Math @ Duke

Publications [#264879] of Guillermo Sapiro
Papers Published
 Bruckstein, AM; Sapiro, G; Shaked, D, Evolutions of planar polygons,
International Journal of Pattern Recognition and Artificial Intelligence, vol. 9 no. 6
(1995),
pp. 9911014 [doi]
(last updated on 2018/03/18)
Abstract: Evolutions of closed planar polygons are studied in this work. In the first part of the paper, the general theory of linear polygon evolutions is presented, and two specific problems are analyzed. The first one is a polygonal analog of a novel affineinvariant differential curve evolution, for which the convergence of planar curves to ellipses was proved. In the polygon case, convergence to polygonal approximation of ellipses, polygonal ellipses, is proven. The second one is related to cyclic pursuit problems, and convergence, either to polygonal ellipses or to polygonal circles, is proven. In the second part, two possible polygonal analogues of the wellknown Euclidean curve shortening flow are presented. The models follow from geometric considerations. Experimental results show that an arbitrary initial polygon converges to either regular or irregular polygonal approximations of circles when evolving according to the proposed Euclidean flows.


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