Anisotropic Distributions on Manifolds: Template Estimation and Most Probable Paths

  • Stefan SommerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9123)


We use anisotropic diffusion processes to generalize normal distributions to manifolds and to construct a framework for likelihood estimation of template and covariance structure from manifold valued data. The procedure avoids the linearization that arise when first estimating a mean or template before performing PCA in the tangent space of the mean. We derive flow equations for the most probable paths reaching sampled data points, and we use the paths that are generally not geodesics for estimating the likelihood of the model. In contrast to existing template estimation approaches, accounting for anisotropy thus results in an algorithm that is not based on geodesic distances. To illustrate the effect of anisotropy and to point to further applications, we present experiments with anisotropic distributions on both the sphere and finite dimensional LDDMM manifolds arising in the landmark matching problem.


Template estimation Manifold Diffusion Geodesics Frame bundle Most probable paths Anisotropy 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.DIKUUniversity of CopenhagenCopenhagenDenmark

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