Convex Optimization for Nonrigid Stereo Reconstruction

We present a method for recovering 3-D nonrigid structure from an image pair taken with a stereo rig. More specifically, we dedicate to recover shapes of nearly inextensible deformable surfaces. In our approach, we represent the surface as a 3-D triangulated mesh and formulate the reconstruction problem as an optimization problem consisting of data terms and shape terms. The data terms are model to image keypoint correspondences which can be formulated as second-order cone programming (SOCP) constraints using
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norm. The shape terms are designed to retaining original lengths of mesh edges which are typically nonconvex constraints. We will show that this optimization problem can be turned into a sequence of SOCP feasibility problems in which the nonconvex constraints are approximated as a set of convex constraints. Thanks to the efficient SOCP solver, the reconstruction problem can then be solved reliably and efficiently. As opposed to previous methods, ours neither involves smoothness constraints nor need an initial estimation, which enables us to recover shapes of surfaces with smooth, sharp and other complex deformations from a single image pair. The robustness and accuracy of our approach are evaluated quantitatively on synthetic data and qualitatively on real data.