Team Geometrica

Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities

Section: Other Grants and Activities

National Actions

ANR Triangles

Participants : Manuel Caroli, Pedro Machado Manhães de Castro, Olivier Devillers, Sylvain Pion, Monique Teillaud.

We lead the Triangles project funded by the anr . The project involves

— the «Laboratoire d'InfoRmatique en Image et Systèmes d'information» (LIRIS), Lyon,

— the «Département d'informatique de l'ENS» and

— the Geometrica team.

Triangulations are essential in many applications, in particular for meshing and shape reconstruction. We want to develop and distribute new results for academic and industrial researchers. The goal of the project is the development of robust and effective algorithms for the manipulation of large sets of points, of mobile sets of points and points in non Euclidean spaces such as periodic spaces (torus, cylinder), projective, oriented projective or hyperbolic spaces. The results obtained will be implemented in the CGAL library and will be applied to computer vision (visual envelopes, camera calibration), fluid dynamics, astronomy, computer graphics and medical applications.

In the Geometrica team, Triangles is co-funding the scholarship of Pedro de Castro (with «Région PACA») and funding traveling and computers. Several meetings have been organized between participants, details can be found on the project's web page.

- Starting date: November 2007

- Duration: 3 years


Participants : Jean-Daniel Boissonnat, Frédéric Chazal, Arijit Ghosh, David Cohen-Steiner, Samuel Hornus.

The aim of this project is to formalize a collaboration between researchers from computational geometry, machine learning and computer vision to study distortions and in particular Bregman divergences, information theory, statistics, Riemannian geometry, and convex analysis.

The other partners of the project are the Université des Antilles et de la Guyane (R. Nock, coordinator), the Ecole Polytechnique (F. Nielsen) and the Lear project-team (C. Schmid).

- Starting date: November 2007

- Duration: 4 years

ANR Galapagos

Participant : Sylvain Pion.

In this project we wish to apply computerized theorem proving tools to two aspects of geometry. The first aspect concerns computational geometry. The second aspect concerns verifying geometric reasoning steps in usual constructions, such as constructions with rules and compass. Other participants in this contract are the universities of Strasbourg and Poitiers, the ENSIEE in Evry and the Ecole Normale Supérieure in Lyon. The leader of the project is the Marelle project-team.

- Starting date: November 2007.

- Duration: 3 years.

ANR GeoTopAl

Participants : Pierre Alliez, Jean-Daniel Boissonnat, Frédéric Chazal, David Cohen-Steiner, Sylvain Pion.

This project aims at developing concepts, methods and algorithms for solving problems in the realm of geometric modeling (of complex shapes), reverse engineering and numerical simulation, as well as visualization. The concepts and methods sought after should be rich enough to accommodate a certain mathematical sophistication, while remaining compatible with the constraints inherent to the development of efficient and certified algorithms. (Certification herein refers to a geometric and topological coherence between the input and the output of an algorithm.) Meeting these two goals simultaneously requires a close collaboration between Mathematics —Differential Topology and Geometry, and Computer Science —Computational Geometry and Solid Modeling. Bridging the gap between these disciplines is not traditional and contributes to the main innovative aspect of this project. The goals pursued cover theoretical and applied aspects. On the one hand, the project aims at developing a mathematical theory for geometric and topological approximation. On the other hand, implementation and efficiency issues of algorithms will also be addressed. In particular, algorithms will be validated on a fairly large spectrum of applications involving 3D models in the scope of Digital Geometry Processing.

This project coordinated by Geometrica also involves researchers from the INRIA team-project ABS, CNRS (Grenoble, ENS Paris), and a representative from the industry holding a PAST position (Visiting Professor from Industry) at the university of Grenoble.

- Starting date: 2006.

- Duration: 3 years.

ANR Gyroviz

Participants : Pierre Alliez, Jean-Daniel Boissonnat, Laurent Saboret, Nader Salman, Mariette Yvinec.

The Gyroviz project was selected by the ANR in the framework of the call Audivisual and Multimedia techniques. The project, which was started December 2007 for three years, involves the SME Sofresud (Toulon, coordinator) and IXSEA and research teams from the CEA, INRIA and SupMECA Toulon. The project addresses the challenge of automatic modeling of 3D physical scenes from located frames. The aim of the project is to couple new accurate inertial sensors with an image acquisition device and efficient reconstruction algorithms to obtain an automatic image-based modeling system.

- Starting date: December 2007.

- Duration: 3 years.

DIGITEO project GAS: Geometry Algorithms and Statistics

Participants : Claire Caillerie, Frédéric Chazal, David Cohen-Steiner, Bertrand Michel, Steve Oudot.

The project GAS was selected by the DIGITEO consortium in the framework of the “Domaines d'Intérêt Majeur” call of the Région Île-de-France. The project intends to explore and to develop new research at the crossing of information geometry, computational geometry and statistics. It started in September 2008 for an expected duration of 2 years. The other partners of the project are the Ecole Polytechnique (F. Nielsen) and the SELECT project-team (G. Celeux, P. Massart).

- Starting date: September 2008.

- Duration: 2 years.


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