Material
|
1. Feature Points.
|
2. Mapping Function.
|
|
3. Dual Reeb Graph.
|
4. Constriction Approximation.
|
|
5. Constriction Enhanced Graph.
|
6. Application to Mesh Deformation.
|
Abstract
This paper describes a novel and unified approach for Reeb graph
construction and simplification as well as constriction approximation on
3D polygonal meshes. The key idea of our algorithm is that discrete
contours - curves carried by the edges of the mesh and approximating the
continuous contours of a mapping function - encode both topological and
geometrical shape characteristics.
Firstly, mesh feature points are computed. Then they are used as
geodesic origins for the computation of an invariant mapping function
that reveals the shape most significant features. Secondly, for each
vertex in the mesh, its discrete contour is computed. As the set of
discrete contours recovers the whole surface, each of them can be
analyzed, both to detect topological changes or constrictions.
Constriction approximations enable Reeb graphs refinement into more
visually meaningful skeletons, that we refer as enhanced topological
skeletons.
Without pre-processing stages and without input parameters, our method
provides nice-looking and affine-invariant skeletons, with satisfactory
execution times. This makes enhanced topological skeletons good
candidates for applications needing high level shape representations,
such as mesh deformation (experimented in this paper), retrieval,
compression, metamorphosis, etc.
BibTeX Entry
@InProceedings{tierny06pacific,
|
author |
= "Tierny, Julien and Vandeborre, Jean-Philippe and Daoudi,
Mohamed", |
|
title |
= "{3}D {M}esh {S}keleton {E}xtraction {U}sing {T}opological and
{G}eometrical {A}nalyses",
|
|
booktitle |
= "14th Pacific Conference on Computer Graphics and
Applications (Pacific Graphics 2006)",
|
|
pages |
= "85-94",
|
|
year |
= "2006",
|
|
address |
= "Taipei, Taiwan",
|
| } |
Updated on October 16th, 2006.
