Segmentation of Medical Images using Fuzzy Mathematical Morphology
Keywords:Fuzzy Logic, Mathematical morphology, Segmentation
Currently, Mathematical Morphology (MM) has become a powerful tool in Digital Image Processing (DIP). It allows processing images to enhance fuzzy areas, segment objects, detect edges and analyze structures. The techniques developed for binary images are a major step forward in the application of this theory to gray level images. One of these techniques is based on fuzzy logic and on the theory of fuzzy sets. Fuzzy sets have proved to be strongly advantageous when representing inaccuracies, not only regarding the spatial localization of objects in an image but also the membership of a certain pixel to a given class. Such inaccuracies are inherent to real images either because of the presence of indefinite limits between the structures or objects to be segmented within the image due to noisy acquisitions or directly because they are inherent to the image formation methods. Our approach is to show how the fuzzy sets specifically utilized in MM have turned into a functional tool in DIP.
 J. Serra, Image Analysis and Mathematical Morphology, Vol. II, London Editorial Academic Press, 1988.
 J. Serra and L. Vincent, “An Overview of Morphologic Filtering”, Circuits, Systems and Signal Processing. vol. 11, pp. 47-108, 1992.
 R. Espin, J. Gomez and M. Lecich, “Compensatory Logic: A Fuzzy aproach decision making”, NAISO'Enterprises Systems', Portugal, 2004.
 T. Deng and H. Heijmans, “Grey-scale Morphology Based on Fuzzy Logic”, Journal of Mathematical
Imaging and Vision, Springer Netherlands, vol. 16, no. 2, pp. 155-171, 2002.
 R. Gonzalez and R. Woods, Digital Image Processing, Editorial Adison –Wesley, 1992.
 E. Dougherty, An Introduction to Morphologic Image Processing, SPIE, Washington, 1992.
 L. Vincent, “Morphologic Greyscale Reconstruction in Image Analysis: Applications and Efficient Algorithms”, IEEE Transactions on Image Processing, vol.2, no.2, pp.176-201, 1993.
 S. Mukhopadhyay and B.Chanda, “Multiscale Morphologic Segmentation of Gray-Scale Images”, IEEE Transactions on Image Processing, vol.12, no.5, pp.533-549, 2003.
 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.
 SDC Morphology Toolbox for MATLAB 5. User’s Guide. SDC Information Systems, 2001.