A Survey Paper on: Fuzzy Mathematical Morphology Techniques for Digital Image Processing

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Abstract:

This paper puts across the various approaches and methods that have been proposed in the context of Fuzzy Mathematical Morphology. The underlying principles of Dilation & Erosion, the structuring elements used in various techniques, the unique variations put forth by researchers, new applications in spatial relationships, decision making, segmentation of medical images have been discussed.

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Periodical:

Advanced Materials Research (Volumes 403-408)

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3469-3475

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November 2011

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[1] Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975).

Google Scholar

[2] Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982).

Google Scholar

[3] Hadwiger, H.: Vorlesungen Über Inhalt, Oberfläche und Isoperimetrie. Springer, Berlin (1957).

DOI: 10.1007/978-3-642-94702-5

Google Scholar

[4] Minkowski, H.: Gesammelte Abhandlungen. Teubner, Leipzig (1911).

Google Scholar

[5] Sternberg, S.R.: Parallel architecture for image processing. In: Proceedings of the Third International IEEE Compsac, Chicago, USA, p.712–717 (1979).

Google Scholar

[6] Sternberg, S.R.: Grayscale morphology. Comput. Vis. Graph. Image Process. 35, 333–355 (1986).

Google Scholar

[7] Birkhoff, G.: Lattice Theory, 3rd edn. AMS, Providence (1993).

Google Scholar

[8] Heijmans, H.J.A.M.: Morphological Image Operators. Academic Press, New York (1994).

Google Scholar

[9] Serra, J.: Image Analysis and Mathematical Morphology. Theoretical Advances, vol. 2. Academic Press, New York (1988).

Google Scholar

[10] A. Resenfield: the fuzzy geometry of image subsets, Patern recognition letters 2, 311-317, (1984).

Google Scholar

[11] M Wu: Fuzzy Morphology and image analysis, Proc of the 9th ICPR , Rome, 453-455, (1988).

Google Scholar

[12] D. Sinha, E.R. Dougherty: An intrinsically fuzzy approach to mathematical morphology , SPIE Vol . 1607 , Boston, Massachusetts, Nov (1991).

Google Scholar

[13] D. Sinha, E.R. Dougherty: Fuzzification of set inclusion, SPIE, VOl 1708 , Orlando , Florida, April (1992).

Google Scholar

[14] Bloch, I. and Maître, H., Fuzzy Mathematical Morphologies: A Comparative Study, Pattern Recognit., 1995, vol. 28, p.1341–1387.

DOI: 10.1016/0031-3203(94)00312-a

Google Scholar

[15] Sinha, D. and Dougherty, E., Fuzzification of Set Inclusion, Theory and Application, Fuzzy Sets and Systems, 1993, vol. 55, p.15–42.

DOI: 10.1016/0165-0114(93)90299-w

Google Scholar

[16] Sinha, D. and Dougherty, E., A General Axiomatic Theory of Intrinsically Fuzzy Mathematical Morphologies, IEEE Transactions of Fuzzy systems, 1995, vol. 3, p.389–403.

DOI: 10.1109/91.481948

Google Scholar

[17] De Baets, B., Kerre, E., and Gupta, M., The Fundamentals of Fuzzy Mathematical Morphology. Part 1: Basic Concepts, Internat. J. Gen. Systems, 1994, vol. 23, p.155–171.

DOI: 10.1080/03081079508908037

Google Scholar

[18] de Baets, B., Kerre, E., and Gupta, M., The Fundamentals of Fuzzy Mathematical Morphology. Part 2: Idempotence, Convexity and Decomposition, Internat. J. Gen. Systems, 1995, vol. 23, p.307–332.

DOI: 10.1080/03081079508908045

Google Scholar

[19] de Baets, B., Generalized Idempotence in Fuzzy MathematicalMorphology, in Fuzzy Techniques in Image Processing (Kerre, E. and Nachtegael, M., Eds. ), Studies in Fuzziness and Soft Computing, Physica, 2000, p.58–75.

DOI: 10.1007/978-3-7908-1847-5_2

Google Scholar

[20] de Baets, B., Fuzzy Morphology: A Logical Approach, in Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics and Neural Network Approach (Ayyub, B. and Gupta, M., Eds. ), Kluwer Academic Publishers, 1997, p.53–67.

