Method and implementation of the formalization system for describing the class of images using nonparametric statistics

The paper deals with the task of formalizing the description of a class of images of a person’s face. The research is aimed at finding methods that increase the accuracy of the description for recognition problems. The existing methods of description are briefly considered, such as nearest neighbor methods, separating hypersurface methods, support hypersurface methods, and probability density function methods. A technique is proposed that makes it possible to reduce the total errors of the first and second kind when describing image classes based on the probability density function. The problem of reconstructing the probability density function is also considered. Based on the experiments carried out, the advantage of the nonparametric Rosenblatt—Parzen method was revealed in comparison with the parametric approach, and a decision was made to apply this method to restore the density function based on experimental data. The recovery of probability density functions based on the Rosenblatt—Parzen method is interrelated with the search for a vector of optimal blur coefficients for each function. To solve this problem, it was proposed to use the gradientless Nelder—Mead method known as the simplex method. As a result:

• The description of the realization of the method of formalized description of the image class based on the reconstruction of the probability density function based on experimental data with the help of the non-parametric Nelder—Mead method was proposed
• Testing of this method was performed in comparison with the classical parametric reconstruction of the probability density function and the advantage of the proposed approach was revealed.