Abstract
In this paper, area preserving geometric multi-scale representations of planar curves are described. This allows geometric smoothing without shrinkage at the same time preserving all the scale-space 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 scale-space 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.
This work was supported in part by grants from the National Science Foundation DMS-8811084 and ECS-9122106, by the Air Force Office of Scientific Research AFOSR-90-0024 and F49620-94-1-00S8DEF, by the Army Research Office DAAL03-91-G-0019, DAAH04-93-G-0332, and DAAL03-92-G-0115, and by the Rothschild Foundation-Yad Hanadiv.
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© 1994 Springer-Verlag Berlin Heidelberg
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Sapiro, G., Tannenbaum, A. (1994). Area and length preserving geometric invariant scale-spaces. In: Eklundh, JO. (eds) Computer Vision — ECCV '94. ECCV 1994. Lecture Notes in Computer Science, vol 801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028376
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DOI: https://doi.org/10.1007/BFb0028376
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