A morphable model for the synthesis of 3D faces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Journal of Computational Physics
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Object correspondence as a machine learning problem
ICML '05 Proceedings of the 22nd international conference on Machine learning
The Visual Computer: International Journal of Computer Graphics
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Setting the boundary free: a composite approach to surface parameterization
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Geometry for robot path planning
Robotica
IEEE Transactions on Image Processing
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We study nonparametric regression between Riemannian manifolds based on regularized empirical risk minimization. Regularization functionals for mappings between manifolds should respect the geometry of input and output manifold and be independent of the chosen parametrization of the manifolds. We define and analyze the three most simple regularization functionals with these properties and present a rather general scheme for solving the resulting optimization problem. As application examples we discuss interpolation on the sphere, fingerprint processing, and correspondence computations between three-dimensional surfaces. We conclude with characterizing interesting and sometimes counterintuitive implications and new open problems that are specific to learning between Riemannian manifolds and are not encountered in multivariate regression in Euclidean space.