On the Information Rates of the Plenoptic Function
The plenoptic function describes the visual information available to an observer at any point in space and time. Samples of the plenoptic function (POF) are seen in video and in general visual content (images, mosaics, panoramic scenes, etc.), and rep- resent large amounts of information. In this paper, we propose a stochastic model to study the compression limits of a simplified version of the plenoptic function. In the proposed framework, we isolate the two fundamental sources of information in the POF: the one representing the camera motion and the other representing the information complexity of the “reality” being acquired and trans- mitted. The sources of information are combined, generating a sto- chastic process that we study in detail. We first propose a model for ensembles of realities that do not change over time. The proposed model is simple in that it enables us to derive precise coding bounds in the information-theoretic sense that are sharp in a number of cases of practical interest. For this simple case of static realities and camera motion, our results indicate that coding practice is in accor- dance with optimal coding from an information-theoretic stand- point. The model is further extended to account for visual realities that change over time. We derive bounds on the lossless and lossy information rates for this dynamic reality model, stating conditions under which the bounds are tight. Examples with synthetic sources suggest that within our proposed model, common hybrid coding using motion/displacement estimation with DPCM performs con- siderably suboptimally relative to the true rate-distortion bound.