## Section: Application Domains

### Shape processing

Many problems encounter in the application of computer sciences started from
measurement data, from which one wants to recover a curve, a surface, or more
generally a shape. This is typically the case in image processing, computer
vision or signal processing. This also appears in computer biology where
*Distance geometry* plays a significant role, for example, in the
reconstruction from NMR experiments, or the analysis of realizable or
accessible configurations. In another domain, scanners which tends
to be more and more easily used yield large set of data points from which
one has to recover compact geometric model.
We are working in collaboration with groups in agronomy on the problems
of reconstruction of branching models (which represent trees or plants).
We are investigating the application of algebraic techniques to these
reconstruction problems.
Geometry is also highly involved in the numerical simulation of physical
problems such as heat conduction, ship hull design, blades and turbines
analysis, mechanical stress analysis. We apply our algebraic-geometric
techniques in the isogeometric approach which use the same (bspline)
formalism to represent both the geometry and the solutions of partial
differential equations on this geometry.