Recovery of relative depth from a single observation using an uncalibrated (real-aperture) camera

In this paper we investigate the challenging problem of recovering the depth layers in a scene from a single defocused observation. The problem is definitely solvable if there are multiple observations. In this paper we show that one can perceive the depth in the scene even from a single observation. We use the inhomogeneous reverse heat equation to obtain an estimate of the blur, thereby preserving the depth information characterized by the defocus. However, the reverse heat equation, due to its parabolic nature, is divergent. We stabilize the reverse heat equation by considering the gradient degeneration as an effective stopping criterion. The amount of (inverse) diffusion is actually a measure of relative depth. Because of ill-posedness we propose a graph-cuts based method for inferring the depth in the scene using the amount of diffusion as a data likelihood and a smoothness condition on the depth in the scene. The method is verified experimentally on a varied set of test cases.