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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">ntv</journal-id><journal-title-group><journal-title xml:lang="ru">Научно-технический вестник информационных технологий, механики и оптики</journal-title><trans-title-group xml:lang="en"><trans-title>Scientific and Technical Journal of Information Technologies, Mechanics and Optics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-1494</issn><issn pub-type="epub">2500-0373</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2226-1494-2025-25-2-261-272</article-id><article-id custom-type="elpub" pub-id-type="custom">ntv-446</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>КОМПЬЮТЕРНЫЕ СИСТЕМЫ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>COMPUTER SCIENCE</subject></subj-group></article-categories><title-group><article-title>Кластеризация пространственных данных с неявно выраженной полигональной структурой на основе топологических подходов</article-title><trans-title-group xml:lang="en"><trans-title>Clustering of spatial data with implicit polygonal structure based on topological approaches</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8482-1479</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Еремеев</surname><given-names>С. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Eremeev</surname><given-names>S. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Еремеев Сергей Владимирович — кандидат технических наук, доцент, доцент.</p><p>Муром, 602264</p></bio><bio xml:lang="en"><p>Sergey V. Eremeev — PhD, Associate Professor, Associate Professor.</p><p>Murom, 602264, sc 56673892800</p></bio><email xlink:type="simple">sv-eremeev@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Муромский институт (филиал) ФГБОУ ВО «Владимирский государственный университет имени Александра Григорьевича и Николая Григорьевича Столетовых»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Murom Institute (Branch) of Vladimir State University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>24</day><month>04</month><year>2025</year></pub-date><volume>25</volume><issue>2</issue><fpage>261</fpage><lpage>272</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Еремеев С.В., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Еремеев С.В.</copyright-holder><copyright-holder xml:lang="en">Eremeev S.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ntv.elpub.ru/jour/article/view/446">https://ntv.elpub.ru/jour/article/view/446</self-uri><abstract><sec><title>Введение</title><p>Введение. Кластеризация является одним из фундаментальных подходов для интеллектуального анализа данных, который в сфере геоинформатики и обработки изображений используется для поиска знаний и скрытых закономерностей пространственной информации. При автоматической векторизации объектов на спутниковых снимках из-за несовершенства этих технологий на линейных и полигональных объектах появляются пропущенные элементы, что препятствует полноценному анализу и визуализации данных. Представлен новый метод кластеризации геометрических примитивов с неявно выраженной полигональной структурой с возможностью устранения неполных данных в векторных моделях.</p></sec><sec><title>Метод</title><p>Метод. Предлагаемый метод основан на итерационном формировании пространственных структур при растяжении исходных объектов линейного типа. В отличие от многих подходов кластеризации элементы группируются в кластеры не по принципу ближайшего евклидова расстояния, а за счет определения ближайшего пересечения между отрезками. Такой подход позволяет корректно разделить рядом стоящие линейные объекты в разные кластеры. Для формирующихся пространственных структур на каждой итерации в зависимости от коэффициента растяжения вычисляются их топологические особенности, что обеспечивает возможность обнаруживать и проводить фильтрацию неявно выраженных полигональных структур.</p></sec><sec><title>Основные результаты</title><p>Основные результаты. Разработанный метод апробирован для кластеризации линейных геометрических примитивов на векторных моделях городской инфраструктуры. Проведено сравнение работы метода с аналогами: k-средних, Density-Based Spatial Clastering of Application with Noise (DBSCAN) и агломеративной кластеризацией. Исследования показали, что с использованием метрики оценки качества кластеризации в виде индексов инерции и Жаккара предложенный метод имеет преимущество в случаях корректного разделения близко расположенных кластеров.