Team Coprin

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Inria / Raweb 2004
Project: Coprin

Project : coprin

Section: New Results


Resolution of geometrical constraints systems by rigidity, consistency and interval analysis

Uncertainty management

Keywords : distance equations, uncertainty.

Participants : Carlos Grandon, Bertrand Neveu.

We have studied how to manage small uncertainties in the parameters of a system of distance equations. The main aim is to approximate the sub-spaces of solutions as precise as possible. Classical interval solvers have difficulties for describing it, because solutions are not isolated points but continuous subspaces. Our work is based on the following idea: we have the solutions of distance equation system without uncertainties (or we compute them), then we use these solutions to determine a dynamic splitting policy of the domains (using these solutions as N-dimensional points to compute a subspace like Voronoi diagrams). Filtering algorithms are then applied to each subspace to obtain boxes containing the solutions of the system with uncertainties.

We have studied the limitations of this method. Despite that the method is complete (no region with solutions is lost), we have found the following difficulties:

We are now studying how to solve these difficulties and how to extend the method to other systems of equations.

Scene Modeling Based on Constraint System Decomposition Techniques

Keywords : computer vision, scene reconstruction, geometric constraints, decomposition.

Participants : Gilles Trombettoni, Marta Wilczkowiak.

This work has been performed in collaboration with Marta Wilczkowiak working in the MOVI project at INRIA RhĂ´nes-Alpes.

In 2002 and 2003, we had designed and implemented a new approach to 3D scene modeling based on geometric constraints (published in 2003 in the main conferences in constraint programming and computer vision). Contrary to the existing methods, we can quickly obtain 3D scene models that respect exactly the given constraints. Our system can describe a large variety of linear and non-linear constraints in a flexible way.

In 2004, this work has been continued in two ways:


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