Paper:

# Image Thresholding Computation Using Atanassov’s Intuitionistic Fuzzy Sets

## H. Bustince, E. Barrenechea, M. Pagola, and R. Orduna

Departamento de Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, s/n, 31006 Pamplona, Navarra, Spain

In this paper, a new thresholding technique using Atanassov’s intuitionistic fuzzy sets (A-IFSs) and restricted dissimilarity functions is introduced. In recent years, various thresholding techniques ([18, 24]) based on fuzzy set theory have been introduced to overcome the problem of non-uniform illumination and inherent image vagueness. In this paper we analyze this task and propose a new method for handling the grayness ambiguity and vagueness during the process of threshold selection.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.2, pp. 187-194, 2007.

- [1] K. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 20, pp. 87-96, 1986.
- [2] K. Atanassov, “Review and new results on intuitionistic fuzzy sets,” IM-MFAIS 1, 1988.
- [3] E. Barrenechea, “Image Thresholding with Interval-valued Fuzzy Sets. Edge Detection. Contrast,” Ph.D. Thesis, Universidad Pública de Navarra, 2005.
- [4] J. C. Bezdek, J. Keller, R. Krisnapuram, and N. R. Pal, “Fuzzy Models and algorithms for pattern recognition and image processing,” The Handbooks of Fuzzy Sets Series, Series Editors: D. Dubois and H. Prade, Kluwer Academic Publishers, Boston/London/Dordrecht, 1999.
- [5] P. Burillo and H. Bustince, “Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets,” Fuzzy Sets and Systems, 78, pp. 81-103, 1996.
- [6] H. Bustince and P. Burillo, “Perturbation of intuitionistic fuzzy relations,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9 (1), pp. 305-316, 2001.
- [7] H. Bustince, J. Kacprzyk, and V. Mohedano, “Intuitionistic fuzzy generators. Application to intuitionistic fuzzy complementation,” Fuzzy Sets and Systems, 114, pp. 485-504, 2000.
- [8] H. Bustince, V. Mohedano, E. Barrenechea, and M. Pagola, “Proximity functions. Application to fuzzy thresholding,” EUSFLAT, 2005.
- [9] H. Bustince, E. Barrenechea, and M. Pagola, “Image thresholding using restricted equivalence functions and maximizing the measures of similarity,” Fuzzy Sets and Systems, In Press, Available Online, 2006.
- [10] T. Chaira and A. K. Ray, “Region extraction using fuzzy similarity measures,” J. Fuzzy Math, 11 (3), pp. 601-607, 2003.
- [11] T. Chaira and A. K. Ray, “Thresholding selection using fuzzy set theory,” Pattern Recognition Letters, 25, pp. 865-874, 2004.
- [12] Z. Chi, H. Yan, and T. Pham, “Optimal image thresholding,” Fuzzy algorithms: with application to image processing and pattern recognition, World Scientific, Singapore, pp. 45-84, 1998.
- [13] C. Cornelis, G. Deschrijver, and E. Kerre, “Intuitionistic Fuzzy Connectives Revisited,” Proceedings of the Ninth International Conference IPMU 2002, Annecy-France, July 1-5, pp. 1839-1844, 2002.
- [14] M. G. Forero, “Fuzzy thresholding and histogram analysis,” Fuzzy Filters for Image Processing, M. Nachtegael, D. Van der Weken, D. Van de Ville, and E. E. Kerre (Eds.), pp. 129-152, Springer, 2003.
- [15] M. G. Forero and O. Rojas, “New formulation in image thresholding using fuzzy logic,” 11th Portuguese conference on pattern recognition RECPAD2000, pp. 117-124, 2000.
- [16] M. G. Forero, E. L. Sierra, J. Alvarez, J. Pech, G. Cristobal, L. Alcalá, and M. Desco, “Automatic sputum color image segmentation for tuberculosis diagnosis,” Proceedings of SPIE: Algorithms and systems for optical information processing, V. Javidi Dahram and Psaltis Demetri (Eds.), Vol.4471, pp. 251-261, 2001.
- [17] C. A. Glasbey, “An analysis of histogram-based thresholding algorithms,” CVGIP: Graphical models and image processing, 55 (6), pp. 532-537, 1993.
- [18] L. K. Huang and M. J. Wang, “Image thresholding by minimizing the measure of fuzziness,” Pattern recognition, 28(1), pp. 41-51, 1995.
- [19] J. S. R. Jan, C. T. Sun, and E. Mizutani, “Fuzzy Sets,” Neuro-fuzzy and soft computing, pp. 13-46, 1997.
- [20] C. V. Jawahar, P. K. Biswas, and A. K. Ray, “Investigations on fuzzy thresholding based on fuzzy clustering,” Pattern Recognition, 30(10), pp. 1605-1613, 1997.
- [21] E. Szmidt and J. Kacprzyk, “Entropy for intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 118(3), pp. 467-477, 2001.
- [22] C. T. Lin and G. Lee, “Fuzzy measures,” Neural fuzzy systems: A neuro-fuzzy synergism to intelligent systems, Prentice Hall, Upper Saddle River, pp. 63-88, 1996.
- [23] N. Otsu, “A threshold selection method from gray level histograms,” IEEE Transactions on Systems, Man and Cybernetics, 9, pp. 62-66, 1979.
- [24] N. R. Pal and S. K. Pal, “A review of image segmentation techniques,” Pattern recognition, 26, pp. 1277-1294, 1993.
- [25] J. R. Parker, “Advanced method in grey-level segmentation,” Algorithms for image processing and computer vision, John Wiley and Sons, New York, pp. 116-149, 1997.
- [26] W. K. Pratt, “Image segmentation,” Digital image processing, John Wiley and Sons, New York, pp. 597-627, 1991.
- [27] M. Sezgin and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation,” J. Electron. Imaging, 13(1), pp. 146-165, 2004.
- [28] P. K. Sahoo, S. Soltani, A. K. C. Wong, and Y. C. Chen, “A survey of thresholding techniques,” Computer vision, graphics and image processing, 41, pp. 233-260, 1988.
- [29] H. R. Tizhoosh, “Image thresholding using type II fuzzy sets,” Pattern Recognition, available on line, 2005.
- [30] R. R. Yager, “On the measure of fuzziness and negation. Part I: Membership in the unit interval,” Intern. J. of General Systems, 5, pp. 221-229, 1979.
- [31] R. R. Yager, “On the measure of fuzziness and negation. Part II Lattices,” Information and Control, 44(3), pp. 236-260, 1979.
- [32] L. A. Zadeh, “Fuzzy sets,” Information Control, 8, pp. 338-353, 1965.