Invariant geometric evolutions of surfaces and volumetric smoothing

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.

Duke Authors

Cited Authors

  • Olver, PJ; Sapiro, G; Tannenbaum, A

Published Date

  • 1997

Published In

  • SIAM Journal on Applied Mathematics

Volume / Issue

  • 57 / 1

Start / End Page

  • 176 - 194

Citation Source

  • SciVal