Affine and Projective Normalization of Planar Curves and Regions

Recent research has showed that invariant indexing can speed up the recognition process in computer vision. Extraction of invariant features can be done by choosing rst a canonical reference frame, and then features in this reference frame. These automatically become invariants. In this paper methods are given where a global and stable approach is used both in choosing the canonical reference frame and in the extraction of invariants for aane and projective transformations. These invariants can be used to recognize fairly general feature conngurations, and they can be used in a semi-local way to recognize occluded objects. In the aane case a unique distinguished reference frame can be chosen in a continuous way with respect to the Hausdorr metric. In the projective case this is impossible, since arbitrarily close to every pair of closed curves exists a projectively equivalent pair. However, by sacriicing uniqueness it is possible to construct useful projective normalization schemes. In the case where more information is at hand, e.g. when the curve has a concavity, the reference frame can still be chosen in a unique way.