Dense Batch Non-Rigid Structure from Motion in a Second

In this paper, we show how to minimise a quadratic function on a set of orthonormal matrices using an efficient semidefinite programming solver with application to dense non-rigid structure from motion. Thanks to the proposed technique, a new form of the convex relaxation for the Metric Projections (MP) algorithm is obtained. The modification results in an efficient single-core CPU implementation enabling dense factorisations of long image sequences with tens of thousands of points into camera pose and non-rigid shape in seconds, i.e., at least two orders of magnitude faster than the runtimes reported in the literature so far. The proposed implementation can be useful for interactive or real-time robotic and other applications, where monocular non-rigid reconstruction is required. In a narrow sense, our paper complements research on MP, though the proposed convex relaxation methodology can also be useful in other computer vision tasks. The experimental part providing runtime evaluation and qualitative analysis concludes the paper.