Dempster-Shafer Evidence Theory for Image Segmentation: Application in Cells Images

Authors: S. Ben Chaabane, M. Sayadi, F. Fnaiech, E. Brassart

Abstract:

In this paper we propose a new knowledge model using the Dempster-Shafer-s evidence theory for image segmentation and fusion. The proposed method is composed essentially of two steps. First, mass distributions in Dempster-Shafer theory are obtained from the membership degrees of each pixel covering the three image components (R, G and B). Each membership-s degree is determined by applying Fuzzy C-Means (FCM) clustering to the gray levels of the three images. Second, the fusion process consists in defining three discernment frames which are associated with the three images to be fused, and then combining them to form a new frame of discernment. The strategy used to define mass distributions in the combined framework is discussed in detail. The proposed fusion method is illustrated in the context of image segmentation. Experimental investigations and comparative studies with the other previous methods are carried out showing thus the robustness and superiority of the proposed method in terms of image segmentation.

Keywords: Fuzzy C-means, Color image, data fusion, Dempster-Shafer's evidence theory

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070659

References:

[1] A. W. C. Liew, S. H. Leung, et W. H. Lau, " Fuzzy image clustering incorporating spatial continuity," IEE Procedings on Vision Image Signal Processing, Vol. 14, no. 2, pp. 185-192, April 2000.
[2] Dempster, Arthur P, "A generalization of Bayesian inference," Journal of the Royal Statistical Society, Series B, Vol. 30, pp. 205-247, 1968.
[3] E. Rignot, R. Chellappa, and P. Dubois, "Unsupervised segmentation of polarimetric SAR data using the covariance matrix," IEEE Transactions Geosciences and Remote Sensing, Vol. 30, pp. 697-705, 1992.
[4] H. D. Cheng, Y. H. Chen, "Fuzzy partition of two dimensional histogram and its application to thresholding," Pattern Recognition, Vol. 32, pp. 825-843, 1999.
[5] H. D. Cheng, X. H. Jiang and Jingli Wang, "Color image segmentation based on homogram thresholding and region merging," Pattern Recognition, Vol. 25, pp. 373-393, 2002.
[6] H. D. Cheng, X. H. Jiang, Ying Sun, Jingli Wang, "Color image segmentation: advances and prospects," Pattern Recognition to appear.
[7] I. Block, H. Maitre, "Fusion of image information under imprecision, in: B. Bouchon-Meunier (Ed.), Aggregation and fusion of imperfect information, series studies in fuzziness," Physica Verlag, Springer, pp. 189-213, 1997.
[8] J. C. Dunn, "A fuzzy relative of the Isodata process and its use in detecting compact well-separated clusters," Journal of Cybernetics, Vol. 3, pp. 32-57, 1974.
[9] J. Basak and D. Mahata, "A Connectionist Model for Corner Detection in Binary and Gray Images," IEEE Transactions on neuronal networks, vol. 11, no.5, September 2000.
[10] K. Raghu, J. M. Keller, "A possibilistic approach to clustering," IEEE Transactions on Fuzzy Systems, Vol. 1, no. 2, 1993.
[11] L. O. Hall, A. M. Bensaid, L. Clarke, R. P. Velthuizen, M. Silbiger, and J.C. Bezdek, " A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain," IEEE Transactions Neural Networks, Vol. 3, pp. 672-681, 1992.
[12] Lotfi A. Zadeh, "Fuzzy sets," Information and Control, Vol. 8, pp. 338- 353, 1965.
[13] Lotfi A. Zadeh, "Fuzzy Sets a Basis for a theory of Possibility," Fuzzy sets and systems, Vol. 1, pp. 3-28, 1978.
[14] M. C. Shin, D. B. Goldgof, K. W. Bowyer et S. Nikiforou, " Comparaison of Edge Detection Algorithms Using a Structure from Motion Task," IEEE Transactions on systems, Man, and cybernetics (SMC 01)-Part B: cybernetics, Vol. 31, no. 4, august 2001.
[15] P. K. Sahoo, S. Soltani and A.K.C Wong, "A survey of thresholding techniques," Comput, Vision Graphics Image Process. Vol. 41, pp. 233-260, 1988.
[16] P. Vannoorenberche, O. Colot and D. de Brucq, "Color image segmentation using dempster-shafer-s theory," Proc. ICIP-99, pp. 300- 304, October 1999.
[17] Shafer, Glenn, "A Mathematical Theory of Evidence," Princeton University Press, 1976.
[18] W. Chumsamrong, P. Thitimajshima, and Y. Rangsanseri, "Synthetic aperture radar (SAR) image segmentation using a new modified fuzzy c-means algorithm," Proceedings of Geoscience and Remote Sensing Symposium, Vol. 2, PP. 624-626, 2000.
[19] Y. Yang, Ch. Zheng and P. Lin, "Fuzzy C-means clustering algorithm with a novel penalty term for image segmentation," Opto-Electronics Rev., Vol. 13, no. 4, 2005.
[20] Y. I. Ohta, T. Kanade, T. Sakai, "Color information for region segmentation," Comput. Graph. and Imag. Proc., Vol. 13, pp. 222-241, 1980.