3D dynamics analysis in Teichmüller space

Dynamics analysis for 3D surface sequence is an important task in vision. In this work, 2D shape analysis method [16] based on Teichmüller space theory is generalized to handle deforming surfaces. Two surfaces are conformally equivalent if they can be mapped to each other by an angle preserving map. Each equivalence class has a unique fingerprint, the conformal module. The Teichmuller space is the shape space of all classes, which is of finite dimension and equipped with a Riemannian metric. Conformal module is treated as the Teichmuller space coordinates. A Sequence of deforming 3D surfaces is converted to a curve in the shape space, which allows more effective 3D dynamics analysis. The method can handle genus zero surfaces with all kinds of topologies and with large deformations. The algorithm for computing Teichmuller coordinates is fully automatic, efficient and robust. Experiments on large scale raw 3D surface sequences for key frame selection, motion symmetry detection and deformation intensity estimation demonstrate the efficiency and efficacy of the method.