The Taub Faculty of Computer Science Events and Talks

The field of shape analysis is rapidly growing. It involves processing of geometric structures for which tools from numerical, metric, diffusion, and differential geometries are exploited. In this thesis we propose to extend the set of classical tools used in this domain by designing new geometries and solving classical problems in the natural spectral domain. We first define a new scale- invariant metric and extend existing procedures to deal with objects that are subject to isometric semi-local scale deformations. Then, we propose an efficient representation for a family of continuous functions defined on a given set of isometrically similar manifolds. To that end, we revisit the definition of classical Principal Component Analysis and regularize its structure exploiting the intrinsic geometry of the given manifold. Finally, we show how the natural basis obtained from the Laplace- Beltrami Operator coupled with the basis provided by classical Principal Component Analysis can be used to effectively describe a given data while accounting for out-of-sample information.