Convergence of morphological operations: Parallel processing implementation.
Item
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Title
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Convergence of morphological operations: Parallel processing implementation.
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Identifier
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AAI9530907
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identifier
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9530907
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Creator
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Ngatchou, Jean-Claude.
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Contributor
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Adviser: Charles R. Giardina
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Date
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1995
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Language
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English
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Publisher
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City University of New York.
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Subject
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Computer Science | Mathematics | Engineering, Electronics and Electrical
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Abstract
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Two primitive morphological operations are considered: Dilation and Erosion. The Convergence Theorems are established for analog signals. The same concept can readily be generalized to image of higher dimension by increasing the spatial domain.;Given two continuous functions f(x) and g(x) of domains (a,b), and (0,1) respectively, a family of partitions is generated from the domain of g(x). A sequence of functions g{dollar}\sb{lcub}n{rcub}{dollar}(x) is then constructed both "Pointwise" and "Stepwise" from that family, which are shown to converge uniformly toward g(x). The Convergence Theorems for the dilation and the erosion, stipulate that the limit of the dilation (erosion) of f(x) by {dollar}g\sb{lcub}n{rcub}{dollar}(x) as n approaches infinity is the dilation (erosion) of f(x) by g(x). In the process of proving the Convergence Theorems, it is shown that the limit as n approaches infinity of the domain of dilation (erosion) of f(x) by {dollar}g\sb{lcub}n{rcub}{dollar}(x) equals the domain of the dilation (erosion) of f(x) by g(x).;Finally, in each case a parallel algorithm is designed using a block diagram. It turns out that n can be viewed as the number of processors needed to approximate the dilation (erosion) of f(x) by g(x) by the digitized version, that is the dilation (erosion) of f(x) by {dollar}g\sb{lcub}n{rcub}{dollar}(x).
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
