  In this work, we address the problem of outlier detection for robust motion
estimation by using modern sparse-low-rank decompositions, i.e., Robust
PCA-like methods, to impose global rank constraints. Robust decompositions have
shown to be good at splitting a corrupted matrix into an uncorrupted low-rank
matrix and a sparse matrix, containing outliers. However, this process only
works when matrices have relatively low rank with respect to their ambient
space, a property not met in motion estimation problems. As a solution, we
propose to exploit the partial information present in the decomposition to
decide which matches are outliers. We provide evidences showing that even when
it is not possible to recover an uncorrupted low-rank matrix, the resulting
information can be exploited for outlier detection. To this end we propose the
Robust Decomposition with Constrained Rank (RD-CR), a proximal gradient based
method that enforces the rank constraints inherent to motion estimation. We
also present a general framework to perform robust estimation for stereo Visual
Odometry, based on our RD-CR and a simple but effective compressed optimization
method that achieves high performance. Our evaluation on synthetic data and on
the KITTI dataset demonstrates the applicability of our approach in complex
scenarios and it yields state-of-the-art performance.
