A t-Norm Based Approach to Edge Detection

In this paper we study a modification of the original method by Genyun Sun et al. [1] for egde detection based on the Law of Universal Gravitation. We analyze the effect of the substitution of the product by other t-norms in the calculation of the gravitatory forces. We construct a fuzzy set where memberships to the edges are extracted from the magnitude of the resulting force on each pixel. To finish, we experimentally proof that the features of each t-norm determine the kind of edges to be detected.

[1]  Q. Y. Ma,et al.  MRI brain image segmentation by multi-resolution edge detection and region selection. , 2000, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[2]  Lei Zhang,et al.  Edge detection by scale multiplication in wavelet domain , 2002, Pattern Recognit. Lett..

[3]  Alan L. Yuille,et al.  A statistical approach to multi-scale edge detection , 2003, Image Vis. Comput..

[4]  James C. Bezdek,et al.  A geometric approach to edge detection , 1998, IEEE Trans. Fuzzy Syst..

[5]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[6]  Jun Shen,et al.  Neuro-fuzzy synergism to the intelligent system for edge detection and enhancement , 2003, Pattern Recognit..

[7]  Qiang Liu,et al.  A novel approach for edge detection based on the theory of universal gravity , 2007, Pattern Recognit..

[8]  Humberto Bustince,et al.  Interval-valued fuzzy sets constructed from matrices: Application to edge detection , 2009, Fuzzy Sets Syst..

[9]  Gleb Beliakov,et al.  Aggregation Functions: A Guide for Practitioners , 2007, Studies in Fuzziness and Soft Computing.

[10]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Wen-June Wang,et al.  A novel edge detection method based on the maximizing objective function , 2007, Pattern Recognit..

[12]  M. J. Frank,et al.  Associative Functions: Triangular Norms And Copulas , 2006 .

[13]  Lily R. Liang,et al.  Competitive fuzzy edge detection , 2003, Appl. Soft Comput..

[14]  Cécile Barat,et al.  Scale-adaptive detection and local characterization of edges based on wavelet transform , 2004, Signal Process..

[15]  J. Canny.  A Computational Approach toEdgeDetection , 1986 .

[16]  In-So Kweon,et al.  Automatic edge detection using 3 x 3 ideal binary pixel patterns and fuzzy-based edge thresholding , 2004, Pattern Recognit. Lett..

[17]  Jussi Parkkinen,et al.  Edge detection in multispectral images using the self-organizing map , 2003, Pattern Recognit. Lett..