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The primary task of machine vision is to utilize a variety of techniques to segment a digital image into meaningful regions, extract the corresponding edges, compute the various features (e.g., area, centroids) and primitives (e.g. lines, corners, curves) that exist in the image, and finally develop some decision rules or grammar structures for interpreting the image content. In conventional vision systems, the operations performed involve making crisp (yes or no) decisions about the regions, features, primitives, regional relationships and overall scene interpretation. However, various degrees of uncertainty exist at each and every stage of the vision system process because these decisions are often based on data that is inexact or ambiguous in nature. Much of the incertitude in the image information can be interpreted in terms of either grayness ambiguity (deciding on the intensity of a pixel) or spatial ambiguity (deciding on the shape and geometry of the regions within the image). Fuzzy morphology is a mathematical tool developed to deal with imprecise or ambiguous information that arises during a subjective evaluation process such as scene interpretation. This mathematical approach transforms a gray scale image into a two-dimensional array of fuzzy singletons called a fuzzy image. The value of each fuzzy singleton reflects the degree to which the pixel possesses some property such as brightness, edgeness, redness, or surface uniformity (i.e., texture). A variety of morphological operations can be performed on the singletons in order to modify the ambiguity associated with the desired property. For the efficient shape representation of objects in a scene, a thinning algorithm for fuzzy images is proposed in this paper. Once the object shape has been thinned to a skeleton-like representation, curve descriptors can be used to transform the generalized shape into a coded form. In essence, this thinning algorithm is used to reduce, or compress, the structural shape information of a vaguely defined object into simplified features for a rule-based description of the object shape.
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