GEOMETRIC INVARIANTS AND OBJECT RECOGNITION

We discuss the role of the general invariance concept in object recognition, and review the classical and recent literature on projective invariance. Invariants help solve major problems of object recognition. For instance, different images of the same object often differ from each other, because of the different viewpoint from which they were obtained. To match the two images, common methods thus need to find the correct viewpoint, a difficult problem that can involve search in a high dimensional space of all possible points of view and/or finding point correspondences. Geometric invariants are shape descriptors, computed from the geometry of the shape, that remain unchanged under geometric transformations such as changing the viewpoint. Thus they can be matched without search. Deformations of objects are another important class of geometric changes for which invariance is useful.