Prof Martin Rumpf

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Speaker

Universität Bonn

Martin Rumpf studied mathematics at Bonn University. He did his PhD in 1992 and was scientific assistant from 1993 to 1996 at the University of Freiburg. In 1996 he became associate professor at Bonn University and in 2001 full professor at Duisburg university. Since 2004 he is full professor for mathematics at Bonn University.
He is studying Riemannian calculus on shape spaces with applications in imaging and in computer graphics. Furthermore, he is interested in microstructures in material science, in shape optimization and in adaptive finite element methods.

Talk

Sparse Principal Component Analysis on Shape Manifolds

This talk discusses the construction of a low-dimensional nonlinear space capturing the variability of a non-rigid shape from a data set of example poses.  The core of the approach is a Sparse Principal Geodesic Analysis (SPGA) on the Riemannian manifold of discrete shells, in which a pose of a non-rigid shape is a point. The SPGA is invariant to rigid body motions of the poses and supports large deformation. Since the Riemannian metric measures the membrane and bending distortions of the shells, the sparsity term forces the modes to describe largely decoupled and localized deformations.