Method for analyzing geometric parameters of particles and constructing their distributions based on micrograph segmentation data using parameterized polygons

Kasyanov A.V., Babina K.A., Parkhomchuk E.V.
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The accurate characterization of particle size and morphology is crucial across numerous scientific and industrial fields. While microscopy is a powerful tool for visualizing particle geometry, traditional image analysis often relies on basic parameters like area and equivalent circular diameter, which are insufficient for describing non-spherical or complex particles. This paper presents a novel methodology for the analysis of particles from micrographs, combining deep learningbased segmentation with parametric polygon approximation. Optical microscopy images were obtained for model systems of increasing complexity: monodisperse polystyrene spheres, SAPO-34 cubes, ZSM-5 hexagonal prisms, and a multi-component mixture of all three. Neural network segmentation was performed using the DLgram01 cloud service, trained on manually annotated images. A custom Python program was developed to process the resulting segmentation polygons. The core of the method involves fitting a parameterized polygon to each segmented particle’s contour. The optimal value of geometric parameters for each particle is determined by minimizing a “dissimilarity” function that measures the discrepancy between the segmentation and the parametric shape. This approach was validated on the simple spherical system, yielding a size distribution consistent with conventional projected diameter methods. For more complex cubic SAPO-34 particles, the rectangle fit revealed deviations from the ideal shape, providing a more complete morphological description than using a single size parameter. In the mixture of particles, the method successfully classified and extracted distinct parameter distributions for each particle type. The results for each class in the mixture were statistically consistent with those obtained from the single-component systems, demonstrating the method’s robustness and accuracy. The proposed methodology provides a powerful and universal tool for automated, high-throughput particle analysis, enabling the extraction of detailed shape parameters and the construction of comprehensive size and morphology distributions for complex particulate systems.

Keywords: neural network, image segmentation, microscopy, particle size analysis
Citation in English: Kasyanov A.V., Babina K.A., Parkhomchuk E.V. Method for analyzing geometric parameters of particles and constructing their distributions based on micrograph segmentation data using parameterized polygons // Computer Research and Modeling, 2026, vol. 18, no. 4, pp. 837-853
Citation in English: Kasyanov A.V., Babina K.A., Parkhomchuk E.V. Method for analyzing geometric parameters of particles and constructing their distributions based on micrograph segmentation data using parameterized polygons // Computer Research and Modeling, 2026, vol. 18, no. 4, pp. 837-853
DOI: 10.20537/2076-7633-2026-18-4-837-853
URL: http://crm-en.ics.org.ru/journal/article/3748/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Kasyanov A.V., Babina K.A., Parkhomchuk E.V.

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