Non-parametric Regression between Riemannian Manifolds

Steinke, F; Hein, M

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Non-parametric Regression between Riemannian Manifolds

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Steinke, F
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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https://papers.nips.cc/paper/3561-non-parametric-regression-between-manifolds.pdf
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Citation

Steinke, F., & Hein, M. (2009). Non-parametric Regression between Riemannian Manifolds. In D. Koller, D. Schuurmans, Y. Bengio, & L. Bottou (Eds.), Advances in neural information processing systems 21 (pp. 1561-1568). Red Hook, NY, USA: Curran.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C497-4

Abstract

This paper discusses non-parametric regression between Riemannian manifolds. This learning problem arises frequently in many application areas ranging from signal processing, computer vision, over robotics to computer graphics. We present a new algorithmic scheme for the solution of this general learning problem based on regularized empirical risk minimization. The regularization functional takes into account the geometry of input and output manifold, and we show that it implements a prior which is particularly natural. Moreover, we demonstrate that our algorithm performs well in a difficult surface registration problem.