Abstract
The article presents the results of a study of the problem of structural synthesis of a vision system and its parametric identification using a new method based on the mathematical apparatus of the theory of modified descriptive image algebras. The theory of modified descriptive image algebras is a mathematical apparatus that allows one to formally describe the processing and analysis of images. In this mathematical apparatus, it is possible to describe the mathematical model of the measurement function of the technical vision system for the selected attribute of the observed object. To develop mathematical models, procedural and parametric transformations of images are used. Any mathematical model in the theory of modified descriptive image algebras has at least one variational parameter. In the course of parametric identification, it is required to calculate their values. This problem is multimodal and always has at least one solution. Numerical methods are usually used to solve the optimization problem. The article describes the algorithm for constructing a mathematical model for measuring the area using procedural and parametric transformations. The parametric identification problem is solved in the form of a nonlinear optimization problem. The visualization of the objective function has been carried out and recommendations for choosing the values of its variational parameters have been formulated. The collection of statistical data was carried out and a histogram was constructed, on the basis of which the distribution law for the measured value is selected. The statistical task of testing the hypothesis with the selected law of distribution of the general population according to the Pearson criterion is solved for a given level of significance. For the unknown parameters of the chosen distribution law, the estimation of confidence intervals was carried out. The materials of the article are applied in nature and have practical value. Using the proposed approach, it is possible to develop a measurement function for any feature of the observed object on a series of images.
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