Math @ Duke

Publications [#264881] of Guillermo Sapiro
Papers Published
 Sapiro, G; Bruckstein, AM, The ubiquitous ellipse,
Acta Applicandae Mathematicae, vol. 38 no. 2
(February, 1995),
pp. 149161, Springer Nature, ISSN 01678019 [doi]
(last updated on 2019/06/25)
Abstract: We discuss three different affine invariant evolution processes for smoothing planar curves. The first one is derived from a geometric heattype flow, both the initial and the smoothed curves being differentiable. 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 Bspline approximations. For this process, the initial curve is a planar polygon, and the smoothed curves are differentiable and even analytic. We show that, in the limit, all three affine invariant smoothing processes collapse any initial curve into an elliptic point. © 1995 Kluwer Academic Publishers.


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