Fuzzy geometry: An overview

The author briefly reviews work on the fuzzy topology and geometry of image subsets, including adjacency, separation, and connectedness; distance and relative position; area, perimeter, and diameter; convexity and starshapedness; and medial axes and thinning.<<ETX>>

[1]  Azriel Rosenfeld,et al.  A Medial Axis Transformation for Grayscale Pictures , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  P. Diamond A note on fuzzy starshaped fuzzy sets , 1990 .

[3]  R. Lowen Convex fuzzy sets , 1980 .

[4]  Azriel Rosenfeld,et al.  Some results on fuzzy (digital) convexity , 1982, Pattern Recognit..

[5]  Sankar K. Pal Fuzzy skeletonization of an image , 1989, Pattern Recognit. Lett..

[6]  Azriel Rosenfeld,et al.  The perimeter of a fuzzy set , 1985, Pattern Recognit..

[7]  Azriel Rosenfeld,et al.  A fuzzy medial axis transformation based on fuzzy disks , 1991, Pattern Recognit. Lett..

[8]  Sankar K. Pal,et al.  Automatic grey level thresholding through index of fuzziness and entropy , 1983, Pattern Recognit. Lett..

[9]  Azriel Rosenfeld,et al.  Image enhancement and thresholding by optimization of fuzzy compactness , 1988, Pattern Recognit. Lett..

[10]  A. Rosenfeld The fuzzy geometry of image subsets , 1984, Pattern Recognit. Lett..

[11]  Zheng Chong-you,et al.  Fuzzy path and fuzzy connectedness , 1984 .

[12]  Azriel Rosenfeld,et al.  Distances between fuzzy sets , 1985, Pattern Recognit. Lett..

[13]  Marie-Christine Jaulent,et al.  A general approach to parameter evaluation in fuzzy digital pictures , 1987, Pattern Recognit. Lett..

[14]  Azriel Rosenfeld,et al.  A Min-Max Medial Axis Transformation , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Jean Chorowicz,et al.  Parametrisable skeletonization of binary and multi-level images , 1990, Pattern Recognit. Lett..

[16]  A. Rosenfeld,et al.  Fuzzy rectangles , 1990, Pattern Recognit. Lett..

[17]  Sankar K. Pal,et al.  A Note on the Quantitative Measure of Image Enhancement Through Fuzziness , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  A. Bogomolny On the perimeter and area of fuzzy sets , 1987 .

[19]  Azriel Rosenfeld,et al.  Thinning Algorithms for Gray-Scale Pictures , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Azriel Rosenfeld,et al.  A Note on the Use of Local MIN and MAX Operations in Digital Picture Processing , 1977 .

[21]  László T. Kóczy On the description of relative position of fuzzy patterns , 1988, Pattern Recognit. Lett..

[22]  Azriel Rosenfeld,et al.  Piecewise Approximation of Pictures Using Maximal Neighborhoods , 1978, IEEE Transactions on Computers.

[23]  Wen-Hsiang Tsai,et al.  A new thinning algorithm for gray-scale images by the relaxation technique , 1990, Pattern Recognit..

[24]  Giorgio Levi,et al.  A Grey-Weighted Skeleton , 1970, Inf. Control..

[25]  A. Rosenfeld The diameter of a fuzzy set , 1984 .

[26]  Fabio Pasian,et al.  Core-line tracing for fuzzy image subsets , 1986, Pattern Recognit. Lett..

[27]  Azriel Rosenfeld,et al.  Fuzzy Digital Topology , 1979, Inf. Control..

[28]  Azriel Rosenfeld,et al.  On connectivity properties of grayscale pictures , 1981, Pattern Recognit..

[29]  Azriel Rosenfeld,et al.  Degree of adjacency or surroundedness , 1984, Pattern Recognit..

[30]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .