Modular large deformation and shape aware metrics in shape analysis

Alain Trouve
École Normale Supérieure de Cachan

The statistical shape analysis remains a core challenging problem mainly because of three mathematical issues: the non functional nature of shapes, the importance of actions of group of transformations and the high dimensionality of shapes variations. The riemannian point of view on shape spaces integrates these three issues within a tractable numerical framework and more recently, modular sub-riemannian approaches on shape spaces have opened the possibility of a more decomposable, shape driven analysis of variations and evolutions. However, in this talk, we will advocate that paradoxically, quite sophisticated tools are still needed to allow a simple and user-friendly incorporation of meaningful prior knowledge into the mathematical shape analysis machinery.

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