New derivation of projective and permutation invariants

A simple and effective method for the representation and computation of the projective and permutation invariants of point sets is presented.These invariants are important in computer vision and pattern recognition.The projective and permutation invariant of four distinct points on a projective line based on a simple symmetric function is derived first.This projective and permutation invariant takes one of the six raw cross ratios of the four points as its value.The computational complexity is low and the discriminating power is retained.Then two functional independent projective and permutation invariants of five points on the projective plane and three functional independent projective and permutation invariants of six points in the space are derived based on the proposed simple symmetric function and the elementary symmetric polynomials.