Minimal non-simple sets on 3D and 4D geometric grids.
Item
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Title
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Minimal non-simple sets on 3D and 4D geometric grids.
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Identifier
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AAI3159211
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identifier
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3159211
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Creator
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Gau, Chyi-jou.
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Contributor
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Adviser: Yung Kong
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Date
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2005
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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
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Abstract
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Ronse introduced the concept of a minimal non-simple ("MNS") set of 1s of a binary image; if no iteration of a proposed parallel thinning algorithm can ever delete an MNS set, then it follows that the proposed algorithm "preserves topology". Ronse, Ma, Kong, Hall, and other authors have solved the problem of finding all those sets of grid points that can be MNS sets of binary images on the 2D and 3D Cartesian grids and the 2D hexagonal grid. This thesis solves the same problem for the 3D face-centered cubic grid (with (18,12)-, (12,18)-, or (12,12)-adjacency) and the 4D Cartesian grid (with (80,8)- or (8,80)-adjacency). Kong's concept of the attachment set of a point in a binary image is used to study of the effect of deleting non-simple 1s and MNS sets. In the attachment set approach, the definition of a simple point (which involves continuous deformation) is independent of the dimensionality and form of the grid and is therefore a convenient basis for our work. At the end of the thesis a staggered tiling system for n-dimensional Euclidean space is proposed. The author believes that thinning algorithms for images on the corresponding n-dimensional grids will be easier to analyze than similar algorithms on n-dimensional Cartesian grids.
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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.
