SFU MOCAD Seminar: Elena Celledoni

Shape analysis is a framework for treating complex data and obtain metrics on spaces of data. Examples are spaces of unparametrized curves, time-signals, surfaces and images. In this talk we discuss structure preservation and deep learning for classifying, analysing and manipulating shapes. A computationally demanding task for estimating distances between shapes, e.g. in object recognition, is the computation of optimal reparametrizations. This is an optimisation problem on the infinite dimensional group of orientation preserving diffeomorphisms. We approximate diffeomorphisms with neural networks and use the optimal control and dynamical systems point of view to deep learning. We will discuss useful geometric properties in this context e.g. reparametrization invariance of the distance function and inherent geometric structure of the data. Another interesting set of related problems arises when learning dynamical systems from (human motion) data.