Date
October 2nd, 2008 (2:00 pm).
Location
TELECOM Lille 1, Universite des Sciences et Technologies de Lille.
Committee
Abstract
With the ongoing development of 3D technologies, 3D shapes are
becoming an interactive media of major importance. Their commonest
representation, the surface mesh, suffers however from high
variability towards standard shape-preserving surface
transformations.It is necessary thus to design intrinsic shape
modeling techniques.
In this thesis, we explore topological modeling by studying Reeb
graph based structures. In particular, we introduce a novel shape
abstraction, called the enhanced topological skeleton, which enables
not only the study of the topological evolution of Morse functions'
level sets but also that of their geometrical evolution. We show the
utility of this intrinsic shape representation in three research
problems related to Computer Graphics and Computer Vision.
First, we introduce the notion of geometrical calculus on Reeb
graphs for the stable and automatic computation of control skeletons
for interactive shape handling.
Then, by introducing the notions of Reeb chart and Reeb pattern, we
propose a new method for partial 3D shape similarity estimation. We
show this approach outperforms the competing methods of the
international SHape REtrieval Contest 2007 by a gain of 14%.
Finally, we present two techniques for the functional decomposition
computation of a 3D shape, both from human perception based
heuristics and from the analysis of time-varying 3D data.
For each of these research problems, concrete applicative examples
are presented to assess the utility of our approach.
Updated on October 14th, 2008.