A Computational Model of View Degeneracy

We quantify the observation by Kender and Freudenstein [24] that degenerate views occupy a significant fraction of the viewing sphere surrounding an object. For a perspective camera geometry, we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a polyhedral object. For a typical recognition system parameterization, view degeneracies typically occur with probabilities of 20% and, depending on the parameterization, as high as 50%. We discuss the impact of view degeneracy on the problem of object recognition and, for a particular recognition framework, relate the cost of object disambiguation to the probability of view degeneracy. To reduce this cost, we incorporate our model of view degeneracy in an active focal length control paradigm that balances the probability of view degeneracy with the camera field of view. In order to validate both our view degeneracy model as well as our active focal length control model, a set of experiments are reported using a real recognition system operating on real images.