3D Human Pose Tracking Priors using Geodesic Mixtu

Authors: Edgar SimoSerra Carme Torras Francesc MorenoNoguer

Publish Date: 2016/08/24

Volume: 122, Issue: 2, Pages: 388-408

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Abstract

We present a novel approach for learning a finite mixture model on a Riemannian manifold in which Euclidean metrics are not applicable and one needs to resort to geodesic distances consistent with the manifold geometry For this purpose we draw inspiration on a variant of the expectationmaximization algorithm that uses a minimum message length criterion to automatically estimate the optimal number of components from multivariate data lying on an Euclidean space In order to use this approach on Riemannian manifolds we propose a formulation in which each component is defined on a different tangent space thus avoiding the problems associated with the loss of accuracy produced when linearizing the manifold with a single tangent space Our approach can be applied to any type of manifold for which it is possible to estimate its tangent space Additionally we consider using shrinkage covariance estimation to improve the robustness of the method especially when dealing with very sparsely distributed samples We evaluate the approach on a number of situations going from data clustering on manifolds to combining pose and kinematics of articulated bodies for 3D human pose tracking In all cases we demonstrate remarkable improvement compared to several chosen baselinesWe would like to thank the three anonymous reviewers for their insights and comments that have significantly contributed to improving this manuscript This work was partly funded by the Spanish MINECO project RobInstruct TIN201458178R and by the ERAnet CHISTERA project IDRESS PCIN2015147Plot of the change Frobenius norm of fracpartial log mu kxipartial mu k We compute the derivative numerically using a first order approximation as there is no analytic form We can see for points near the center there is small change in the derivative and thus little error in the approximation we make by considering the derivative to be constant For visualization purposes we only display points with a change of under 10 units

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