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. Google Scholar

[2]

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

[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. Google Scholar

[4]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[9]

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

[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. Google Scholar

[11]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[15]

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

[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. Google Scholar

[17]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

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. Google Scholar

[2]

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

[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. Google Scholar

[4]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[9]

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

[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. Google Scholar

[11]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[15]

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

[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. Google Scholar

[17]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

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