A Mathematical Model for Wind Velocity Field Reconstruction and Visualization Taking into Account the Topography Influence.

In this paper, we propose a global modelling for vector field approximation from a given finite set of vectors (corresponding to the wind velocity field or marine currents). In the modelling, we propose using the minimization on a Hilbert space of an energy functional that includes a fidelity criterion to the data and a smoothing term. We discretize the continuous problem using a finite elements method.

A Level Set-Based Model for Image Segmentation under Geometric Constraints and Data Approximation.

In this paper, we propose a new model for image segmentation under geometric constraints. We define the geometric constraints and we give a minimization problem leading to a variational equation. This new model based on a minimal surface makes it possible to consider many different applications from image segmentation to data approximation.

On the construction of topology-preserving deformation fields.

In this paper, we investigate a new method to enforce topology preservation on deformation fields. The method is composed of two steps. The first one consists in correcting the gradient vector fields of the deformation at the discrete level, in order to fulfill a set of conditions ensuring topology preservation in the continuous domain after bilinear interpolation.