The features for recognition of projectively deformed point sets

The paper deals with features of a point set which are invariant with respect to the projective transform. First, some properties of the area of a triangle under a projective transform and the cross-ratio are discussed. Two types of projective triangular invariants of point sets are derived. One of them is a quotient of two different products of the areas of triangles formed by the vertices of the polygon. It is invariant to the labeling of the vertices. The number of the features is discussed and a method for its reduction is presented. The other type of features is expressed as functions of a five-point cross-ratios and it is invariant to the choice of labeling of the points. The possibility of the normalization of these invariants is shown. The performance of the features is demonstrated by numerical experiments.