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Processing gray-scale realizations of images that are ide- ally binary (such as gray-scale realizations of printed characters) is problematic due to the fact that gray-scale processing should be con- sistent with the binary nature of the ideal image. Essentially, any final decision (such as the recognition of a specific character at a spe- cific 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 re- alizations of ideal gray-scale images. These should not be expected to lead, ipso facto, to decision procedures appropriate to 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. The theory of fuzzy mathematical morphology has been fully char- acterized in terms of a set of axioms for subset fuzzzfication. Within the general framework there exists an infinite number of realizations of fuzzy mathematical morphology and the determination of which the- ory is relevant is application dependent; nevertheless, there does exist a general paradigm for the construction of fuzzy algorithms from cor- responding binary algorithms. In this chapter 'we discuss this general paradigm for algorithm construction, and in particular, we discuss morphological algorithms for smoothing, geometric filtering, edge de- tection, object detection, and peak detection. The efficacy of these algorithms are underlined by the various simulations presented herein.
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