Visual Information Theory and Visual Representation for Achieving Provable Bounds in Vision-Based Control and Decision.

摘要

This project pursued the development of representations of visual data suitable for control and decision tasks. The fundamental premise is that traditional notions of information developed in support of communication engineering -- where the task is reproduction of the source data, and nuisance factors can be easily characterized statistically -- are unsuited to visual inference, where the task is decision or control, and the data formation process include scaling (that makes the continuous limit relevant) and occlusion (that makes control relevant). Specifically, the task (or classes of task) inform what portion of the data is "informative" and what is "nuisance variability." One of the peculiarities of visual processing is that most of the complexity in visual data can be ascribed to nuisance factors that affect the data but are irrelevant to the task. This notion has been made precise in [16], preceding the commencement of this project, where it was shown that the quotient of the (infinite-dimensional) set of image modulo changes of viewpoint and illumination is supported on a set of measure zero of the image domain. So, for any task that requires invariance to viewpoint and illumination (such as object detection, localization, recognition, categorization), a zero-measure set contains as much "information" as the original data. In other words, information is a thin set of visual data, for decision and control tasks. The development of a theory of information in support of decision and control tasks, specific to visual data, is a long-term goal that has been under development since 2007, and will continue for the foreseeable future. During the course of this project, significant progress has been registered in a number of areas critical to such a development, which is described below.