A Measure of Vision Distance for Optimization of Camera Networks

is dissertation proposes a solution to the problem of multi-camera deployment for optimization of visual coverage and image quality. Image quality and coverage are, by nature, difficult to quantify objectively. However, the chief difficulty is that, in the most general case, image quality and coverage are functions of many parameters, thus making any model of the vision system inherently complex. Additionally, these parameters are members of metric spaces that are not compatible amongst themselves under any known operators. is dissertation borrows the idea of transforming the mathematical definitions that describe the vision system into geometric constraints, and sets out to construct a geometrical model of the vision system. e vision system can be divided into two different concepts: the camera and the task. Whereas the camera has a set of parameters that describe it, the task also has a set of task parameters that quantify the visual requirements. e definition of the proposed geometric model involves the construction of a tensor; a mathematical construct of high dimensionality which enables a representation of the camera or the task. e tensor-based representation of these concepts is a powerful tool because it brings a large tool set from various disciplines such as differential geometry. e contributions of this dissertation are twofold. Firstly, a new distance function that effectively measures the distance between two visual entities is presented based on the geometrical model of the vision system. A visual entity may be a camera or a task. is distance is termed the Vision Distance and it measures the closeness to the optimal state for the configuration between the camera and the task. Lastly, a deployment method for multi-camera networks based on convex optimization is presented. Using second-order cone programming, this work shows how to optimize the position and orientation of a camera for maximum coverage of a task. is dissertation substantiates all of these claims. e vision distance is validated and compared to an existing model of visual coverage. Additionally, simulations, experiments, and comparisons show the efficacy of the proposed deployment method.