Video-based descriptors for object recognition
Image and Vision Computing
| Hi-index | 0.00 |
We tackle the problem of compression in the context of decision and control tasks, as opposed to data transmission and storage tasks implicit in traditional communications theory. We focus on the simplest task (binary decision) for channels subject to scaling and occlusion phenomena, ubiquitous in remote sensing and imaging data. In order to extend Rate-Distortion theory, we characterize the tradeoff between decision performance (expected risk) and resources ("rate"). We show that, in the presence of scaling and occlusions, in order to trade off the expected risk, it is necessary to exercise control on the sensing process. Thus the natural generalization of "rate" is not the volume of the data provided by the sensor, but the amount of control authority that can be exercised on it, measured by the volume of the reachable set and the energy of the input. Scaling poses a challenge to traditional Sampling Theory, as there is no Nyquist Frequency, or complexity bound, that can result in a sufficient discretization. This makes the continuous limit in the analysis relevant. Occlusions poses a challenge to worst-case performance bounds (if the object of interest is not manifest in the data, the probability of error in the decision is no better than "chance", i.e., what is offered by the prior). We prove that, when both occlusion and scaling are present, average performance (expected error) is also at chance (Sect. 1 of [1]) if the data is processed in a passive manner. However, we show that if the sensor is afforded infinite control authority (full reach ability, infinite energy), the expected error can be made arbitrarily small (asymptotically) (Sect. 2 of [1]). In between these two extrema, the amount of control authority, that depends on the geometry of state-space (reachable volume and on the energy of the input, trades off performance in the task (expected error). We prove the extremal cases analytically, and characterize the tradeoff empirically (Sect. 3 of [1] and the figure below). We envision, eventually, a Control-Recognition Theory enabling a paradigm shift from a pure exploitation scenario (given the available data, make the best possible decision) to a joint exploration-exploitation scenario (given a desired performance, enact the best sensing-control sequence that achieves it).