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Optimal morphological pattern restoration from noisy binary images

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2 Author(s)
Schonfeld, D. ; Dept. of Electr. & Comput. Eng., Johns Hopkins Univ., Baltimore, MD, USA ; Goutsias, J.

A theoretical analysis of morphological filters for the optimal restoration of noisy binary images is presented. The problem is formulated in a general form, and an optimal solution is obtained by using fundamental tools from mathematical morphology and decision theory. Consideration is given to the set-difference distance function as a measure of comparison between images. This function is used to introduce the mean-difference function as a quantitative measure of the degree of geometrical and topological distortion introduced by morphological filtering. It is proved that the class of alternating sequential filters is a set of parametric, smoothing morphological filters that best preserve the crucial structure of input images in the least-mean-difference sense

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:13 ,  Issue: 1 )