The Variational Structure of Disparity and Regularization of 4D Light Fields

Unlike traditional images which do not offer information for different directions of incident light, a light field is defined on ray space, and implicitly encodes scene geometry data in a rich structure which becomes visible on its epipolar plane images. In this work, we analyze regularization of light fields in variational frameworks and show that their variational structure is induced by disparity, which is in this context best understood as a vector field on epipolar plane image space. We derive differential constraints on this vector field to enable consistent disparity map regularization. Furthermore, we show how the disparity field is related to the regularization of more general vector-valued functions on the 4D ray space of the light field. This way, we derive an efficient variational framework with convex priors, which can serve as a fundament for a large class of inverse problems on ray space.