Monocular Template-Based Tracking of Inextensible Deformable Surfaces under L ₂-Norm

Abstract

We present a method for recovering the 3D shape of an inextensible deformable surface from a monocular image sequence. State-of-the-art method on this problem [1] utilizes L _∞-norm of reprojection residual vectors and formulate the tracking problem as a Second Order Cone Programming (SOCP) problem. Instead of using L _∞ which is sensitive to outliers, we use L ₂-norm of reprojection errors. Generally, using L ₂ leads a non-convex optimization problem which is difficult to minimize. Instead of solving the non-convex problem directly, we design an iterative L ₂-norm approximation process to approximate the non-convex objective function, in which only a linear system needs to be solved at each iteration. Furthermore, we introduce a shape regularization term into this iterative process in order to keep the inextensibility of the recovered mesh. Compared with previous methods, ours performs more robust to outliers and large inter-frame motions with high computational efficiency. The robustness and accuracy of our approach are evaluated quantitatively on synthetic data and qualitatively on real data.

This work was supported by National Natural Science Foundation of China under Grant 60833009, National 973 Key Basic Research Program of China under Grant 2006CB303103, and Graduate Innovation Foundation of SJTU.