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The second-order sharpening of blurred smooth borders


Author: Blair Swartz
Journal: Math. Comp. 52 (1989), 675-714, S35
MSC: Primary 65D99; Secondary 65P05
DOI: https://doi.org/10.1090/S0025-5718-1989-0983313-8
MathSciNet review: 983313
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Abstract: The problem is to approximate, with local second-order accuracy, the smooth boundary separating a black and a white region in the plane, given discretely located gray values associated with a blurring of that border. "Second-order", here, is with respect to the size h of the scale of the prescribed blurring. The locally determined approximations are line segments. The algorithms discussed here can result in second-order accuracy, but they may not in certain geometric circumstances. Typical local curvature estimates based on adjacent line segments do not converge, but an atypical one does. Consideration of a class of scaled blurrings leads to a type of blurring of borders which is particularly easy for a computer to undo locally, yielding a line which is locally second-order accurate. Some extensions to three (and more) dimensions are appended.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1989-0983313-8
Keywords: Blurred, boundary, border, edge, curve, surface, interface, approximation, reconstruction
Article copyright: © Copyright 1989 American Mathematical Society

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