A Differential-geometric Approach for Globally Solving a Non-convex, Discontinuous Depth Estimation Problem for Plenoptic Camera Images

Abstract

In this paper, we address the problem of estimating a scene's three-dimensional geometry from plenoptic camera images. Existing approaches for this problem have emphasized the development of sharpness and contrast measures for distinguishing between in-/out-of-focus image regions. The ways in which these measures are aggregated can yield erroneous, localized distance fluctuations, though. To deal with such fluctuations, post-processing smoothing techniques can be applied. However, they may remove fine-scale, non-erroneous depth structures and edges. Here, we propose a non-convex, discontinuous cost-function that simultaneously combines and regularizes sharpness and contrast so that valid depth transitions are better preserved. We implicitly convert this function into one that is continuous and (quasi-)convex by optimizing it on the non-positively-curved Riemannian manifold of depth maps with a learned metric.