A New Approach to Image Segmentation via Fuzzification of Rènyi Entropy of Generalized Distributions
In this paper, we propose a novel approach for image
segmentation via fuzzification of Rènyi Entropy of Generalized
Distributions (REGD). The fuzzy REGD is used to precisely measure
the structural information of image and to locate the optimal
threshold desired by segmentation. The proposed approach draws
upon the postulation that the optimal threshold concurs with
maximum information content of the distribution. The contributions
in the paper are as follow: Initially, the fuzzy REGD as a measure of
the spatial structure of image is introduced. Then, we propose an
efficient entropic segmentation approach using fuzzy REGD.
However the proposed approach belongs to entropic segmentation
approaches (i.e. these approaches are commonly applied to grayscale
images), it is adapted to be viable for segmenting color images.
Lastly, diverse experiments on real images that show the superior
performance of the proposed method are carried out.
[1] W.Y. Ma and B.S. Manjunath, "Edge flow: A framework of boundary
detection and image segmentation". In: IEEE Conference on Computer
Vision and Pattern Recognition, San Juan, Puerto Rico, 1997, pp. 744-
749.
[2] C.Y. Xu and L.P. Jerry, "Snakes, shapes, and gradient vector flow," IEEE
Trans. Image Process, 7 (3), 1998, pp. 359-369.
[3] Y.N. Deng, B.S. Manjunath, "Unsupervised segmentation of color-
texture regions in images and video," IEEE Trans. Pattern Anal. Mach.
Intell, 23 (8), 2001, 800-810.
[4] S.C. Zhu and Y. Alan, "Region competition: Unifying snakes, region
growing, and Bayes/MDL for multiband image segmentation," IEEE
Trans. Pattern Anal. Mach. Intell. 18 (9), 1996, pp. 884-900.
[5] G.-P Daniel., G. Chuang, "Extensive partition operators, gray-level
connected operators, and region merging/classification segmentation
algorithms: Theoretical links," IEEE Trans. Image Process. 10 (9), 2001,
pp. 1332-1345.
[6] K.S. Punam and K.U Jayaram. "Optimum image thresholding via class
uncertainty and region homogeneity," IEEE Trans. Pattern Recog. Mach.
Intell. 23 (7), 2001, pp. 689-706.
[7] Y. Zhang, B. Michael and S. Stephen, "Segmentation of brain images
through a hidden Markov random field model and the expectationmaximization algorithm," IEEE Trans. Med. Image, 20 (1), 2001, pp. 45-
57.
[8] J. Mohanalin, P. K. Kalra, N. Kumar, "Tsallis Entropy based
Microcalcification Segmentation", ICGST-GVIP Journal, ISSN 1687-
398X, Volume (9), Issue (I), 2009.
[9] C. Tsallis, S. Abe, Y. Okamoto, "Nonextensive Statistical Mechanics and
its Applications," In: Series Lecture Notes in Physics. Springer, Berlin,
2001.
[10] M. Portes de Albuquerque, I.A. Esquef, A.R. Gesualdi "Image
thresholding using Tsallis entropy," in: Pattern Recognition Letters, vol.
25, 2004, pp. 1059-1065.
[11] C. E. Shannon and W. Weaver, "The Mathematical Theory of
Communication," Urbana, University of Illinois Press, 1949.
[12] A. Rènyi, "On a theorem of P. Erdos and its application in information
theory," Mathematica, vol. 1, 1959, pp. 341-344.
[13] D. Strzałka and F. Grabowski, "Towards possible q-generalizations of
the Malthus and Verhulst growth models", Physica A, Vol.387, Issue 11,
2008, pp. 2511-2518.
[14] B. Singh and A. Partap, "Edge Detection in Gray Level Images based on
the Shannon Entropy," Journal. of Computer Sci. 4 (3), 2008, pp. 186-
191.
[15] C. Tsallis and M.P Albuquerque, "Are citations of scientific paper a case
of nonextensivity?" Euro. Phys. J. B 13, 2000, pp. 777-780.
[16] L. A. Zadeh, "Fuzzy sets," Inform. and Control, vol. 8, no. 1, pp.338-
353, 1965.
[17] W. Tatsuaki and S. Takeshi "When nonextensive entropy becomes
extensive," Physica A 301, 2001, pp. 284-290.
[18] R. C. Gonzalez and R. E. Woods, "Digital Image Processing Using
Matlab" Prentice Hall, Inc, Upper Saddle River, NJ, 2nd Edition, 2003.
[19] I. Levner and Hong Zhang, "Classification-Driven Watershed
Segmentation," IEEE Transactions on Image Processing vol. 16, Issue
5, May 2007, pp.1437-1445.
[1] W.Y. Ma and B.S. Manjunath, "Edge flow: A framework of boundary
detection and image segmentation". In: IEEE Conference on Computer
Vision and Pattern Recognition, San Juan, Puerto Rico, 1997, pp. 744-
749.
