Sparse Bayesian learning for image rectification with transform invariant low-rank textures

A Bayesian version of transform invariant low-rank textures (TILT) is proposed.The robust Bayesian TILT can handle more complex cases, especially with corruptions.Theoretical analyses and statistical evidences of the Bayesian TILT are provided.Variational Bayesian approach is exploited to implement the Bayesian inference. Comparing to the low-level local features, transform invariant low-rank textures (TILT) can in some sense globally rectify a large class of low-rank textures in 2D images, and thus more accurate and robust. However, the existing algorithms based on the alternating direction method (ADM) and the linearized alternating direction method with adaptive penalty (LADMAP), suffer from the weak robustness and the local minima, especially with plenty of corruptions and occlusions. In this paper, instead of exploiting optimization methods, we propose to build a hierarchical Bayesian model to TILT and then a variational method is implemented for Bayesian inference. Instead of point estimation, the proposed Bayesian approach introduces the uncertainty of the parameters, which has been proven to have much less local minima. Experimental results on both synthetic and real data indicate that our new algorithm outperforms the existing algorithms especially for the case with corruptions and occlusions.