Lossy compression of active sources

In computer vision, an active vision source is a sensor that explores its environment in an active way, deciding to investigate parts of the environment in greater depth based on what it currently sees. We study the problem of determining the rate required to compress the output of an active vision source to within a desired fidelity. In order to make the problem analytically tractable, we assume that the environment is memoryless and gain insights into the distinction between compression of passive and active sources. We show that modelling of the sources is crucial by considering two extreme cases: adversarially active sources and helpful active sources. The theory of arbitrarily varying sources is useful for these purposes and we expand on it by allowing the party controlling the variation in the source to have partial or noisy observations of the environment. We give several examples showing that there is a large difference in the rate required to compress active sources that are adversarially modelled and active sources that are jointly optimized with the coding system. The results suggest that when active sources are part of a networked system where rate comes at a premium, large savings can be reaped by jointly optimizing the coding system with the computer vision system.