Robust Statistical Estimation and Segmentation of Multiple Subspaces

We study the problem of estimating a mixed geometric model of multiple subspaces in the presence of a significant amount of outliers. The estimation of multiple subspaces is an important problem in computer vision, particularly for segmenting multiple motions in an image sequence. We first provide a comprehensive survey of robust statistical techniques in the literature, and identify three main approaches for detecting and rejecting outliers. Through a careful examination of these approaches, we propose and investigate three principled methods for robustly estimating mixed subspace models: random sample consensus, the influence function, and multivariate trimming. Using a benchmark synthetic experiment and a set of real image sequences, we conduct a thorough comparison of the three methods