Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing

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 R(exp n), they write down a general expression for any G-invariant hypersurface geometric evolution in R(exp n). As an application, they derive the simplest affine invariant flow for surfaces.

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Document Details

Document Type
Technical Report
Publication Date
Apr 15, 1994
Accession Number
ADA455853

Entities

People

  • Allen Tannenbaum
  • Guillermo Sapiro
  • Peter Olver

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Calculus Of Variations
  • Change Detection
  • Curvature
  • Differential Equations
  • Differential Geometry
  • Equations
  • Geometric Forms
  • Geometry
  • Heat Transmission
  • Image Processing
  • Lie Groups
  • Lines (Geometry)
  • Partial Differential Equations
  • Personal Information Managers
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Graph Algorithms and Convex Optimization.