A quantitative analysis of view degeneracy and its use for active focal length control

We quantify the observation by Kender and Freudenstein (1987) that degenerate views occupy a significant fraction of the viewing sphere surrounding an object. This demonstrates that systems for recognition must explicitly account for the possibility of view degeneracy. We show that view degeneracy cannot be detected from a single camera viewpoint. As a result, systems designed to recognize objects from a single arbitrary viewpoint must be able to function in spite of possible undetected degeneracies, or else operate with imaging parameters that cause acceptably low probabilities of degeneracy. To address this need, we give a prescription for active control of focal length that allows a principled tradeoff between the camera field of view and probability of view degeneracy