АНАЛІЗ МАТЕМАТИЧНИХ МОДЕЛЕЙ ТА МЕТОДІВ ВИЯВЛЕННЯ ЗМІН 3D СЕРЕДОВИЩА ЗА ЗОБРАЖЕННЯМИ

Oleg Chertov; Serhii Sakharov

doi:10.20535/kpisn.2025.3.336383

Authors

Oleg Chertov National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Faculty of Applied Mathematics, Applied Mathematics Department, Kyiv, Ukraine https://orcid.org/0000-0003-0087-1028
Serhii Sakharov National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Faculty of Applied Mathematics, Applied Mathematics Department, Kyiv, Ukraine https://orcid.org/0009-0001-0943-023X

DOI:

https://doi.org/10.20535/kpisn.2025.3.336383

Keywords:

3D environment changes, point clouds, digital twin, computer vision, machine learning

Abstract

Background. Automated detection of changes in three-dimensional (3D) environments constitutes a fundamental challenge in the development and maintenance of urban infrastructure digital twins, environmental monitoring systems, and facility security applications. Current methodologies exhibit limitations in uncertainty quantification, computational scalability for large-scale datasets, and semantic information integration. Existing reviews predominantly emphasize technical implementations or domain-specific applications, with insufficient attention to the particularities of the mathematical methods used. This gap impedes the principled selection of algorithms for digital twin actualization.

Objective. To provide a comprehensive systematization and comparative analysis of mathematical models and computational methods for three-dimensional environmental change detection. To establish a taxonomic framework that delineates methodological advantages, constraints, and applicability domains. To formulate evidence-based recommendations for method selection across diverse monitoring scenarios of 3D environment.

Methods. We conducted a systematic analysis encompassing classical geometric approaches for point cloud registration and comparison, statistical frameworks for uncertainty quantification, and contemporary machine learning paradigms for automated change classification. Formal mathematical representations were developed for three-dimensional data structures, change typologies, and corresponding evaluation metrics.

Results. A unified mathematical framework for characterizing diverse change phenomena in three-dimensional environments was established, providing a theoretical foundation for automated digital twin synchronization. Method selection criteria were derived based on data properties and application-specific requirements. Empirical evidence demonstrates that hybrid architectures integrating geometric primitives with machine learning techniques achieve superior accuracy while preserving interpretability in digital environment model updates.

Conclusions. The proposed systematic framework facilitates principled method selection for specific change detection applications. Future research directions include the development of self-adaptive algorithms with autonomous parameter optimization and the incorporation of semantic reasoning through advanced deep learning architectures.

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ANALYSIS OF MATHEMATICAL MODELS AND METHODS FOR 3D ENVIRONMENT CHANGE DETECTION FROM IMAGERY

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