[2] C.Y. Xu and L.P. Jerry, "Snakes, shapes, and gradient vector flow," IEEE
Trans. Image Process, 7 (3), 1998, pp. 359-369.
[3] Y.N. Deng, B.S. Manjunath, "Unsupervised segmentation of color-
texture regions in images and video," IEEE Trans. Pattern Anal. Mach.
Intell, 23 (8), 2001, 800-810.
[4] S.C. Zhu and Y. Alan, "Region competition: Unifying snakes, region
growing, and Bayes/MDL for multiband image segmentation," IEEE
Trans. Pattern Anal. Mach. Intell. 18 (9), 1996, pp. 884-900.
[5] G.-P Daniel., G. Chuang, "Extensive partition operators, gray-level
connected operators, and region merging/classification segmentation
algorithms: Theoretical links," IEEE Trans. Image Process. 10 (9), 2001,
pp. 1332-1345.
[6] K.S. Punam and K.U Jayaram. "Optimum image thresholding via class
uncertainty and region homogeneity," IEEE Trans. Pattern Recog. Mach.
Intell. 23 (7), 2001, pp. 689-706.
[7] Y. Zhang, B. Michael and S. Stephen, "Segmentation of brain images
through a hidden Markov random field model and the expectationmaximization algorithm," IEEE Trans. Med. Image, 20 (1), 2001, pp. 45-
57.
[8] J. Mohanalin, P. K. Kalra, N. Kumar, "Tsallis Entropy based
Microcalcification Segmentation", ICGST-GVIP Journal, ISSN 1687-
398X, Volume (9), Issue (I), 2009.
[9] C. Tsallis, S. Abe, Y. Okamoto, "Nonextensive Statistical Mechanics and
its Applications," In: Series Lecture Notes in Physics. Springer, Berlin,
2001.
[10] M. Portes de Albuquerque, I.A. Esquef, A.R. Gesualdi "Image
thresholding using Tsallis entropy," in: Pattern Recognition Letters, vol.
25, 2004, pp. 1059-1065.
[11] C. E. Shannon and W. Weaver, "The Mathematical Theory of
Communication," Urbana, University of Illinois Press, 1949.
[12] A. Rènyi, "On a theorem of P. Erdos and its application in information
theory," Mathematica, vol. 1, 1959, pp. 341-344.
[13] D. Strzałka and F. Grabowski, "Towards possible q-generalizations of
the Malthus and Verhulst growth models", Physica A, Vol.387, Issue 11,
2008, pp. 2511-2518.
[14] B. Singh and A. Partap, "Edge Detection in Gray Level Images based on
the Shannon Entropy," Journal. of Computer Sci. 4 (3), 2008, pp. 186-
191.
[15] C. Tsallis and M.P Albuquerque, "Are citations of scientific paper a case
of nonextensivity?" Euro. Phys. J. B 13, 2000, pp. 777-780.
[16] L. A. Zadeh, "Fuzzy sets," Inform. and Control, vol. 8, no. 1, pp.338-
353, 1965.
[17] W. Tatsuaki and S. Takeshi "When nonextensive entropy becomes
extensive," Physica A 301, 2001, pp. 284-290.
[18] R. C. Gonzalez and R. E. Woods, "Digital Image Processing Using
Matlab" Prentice Hall, Inc, Upper Saddle River, NJ, 2nd Edition, 2003.
[19] I. Levner and Hong Zhang, "Classification-Driven Watershed
Segmentation," IEEE Transactions on Image Processing vol. 16, Issue
5, May 2007, pp.1437-1445.
@article{"International Journal of Electrical, Electronic and Communication Sciences:54349", author = "Samy Sadek and Ayoub Al-Hamadi and Axel Panning and Bernd Michaelis and Usama Sayed", title = "A New Approach to Image Segmentation via Fuzzification of Rènyi Entropy of Generalized Distributions", abstract = "In this paper, we propose a novel approach for image
segmentation via fuzzification of Rènyi Entropy of Generalized
Distributions (REGD). The fuzzy REGD is used to precisely measure
the structural information of image and to locate the optimal
threshold desired by segmentation. The proposed approach draws
upon the postulation that the optimal threshold concurs with
maximum information content of the distribution. The contributions
in the paper are as follow: Initially, the fuzzy REGD as a measure of
the spatial structure of image is introduced. Then, we propose an
efficient entropic segmentation approach using fuzzy REGD.
However the proposed approach belongs to entropic segmentation
approaches (i.e. these approaches are commonly applied to grayscale
images), it is adapted to be viable for segmenting color images.
Lastly, diverse experiments on real images that show the superior
performance of the proposed method are carried out.", keywords = "Entropy of generalized distributions, entropy
fuzzification, entropic image segmentation.", volume = "3", number = "8", pages = "1561-6", }
