Incorporating constraints and prior knowledge into factorization algorithms - an Application to 3D recovery
Matrix factorization is a fundamental building block in many computer vision and machine learning algorithms. For example, the problem of ''structure from motion'' in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations may be reduced to a low rank factorization problem. When all the 2D locations are known, singular value decomposition yields a least squares factorization of the measurements matrix. But in realistic scenarios, some of the data is missing, the measurements have correlated noise, and the scene may contain multiple objects. Under these conditions, most existing factorization algorithms fail while human perception is relatively unchanged. This work presents an EM algorithm for matrix factorization while taking advantage of prior information as well as imposing strict constraints on the resulting matrix factors. We present results on challenging sequences.