DOI: 10.1007/978-1-4615-5473-8_4

Google Scholar

[21] Kosko, B., Neural Networks and Fuzzy Systems, Prentice Hall, (1991).

Google Scholar

[22] Serra, J., Image Analysis and Mathematical Morphology, London: Academic, (1982).

Google Scholar

[23] Serra, J., Image Analysis and Mathematical Morphology: Theoretical Advances, Academic, (1988).

Google Scholar

[24] Dubois, D., Fargier, H., and Prade, H., Beyond Min Aggregation in Multicriteria Decision: Ordered Weighted Min, Leximin, in The Ordered Weighted Averaging Operators—Theory and Applications, (Yager, R. and Kacprzyk, J., Eds. ), Kluwer Academics Publishers, (1997).

DOI: 10.1007/978-1-4615-6123-1_15

Google Scholar

[25] Grabisch, M., Fuzzy Integral in Multicriteria Decision Making, Fuzzy Sets and Systems, 1994, vol. 69, p.279–289.

DOI: 10.1016/0165-0114(94)00174-6

Google Scholar

[26] Grabisch, M., Murofushi, T., and Sugeno, M., Fuzzy Measure of Fuzzy Events Defines by Fuzzy Integrals, Fuzzy sets and systems, 1991, vol. 50, p.293–313.

DOI: 10.1016/0165-0114(92)90227-u

Google Scholar

[27] Sugeno, M., Theory of Fuzzy Integral and Its Applications, PhD thesis, Tokyo Inst. of Technology, (1974).

Google Scholar

[28] Tahani, H. and Keller, J., Information Fusion in Computer Vision Using Fuzzy Integral, IEEE Trans. on System, Man and Cybernetics, 1990, vol. 20, p.733–741.

DOI: 10.1109/21.57289

Google Scholar

[29] Yager, R., On Ordered Weighted Averaging Aggregation Operators in Multi-criteria Decision Making, IEEE Trans. on SMC, 1988, vol. 18, p.183–190.

DOI: 10.1109/21.87068

Google Scholar

[30] I. Bloch, H Maitre: Constructing a fuzzy mathematical morphology- alternative ways, (1993).

Google Scholar

[31] Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965).

Google Scholar

[32] Bandler, W., Kohout, L.: Fuzzy power sets and fuzzy implication operators. Fuzzy Sets Syst. 4(1), 13–30 (1980).

DOI: 10.1016/0165-0114(80)90060-3

Google Scholar

[33] Kitainik, L.: Fuzzy Decision Procedures with Binary Relations. Kluwer Academic, Dordrecht (1993).

Google Scholar

[34] Sinha, D., Dougherty, R.: Fuzzification of set inclusion: theory and applications. Fuzzy Sets Syst. 55(1), 15–42 (1993).

DOI: 10.1016/0165-0114(93)90299-w

Google Scholar

[35] Sinha, D., Sinha, P., Dougherty, E.R., Batman, S.: Design and analysis of fuzzy morphological algorithms for image processing. IEEE Trans. Fuzzy Syst. 5(4), 570–578 (1997).

DOI: 10.1109/91.649909

Google Scholar

[36] R. Krishnapuram, J. Keller, and Y. Ma, Quantitative Analysis of Properties and Spatial Relations of Fuzzy Image Regions, iEEE Trans Fuzzy Systems, v. 1, no. 3, pp.222-233. (1993).

DOI: 10.1109/91.236554

Google Scholar

[37] Paul D. Gader: Fuzzy Spatial Relations Based on Fuzzy Morphology – IEEE, (1997).

Google Scholar

[38] F. Zana and J.C. Klein, Segmentation of Vessel-Like Patterns using Mathematical Morphology and Curvature Evaluation, IEEE Transactions on Image Processing, vol. 10, no. 7, pp.1010-1019, (2001).

DOI: 10.1109/83.931095

Google Scholar

[39] Bouchet A, Pastore J, Ballarin V : Segmentation of medical Imagesusing fuzzy mathematical morphology, (2007).

Google Scholar

[40] Jinsung Oh and Luis. F Chaparro : Adaptive fuzzy morphological filtering of impulse noise in images.

Google Scholar