Invariant geometric evolutions of surfaces and volumetric smoothing
Author(s)
Olver, Peter
Sapiro, Guillermo
Tannenbaum, Allen R.
Advisor(s)
Editor(s)
Collections
Supplementary to:
Permanent Link
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.
Sponsor
Date
1997-02
Extent
Resource Type
Text
Resource Subtype
Article