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2001, 23(7), pp 689–706. ; Hilton, A. Estimation of Fuzzy Gaussian Mixture and Unsupervised Statistical Image Segmentation. IEEE Trans. Image Proc. 1997, 6(3), pp 425– 440. ; Flores-Mangas, F. Classification of Anatomical Structures in MR Brain Images Using Fuzzy Parameters. IEEE Trans. Biomed. Eng. 2004, 51(9), pp 1599–1608. ; Lui, Y. ; Freimanis, R. I. A Novel Approach to Microcalcification Detection Using Fuzzy Logic Technique. IEEE Trans. Med. Imag. 1998, 17(3) pp 442–450. Udupa, J. ; Samarasekera, S.

Dutta Majumder, D. Correlation Between Two Fuzzy Membership Functions. Fuzzy Sets Syst. 1985, 17, pp 23–38. 12. Pal, N. ; Pal, S. K. Higher Order Fuzzy Entropy and Hybrid Entropy of a Set. Inform. Sci. 1992, 61 pp 211–231. 13. ; Termini, S. A Definition of a Non Probabilistic Entropy in the Setting of Fuzzy Set Theory. Inform. Control 1972, 20, pp 301–312. 14. Shannon, C. E. A Mathematical Theory of Communication. Bell. Syst. Tech. J. 1948, 27, p 379. 15. Pal, N. ; Pal, S. K. Entropic Thresholding.

Note that the original image cannot be reconstructed, like the other conventional techniques of gray skeleton extraction (2–85) from the fuzzy skeleton obtained here. The second method is based on fuzzy medial axis transformation (FMAT) (28) using the concept of fuzzy disks. A fuzzy disk with center P is a fuzzy set in which membership depends only on the distance from P. For any fuzzy set f, a maximal fuzzy disk gP f ≤ f exists centered at every point P, and f is the sup of the gP f s. ) Let us call a set Sf of points f-sufficient if every gP f ≤ gQ f for some set of Q in Sf ; evidently f is then the sup of the gQ f s.

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