A variational model for segmentation of overlapping objects with additive intensity value

IEEE Transactions on Image Processing

Volumn 20, Issue 6, 2011, Pages 1495-1503

  Law, Yan Nei ^a   Lee, Hwee Kuan ^a   Liu, Chaoqiang ^b   Yip, Andy M ^b  

^a BIOINFORMATICS INSTITUTE   (Singapore)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Additive intensity; Euler's elastica; image segmentation; level set methods; MumfordShah model; overlapping objects

Indexed keywords

ADDITIVITY; EULER'S ELASTICA; GEOMETRIC QUANTITIES; HARD CONSTRAINTS; INTENSITY VALUES; LEVEL SET METHOD; LEVEL SET METHODS; MULTIPLE CHANNELS; MULTIPLE OBJECTS; MUMFORD SHAH MODEL; OBJECT BOUNDARIES; OPTIMIZATION PROBLEMS; OVERLAPPING OBJECTS; PRIORI KNOWLEDGE; REAL IMAGES; SEGMENTATION RESULTS; SOFT CONSTRAINT; STABILITY CONDITION; VARIATIONAL MODELS;

CONSTRAINT THEORY; DROP BREAKUP; EVOLUTIONARY ALGORITHMS; LEVEL MEASUREMENT; NUMERICAL METHODS;

IMAGE SEGMENTATION;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; THEORETICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, THEORETICAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SUBTRACTION TECHNIQUE;

EID: 79957500803     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2010.2095868     Document Type: Article

References (20)

1. N. Geva-Zatorsky, N. Rosenfeld, S. Itzkovitz, R. Milo, E. Sigal, A. Dekel, T. Yarnitzky, P. Liron, Y. Polak, G. Lahav, and U. Alon, "Oscillations and variability in the system p53 system," Mol. Syst. Biol., vol. 2, no. 0033, 2006.
2. D. Mumford and J. Shah, "Optimal approximation by piecewise smooth functions and associated variational problems," Commun. Pure Appl. Math., vol. 42, pp. 577-685, 1989.
3. D. Cremers, M. Rousson, and R. Deriche, "A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape," Int. J. Comput. Vis., vol. 72, no. 2, pp. 195-215, 2007. (Pubitemid 46094760)
4. J. Shen, "A stochastic-variational model for soft Mumford-Shah segmentation," Int. J. Biomed. Imag., vol. 2006, no. Article ID 92329, 2006.
5. M. Nitzberg and D. Mumford, "The 2.1D sketch," in Proc. 3rd Intl. Conf. Computer Vision, 1990, pp. 138-144.
6. M. Nitzberg, D. Mumford, and T. Shiota, Filtering, Segmentation, and Depth. New York: Springer-Verlag, 1993.
7. W.Zhu, T. Chan, and S. Esedoglu, "Segmentation with depth:Alevel set approach," SIAM J. Sci. Comput., vol. 28, no. 5, pp. 1957-1973, 2006.
8. S. Esedoglu and R. March, "Segmentation with depth but without detecting junctions," J. Math. Imag. Vis., vol. 18, pp. 7-15, 2003.
9. W. Zhu and T. Chan, "A variational model for capturing illusory contours using curvature," J. Math. Imag. Vis., vol. 27, pp. 29-40, 2007. (Pubitemid 46122366)
10. D. Mumford, "Elastica and computer vision," Alg. Geom. Appl., pp. 491-506, 1994.
11. A. Masnou and J.-M.Morel, "Level-lines based disocclusion," in Proc. 5th IEEE Int. Conf. Image Process, 1998, vol. 3, pp. 259-263.
12. T. Chan, S. Kang, and J. Shen, "Euler's elastica and curvature based inpaintings," SIAM J. Appl. Math., vol. 63, no. 2, pp. 564-592, 2002.
13. L. A.Vese and T. F. Chan, "A multiphase level set framework for image segmentation using the Mumford and Shah model," Int. J. Comput. Vis., vol. 50, no. 3, pp. 271-293, 2002. (Pubitemid 35377416)
14. S. Osher and J. A. Sethian, "Fronts propogating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation," J. Comput. Phys., vol. 79, pp. 12-49, 1988.
15. T. F. Chan and L. A. Vese, "Active contours without edges," IEEE Trans. Image Process, vol. 10, no. 2, pp. 266-277, Feb. 2001. (Pubitemid 32254596)
16. J. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd ed. Philadelphia, PA: SIAM, 2007.
17. P. Smereka, "Semi-implicit level set methods for curvature and surface diffusion motion," J. Sci. Comput., vol. 19, pp. 439-456, 2003.
18. D. Chopp and J. Sethian, "Motion by intrinsic Laplacian of curvature," Interfaces Free Bound., vol. 1, pp. 1-18, 1999.
19. C. Schönlieb, A. Bertozzi, M. Burger, and L. He, "Image inpainting using a fourth-order total variation flow," UCLA CAM Rep., vol. 09-34, 2009.
20. Y. Law, H. Lee, and A. Yip, "A multi-resolution stochastic level set method for Mumford-Shah image segmentation," IEEE Trans. Image Process., vol. 17, no. 12, pp. 2289-2300, Dec. 2008.