Point-based projective invariants

The paper deals with features of a 2-D point set which are invariant with respect to a projective transform. First, projective invariants for five-point sets, which are simultaneously invariant to the projective transform and to permutation of the points, are derived. They are expressed as functions of five-point cross-ratios. Then, the invariants for more than five points are derived. The algorithm for searching the correspondence between the points of two 2-D point sets is presented. The algorithm is based on the comparison of two projective and permutation invariants of five-tuples of the points. The best-matched five tuples are then used for the computation of the projective transformation and that with the maximum of corresponding points is used. Stability and discriminability of the features and behavior of the searching algorithm are demonstrated by numerical experiments. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.