On the Information Rates of the Plenoptic Function

TL;DR

This paper models the plenoptic function to analyze its compression limits, separating camera motion and scene complexity, and provides theoretical bounds that inform optimal coding strategies for static and dynamic visual content.

Contribution

It introduces a stochastic model for the plenoptic function that isolates key information sources and derives sharp coding bounds for static and dynamic scenes.

Findings

Coding practice aligns with theoretical bounds for static scenes.

Dynamic scenes require more complex coding strategies, with simple methods performing suboptimally.

The model provides conditions for tight bounds on lossless and lossy information rates.

Abstract

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.