From Shape Matching to Shape Mechanics: Geometry and Dynamics
During the last decades, the study of shape spaces has been driven by the accelerated development of imaging techniques in biomedical engineering and the emergence of computational anatomy. Starting from the basic and hard problems of shape comparison, shape matching and modeling shape populations, a fascinating landscape is appearing involving infinite dimensional manifolds, Lie groups, Riemannian geometry, Hamiltonian systems and Statistics. Its connection with many existing mathematical theories, sometimes outside the usual scope of the imaging community, and the growing need for effective tools in shape analysis, provide an exciting playground for inter-disciplinary research and collaborations. This talks will visit some hot spots in this landscape and some challenges driven by anatomical growth modeling.
Alain Trouvé, Ecole Normale Supérieure, France