Math @ Duke

Publications [#264845] of Guillermo Sapiro
Papers Published
 Sapiro, G; Tannenbaum, A, Area and length preserving geometric invariant scalespaces, edited by Eklundh, JO,
Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 801 LNCS
(January, 1994),
pp. 449458, SPRINGER, ISBN 9783540579571 [html], [doi]
(last updated on 2019/06/25)
Abstract: © SpringerVerlag Berlin Heidelberg 1994. In this paper, area preserving geometric multiscale representations of planar curves are described. This allows geometric smoothing without shrinkage at the same time preserving all the scalespace properties. The representations are obtained deforming the curve via invariant geometric heat flows while simultaneously magnifying the plane by a homethety which keeps the enclosed area constant. The flows are geometrically intrinsic to the curve, and exactly satisfy all the basic requirements of scalespace representations. In the case of the Euclidean heat flow for example, it is completely local as well. The same approach is used to define length preserving geometric flows. The geometric scalespaces are implemented using an efficient numerical algorithm.


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