Title:
Invariant geometric evolutions of surfaces and volumetric smoothing
Invariant geometric evolutions of surfaces and volumetric smoothing
Author(s)
Olver, Peter
Sapiro, Guillermo
Tannenbaum, Allen R.
Sapiro, Guillermo
Tannenbaum, Allen R.
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Abstract
The study of geometric flows for smoothing, multiscale representation, and analysis of
two- and three-dimensional objects has received much attention in the past few years. In this paper,
we first survey the geometric smoothing of curves and surfaces via geometric heat-type flows, which
are invariant under the groups of Euclidean and affine motions. Second, using the general theory of differential invariants, we determine the general formula for a geometric hypersurface evolution which is invariant under a prescribed symmetry group. As an application, we present the simplest a affine invariant flow for (convex) surfaces in three-dimensional space, which, like the affine-invariant curve
shortening flow, will be of fundamental importance in the processing of three-dimensional images.
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Date Issued
1997-02
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Text
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Article