Homeomorphic alignment of weighted trees

Motion capture, a currently active research area, needs estimation of the pose of the subject. For this purpose, we match the tree representation of the skeleton of the 3D shape to a pre-specified tree model. Unfortunately, the tree representation can contain vertices that split limbs in multiple parts, which do not allow a good match by usual methods. To solve this problem, we propose a new alignment, taking into account the homeomorphism between trees, rather than the isomorphism, as in prior works. Then, we develop several computationally efficient algorithms for reaching real-time motion capture.