A Geometric Approach to Motion Tracking in Manifolds

In many multi-dimensional tracking problems, the quantities of interest are restricted to a manifold in observation space. Learning the manifold shape is a necessary step for dimensionality reduction, which in turn allows faster and more robust tracking performance. For manifolds with arbitrary topology, learning the shape from noisy scattered data is not trivial. This paper presents a geometric approach that is valid for arbitrary manifold dimension and topology. An approximation of the tangent bundle is computed by region growing, making it possible to estimate a set of manifold charts. A tracking algorithm which takes advantage of the geometric information thus found is also presented. Copyright © 2002 IFAC