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 and 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), 304-309. doi: 10.1109/83.661180.

[2]

V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours, Int. J. Comput. Vis., 22 (1997), 61-79. 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), 130-141. doi: 10.1006/jvci.1999.0442.

[4]

T. F. Chan and L. A. Vese, Active contours without edges, IEEE Trans. Image Process., 10 (2001), 266-277. 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), 267-285. 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, 08-75, 2008.

[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), 1155-1174. 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), 158-175. doi: 10.1109/34.368173.

[9]

M. Moelich, "Logic Models for Segmentation and Tracking,'' Ph.D thesis, University of California, Los Angeles, 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), 12-49. 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, New York, 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), 187-197. 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, 02-39, 2002.

[14]

B. Sandberg and T. F. Chan, A logic framework for active contours on multi-channel images, J. Visual Comm. Image Rep., 16 (2005), 333-258. doi: 10.1016/j.jvcir.2004.08.005.

[15]

G. Sapiro, Color snakes, Comput. Vis. Image Und., 68 (1997), 247-253. 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), 1582-1586. doi: 10.1109/83.541429.

[17]

J. Shah, Curve evolution and segmentation functionals: Applications to color images, in "Proceedings of the International Conference on Image Processing,'' (1996), 461-464.

[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), 1169-1186. 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), 271-293. 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), 179-195. 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), 884-900. 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), 304-309. doi: 10.1109/83.661180.

[2]

V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours, Int. J. Comput. Vis., 22 (1997), 61-79. 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), 130-141. doi: 10.1006/jvci.1999.0442.

[4]

T. F. Chan and L. A. Vese, Active contours without edges, IEEE Trans. Image Process., 10 (2001), 266-277. 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), 267-285. 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, 08-75, 2008.

[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), 1155-1174. 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), 158-175. doi: 10.1109/34.368173.

[9]

M. Moelich, "Logic Models for Segmentation and Tracking,'' Ph.D thesis, University of California, Los Angeles, 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), 12-49. 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, New York, 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), 187-197. 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, 02-39, 2002.

[14]

B. Sandberg and T. F. Chan, A logic framework for active contours on multi-channel images, J. Visual Comm. Image Rep., 16 (2005), 333-258. doi: 10.1016/j.jvcir.2004.08.005.

[15]

G. Sapiro, Color snakes, Comput. Vis. Image Und., 68 (1997), 247-253. 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), 1582-1586. doi: 10.1109/83.541429.

[17]

J. Shah, Curve evolution and segmentation functionals: Applications to color images, in "Proceedings of the International Conference on Image Processing,'' (1996), 461-464.

[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), 1169-1186. 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), 271-293. 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), 179-195. 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), 884-900. doi: 10.1109/34.537343.

[1]

Fan Jia, Xue-Cheng Tai, Jun Liu. Nonlocal regularized CNN for image segmentation. Inverse Problems and Imaging, 2020, 14 (5) : 891-911. doi: 10.3934/ipi.2020041

[2]

Ye Yuan, Yan Ren, Xiaodong Liu, Jing Wang. Approach to image segmentation based on interval neutrosophic set. Numerical Algebra, Control and Optimization, 2020, 10 (1) : 1-11. doi: 10.3934/naco.2019028

[3]

Dominique Zosso, Jing An, James Stevick, Nicholas Takaki, Morgan Weiss, Liane S. Slaughter, Huan H. Cao, Paul S. Weiss, Andrea L. Bertozzi. Image segmentation with dynamic artifacts detection and bias correction. Inverse Problems and Imaging, 2017, 11 (3) : 577-600. doi: 10.3934/ipi.2017027

[4]

Shi Yan, Jun Liu, Haiyang Huang, Xue-Cheng Tai. A dual EM algorithm for TV regularized Gaussian mixture model in image segmentation. Inverse Problems and Imaging, 2019, 13 (3) : 653-677. doi: 10.3934/ipi.2019030

[5]

Jianping Zhang, Ke Chen, Bo Yu, Derek A. Gould. A local information based variational model for selective image segmentation. Inverse Problems and Imaging, 2014, 8 (1) : 293-320. doi: 10.3934/ipi.2014.8.293

