February  2012, 6(1): 95-110. doi: 10.3934/ipi.2012.6.95

A multiphase logic framework for multichannel image segmentation

1. 

Department of Mathematics, UCLA, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, United States, United States

2. 

The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

Received  November 2010 Revised  August 2011 Published  February 2012

We propose a novel framework for energy-based multiphase segmentation over multiple channels. The framework allows the user to combine the information from each channel as the user sees fit, and thus allows the user to define how the information from each channel should influence the result. The framework extends the two-phase Logic Framework [J. Vis. Commun. Image R. 16 (2005) 333-358] model. The logic operators of the Logic Framework are used to define objective functions for multiple phases and a condition is defined that prevents conflict between energy terms. This condition prevents local minima that may occur using ad hoc methods, such as summing the objective functions of each region.
Citation: Matthew S. Keegan, Berta Sandberg, Tony F. Chan. A multiphase logic framework for multichannel image segmentation. Inverse Problems & Imaging, 2012, 6 (1) : 95-110. doi: 10.3934/ipi.2012.6.95
References:
[1]

P. Blomgren and T. F. Chan, Color TV: Total variation methods for restoration for vector-valued images,, IEEE Trans. Image Process., 7 (1998), 304. doi: 10.1109/83.661180.

[2]

V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours,, Int. J. Comput. Vis., 22 (1997), 61. doi: 10.1023/A:1007979827043.

[3]

T. F. Chan, B. Y. Sandberg and L. A. Vese, Active contours without edges for vector-valued images,, J. Visual Comm. Image Rep., 11 (2000), 130. doi: 10.1006/jvci.1999.0442.

[4]

T. F. Chan and L. A. Vese, Active contours without edges,, IEEE Trans. Image Process., 10 (2001), 266. doi: 10.1109/83.902291.

[5]

G. Chung and L. A. Vese, Image segmentation using a multilayer level-set approach,, Comput. Vis. Sci., 12 (2009), 267. doi: 10.1007/s00791-008-0113-1.

[6]

V. Israel-Jost, J. Darbon, E. D. Angelini and I. Bloch, Multi-phase and multi-channel region segmentation and application in brain mri,, UCLA Department of Mathematics CAM Report, (2008), 08.

[7]

J. Lie, M. Lysaker and X.-C. Tai, A variant of the level set method and applications to image segmentation,, Math. Comp., 75 (2006), 1155. doi: 10.1090/S0025-5718-06-01835-7.

[8]

R. Malladi, J. A. Sethian and B. C. Vemuri, Shape modelling with front propagation,, IEEE Trans Pat. Anal. Mach. Intell., 17 (1995), 158. doi: 10.1109/34.368173.

[9]

M. Moelich, "Logic Models for Segmentation and Tracking,'', Ph.D thesis, (2004).

[10]

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations,, J. Comput. Phys., 79 (1988), 12. doi: 10.1016/0021-9991(88)90002-2.

[11]

S. J. Osher and R. P. Fedkiw, "Level Set Methods and Dynamic Implicit Surfaces,'', Springer-Verlag, (2002).

[12]

C. Samson, L. Blanc-Féraud, G. Aubert and J. Zerubia, A level set model for image classification,, Int. J. Comput. Vis., 40 (2000), 187. doi: 10.1023/A:1008183109594.

[13]

B. Sandberg, T. Chan and L. Vese, A level-set and gabor-based active contour algorithm for segmenting textured images,, UCLA Department of Mathematics CAM report, (2002), 02.

[14]

B. Sandberg and T. F. Chan, A logic framework for active contours on multi-channel images,, J. Visual Comm. Image Rep., 16 (2005), 333. doi: 10.1016/j.jvcir.2004.08.005.

[15]

G. Sapiro, Color snakes,, Comput. Vis. Image Und., 68 (1997), 247. doi: 10.1006/cviu.1997.0562.

[16]

G. Sapiro and D. L. Ringach, Anisotropic diffusion of multivalued images with applications to color filtering,, IEEE Trans. Image Process., 5 (1996), 1582. doi: 10.1109/83.541429.

[17]

J. Shah, Curve evolution and segmentation functionals: Applications to color images,, in, (1996), 461.

[18]

A. Tsai, A. Yezzi and A. S. Willsky, Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation and magnification,, IEEE Trans. Image Process., 10 (2001), 1169. doi: 10.1109/83.935033.

[19]

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., 50 (2002), 271. doi: 10.1023/A:1020874308076.

