Recovering thin structures via nonlocal-means regularization with application to depth from defocus

We propose a novel scheme to recover depth maps containing thin structures based on nonlocal-means filtering regularization. The scheme imposes a distributed smoothness constraint by relying on the assumption that pixels with similar colors are likely to belong to the same surface, and therefore can be used jointly to obtain a robust estimate of their depth. This scheme can be used to solve shape-from-X problems and we demonstrate its use in the case of depth from defocus. We cast the problem in a variational framework and solve it by linearizing the corresponding Euler-Lagrange equations. The linearized system is then inverted by using efficient numerical methods such as successive overrelaxations or more general methods such as conjugate gradient when the system is not diagonally dominant. One of the main benefits of this formulation is that it can handle the regularization of highly fragmented surfaces, which require large neighborhood structures typically difficult to solve efficiently with graph-based methods. We compare the performance of the proposed algorithm with methods recently proposed in the literature that are analogous to neighborhood filters. Finally, experimental results are shown on synthetic and real data.