TY - JOUR T1 - Large-scale matrix factorization with missing data under additional constraints JF - Advances in Neural Information Processing Systems Y1 - 2010 A1 - Mitra, K. A1 - Sheorey,S. A1 - Chellapa, Rama AB - Matrix factorization in the presence of missing data is at the core of many com-puter vision problems such as structure from motion (SfM), non-rigid SfM and photometric stereo. We formulate the problem of matrix factorization with miss- ing data as a low-rank semidefinite program (LRSDP) with the advantage that: 1) an efficient quasi-Newton implementation of the LRSDP enables us to solve large-scale factorization problems, and 2) additional constraints such as ortho- normality, required in orthographic SfM, can be directly incorporated in the new formulation. Our empirical evaluations suggest that, under the conditions of ma- trix completion theory, the proposed algorithm finds the optimal solution, and also requires fewer observations compared to the current state-of-the-art algorithms. We further demonstrate the effectiveness of the proposed algorithm in solving the affine SfM problem, non-rigid SfM and photometric stereo problems. VL - 23 ER -