Local invariants for recognition

Geometric invariants are shape descriptors that remain unchanged under geometric transformations such as projection or changing the viewpoint. A new method of obtaining local projective and affine invariants is developed and implemented for real images. Being local, the Invariants are much less sensitive to occlusion than global invariants. The invariants´ computation is based on a canonical method. This consists of defining a canonical coordinate system by the intrinsic properties of the shape, independently of the given coordinate system. Since this canonical system is independent of the original one, it is invariant and all quantities defined in it are invariant. The method was applied without the use of a curve parameter. This was achieved by fitting an implicit polynomial to an arbitrary curve in a vicinity of each curve point. Several configurations are treated: a general curve without any correspondence and curves with known correspondences of one or two feature points or lines. Experimental results for different 2D objects in 3D space are presented