Journal of Electronic ImagingFuzzy uncertainty measures in image processing
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A gray-tone image taken of a real scene will contain inherent ambiguities due to light dispersion on the physical surfaces. The neighboring pixels may have very different intensity values and yet they may represent the same surface region. A fuzzy set theoretic approach for representing, processing, and quantitatively evaluating the information in gray-tone images is presented in this paper. The gray-tone digital image is mapped into a two-dimensional array of singletons called a fuzzy image. The value of each fuzzy singleton represents the degree to which a pixel intensity can be associated with some vaguely defined visual property γ. For illustrative purposes, the visual properties related to the notion of a uniform surface are investigated. The inherent ambiguity in the surface information can be modified by performing a variety of fuzzy mathematical operations on the singletons. Once the fuzzy image processing operations are completed, the modified fuzzy image can be converted back to a gray-tone image representation. The ambiguity associated with the processed fuzzy image is quantitatively evaluated by measuring the uncertainty present both before and after processing. Computer simulations are presented to illustrate some of these notions.