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Invariant geometric evolutions of surfaces and volumetric smoothing

Publication ,  Journal Article
Olver, PJ; Sapiro, G; Tannenbaum, A
Published in: SIAM Journal on Applied Mathematics
January 1, 1997

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 Scholars

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Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

January 1, 1997

Volume

57

Issue

1

Start / End Page

176 / 194

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Olver, P. J., Sapiro, G., & Tannenbaum, A. (1997). Invariant geometric evolutions of surfaces and volumetric smoothing. SIAM Journal on Applied Mathematics, 57(1), 176–194. https://doi.org/10.1137/s0036139994266311
Olver, P. J., G. Sapiro, and A. Tannenbaum. “Invariant geometric evolutions of surfaces and volumetric smoothing.” SIAM Journal on Applied Mathematics 57, no. 1 (January 1, 1997): 176–94. https://doi.org/10.1137/s0036139994266311.
Olver PJ, Sapiro G, Tannenbaum A. Invariant geometric evolutions of surfaces and volumetric smoothing. SIAM Journal on Applied Mathematics. 1997 Jan 1;57(1):176–94.
Olver, P. J., et al. “Invariant geometric evolutions of surfaces and volumetric smoothing.” SIAM Journal on Applied Mathematics, vol. 57, no. 1, Jan. 1997, pp. 176–94. Scopus, doi:10.1137/s0036139994266311.
Olver PJ, Sapiro G, Tannenbaum A. Invariant geometric evolutions of surfaces and volumetric smoothing. SIAM Journal on Applied Mathematics. 1997 Jan 1;57(1):176–194.

Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

January 1, 1997

Volume

57

Issue

1

Start / End Page

176 / 194

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics