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Multi-Phase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance

  • Motong Qiao (a1), Wei Wang (a2) and Michael Ng (a3)

Abstract

We present a multi-phase image segmentation method based on the histogram of the Gabor feature space, which consists of a set of Gabor-filter responses with various orientations, scales and frequencies. Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function, which is a metric to measure the distance of two histograms. The energy functional is minimized by alternative minimization method and the existence of closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2. We test our model on both simple synthetic texture images and complex natural images with two or more phases. Experimental results are shown and compared to other recent results.

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Corresponding author

*Corresponding author.Email:qiao.motong@gmail.com

References

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[1]The Berkeley Segmentation Dataset and Benchmark, http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/.
[2]Braides, A. and Maso, G. D., Non-local approximation of the Mumford-Shah functional, Calculus of Variations and Partial Differential Equations, 5(4) (1997), 293322.
[3]Bresson, X., Vandergheynst, P. and Thiran, J. P., A variational model for object segmetation using boundary information and shape prior driven by the Mumford-Shah functional, Int. J. Comput. Vision, 68(2) (2006), 145162.
[4]Bresson, X., Esedoglu, S., Vandergheynst, P., Tharan, J. P. and Osher, S., Fast global minimization of the active contour/snake model, J. Math. Imaging Vision, 28 (2007), 151167.
[5]Bae, E., Yuan, J. and Tai, X-C., Global minimization for continuous multiphase partitioning problems using a dual approach, Int. J. Comput. Vision, 92(1) (2011), 112129.
[6]Caselles, V., Geometric models for active contours, International Conference on Image Processing, 3 (1995), 912.
[7]Caselles, V., Kimmel, R. and Sapiro, G., Geodesic active contours, Int. J. Cumput. Vision, 22(1) (1997), 6179.
[8]Chan, T. and Vese, L., Active contours without edges, IEEE Tran. Image Process., 10(2) (2001).
[9]Chan, T., Esedoglu, S. and Nikolova, M., Algorithms for finding global minimizers of image segmentation and denoising models, SIAM J. Appl. Math., 66(5) (2006), 16321648.
[10]Chan, T., Sandberg, B. and Vese, L., Active contours without edges for vector-valued images, J. Visual Commun. Image Representation, 11(2) (2000), 130141.
[11]Chan, T., Esedoglu, S. and Ni, K., Histogram based segmentation using wasserstein distances, scale space and variational methods in computer vision, Lecture Notes in Computer Science, 4485 (2007), 697708.
[12]Chambolle, A., Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations, SIAM J. Appl. Math., 55(3) (1995), 827863.
[13]Chambolle, A., An algorithm for total variation minimization and application, J. Math. Image Vision, 20 (2004), 8997.
[14]Chung, G. and Vese, L., Image segmentation using a multilayer level-set approach, Comput. Visual. Science, 12(6) (2009), 267285.
[15]Cohen, L. D., On active contour models and balloons, CVGIP: Image Understanding, 53(2) (1991), 211218.
[16]Georgiou, T., Michailovich, O., Rathi, Y., Malcolm, J. and Tannenbaum, A., Distribution metrics and image segmentation, Linear Algebra and Its Applications, 405 (2007), 663672.
[17]Gobbino, M., Finite difference approximation of the Mumford-Shah functional, Commun. Pure Appl. Math., 51(2) (1998), 197228.
[18]Goldenberg, R., Kimmel, R., Rivlin, E. and Rudzsky, M., Fast geodesic active contours, IEEE Tran. Image Process., 10(10) (2001), 14671475.
[19]Houhou, N. and Thiran, J. P., Fast texture segmentation model based on the shape operator and active contour, IEEE Conference on Computer Vision and Pattern Recognition, 1-8, 2008.
[20]Houhou, N., Thiran, J. P. and Bresson, X., Fast texture segmentation based on semi-local region descriptor and active contour, Numer. Math. Theory Meth. Appl., 2(4) (2009), 445468.
[21]Huang, Y., Ng, M. K. and Wen, Y. W., A fast total variation minimization method for image restoration, Multiscale Model. Simul., 7 (2008), 774795.
[22]Jain, A. K. and Farrokhnia, F., Unsupervised texture segmentation using gabor filters, Pattern Recognition, 24(12) (1991), 11671186.
[23]Kass, M., Witkin, A. and Terzopoulos, D., Snakes: active contour models, Int. J. Comput. Vision, 1 (1988), 321331.
[24]Kantorovich, L., On the translocation of masses, C. R. (Doklady) Acad. Sci. URSS (N.S.), (37) (1942), 199201.
