Algorithm of classification and recovery of the distorted $n$-dimensional group pointwise objects on the basis of combinatorial search of fragments

The algorithm of classification of multidimensional group pointwise objects samples is presented. Search is carried out on the basis of combinatorial search of proportionate fragments of matrixes of pairwise relations on a set of templates. The decision on assignment of the sample to this or that template is made according to criterion of the minimum Euclidean distance. The presented approach to recognition allows one to synthesize invariant (concerning rotation, scaling or offset of system of co-ordinates) descriptions of secondary signs and to use quite a powerful toolkit of the theory of multidimensional and metric scaling in compensating distortions of the recognized group pointwise objects images. The algorithm implements a procedure of statistical tests of Monte-Carlo, within the frames of which each point, allocated in a random way in a prospective neighborhood of required coordinates, is checked by condition of the minimum of the quadratic similarity measure. The paper gives an example and the results of using the algorithm for identification and recovery of the distorted radio images exposed to coordinate noises and presented by sampling of templates of “brilliant” points.