[6]

Lu Tan, Ling Li, Senjian An, Zhenkuan Pan. Nonlinear diffusion based image segmentation using two fast algorithms. Mathematical Foundations of Computing, 2019, 2 (2) : 149-168. doi: 10.3934/mfc.2019011

[7]

Ruiliang Zhang, Xavier Bresson, Tony F. Chan, Xue-Cheng Tai. Four color theorem and convex relaxation for image segmentation with any number of regions. Inverse Problems and Imaging, 2013, 7 (3) : 1099-1113. doi: 10.3934/ipi.2013.7.1099

[8]

Balázs Kósa, Karol Mikula, Markjoe Olunna Uba, Antonia Weberling, Neophytos Christodoulou, Magdalena Zernicka-Goetz. 3D image segmentation supported by a point cloud. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 971-985. doi: 10.3934/dcdss.2020351

[9]

Jie Huang, Xiaoping Yang, Yunmei Chen. A fast algorithm for global minimization of maximum likelihood based on ultrasound image segmentation. Inverse Problems and Imaging, 2011, 5 (3) : 645-657. doi: 10.3934/ipi.2011.5.645

[10]

Liam Burrows, Weihong Guo, Ke Chen, Francesco Torella. Reproducible kernel Hilbert space based global and local image segmentation. Inverse Problems and Imaging, 2021, 15 (1) : 1-25. doi: 10.3934/ipi.2020048

[11]

Maika Goto, Kazunori Kuwana, Yasuhide Uegata, Shigetoshi Yazaki. A method how to determine parameters arising in a smoldering evolution equation by image segmentation for experiment's movies. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 881-891. doi: 10.3934/dcdss.2020233

[12]

Baoli Shi, Zhi-Feng Pang, Jing Xu. Image segmentation based on the hybrid total variation model and the K-means clustering strategy. Inverse Problems and Imaging, 2016, 10 (3) : 807-828. doi: 10.3934/ipi.2016022

[13]

Yupeng Li, Wuchen Li, Guo Cao. Image segmentation via $ L_1 $ Monge-Kantorovich problem. Inverse Problems and Imaging, 2019, 13 (4) : 805-826. doi: 10.3934/ipi.2019037

[14]

Qianting Ma, Tieyong Zeng, Dexing Kong, Jianwei Zhang. Weighted area constraints-based breast lesion segmentation in ultrasound image analysis. Inverse Problems and Imaging, 2022, 16 (2) : 451-466. doi: 10.3934/ipi.2021057

[15]

Ibrar Hussain, Haider Ali, Muhammad Shahkar Khan, Sijie Niu, Lavdie Rada. Robust region-based active contour models via local statistical similarity and local similarity factor for intensity inhomogeneity and high noise image segmentation. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022014

[16]

Micol Amar, Andrea Braides. A characterization of variational convergence for segmentation problems. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 347-369. doi: 10.3934/dcds.1995.1.347

[17]

Sung Ha Kang, Berta Sandberg, Andy M. Yip. A regularized k-means and multiphase scale segmentation. Inverse Problems and Imaging, 2011, 5 (2) : 407-429. doi: 10.3934/ipi.2011.5.407

[18]

Dana Paquin, Doron Levy, Eduard Schreibmann, Lei Xing. Multiscale Image Registration. Mathematical Biosciences & Engineering, 2006, 3 (2) : 389-418. doi: 10.3934/mbe.2006.3.389

[19]

Antoni Buades, Bartomeu Coll, Jose-Luis Lisani, Catalina Sbert. Conditional image diffusion. Inverse Problems and Imaging, 2007, 1 (4) : 593-608. doi: 10.3934/ipi.2007.1.593

[20]

Michael K. Ng, Chi-Pan Tam, Fan Wang. Multi-view foreground segmentation via fourth order tensor learning. Inverse Problems and Imaging, 2013, 7 (3) : 885-906. doi: 10.3934/ipi.2013.7.885

2020 Impact Factor: 1.639

Metrics

  • PDF downloads (87)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]