Maks Ovsjanikov will defend his habilitation thesis next week on May, 19th. It will take place at Télécom ParisTech, 46 rue Barrault, Paris, amphi Estaunié.
Abstract: The work presented in my habilitation dissertation describes a set of approaches for analyzing and processing 3D shapes and their relations. The main unifying theme of this work is the observation that many concepts in geometric data analysis can be considered, both in theory and in practice, as linear operators acting on real-valued functions defined on the shapes. Although this point of view has been common in some areas of mathematics, such as dynamical systems, representation theory or parts of differential geometry, it has only recently been adopted in digital geometry processing, where it has led to novel insights and efficient algorithms for a wide variety of problems including shape matching, tangent vector field analysis and shape comparison to name a few. I will give an overview of these and related techniques and demonstrate, in particular, how the functional operator point of view can be helpful in a variety of practical settings, both by providing a common language in which many operations can be expressed and by enabling the use of classical linear-algebraic tools in novel, and sometimes unexpected scenarios.