Publications [#264902] of Guillermo Sapiro

Papers Published

1. Olver, PJ; Sapiro, G; Tannenbaum, A, Invariant geometric evolutions of surfaces and volumetric smoothing, SIAM Journal on Applied Mathematics, vol. 57 no. 1 (January, 1997), pp. 176-194, Society for Industrial & Applied Mathematics (SIAM) [doi]
   (last updated on 2025/02/02)

   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 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.