Postdoc proposal
Topological properties and shape characteristics for idealized models

Advisors

Jean-Claude Léon	Franck Hétroy
SIREP/G-SCOP	LJK/EVASION
E-mail : Jean-Claude.Leon@grenoble-inp.fr	E-mail : Franck.Hetroy@imag.fr
Tel. : 04 76 82 51 27	Tel. : 04 76 61 55 04

Context

Shape characterization for non-manifold models is based on geometrical and topological concepts. In the past, topological aspects have been adressed from both a local point of view, with data structures conveying the connections between the components of non-manifold models, and a global one, with the Euler-Poincaré theorem and Betti numbers. The main difficulty with respect to non-manifold models is to get global topological characteristics which are related to their shape. Such topological parameters help classifying objects, thus distinguishing them.

Objectives

The main stages of this postdoctoral project are the following:

participation to the study [LF08, LFH09] of shape classification for manifold-connected components [HF07] of a non-manifold simplicial complex:
- identification of topological properties of non-manifolds derived from 2-manifold with singularities;
- study of different classes of non-manifold objects, with respect to the orientation notion;
- specification of a generic data structure to describe non-manifold objects, based on these properties;
- creation of algorithms to compute shape characteristics for manifold-connected components;
participation to the study, initiated by J.C. Léon and L. de Floriani, of properties of non-manifold objects made of several manifold-connected components, based on hypergraphs:
- adaptation to objects with several manifold-connected components of global topological properties identified for objects with a single manifold-connected component;
- specification a data structure to describe non-manifold objects, based on these properties;
- creation of algorithms to compute shape characteristics for non-manifold objects made of several manifold-connected components.

They will be adressed in collaboration with the two advisors and Leila de Floriani from Genova University in Italy. A stay in Genova is planned.

Pre-requisites

Candidates must have defended a PhD thesis in computer science or applied maths, and have a strong background on computational geometry. Required skills also include geometric modeling, computer graphics, object-oriented programming and the ability to work in a team in an international context. Candidates must agree to spend several weeks in Genova to work with our Italian partner.

Keywords : topology, non-manifold, singularity, manifold-connected component, Betti number, hypergraph, knot theory.

Application conditions, duration and salary

To apply, candidates must:

be under 35;
have defended their PhD thesis less than 3 years ago;
have carried out research work outside Grenoble.

This is a 6-month offer, with a start date in autumn 2009. The gross salary will be about 2350 EUR per month.

References

[HF07] A. Hui and L. de Floriani. A two-level topological decomposition for non-manifold simplicial shapes. Solid and Physical Modeling Conference, 2007.
[LF08] J.C. Léon and L. de Floriani. Contribution to a taxonomy of non-manifold models based on topological properties. ASME DETC CIE conference, 2008.
[LFH09] J.C. Léon, L. de Floriani and F. Hétroy. Classification of non-manifold singularities from transformations of 2-manifolds. IEEE International Conference on Shape Modeling and Applications (SMI), 2009.