Recognition with Invariants

Invariant measures like the cross ratio contain shape information. This can be used in several ways, for instance to identify objects seen by a camera. For simplicity, we will restrict ourselves to planar objects here, so that the mapping from scene points to image ones is one to one. The full 3D case is harder. For example, no 3D invariant can be extracted from a single perspective image of a set of general 3D points, unless something further is known about the point configuration (for instance, that some of them are coplanar). For 3D invariants from two images, see [7]. For an overview of projective invariants for planar shape recognition, see [22].