The object of the research is the statistical analysis of angular and linear coordinates obtained from the technical vision system (TVS). The subject of the research is a linear regression model constructed based on the coordinates of the objects. The goal of the research is to conduct a statistical analysis of the observed objects to determine their coordinate relationships and to build an optimal regression model. Multivariate linear regression is considered using the example of three observed objects, each of which has four features within a specified coordinate range. Two coordinate features are defined on the camera matrix as pixel coordinates x and y in Cartesian axes, while the third and fourth features are recognized by technical vision as the object's distance z and its angular rotation of the image. The main task is to determine the optimal regression line, which will represent the trajectory of the main optical axis of the camera during the video recording of the objects. The software part is implemented using Python in the PyCharm environment, according to the presented mathematical framework. Training of the regression model has been conducted using programming gradient descent loops based on the system of equations for the slope and shift coefficients of the linear function. The coordinate dependencies are considered from the perspective of correlation. A heat map is presented that reflects the degree of the Pearson correlation coefficient. Using the mean squared error (MSE) function, an optimal regression model has been built, which, due to the chosen coordinate intervals, has a linear coverage of the observed objects within the camera's field of view. Machine learning regression using gradient descent has minimized the slope error of the regression line. The work aims to increase the accuracy of the statistical analysis of the observed objects and the linear regression model constructed based on the coordinates of these objects. The results presented can be applied in combined guidance and video surveillance systems. In this case, the video surveillance channel will determine the coordinates of the object, while the guidance system will align the main optical axis along the optimal linear trajectory. The determination of more precise and in-depth statistical analysis of the angular and linear coordinates of several observed objects using machine learning is an evolving direction for modern systems of statistical analysis.
Mihed et al. (Thu,) studied this question.