Image Edge Detection: A New Approach Based on Fuzzy Entropy and Fuzzy Divergence

In image pre-processing, edge detection is a non-trivial task. Sometimes, images are affected by vagueness so that the edges of objects are difficult to distinguish. Hence, the usual edge-detecting operators can give unreliable results, thus necessitating the use of fuzzy procedures. In literature, Chaira and Ray approach is a popular technique for fuzzy edge detection in which fuzzy divergence formulation is exploited. However, this approach does not specify the threshold technique must be applied. Then, in this work, starting from Chairy and Ray procedure, we present a new fuzzy edge detector based on both fuzzy divergence (thought and proved to be a distance) and fuzzy entropy minimization for the thresholding sub-step in gray-scale images. Eddy currents, thermal infrared, and electrospinning images were used to test the proposed procedure after their fuzzification by a suitable adaptive S-shaped fuzzy membership function. Moreover, the fuzziness content of each image has been quantified by new specific indices proposed here and formulated in terms of fuzzy divergence. The results have been evaluated by suitable assessment metrics here formulated and are considered to be encouraging when qualitatively and quantitatively compared with those obtained by some well-known I- and II-order edge detectors.