3D orthographic reconstruction based on robust factorization method with outliers

It is well known that both shape and motion can he factorized directly from the measurement matrix constructed from feature points trajectories under orthographic camera model. In practical applications, the measurement matrix might he contaminated by noises and contains outliers and missing values. A direct SVD (singular value decomposition) to the measurement matrix with outliers would yield erroneous result. In this paper we present a new algorithm for computing SVD by linear l₁-norm regression and apply it to structure from motion problem. It is robust to outliers and can handle missing data naturally. The linear regression problem is solved using weighted-median algorithm and is simple to implement. The proposed robust factorization method with outliers can improve the reconstruction result remarkably. Quantitative and qualitative experiments illustrate the good performance of our approach.