Accurate Structure Recovery via Weighted Nuclear Norm: A Low Rank Approach to Shape-from-Focus

Abstract

In recent years, weighted nuclear norm minimization (WNNM) approach has been attracting much interest in computer vision and machine learning. Due to the ability of WNNM to preserve large-scale sharp discontinuities and small-scale fine details more effectively, we propose to use it as a regularizer to recover the 3D structure using shape-from-focus (SFF). Initially, we estimate the All-in-focus image and subsequently 3D structure is recovered using space-variantly blurred observations from the SFF stack. Since estimation of 3D shape is a severely ill-posed problem, we use weighted nuclear norm as a regularizer in the proposed algorithm. Finally, the estimated shape profile is post-processed to compensate for the effect of specular reflections in the observations on shape reconstruction. We conducted several experiments on various synthetic and real-world datasets and our results confirm that the proposed method outperforms other state-of-the-art techniques.