Discrete optimization of the multiphase piecewise constant Mumford-Shah functional

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

Volumn 6819 LNCS, Issue , 2011, Pages 233-246

  El Zehiry, Noha ^a   Grady, Leo ^a  

^a SIEMENS CORPORATE RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE SOLUTION; DE-NOISING; DISCRETE OPTIMIZATION; ENERGY FUNCTIONALS; ENERGY FUNCTIONS; GLOBAL OPTIMUM; GRADIENT DESCENT; GRAPH REPRESENTATION; LEVEL SET; LEVEL SETS METHODS; LOCAL OPTIMA; MULTI-CLASS; MUMFORD SHAH MODEL; MUMFORD-SHAH; MUMFORD-SHAH FUNCTIONALS; OPTIMAL SOLUTIONS; PIECEWISE CONSTANT; PRIOR INFORMATION; RECURSIVE BISECTION;

COMPUTER VISION; NUMERICAL METHODS; OPTIMIZATION;

IMAGE SEGMENTATION;

EID: 80051777769     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-23094-3_17     Document Type: Conference Paper

References (27)

1. Bruckstein, A.M., Netravali, A.N., Richardson: Epi-convergence of discrete elastica. Applicable Analysis 79, 137-171 (1997)
2. El-Zehiry, N.Y., Sahoo, P., Xu, S., Elmaghraby, A.: Graph cut optimization for the Mumford Shah model. In: Proccedings of VIIP (August 2007)
3. Grady, L., Alvino, C.: The piecewise smooth Mumford-Shah functional on an arbitrary graph. IEEE Trans. on Image Proc. 18, 2547-2561 (2009)
4. Darbon, J., Sigelle, M.: A Fast and Exact Algorithm for Total Variation Minimization. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3522, pp. 351-359. Springer, Heidelberg (2005) (Pubitemid 41351469)
5. Hammer, P.L., Hansen, P., Simeone, B.: Roof duality, complementation and persistency in quadratic 01 optimization. Mathematical Programming 28, 121-155 (1984) (Pubitemid 14569633)
6. Kolmogorov, V., Rother, C.: Minimizing nonsubmodular functions with graph cutsa review. IEEE Trans. Pattern Anal. Mach. Intell. 29, 1274-1279 (2007) (Pubitemid 46838518)
7. Rother, C., Kolmogorov, V., Lempitsky, V., Szummer, M.: Optimizing binary MRFs via extended roof duality. In: Computer Vision and Pattern Recognition - CVPR, vol. 5302, pp. 248-261 (2007)
8. Vese, L.A., Chan, T.F.: A multiphase level set framework for image segmentation using the mumford and shah model. International Journal of Computer Vision 50, 271-293 (2002) (Pubitemid 35377416)
9. Ni, K., Hong, B.-W., Soatto, S., Chan, T.: Unsupervised multiphase segmentation: A recursive approach. Computer Vision and Image Understanding 113, 502-510 (2009)
10. Jeon, M., Alexander, M., Pedrycz, W., Pizzi, N.: Unsupervised hierarchical image segmentation with level set and additive operator splitting. Pattern Recognition Letters 26
11. El-Zehiry, N.Y., Elmaghraby, A.: Brain MRI tissue classification using graph cut optimization of the mumford-shah functional. In: IVCNZ, New Zealand, pp. 321-326 (2007)
12. Bae, E., Tai, X.-C.: Graph cut optimization for the piecewise constant level set method applied to multiphase image segmentation. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 1-13. Springer, Heidelberg (2009)
13. Bae, E., Tai, X.-C.: Efficient Global Minimization for the Multiphase Chan-Vese Model of Image Segmentation. In: Cremers, D., Boykov, Y., Blake, A., Schmidt, F.R. (eds.) EMMCVPR 2009. LNCS, vol. 5681, pp. 28-41. Springer, Heidelberg (2009)
14. Bresson, X., Esedognlu, S., Vandergheynst, P., Thiran, J.P., Osher, S.: Fast global minimization of the active contour/snake model. Journal of Math. Imag. and Vis. 2, 151-167 (2007) (Pubitemid 47312505)
15. Badshah, N., Chen, K.: On two multigrid algorithms for modeling variational multiphase image segmentation. Trans. Img. Proc. 18, 1097-1106 (2009)
16. Vazquez-Reina, A., Miller, E., Pfister, H.: Multiphase geometric couplings for the segmentation of neural processes. In: CVPR, pp. 2020-2027 (2009)
17. Simon, H., Teng, S.-H.: How good is recursive bisection? SIAM Journal on Scientific Computing 18, 1436-1445 (2001) (Pubitemid 127642160)
18. Delong, A., Boykov, Y.: Global optimal segmentation of multi-region objects. In: ICCV, vol. 1, pp. 26-33 (2009)
19. Ramalingam, S., Kohli, P., Alahari, K., Torr, P.H.S.: Exact inference in multi-label crfs with higher order cliques. In: CVPR (2008)
20. Ishikawa, H.: Exact optimization for Markov random fields with convex priors. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 1333-1336 (2003)
21. Rother, C., Kolmogorov, V., Lempitsky, V.S., Szummer, M.: Optimizing binary MRFs via extended roof duality. In: CVPR (2007)
22. Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Transactions on Image Processing 10, 266-277 (2001) (Pubitemid 32254596)
23. Kolmogorov, V., Boykov, Y.: What metrics can be approximated by geo-cuts, or global optimization of length/area and flux. In: International Conference on Computer Vision, ICCV 2005, vol. 1, pp. 564-571 (2005) (Pubitemid 44055006)
24. Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? IEEE Trans. on Patt. Anal. and Mach. Int. 26, 147-159 (2004)
25. Boros, E., Hammer, P.L., Tavares, G.: Preprocessing of unconstrained quadratic binary optimization. Technical Report RRR 10-2006, RUTCOR (2006)
26. Kolmogorov, V.: Graph based algorithms for scene reconstruction from two or more views, PhD thesis, Cornell University (2003)
27. Collins, D.L., Zijdenbos, A.P., Kollokian, V., Sled, J.G., Kabani, N.J., Holmes, C.J., Evans, A.C.: Design and construction of a realistic digital brain phantom. IEEE Trans. Med. Imaging 17, 463-468 (1998) (Pubitemid 128747700)