Motion tracking in manifolds with tangent bundle approximation

Abstract

In multi-dimensional tracking problems, the parameter.; to track are often restricted to a manifold embedded in observation space. Learning the manifold shape is useful for dimensionality reduction, lightening the computational load and simplifying the related problem of learning the dynamics. For manifolds with arbitrary topology, learning the shape from noisy scattered data presents several difficuties. This paper presents a geometric approach that addresses such difficulties. The proposed Tangent Bundle Approximation (TBA) algorithm is valid for arbitrary manifold dimension and topology. An approximation of the tangent bundle is computed, making it possible to estimate a set of manifold charts. This geometric information is then used to estimate the trajectory dynamics with a standard spline algorithm. Experimental results are presented for face tracking based on a real video sequence. The proposed method is general in scope and can be applied in any tracking problem, provided that the manifold restriction is verified.