In the metamorphosis approach the space of images is considered as a Riemannian manifold. In this talk, we focus on the computation of time discrete geodesics defined as minimizers of time discrete path energies. Here, images are either considered as square-integrable intensity functions or regarded as a superposition of sparse signals convoluted with structure classifying learned kernels. In the first case, the Gamma-convergence of the time discrete model to the time continuous model is discussed.

This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .

Authors:

Alexander Effland (Universität Bonn)

Benjamin Berkels (RWTH Aachen University)

Martin Rumpf (University of Bonn)

Erich Kobler (Graz University of Technology)

Thomas Pock (Graz University of Technology)

Keywords:

convolutional network, gamma-convergence, geodesics, image metamorphosis, image registration, image representation, nonlinear optimization, time discretization