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

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.