The CMA-ES on Riemannian manifolds to reconstruct shapes in 3-D voxel images

Authors:
Sebastian Colutto;Florian Frühauf;Matthias Fuchs;Otmar Scherzer
Affiliations:
Infmath Imaging Group, University of Innsbruck, Innsbruck, Austria;MED-EL GmbH, Innsbruck Austria and Infmath Imaging Group, University of Innsbruck, Innsbruck, Austria and IMCC, MathConsult GmbH, Linz, Austria;GP Solar Inspect GmbH, Planegg, Germany and Infmath Imaging Group, University of Innsbruck, Innsbruck, Austria and University of Linz, Linz, Austria;Computational Science Center, University of Vienna, Vienna, Austria and Infmath Imaging Group, University of Innsbruck, Innsbruck, Austria and Radon Institute of Computational and Applied Mathemat ...
Venue:
IEEE Transactions on Evolutionary Computation
Year:
2010

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Abstract

The covariance matrix adaptation evolution strategy (CMA-ES) has been successfully used to minimize functionals on vector spaces. We generalize the concept of the CMA-ES to Riemannian manifolds and evaluate its performance in two experiments. First, we minimize synthetic functionals on the 2-D sphere. Second, we consider the reconstruction of shapes in 3-D voxel data. A novel formulation of this problem leads to the minimization of edge and region-based segmentation functionals on the Riemannian manifold of parametric 3-D medial axis representation. We compare the results to gradient-based methods on manifolds and particle swarm optimization on tangent spaces and differential evolution.