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The CMA-ES on Riemannian Manifolds to Reconstruct Shapes in 3-D Voxel Images

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4 Author(s)
Colutto, S. ; Infmath Imaging Group, Univ. of Innsbruck, Innsbruck, Austria ; Fruhauf, F. ; Fuchs, M. ; Scherzer, O.

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.

Published in:

Evolutionary Computation, IEEE Transactions on  (Volume:14 ,  Issue: 2 )