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
Personal Author(s):
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.
Descriptors:
- *IMAGE PROCESSING
- *PARTIAL DIFFERENTIAL EQUATIONS
- *THREE DIMENSIONAL FLOW
- *INVARIANCE
- *DIFFERENTIAL GEOMETRY
- *SMOOTHING(MATHEMATICS)
- DEFORMATION
- GRAPHS
- SURFACES
- DIFFUSION
- LIE GROUPS
- CURVES(GEOMETRY)
- HEAT
- EULER EQUATIONS
- COMPUTER GRAPHICS
- MATHEMATICAL FILTERS
- BOUNDARY VALUE PROBLEMS
- EVOLUTION(GENERAL)
Subject Categories:
- Numerical Mathematics
- Theoretical Mathematics
- Cybernetics
- Fluid Mechanics