Proximal robust factorization for piecewise planar reconstruction

In this paper, we aim to obtain a dense piecewise planar reconstruction of the scene from multiple image frames based on a factorization framework. Integrating all the relevant constraints in a global objective function, we are able to effectively leverage on the scene smoothness prior afforded by the dense formulation, as well as imposing the necessary algebraic constraints required by the shape matrix. These constraints also help to robustly decompose the measurement matrix into the underlying low-rank subspace and the sparse outlier part. Numerically, we achieve the constrained factorization and decomposition via modifying a recently proposed proximal alternating robust subspace minimization algorithm. The results show that our algorithm is effective in handling real life sequences, and outperforms other algorithms in recovering motions and dense scene estimate.