  The {\it plenoptic function} (Adelson and Bergen, 91) 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,
and represent large amounts of information. In this paper we propose a
stochastic model to study the compression limits 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 transmitted. The
sources of information are combined, generating a stochastic 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
accordance with optimal coding from an information-theoretic standpoint. 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 in the presence of scene dynamics,
simple hybrid coding using motion/displacement estimation with DPCM performs
considerably suboptimally relative to the true rate-distortion bound.
