Vertex-based features for recognition of projectively deformed polygons

摘要

The paper deals with features of a general polygon which are invariant with respect to projective transform. First, some properties of the area of a triangle under projective transform are discussed. New projective triangular invariants of polygons are derived as the quotient of two different products of the areas of triangles formed by the vertices of the polygon. The features are proved to be invariant to numbering of the vertices of the polygon. The number of projective triangular invariants for polygons with a given number of vertices is derived. A method for reduction of the number of invariants in the case of polygons with a high number of vertices is presented. Numerical experiments dealing with three octagons and one polygon with 18 vertices deformed by projective transforms are described.