Institute of Image Processing and Pattern Recognition,Shanghai Jiao Tong University, Shanghai 200240, China.
IEEE Trans Image Process. 2010 Feb;19(2):512-21. doi: 10.1109/TIP.2009.2038115. Epub 2009 Dec 8.
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(infinity)-norm of reprojection residual vectors and formulate the tracking problem as a Second-Order Cone Programming (SOCP) problem. Instead of using L(infinity) 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.
我们提出了一种从单目图像序列中恢复不可伸缩变形表面的三维形状的方法。在这个问题上的最新方法，利用重投影残差向量的 L(infinity)范数，并将跟踪问题表述为二阶锥规划（SOCP）问题。我们不使用对离群值敏感的 L(infinity)，而是使用重投影误差的 L(2)范数。通常，使用 L(2)会导致非凸优化问题，难以最小化。我们不直接解决非凸问题，而是设计一个迭代的 L(2)范数逼近过程来逼近非凸目标函数，其中在每次迭代中只需要求解一个线性系统。此外，我们在这个迭代过程中引入了一个形状正则化项，以保持恢复网格的不可伸缩性。与以前的方法相比，我们的方法在处理图像噪声、离群值和大的帧间运动时具有更高的鲁棒性和计算效率。我们的方法的鲁棒性和准确性在合成数据和真实数据上进行了定量评估。
