Abstract Unlike traditional images which do not offer information for different directions of incident light, a light ?eld is ?ned 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 ?elds in variational frameworks and show that their variational structure is induced by disparity, which is in t context best understood as a vector ?eld on epipolar plane image space. We derive differential constraints on this vector ?eld to enable consistent disparity map regularization. Furthermore, we show how the disparity ?eld is related to the regularization of more general vector-valued functions on the 4D ray space of the light ?eld. This way, we derive an ef?cient variational framework with convex priors, which can serve as a fundament for a large class of inverse problems on ray space.