A model based factorization approach for dense 3D recovery from monocular video

Feature track matrix factorization based methods have been attractive solutions to the structure-from-motion (Sfm) problem. Group motion of the feature points is analyzed to get the 3D information. It is well known that the factorization formulations give rise to rank deficient system of equations. Even when enough constraints exist, the extracted models are sparse due the unavailability of pixel level tracks. Pixel level tracking of 3D surfaces is a difficult problem, particularly when the surface has very little texture as in a human face. Only sparsely located feature points can be tracked and tracking errors are inevitable along rotating low texture surfaces. However, the 3D models of an object class lie in a subspace of the set of all possible 3D models. We propose a novel solution to the structure-from-motion problem which utilizes the high-resolution 3D obtained from range scanner to compute a basis for this desired subspace. Adding subspace constraints during factorization also facilitates removal of tracking noise which causes distortions outside the subspace. We demonstrate the effectiveness of our formulation by extracting dense 3D structure of a human face and comparing it with a well known structure-from-motion algorithm due to brand.