Math @ Duke

Publications [#264902] of Guillermo Sapiro
Papers Published
 Olver, PJ; Sapiro, G; Tannenbaum, A, Invariant geometric evolutions of surfaces and volumetric smoothing,
Siam Journal on Applied Mathematics, vol. 57 no. 1
(February, 1997),
pp. 176194, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/06/25)
Abstract: The study of geometric flows for smoothing, multiscale representation, and analysis of two and threedimensional 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 heattype 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 affine invariant flow for (convex) surfaces in threedimensional space, which, like the affineinvariant curve shortening flow, will be of fundamental importance in the processing of threedimensional images.


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