Monocular 3-D Tracking of Inextensible Deformable Surfaces Under $L_2$ -Norm

We present a method for recovering the 3-D shape of an inextensible deformable surface from a monocular image sequence. State-of-the-art methods on this problem, utilize
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 nonconvex optimization problem which is difficult to minimize. Instead of solving the nonconvex problem directly, we design an iterative
L

₂
-norm approximation process to approximate the nonconvex 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 image noises, outliers and large interframe motions with high computational efficiency. The robustness and accuracy of our approach are evaluated quantitatively on synthetic data and qualitatively on real data.