Technical Report CIS9304

TR#:CIS9304
Class:CIS
Title: THE UBIQUITOUS ELLIPSE.
Authors: G. Sapiro and A.M. Bruckstein
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Abstract:

We discuss three different affine invariant evolution processes for smoothing planar curves. The first one is derived from a geometric heat-type flow, both the initial and the smoothed curves being continuous. The second smoothing process is obtained from a discretization of this affine heat equation. In this case the curves are represented by planar polygons. The third process is based on B-Spline approximations. For this process, the initial curve is a planar polygon, and the smoothed curves are continuous. We show that, in the limit, all three affine invariant smoothing processes collapse any initial curve into an elliptic point.

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