Efficient edge detection using simplified Gabor wavelets
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on cybernetics and cognitive informatics
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Analyzes the statistical properties of the basic binary and multilevel morphological operations with both 1-D and 2D structuring elements. Very simple expressions for the output distribution of erosion and opening are derived in the case of any independent identically or nonidentically distributed inputs. The probability relations between erosion and dilation, also between opening and closing, are developed. The output expectation bias and variances are analyzed and computed to show the efficiency of morphological operations for noise supression. As applications of theoretical results, the effects of the morphological operations on noisy signals are illustrated by several examples. The study reveals certain interesting phenomena. For example, the output variances of opening for some input distributions are greater than those of erosion, and morphological operations perform better than median filters in edge preservation