On the Application of Curvature Operators to Problems of Object Recognition in Images

This paper is dedicated to the solution of the problem of classifying objects in images using classical machine learning methods. Approximate values of the Gaussian and mean curvatures of the surface of the luminance function plot for each color component of a point in the image were chosen as sources for generating the feature vector. The basis for applying these values is the classical theorems on the uniqueness and stability of solutions to Dirichlet boundary value problems for the corresponding partial differential equations. The above approximate values are calculated using Sobel operators, an implementation of which is built into the OpenCV computer vision library. Testing was conducted on several datasets using various machine learning methods. The results demonstrated the high effectiveness of the proposed method for detecting objects with distinct shapes.