[25]Kichenassamy, S., Gradient flows and geometric active contour models, 5th International Conference on Computer Vision, 810815, 1995.
[26]Klir, G. J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, ISBN 978-0-13-101171-7, 1995.
[27]Lie, J., Lysaker, M. and Tai, X. C., A binary level set model and some applications to Mumford-Shah image segmentation, IEEE Trans. Image Processing, 15(5) (2006), 11711181.
[28]Lie, J., Lysaker, M. and Tai, X. C., Piecewise constant level set methods and image segmentation, Scale Space and PDE Methods in Computer Vision, 3459 (2005), 573584.
[29]Li, F., Ng, M. K., Zeng, T. Y. and Shen, C., A multiphase image segmentation method based on fuzzy region competition, SIAM J. Image. Sciences, 3(3) (2010), 277299.
[30]Li, F. and Ng, M. K., Kernel density estimation based multiphase fuzzy region competition method for texture image segmentation, Commun. Comput. Phys., 8 (2010), 623641.
[31]Li, W., Mao, K., Zhang, H. and Chai, T., Selection of gabor filters for improved texture feature extraction, Proceedingsof IEEE 17th International Conferenceon Image Processing, 361364, 2010.
[32]Ma, L. Y. and Yu, J., Texture segmentation based on local feature histograms, 18th IEEE International Conference on Image Processing, ICIP 2011, 33493352, 2011.
[33]Michailovich, O., Rathi, Y. and Tannenbaum, A., Image segmentation using active contours driven by the Bhattacharyya gradient flow, IEEE Tran. Image Process., 16(11) (2007).
[34]Mory, B. and Ardon, R., Variation segmentation using fuzzy region competition and local non-parametric probability density funtions, 11th IEEE International Conference on Computer Vision, ICCV 2007, 18, 2007.
[35]Mory, B. and Ardon, R., Fuzzy region competition: a convex two-phase segmentation framework, scale space and variational methods in computer vision, Lecture Notes in Computer Science, 4485 (2007), 214226, 2007.
[36]Mumford, D. and Shah, J., Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., 42 (1989), 577685.
[37]Ni, K., Bresson, X., Chan, T. and Esedoglu, S., Local histogram based segmentation using the Wasserstein distance, Int. J. Comput. Vision, 84(1) (2009), 97111.
[38]Osher, S. and Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys., 79 (1998), 1249.
[39]Paragios, N. and Deriche, R., Geodesic active regions and level set methods for supervised texture segmentation, Int. J. Comput. Vision, 46(3) (2002), 223247.
[40]Rachev, S. and Ruschendorf, L., Mass Transportation Problems, Vol. I: Theory, Vol. II: Applications Probability and Its Applications, Springer-Verlag, New York, 1998.
[41]Sandberg, B., Chan, T. and Vese, L., A level-set and gabor based active contour algorithm for segmenting textured images, UCLA Comput. Appl. Math., Rep. 02-39, 2002.
[42]Sagiv, C., Sochen, N. A. and Zeevi, Y. Y., Integrated active contours for texture segmentation, IEEE Tran. Image Process., 15(6) (2006).
[43]Sagiv, C., Sochen, N. A. and Zeevi, Y. Y., Geodesic active contours applied to texture feature space, Proc. Scale-Space and Morphology in Computer Vision, Kerckhove, M., Ed. Berlin, Germany: Springer-Verlag, 2106 (2001), 344352.
[44]Thomas, B. and Daniel, C., On local region models and a statistical interpretation of the piece-wise smooth Mumford-Shah functional, Scale Space and Variational Methods in Computer Vision, 4485 (2007), 203213.
[45]Vese, L. and Chan, T., A multiphase level set framework for image segmentation using the Mumford and Shah Model, Int. J. Comput. Vision, 50(3) (2002), 271293.
[46]Wang, Y., Xiong, Y., Lv, L., Zhang, H., Cao, Z. and Zhang, D., Vector-valued Chan-Vese model driven by local histogram for texture segmentation, 17th IEEE International Conference on Image Processing, ICIP 2010, 645648, 2010.
[47]Xie, X., Level set based segmentation using local feature distribution, 2010 International Conference on Pattern Recognition, 2010.
[48]Yuan, H. and Zhang, X. P., Texture image retrieval based on a gaussian mixture model and similarity measure using a kullback divergence, IEEE International Conference on Multimedia and Expo, 2004.
[49]Yuan, J., Bae, E., Tai, XC. and Boykov, Y., A continuous max-flow approach to Potts model, Computer Vision–ECCV 2010, 379392, 2010.
[50]Zhu, S. C. and Yuille, A. L., A unified theory for image segmentation: region competition and its analysis, Harvard Robotics Laboratory Technical Report 95-7, 1995.
[51]Zhu, S. C. and Yuille, A. L., Region competition: unifying snakes, region growing and Bayes/MDL for multi-band image segmentation, IEEE Trnas. Pattern Anal. Machine Intell., 18 (1996), 884900.

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