Topology-Preserving Deformations of Fuzzy Digital Pictures
This chapter considers the topology of two-dimensional fuzzy digital pictures, and discusses topology-preserving deformations of these fuzzy pictures that generalize deformations of two-valued digital pictures. It is shown that an arbitrary fuzzy picture can be transformed by this type of deformation into a coherent fuzzy picture. As another application, it is shown that the genus of a fuzzy picture is a linear combination of local property values.
KeywordsFuzzy Subset Local Operation Simple Point Local Connectedness Hexagonal Array
Unable to display preview. Download preview PDF.
- 1.Dyer C.R. and Rosenfeld A., Thinning algorithms for gray-scale pictures,IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 1, pp. 88–89, 1979Google Scholar
- 2.Nakamura A. and Aizawa K., Connectedness of coherent fuzzy pictures,Information Sciences, Vol. 61, pp. 123–133, 1992Google Scholar
- 3.Nakamura A. and Rosenfeld A., Deformations of fuzzy pictures,in: “Proceedings of JCIS’97 — Joint Conference on Information Sciences”, Vol. 3, pp. 273276, 1997Google Scholar
- 5.Rosenfeld A., Fuzzy digital topology,Information and Control, Vol. 40, pp. 7687, 1979Google Scholar
- 6.Rosenfeld A., On connectivity properties of grayscale pictures,Pattern Recognition, Vol. 16, pp. 47–50, 1983Google Scholar