Abstract
Decomposing a polygonal mesh into meaningful sub-components is a major challenge in computer graphics. This operation can be summed up as a discrimination process where meaningful sub-components are identified and optionally linked to each other into a graph representation.
Morse and Reeb graph theories are two powerful mathematical tools that respectively enable to identify topological points of interest over the mesh and to capture their connectivity relations into a graph structure.
In this report, we propose a new method for meaningful mesh topological
decomposition, based on Morse and Reeb graph theories. With this aim, we
develop a new feature point extraction algorithm, in order to compute a
meaningful PL function. We also propose a novel Reeb graph constructing
algorithm that brings a solution to the over-identification of critical
points over PL functions.
Resulting Reeb graphs present several interesting properties such as invariance to standard geometric transformations and to model pose.
BibTeX Entry
@TechReport{tierny05
|
author |
= "Julien Tierny and Tarik Filali-Ansary and Jean-Philippe
Vandeborre",
|
|
title |
= "A {N}ovel {M}ethod for {C}ontructing {M}eaningful {R}eeb
{G}raphs from {PL} {F}unctions over
2-manifolds",
|
|
institution |
= "Laboratoire d'Informatique Fondamentale de Lille (LIFL -
UMR USTL/CNRS 8022)",
|
|
number |
= "05-2005", |
|
year |
= "2005", |
|
month |
= "December", |
| } |
Updated on May 15th, 2006.