The discrete projective transformations on the coordinate plane

The direct and inverse Discrete Projective Transformations (DPT) have been found and analyzed. Hie transformations are based on the fundamental property of the cross ratio of the four co-linear points to be the projective invariant. The operators of the transformation are determined in the three dimensional local basis, through coordinates of the four points on the two-dimensional plane. The main proprties of DPT are: optimal linear classification of points on the family of linear and (or) quadratic functions, decrease of the power of the polynomial by two, invariant with respect to the shift and stable to errors of measurements every where, exept two noise points. The examples of using DPT for solving some practical problems are given (pattern recognition and filtration of points on the samples of tracks and so on).