Abstract
The paper describes an algorithm for image segmentation using fuzzy entropy measure. The relation between the fuzzy entropy of an image domain and the fuzzy entropy of its subdomains is explored as a uniformity predicate. With the aim of implementing the model, we have introduced a well known technique of Problem Solving. The most important roles of our model are played by the Evaluation Function (EF) and the Control Strategy. So the EF is related to the ratio between the fuzzy entropy of one region or zone of the picture and the fuzzy entropy of the entire picture. The Control Strategy determines the optimal path in the search tree (quadtree) so that the nodes of the optimal path have minimal fuzzy entropy. The paper shows some comparisons between the proposed algorithm and classical edge detection techniques.
Chapter PDF
References
R.C. Gonzales and P. Wintz, Digital Image Processing, 2nd Edn. Addison-Wesley, Reading Mass. (1987).
R. Rosenfeld and A.C. Kak, Digital Picture Processing, 2nd Edn. v.2, Academic Press, N.Y. (1982).
D.C. Marr and E. Hildreth, “Theory of edge detection”, Proc. R. Soc. London B 207, 187–217 (1980).
B. Born. Robot Vision, MIT Press, Cambridge, Mass. (1986).
J. Canny, “A computation approach to edge detection”, IEEE Trans. on Pattern Analysis Mach. Intell., PAMI-8, 679–698 (1986).
M.A. Gennert, “Detecting half-edges and vertices in images”, Proc. IEEE Int. Conf. Comput. Vision Pattern Recogn., 552–557 (1986).
V.S. Nalwa and T.O. Binford, “On detecting edges”, IEEE Trans. on Pattern Analysis Mach. Intell., PAMI-6, 699–714 (1986).
M.M. Fleck, “Some defects in finite-difference edge finders”, IEEE Trans. on Pattern Analysis Mach. Intell., PAMI-14, 337–345 (1992).
Y.G. Leclerc, “Capturing the local structure in image discontinuities in two dimensions”. Proc. IEEE Int. Conf. Comput. Vision Pattern Recogn., 34–38 (1985).
P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion”, IEEE Trans. on Pattern Analysis Mach. Intell., PAMI-12, 629–639 (1990)
P. Saint Marc, J. Chen and G. Medioni, “Adaptive smoothing: a general tool for early vision”, IEEE Trans. on Pattern Analysis Mach. Intell., PAMI-13, 514–530 (1991).
W.E. Higgins and C. Hsu, “Edge detection using two dimensional local structure information”, Pattern Recognition, 27, 277–294 (1994).
S.D. Yanowitz and A.M. Brukstein, “A new method for image segmentation”, Comput. Vision Graphics Image Processing, 46, 82–95 (1989).
T. Tart, P.J. Flynn and A.K. Jain, “Segmentation of document images”, IEEE Trans. on Pattern Analysis Mach. Intell., PAMI-11, 1322–1329 (1989).
T. W. Ridler and S. Calvard, “Picture thresholding using an iterative selection method”, IEEE Trans. on System Man and Cybern., SMC-8, 630–632 (1978).
P.K. Sahoo, S. Soltani, A.K.C. Wong and Y.C. Chen, “A survey of thresholding techniques”. Comput. Vision Graphics Image Processing, v.41, 233–260 (1988).
N.R. Pal and S.K. Pal, “Object-background segmentation using a new definition of entropy”, IEE Proc., Pt, 136, 284–295 (1989).
N.R. Pal and D. Bhandari, “On object-background classification”, Int. J. Syst. Sci., 23, 1903–1920 (1992).
A.S. Abutaleb, “Automatic thresholding of grey level pictures using two-dimensional entropy”, Comput. Vision Graphics Image Processing, 47, 22–32 (1989).
P.J. Burt, T. Hong and A. Rosenfeld, “Segmentation and estimation on image properties through cooperative hierarchical computation”, IEEE Trans. on System Man and Cybern., v.11, n.12 (1981).
Y. Nakagawa and A. Rosenfeld, “Some experiments on variable thresholding”, Pattern Recognition, 11, 191–204 (1979).
J. Kittler and J. Illingworth, “Minimum error thresholding”, Pattern Recognition, 19, 41–47 (1986).
S.Vitulano, C.Di Ruberto and M.Nappi, “A.I. based image segmentation”, Lectures Notes in Computer Science, Proc. of Int. Conf. of Image Analysis and Processing, C. Braccini, L. De Floriani, G. Vernazza (Eds.), Springer Verlag, 974, 429–434 (1995).
S. Tanimoto, M. Savini and S. Vitulano, “Allocation in attention vision”, Human and Machine Vision, Proc. of the Third Int. Workshop on Perception, V. Cantoni (Ed.), Plenum Press, 171–180 (1994).
S.L. Horowitz and T. Pavlidis, “Picture segmentation by a directed split and merge procedure”, Proc of the Second Intern. Joint Conf on Pattern Recognition, pp.424–433, Copenhagen, Aug. (1974).
N.J. Nilsson, Principles of Artificial Intelligence, Springer Verlag (1982).
S.Z. Selim and M.A. Ismail, “Soft clustering of multidimensional data: a semi-fuzzy clustering approach”, Pattern Recognition, 15, 559–568 (1984).
M.S. Kamel and S.Z. Selim, “A thresholded fuzzy k-means algorithm for semi-fuzzy clustering”, Pattern Recognition, 24, 825–833 (1991).
Q. Zhang and R.D. Boyle, “A new clustering algorithm with multiple runs of iterative procedures”, Pattern Recognition, 24, 835–848 (1991).
M. Nappi and S. Vitulano, “A new more efficient k-means algorithm for clustering”, Proc. of the Thirteenth IASTED Int. Conf., Applied Informatics, ed. M. H. Hamza, pp. 324–327 (1995).
R.M. Haralick, “Digital step edges from zero crossing of second directional derivatives”, IEEE Trans. on Pattern Analysis Mach. Intell., PAMI-6, 58–68 (1984).
S. Vitulano, C. Di Ruberto, M. Nappi, “Biomedical Image Processing”, Proc. III IEEE ICECS '96, Oct. 13–16, Rodos, v.2, pp. 1116–1119 (1996).
B.Kosko, “Fuzzy Thinking: the New Science of Fuzzy Logic”, Hyperion Ed. (1993).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Di Ruberto, C., Nappi, M., Vitulano, S. (1997). Image segmentation by means of fuzzy entropy measure. In: Del Bimbo, A. (eds) Image Analysis and Processing. ICIAP 1997. Lecture Notes in Computer Science, vol 1310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63507-6_204
Download citation
DOI: https://doi.org/10.1007/3-540-63507-6_204
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63507-9
Online ISBN: 978-3-540-69585-1
eBook Packages: Springer Book Archive