Shape detection via fuzzy morphology

Abstract

Processing gray-scale realizations of images that are ideally binary (such as gray-scale realizations of printed characters) is problematic due to the fact that gray-scale processing should be consistent with the binary nature of the ideal image. Essentially, any final decision (such as the recognition of a specific character at a specific location) should reflect the content of the ideal image, which is generally unknown. Too often, a gray-scale realization of an ideal binary image is processed using methods appropriate for gray-scale realizations of ideal gray- scale images. These should not be expected to lead to decision procedures appropriate for binary images. Fuzzy morphological algorithms do not assume probabilistic knowledge of the degradation process; however, they mirror the processing that one would have performed were the ideal binary image known. Thus, they lead to decision procedures consistent with those that would have been taken following processing of the ideal binary image. In this paper we discuss the fuzzy hit-or-miss transform based shape detectors that are capable of detecting geometric shapes in the presence of considerable additive as well as subtractive random noise. There exists an infinite number of realizations of this shape detector and the determination of which detector is suitable is application dependant; nevertheless, there exist a general set of heuristics for selecting the appropriate realization. We also carry out extensive noise- sensitivity analysis for a few of these shape detectors.