Barkova A.Yu., Klyachin V.A. On the Application of Curvature Operators to Problems of Object Recognition in Images

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https://doi.org/10.15688/mpcm.jvolsu.2026.2.2

Anastasia Y. Barkova
Master’s Student of the MOSm-251 Group, Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Vladimir A. Klyachin
Doctor of Sciences (Physics and Mathematics), Head of Department of Computer Sciences and Experimental Mathematics, Volgograd State University
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https://orcid.org/0000-0003-1922-7849

Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. 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.

Key words: image classification, Gaussian curvature, mean curvature, Sobel operator, machine learning.

Barkova A.Yu., Klyachin V.A. On the Application of Curvature Operators to Problems of Object Recognition in Images is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 29 No. 2 2026, pp. 20-29

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