Section: New Results

A sub-Riemannian modular approach for diffeomorphic deformations

Participants : Barbara Gris [Correspondant] , Stanley Durrleman, Alain Trouvé.

We develop a generic framework to build large deformations from a combination of base modules. These modules constitute a dynamical dictionary to describe transformations. The method, built on a coherent sub-Riemannian framework, defines a metric on modular deformations and characterises optimal deformations as geodesics for this metric. We present a generic way to build local affine transformations as deformation modules, and display examples.

More details in [27] .

Figure 4. Initial position of deformation modules and their control parameters (left) leads to the construction of local scaling (cyan), rotation (red) and translation (green) (right), which combine together to deform the blue shape into the black one.