Joint Estimation of Depth Map and Focus Image in SFF: An Optimization Framework by Sparsity Approach

In this paper, we addressed the problem of estimating the 3D structure of an object from Shape-from-focus (SFF) cue by utilizing sparsity techniques. A set of space-variantly defocused images acquired with respect to relative motion between image capturing device and the specimen is considered to obtain the shape and depth of the 3D target image by calculating the focus points. The estimation of clear image and 3D shape is posed as an inverse-problem. As inverse problems are typically ill-posed and has several solutions. Hence we use a prior information to regularize the solution. In this work, we have shown the results for various types of sparsity based and Markov random field priors and their effects on the solution of the ill-posed shape estimation problem. Initially, latent clear image of the 3D target is well reconstructed from the huge stack of captured images. We have shown the experimental results for various synthetic and real case with different priors and optimization techniques. Since, we need to employ the integral stack of space-variantly defocused pictures, we analyze the possibility of estimation of both the focused image and the 3D structure of the target image. Since, this work is a severely ill-posed inverse-problem we use prior information of both the quantities to be estimated in an alternating minimization approach.