The secondorder sharpening of blurred smooth borders
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 Math. Comp. 52 (1989), 675714 Request permission
Abstract:
The problem is to approximate, with local secondorder 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. "Secondorder", 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 secondorder 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 secondorder accurate. Some extensions to three (and more) dimensions are appended.References

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Additional Information
 © Copyright 1989 American Mathematical Society
 Journal: Math. Comp. 52 (1989), 675714
 MSC: Primary 65D99; Secondary 65P05
 DOI: https://doi.org/10.1090/S00255718198909833138
 MathSciNet review: 983313