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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Daniel Tenbrinck
University of Muenster
Title: Graph Methods for Manifold-Valued Data

Abstract: Due to recent technological advances in the development of modern sensors new imaging modalities have emerged for which the acquired data values are given on a Riemannian manifold. This is the case, e.g., when dealing with Interferometric Synthetic Aperture Radar (InSAR) data consisting of phase values or data obtained in Diffusion Tensor Magnetic Resonance Imaging (DT-MRI), where each measurement is a positive definite matrix of size 3x3. Furthermore, the data might not be given on a rectangular pixel grid but on a surface or a manifold itself. For these emerging imaging fields novel image processing techniques have to be developed and adapted.

In this talk we present a framework for processing discrete manifold-valued data, for which the underlying (sampling) topology is modeled by a graph. We introduce the notion of a manifold-valued derivative on a graph and based on this deduce a family of manifold-valued graph p-Laplacian operators. We propose an efficient numerical scheme to compute a solution to the corresponding parabolic PDEs and apply this algorithm to different manifold-valued data, illustrating the diversity and flexibility of the proposed framework.

This is joint work with Ronny Bergmann (TU Kaiserslautern).

Recording: http://mm.math.cmu.edu/recordings/cna/DanielTenbrinck_small2.mp4
Date: Thursday, February 23, 2017
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Slepcev