Abstract
Type II fuzzy sets are high-level representation of vague data with, compared to ordinary fuzzy sets, greater capability for uncertainty management. Theoretical aspects of type II fuzzy systems have been extensively investigated, and the research is still ongoing. Many image processing tasks accompanied with different types of imperfection. In this chapter, the applications of type II fuzzy sets for image segmentation will be discussed. Global and spatial type II segmentation schemes will be systematically introduced and examples will be provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, Vol. 78, pp. 305–316, 1996.
T. Chaira, A.K. Ray, Segmentation using fuzzy divergence, Pattern Recognition Letters, Vol. 24(12), pp. 1837–1844, 2003.
Z. Chi, H. Yan, T. Pham, Fuzzy Algorithms with Applications to Image Processing and Pattern Recognition, World Scientific, Singapore, 1997.
A. De Luca, S. Termini, A definition of a nonprobabilistic entropy in the setting of fuzzy set theory, Information and Control, Vol. 20, pp. 301–312, 1972.
R.M. Haralick, Image segmentation survey, in Fundamentals in Computer Vision, O. D. Faugeras (ed.), Cambridge University Press, Cambridge, pp. 209–224, 1983.
L.K. Huang, M.J. Wang, Image thresholding by minimizing the measure of fuzziness. Pattern Recognition, Vol. 28, pp. 41–51, 1995.
C.V. Jawahar, P.K. Biswas, A.K. Ray, Investigations on Fuzzy Thresholding Based on Fuzzy Clustering, Patern Recognition, Vol. 30(10), pp. 1605–1613, 1997.
C.V. Jawahar, P.K. Biswas, A.K. Ray, Analysis of fuzzy thresholding schemes, Patern Recognition, Vol. 33(8), pp. 1339–1349, 2000.
A. Kaufmann, Introduction to the Theory of Fuzzy Subsets - Fundamental Theoretical Elements, Vol. 1. Academic Press, New York, 1975.
R. Krishnapuram, J.M. Keller, A possibilistic approach to clustering, IEEE Transactions on Fuzzy Systems, Vol. 1(2), pp. 98–110, 1993.
R. Kruse, F. Höppner, F., Klawonn, Fuzzy-Clusteranalyse (in German), Vieweg, Braunschweig, 1997.
K.C. Lin, Fast image thresholding by finding the zero(s) of the first derivative of between-class variance, Machine Vision and Applications, Vol. 13(5-6), pp. 254–262, 2003.
J.M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems, Prentice Hall, USA, 2001.
J.M. Mendel and R.I. Bob John, Type-2 Fuzzy Sets Made Simple, IEEE Transactions on Fuzzy Systems, Vol. 10(2), pp. 117–127, 2002.
H.B. Mitchell, Pattern recognition using type-II fuzzy sets, Information Sciences, Vol. 170, pp. 409–418, 2005.
P.L. Rosin, Unimodal thresholding, Pattern Recognition, Vol. 34(11), pp. 2083–2096, 2001.
S.K. Pal, A. Ghosh, A., Fuzzy geometry in image analysis, Fuzzy Sets and Systems, Vol. 48, pp. 23–40, 1992.
S.K. Pal, A. Rosenfeld, Image enhancement and thresholding by optimization of fuzzy compactness, Pattern Recognition Letters, Vol. 7, pp. 77–86, 1988.
N.R. Pal, S.K. Pal, A Review on Image Segmentation Techniques. Pattern Recognition, Vol. 26, pp. 1277–1294, 1993.
S.K. Pal, A. Ghosh, Index of area coverage of fuzzy image subsets and object extraction, Pattern Recognition Letters, Vol. 11, pp. 831–841, 1990.
N.R. Pal, D. Bhandari, D.D. Majumder, Fuzzy divergence, probability measure of fuzzy events and image thresholding, Patern Recognition Letters, Vol. 13, pp. 857–867, 1992.
S.K. Pal, C.A. Murthy, Fuzzy thresholding: mathematical framework, bound functions and weighted moving average technique, Pattern Recognition Letters, Vol. 11, pp. 197–206, 1990.
N.R. Pal, J.C. Bezdek, Measures of Fuzziness: A Review and several New Classes,. In: Yager, R.R., Zadeh, L.A. (eds.): Fuzzy Sets, Neural Networks, and Soft Computing, Van Nostrand Reinhold, New York, pp. 194–212, 1994.
R. Sambuc, Functions Φhi-flous. Aplication a laide au diagnostic en pathologie thyrodene, Thse, Universite de Marseille, 1975.
B. Sankur, M. Sezgin, Survey over image thresholding techniques and quantitative performance evaluation, Journal of Electronic Imaging, Vol. 13(1), pp. 146–165, 2004.
L. Snidaro, G.L. Foresti, Real-time thresholding with Euler numbers, Pattern Recognition Letters, Vol. 24(9-10), pp. 1543–1554, 2003.
W. Tao, H. Burkhardt, An Effective Thresholding Method Using a Fuzzy Compactness Measure, Proc. of 12th ICIP, Vol. 1, pp. 47–51, 1994.
H.R. Tizhoosh, Über Binarisierung und Potentiale der Fuzzy-Ansätze. In: Kruse, R., Dassow, J., Informatik’98, Springer, pp. 97–106, 1998.
H.R. Tizhoosh, Fuzzy Image Processing (in German), Springer, Heidelberg, Germany, 1998.
H.R. Tizhoosh, G. Krell, T. Lilienblum, C.J. Moore, B. Michaelis, Enhancement and Associative Restoration of Electronic Portal Images in Radiotherapy. International Journal of Medical Informatics, Elsevier Science Ireland, Vol. 49(2), pp. 157–171, 1998.
H.R. Tizhoosh, H. Hauß ecker, H., Fuzzy Image Processing: An Overview. In: Jähne, B., Hauß ecker, H., Geiß ler, P. (Eds.), Handbook on Computer Vision and Applications, Academic Press, Boston, 1998.
H.R. Tizhoosh, Image Thresholding Using Type II Fuzzy Sets, Pattern Recognition, Vol. 38, pp. 2363–2372, 2005.
H. Yan, Unified formulation of a class of image thresholding techniques, Pattern Recognition, Vol. 29(12), pp. 2025–2032, 1996.
W. A. Yasnoff, J. K. Mui, and J. W. Bacus, Error measures for scene segmentation, Pattern Recogn, Vol. 9, pp. 217–231, 1977.
Q. Wang, Z. Chi, R. Zhao, Image Thresholding by Maximizing the Index of Nonfuzziness of the 2-D Grayscale Histogram, Computer Vision and Image Understanding, Vol. 85(2), pp. 100–116, 2002.
S.D. Zenzo, L. Cinque, S. Levialdi, S., Image Thresholding Using Fuzzy Entropies, SMC, Vol. 28(1), pp. 15–23, 1998.
L.A. Zadeh, Fuzzy sets, Information and Control, Vol. 8, pp. 338–353, 1965.
Y. Zhang, A survey on evaluation methods for image segmentation, Pattern Recognition, Vol. 29(8), pp. 1335–1346, 1996.
Y.-J. Zhang, Advances in Image And Video Segmentation, IRM Press, 2006.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Tizhoosh, H.R. (2008). Type II Fuzzy Image Segmentation. In: Bustince, H., Herrera, F., Montero, J. (eds) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Studies in Fuzziness and Soft Computing, vol 220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73723-0_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-73723-0_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73722-3
Online ISBN: 978-3-540-73723-0
eBook Packages: EngineeringEngineering (R0)