[20]

H.-K. Zhao, T. Chan, B. Merriman and S. Osher, A variational level set approach to multiphase motion,, J. Comput. Phys., 127 (1996), 179. doi: 10.1006/jcph.1996.0167.

[21]

S. C. Zhu and A. Yuille, Region competition: Unifying snakes, region growing, and bayesian/mdl for multiband image segmentation,, IEEE Trans Pat. Anal. Mach. Intell., 18 (1996), 884. doi: 10.1109/34.537343.

show all references

References:
[1]

P. Blomgren and T. F. Chan, Color TV: Total variation methods for restoration for vector-valued images,, IEEE Trans. Image Process., 7 (1998), 304. doi: 10.1109/83.661180.

[2]

V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours,, Int. J. Comput. Vis., 22 (1997), 61. doi: 10.1023/A:1007979827043.

[3]

T. F. Chan, B. Y. Sandberg and L. A. Vese, Active contours without edges for vector-valued images,, J. Visual Comm. Image Rep., 11 (2000), 130. doi: 10.1006/jvci.1999.0442.

[4]

T. F. Chan and L. A. Vese, Active contours without edges,, IEEE Trans. Image Process., 10 (2001), 266. doi: 10.1109/83.902291.

[5]

G. Chung and L. A. Vese, Image segmentation using a multilayer level-set approach,, Comput. Vis. Sci., 12 (2009), 267. doi: 10.1007/s00791-008-0113-1.

[6]

V. Israel-Jost, J. Darbon, E. D. Angelini and I. Bloch, Multi-phase and multi-channel region segmentation and application in brain mri,, UCLA Department of Mathematics CAM Report, (2008), 08.

[7]

J. Lie, M. Lysaker and X.-C. Tai, A variant of the level set method and applications to image segmentation,, Math. Comp., 75 (2006), 1155. doi: 10.1090/S0025-5718-06-01835-7.

[8]

R. Malladi, J. A. Sethian and B. C. Vemuri, Shape modelling with front propagation,, IEEE Trans Pat. Anal. Mach. Intell., 17 (1995), 158. doi: 10.1109/34.368173.

[9]

M. Moelich, "Logic Models for Segmentation and Tracking,'', Ph.D thesis, (2004).

[10]

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations,, J. Comput. Phys., 79 (1988), 12. doi: 10.1016/0021-9991(88)90002-2.

[11]

S. J. Osher and R. P. Fedkiw, "Level Set Methods and Dynamic Implicit Surfaces,'', Springer-Verlag, (2002).

[12]

C. Samson, L. Blanc-Féraud, G. Aubert and J. Zerubia, A level set model for image classification,, Int. J. Comput. Vis., 40 (2000), 187. doi: 10.1023/A:1008183109594.

[13]

B. Sandberg, T. Chan and L. Vese, A level-set and gabor-based active contour algorithm for segmenting textured images,, UCLA Department of Mathematics CAM report, (2002), 02.

[14]

B. Sandberg and T. F. Chan, A logic framework for active contours on multi-channel images,, J. Visual Comm. Image Rep., 16 (2005), 333. doi: 10.1016/j.jvcir.2004.08.005.

[15]

G. Sapiro, Color snakes,, Comput. Vis. Image Und., 68 (1997), 247. doi: 10.1006/cviu.1997.0562.

[16]

G. Sapiro and D. L. Ringach, Anisotropic diffusion of multivalued images with applications to color filtering,, IEEE Trans. Image Process., 5 (1996), 1582. doi: 10.1109/83.541429.

[17]

J. Shah, Curve evolution and segmentation functionals: Applications to color images,, in, (1996), 461.

[18]

A. Tsai, A. Yezzi and A. S. Willsky, Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation and magnification,, IEEE Trans. Image Process., 10 (2001), 1169. doi: 10.1109/83.935033.

[19]

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., 50 (2002), 271. doi: 10.1023/A:1020874308076.

[20]

H.-K. Zhao, T. Chan, B. Merriman and S. Osher, A variational level set approach to multiphase motion,, J. Comput. Phys., 127 (1996), 179. doi: 10.1006/jcph.1996.0167.

[21]

S. C. Zhu and A. Yuille, Region competition: Unifying snakes, region growing, and bayesian/mdl for multiband image segmentation,, IEEE Trans Pat. Anal. Mach. Intell., 18 (1996), 884. doi: 10.1109/34.537343.

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