Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-01T01:17:19.730Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  03 June 2015

Motong Qiao ,
Wei Wang  and
Michael Ng
Motong Qiao*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Wei Wang
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, China
Michael Ng
Affiliation:
Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
*
*Corresponding author.Email:qiao.motong@gmail.com
Get access

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.

Keywords

68U10Multi-phase texture segmentationWasserstein distanceGabor filterMumford-Shah model
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 5 , May 2014 , pp. 1480 - 1500
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]The Berkeley Segmentation Dataset and Benchmark, http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/.Google Scholar
[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), 293–322.Google Scholar
[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), 145–162.Google Scholar
[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), 151–167.CrossRefGoogle Scholar
[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), 112–129.Google Scholar
[6]Caselles, V., Geometric models for active contours, International Conference on Image Processing, 3 (1995), 9–12.Google Scholar
[7]Caselles, V., Kimmel, R. and Sapiro, G., Geodesic active contours, Int. J. Cumput. Vision, 22(1) (1997), 61–79.Google Scholar
[8]Chan, T. and Vese, L., Active contours without edges, IEEE Tran. Image Process., 10(2) (2001).Google ScholarPubMed
[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), 1632–1648.Google Scholar
[10]Chan, T., Sandberg, B. and Vese, L., Active contours without edges for vector-valued images, J. Visual Commun. Image Representation, 11(2) (2000), 130–141.Google Scholar
[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), 697–708.Google Scholar
[12]Chambolle, A., Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations, SIAM J. Appl. Math., 55(3) (1995), 827–863.Google Scholar
[13]Chambolle, A., An algorithm for total variation minimization and application, J. Math. Image Vision, 20 (2004), 89–97.Google Scholar
[14]Chung, G. and Vese, L., Image segmentation using a multilayer level-set approach, Comput. Visual. Science, 12(6) (2009), 267–285.Google Scholar
[15]Cohen, L. D., On active contour models and balloons, CVGIP: Image Understanding, 53(2) (1991), 211–218.Google Scholar
[16]Georgiou, T., Michailovich, O., Rathi, Y., Malcolm, J. and Tannenbaum, A., Distribution metrics and image segmentation, Linear Algebra and Its Applications, 405 (2007), 663–672.Google Scholar
[17]Gobbino, M., Finite difference approximation of the Mumford-Shah functional, Commun. Pure Appl. Math., 51(2) (1998), 197–228.3.0.CO;2-6>CrossRefGoogle Scholar
[18]Goldenberg, R., Kimmel, R., Rivlin, E. and Rudzsky, M., Fast geodesic active contours, IEEE Tran. Image Process., 10(10) (2001), 1467–1475.Google Scholar
[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.Google Scholar
[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), 445–468.Google Scholar
[21]Huang, Y., Ng, M. K. and Wen, Y. W., A fast total variation minimization method for image restoration, Multiscale Model. Simul., 7 (2008), 774–795.CrossRefGoogle Scholar
[22]Jain, A. K. and Farrokhnia, F., Unsupervised texture segmentation using gabor filters, Pattern Recognition, 24(12) (1991), 1167–1186.Google Scholar
[23]Kass, M., Witkin, A. and Terzopoulos, D., Snakes: active contour models, Int. J. Comput. Vision, 1 (1988), 321–331.Google Scholar
[24]Kantorovich, L., On the translocation of masses, C. R. (Doklady) Acad. Sci. URSS (N.S.), (37) (1942), 199–201.Google Scholar
[25]Kichenassamy, S., Gradient flows and geometric active contour models, 5th International Conference on Computer Vision, 810–815, 1995.Google Scholar
[26]Klir, G. J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, ISBN 978-0-13-101171-7, 1995.Google Scholar
[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), 1171–1181.Google Scholar
[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), 573–584.Google Scholar
[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), 277–299.CrossRefGoogle Scholar
[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), 623–641.Google Scholar
[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, 361–364, 2010.Google Scholar
[32]Ma, L. Y. and Yu, J., Texture segmentation based on local feature histograms, 18th IEEE International Conference on Image Processing, ICIP 2011, 3349–3352, 2011.Google Scholar
[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).Google Scholar
[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, 1–8, 2007.Google Scholar
[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), 214–226, 2007.Google Scholar
[36]Mumford, D. and Shah, J., Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., 42 (1989), 577–685.Google Scholar
[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), 97–111.Google Scholar
[38]Osher, S. and Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys., 79 (1998), 12–49.Google Scholar
[39]Paragios, N. and Deriche, R., Geodesic active regions and level set methods for supervised texture segmentation, Int. J. Comput. Vision, 46(3) (2002), 223–247.Google Scholar
[40]Rachev, S. and Ruschendorf, L., Mass Transportation Problems, Vol. I: Theory, Vol. II: Applications Probability and Its Applications, Springer-Verlag, New York, 1998.Google Scholar
[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.Google Scholar
[42]Sagiv, C., Sochen, N. A. and Zeevi, Y. Y., Integrated active contours for texture segmentation, IEEE Tran. Image Process., 15(6) (2006).Google Scholar
[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), 344–352.CrossRefGoogle Scholar
[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), 203–213.Google Scholar
[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), 271–293.CrossRefGoogle Scholar
[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, 645–648, 2010.Google Scholar
[47]Xie, X., Level set based segmentation using local feature distribution, 2010 International Conference on Pattern Recognition, 2010.Google Scholar
[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.Google Scholar
[49]Yuan, J., Bae, E., Tai, XC. and Boykov, Y., A continuous max-flow approach to Potts model, Computer Vision–ECCV 2010, 379–392, 2010.Google Scholar
[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.Google Scholar
[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), 884–900.Google Scholar