Rigid Structure from Motion from a Blind Source Separation Perspective

Abstract

We present an information theoretic approach to define the problem of structure from motion (SfM) as a blind source separation one. Given that for almost all practical joint densities of shape points, the marginal densities are non-Gaussian, we show how higher-order statistics can be used to provide improvements in shape estimates over the methods of factorization via Singular Value Decomposition (SVD), bundle adjustment and Bayesian approaches. Previous techniques have either explicitly or implicitly used only second-order statistics in models of shape or noise. A further advantage of viewing SfM as a blind source problem is that it easily allows for the inclusion of noise and shape models, resulting in Maximum Likelihood (ML) or Maximum a Posteriori (MAP) shape and motion estimates. A key result is that the blind source separation approach has the ability to recover the motion and shape matrices without the need to explicitly know the motion or shape pdf. We demonstrate that it suffices to know whether the pdf is sub-or super-Gaussian (i.e., semi-parametric estimation) and derive a simple formulation to determine this from the data. We provide extensive experimental results on synthetic and real tracked points in order to quantify the improvement obtained from this technique.