Accession Number:

ADA455853

Title:

Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing

Descriptive Note:

Research paper

Corporate Author:

MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS

Report Date:

1994-04-15

Pagination or Media Count:

38.0

Abstract:

The study of geometric flows for smoothing, multi-scale representation and the analysis of two-dimensional and three-dimensional objects has received much attention in the past few years. In this paper, the authors first present results mainly related to Euclidean invariant geometric smoothing of three-dimensional surfaces. They describe results concerning the smoothing of graphs images via level sets of geometric heat-type flows. Then they deal with proper three-dimensional flows. These flows are governed by functions of the principal curvatures of the surface, such as the mean and Gaussian curvatures. Then, given a transformation group G acting on Rexp n, they write down a general expression for any G-invariant hypersurface geometric evolution in Rexp n. As an application, they derive the simplest affine invariant flow for surfaces.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics
  • Cybernetics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE