRUCTURES; PIECEWISE-CONSTANT SEGMENTATION;

IMAGE SEGMENTATION;

EID: 33645682856     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11585978_29     Document Type: Conference Paper

References (30)

1. L. Ambrosio, V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence, Comm. Pure Appl. Math., 43, 999-1036, 1990.
2. L. Ambrosio, V.M. Tortorelli, On the Approximation of Free Discontinuity Problems, Bollettino U.M.I. (7) 6-B, 105-123, 1992.
3. x F(x,f(x), f′(x)), Arkiv for mathematik 6(1): 33-&, 1965.
4. R.E. Caflisch, M.F. Gyure, B. Merriman, S.J. Osher, G. Ratsch, D.D. Vvedensky, J.J. Zinck, Island dynamics and the level set method for epitaxial growth, Applied Mathematics Letters 12(4): 13-22, 1999.
5. V. Caselles, F. Catté, T. Coll, F. Dibos, A geometric model for active contours in image-processing, Numerische Mathematik, 66(1): 1-31, 1993.
6. V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, IJCV 22(1): 61-79, 1997.
7. V. Caselles, J.M. Morel, C. Sbert, An axiomatic approach to image interpolation, IEEE Transactions on IP 7(3): 376-386, 1998.
8. T.F. Chan, B.Y. Sandberg, L.A. Vese, Active contours without edges for vector-valued images, JVCIR, 11(2): 130-141, 2000.
9. T. F. Chan, L. Vese, An active contour model without edges, LNCS 1682, 141-151, 1999.
10. T.F. Chan, L.A. Vese, Active contours without edges, IEEE Transactions on IP 10(2): 266-277, 2001.
11. T.F. Chan, L. A. Vese, Level Set Algorithm for Minimizing the Mumford-Shah Functional in Image Processing, IEEE Workshop on VLSM, 161-168, 2001.
12. L.D. Cohen, Avoiding local minima for deformable curves in image analysis, in Curves and Surfaces with Applications in CAGD, A. Le Méhauté, C. Rabut, and L.L. Schumaker (eds.), 77-84, 1997.
13. L. Cohen, E. Bardinet, and N. Ayache, Surface reconstruction using active contour models, Proc. SPIE 93 Conference on Geometric Methods in Computer Vision, San Diego, CA, July 1993.
14. M.F. Gyure, C. Ratsch, B. Merriman, R.E. Caflisch, S. Osher, J.J. Zinck, D.D. Vvedensky, Level-set methods for the simulation of epitaxial phenomena, Physical Review E 58(6): R6927-R6930 Part A, 1998.
15. S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, A. Yezzi Jr., Conformal curvature flows: from phase transitions to active vision, Arch. Rational Mech. Anal. 134(3): 275-301, 1996.
16. G. Koepfler, C. Lopez, J.-M. Morel, A multiscale algorithm for image segmentation by variational method, SIAM J. Num. Analysis, 31(1): 282-299, 1994.
17. J. Lie, M. Lysaker, X.-C. Tai, Piecewise Constant Level Set Methods and Image Segmentation, LNCS 3459: 573-584, 2005.
18. R. Malladi, J.A. Sethian, B.C. Vemuri, Shape modeling with front propagation - a level set approach, IEEE Tr. PAMI, 17(2): 158-175, 1995.
19. J.M. Morel, S. Solimini, Density estimates for the boundaries of optimal segmentations, CRASS I-Mathematique 312(6): 429-432, 1991.
20. D. Mumford, J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 42:577-685, 1989.
21. N. Paragios, R. Deriche, Unifying boundary and region-based information for geodesic active tracking, Proc. CVPR 1999, Vol. 2: 23-25, 1999.
22. N. Paragios, R. Deriche, Geodesic active regions: A new framework to deal with frame partition problems in computer vision, JVCIR 13(1-2): 249-268, 2002.
23. N. Paragios, R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation, IJCV 46(3): 223-247, 2002.
24. C. Samson, L. Blanc-Féraud, G. Aubert, J. Zérubia, A level set model for image classification, LNCS 1682, 306-317, 1999.
25. C. Samson, L. Blanc-Féraud, G. Aubert, J. Zérubia, A level set model for image classification, IJCV 40(3): 187-197, 2000.
26. A. Tsai, A. Yezzi, A.S. Willsky, Curve evolution implementation of the MumfordShah functional for image segmentation, denoising, interpolation, and magnification, IEEE Transactions on IP, 10(8):1169-1186, 2001.
27. L.A. Vese and T.F. Chan, A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model, IJCV 50(3): 271-293, 2002.
28. L. Vese, Multiphase Object Detection and Image Segmentation in "Geometric Level Set Methods in Imaging, Vision and Graphics", S. Osher and N. Paragios (eds), Springer Verlag, 175-194, 2003.
29. H.-K. Zhao, T. Chan, B. Merriman, and S. Osher, Variational level set approach to multiphase motion, JCP 127(1): 179-195, 1996.
30. S.C. Zhu and A. Yuille, Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation, IEEE Transactions on PAMI, 18(9): 884-900, 1996.