Probabilistic Aane Invariants for Recognition

Under a weak perspective camera model, the image plane coordinates in diierent views of a planar object are related by an aane transformation. Because of this property, researchers have attempted to use aane invariants for recognition. However, there are two problems with this approach: (1) objects or object classes with inherent variability cannot be adequately treated using invariants; and (2) in practice the calculated aane invariants can be quite sensitive to errors in the image plane measurements. In this paper we use probability distributions to address both of these diiculties. Under the assumption that the feature positions of a planar object can be modeled using a jointly Gaussian density, we have derived the joint density over the corresponding set of aane coordinates. Even when the assumptions of a planar object and a weak perspective camera model do not strictly hold, the results are useful because deviations from the ideal can be treated as deformability in the underlying object model.