</p></sec><sec><title>Обсуждение</title><p>Обсуждение. Полученные результаты могут быть использованы в геоинформационных системах для актуализации векторных данных после применения технологий автоматической векторизации объектов на спутниковых снимках.</p></sec></abstract><trans-abstract xml:lang="en"><p>Clustering is one of the fundamental approaches for data mining, which in the field of geoinformatics and image processing is used to search for knowledge and hidden patterns of spatial information. During automatic vectorization of objects on satellite images due to imperfections of these technologies, missing elements appear on linear and polygonal objects, which prevent full-fledged data analysis and visualization. The paper considers the problem of clustering geometric primitives with implicit polygonal structure with the possibility of eliminating incomplete data in vector models. The proposed method is based on the iterative formation of spatial structures by stretching the original linear objects. Unlike many clustering approaches, elements are grouped into clusters not by the principle of nearest Euclidean distance, but by determining the nearest intersection between segments. This approach allows us correctly dividing adjacent objects into different clusters. For the spatial structures formed at each iteration, their topological features are calculated depending on the stretching coefficient, which makes it possible to detect and filter implicit polygonal structures. The developed method is tested for clustering of linear geometric primitives on vector models of urban infrastructure. The performance of the method is compared with its competitors: k-means, DBSCAN, and agglomerative clustering. The research has shown that using the clustering quality assessment metric in the form of inertia and Jaccard indices, the proposed method has an advantage due to the correct separation of closely located clusters.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>кластеризация пространственной информации</kwd><kwd>топологический анализ данных</kwd><kwd>гомотетия</kwd><kwd>геоинформационные системы</kwd><kwd>оценка качества кластеризации</kwd></kwd-group><kwd-group xml:lang="en"><kwd>spatial information clustering</kwd><kwd>topological data analysis</kwd><kwd>homothety</kwd><kwd>geographic information systems</kwd><kwd>clustering quality assessment</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при финансовой поддержке Российского научного фонда в рамках научного проекта№ 23-21-10064. Автор выражает благодарность магистру в области информационных систем Егай Марии Владимировне за помощь в подготовке исходных данных и проведении экспериментов</funding-statement><funding-statement xml:lang="en">This study was supported by the Russian Science Foundation, project no. 23-21-10064. The author expresses gratitude to the Master of Information Systems, Maria Vladimirovna Egay, for her assistance in preparing the initial data and conducting the experiments</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Воробьев А.В., Воробьева Г.Р. Геоинформационная система динамической пространственной кластеризации распределенных источников данных // Вестник Томского государственного университета. Управление, вычислительная техника и информатика. 2023. № 64. С. 61–73. https://doi.org/10.17223/19988605/64/7</mixed-citation><mixed-citation xml:lang="en">Vorobev A.V., Vorobeva G.R. Geoinformation system for dynamic spatial clustering of distributed data sources. Tomsk State University Journal of Control and Computer Science, 2023, no. 64, pp. 61–73. (in Russian). https://doi.org/10.17223/19988605/64/7</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Еремеев С.В., Абакумов А.В., Андрианов Д.Е., Богоявленский И.В., Никонов Р.А. Обнаружение многолетних бугров пучения с использованием декомпозиции цифровых моделей рельефа по топологическим признакам // Современные проблемы дистанционного зондирования Земли из космоса. 2023. Т. 20. № 6. С. 129–143. https://doi.org/10.21046/2070-7401-2023-20-6-129-143</mixed-citation><mixed-citation xml:lang="en">Eremeev S.V., Abakumov A.V., Andrianov D.E., Bogoyavlensky I.V., Nikonov R.A. Detection of perennial heaving mounds in digital elevation model images using decomposition by topological features. Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2023, vol. 20, no. 6, pp. 129–143. (in Russian). https://doi.org/10.21046/2070-7401-2023-20-6-129-143</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Еремеев С.В., Абакумов А.В., Андрианов Д.Е., Ширабакина Т.А. Метод векторизации спутниковых снимков на основе их разложения по топологическим особенностям // Информатика и автоматизация. 2023. Т. 22. № 1. С. 110–145. https://doi.org/10.15622/ia.22.1.5</mixed-citation><mixed-citation xml:lang="en">Eremeev S.V., Abakumov A.V., Andrianov D.E., Shirabakina T.A. Vectorization method of satellite images based on their decomposition by topological features. Informatics and Automation, 2023, vol. 22, no. 1, pp. 110–145. (in Russian). https://doi.org/10.15622/ia.22.1.5</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Lin X., Zhou Y., Liu Y., Zhu C. A comprehensive review of image line segment detection and description: taxonomies, comparisons, and challenges // IEEE Transactions on Pattern Analysis and Machine Intelligence. 2024. V. 46. N 12. P. 8074–8093. https://doi.org/10.1109/tpami.2024.3400881</mixed-citation><mixed-citation xml:lang="en">Lin X., Zhou Y., Liu Y., Zhu C. A comprehensive review of image line segment detection and description: taxonomies, comparisons, and challenges. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024, vol. 46, no. 12, pp. 8074–8093. https://doi.org/10.1109/tpami.2024.3400881</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang C., He Y., Fraser C.S. Spectral clustering of straight-line segments for roof plane extraction from airborne LiDAR point clouds // IEEE Geoscience and Remote Sensing Letters. 2018. V. 15. N 2. P. 267–271. https://doi.org/10.1109/LGRS.2017.2785380</mixed-citation><mixed-citation xml:lang="en">Zhang C., He Y., Fraser C.S. Spectral clustering of straight-line segments for roof plane extraction from airborne LiDAR point clouds. IEEE Geoscience and Remote Sensing Letters, 2018, vol. 15, no. 2, pp. 267–271. https://doi.org/10.1109/LGRS.2017.2785380</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Zang D., Wang J., Zhang X., Yu J. Semantic extraction of roof contour lines from airborne lidar building point clouds based on multidirectional equal-width banding // IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. 2024. V. 17. P. 16316– 16328. https://doi.org/10.1109/jstars.2024.3422973</mixed-citation><mixed-citation xml:lang="en">Zang D., Wang J., Zhang X., Yu J. Semantic extraction of roof contour lines from airborne lidar building point clouds based on multidirectional equal-width banding. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2024, vol. 17, pp. 16316–16328. https://doi.org/10.1109/jstars.2024.3422973</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Xin X., Huang W., Zhong S., Zhang M., Liu Z. Xie Z. Accurate and complete line segment extraction for large-scale point clouds // International Journal of Applied Earth Observation and Geoinformation. 2024. V. 128. P. 103728. https://doi.org/10.1016/j.jag.2024.103728</mixed-citation><mixed-citation xml:lang="en">Xin X., Huang W., Zhong S., Zhang M., Liu Z. Xie Z. Accurate and complete line segment extraction for large-scale point clouds. International Journal of Applied Earth Observation and Geoinformation, 2024, vol. 128, pp. 103728. https://doi.org/10.1016/j.jag.2024.103728</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Miroshnichenko S.Yu., Titov V.S., Dremov E.N., Mosin S.A. Hough transform application to digitize rectangular spatial objects on aerospace imagery //sPIIRAS Proceedings. 2018. N 5 (60). P. 189–215. https://doi.org/10.15622/sp.60.7</mixed-citation><mixed-citation xml:lang="en">Miroshnichenko S.Yu., Titov V.S., Dremov E.N., Mosin S.A. Hough transform application to digitize rectangular spatial objects on aerospace imagery. SPIIRAS Proceedings, 2018, no. 5 (60), pp. 189–215. https://doi.org/10.15622/sp.60.7</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Teplyakov L., Erlygin L., Shvets E. LSDNet: Trainable modification of LSD algorithm for real-time line segment detection // IEEE Access. 2022. V. 10. P. 45256–45265. https://doi.org/10.1109/ACCESS.2022.3169177</mixed-citation><mixed-citation xml:lang="en">Teplyakov L., Erlygin L., Shvets E. LSDNet: Trainable modification of LSD algorithm for real-time line segment detection. IEEE Access, 2022, vol. 10, pp. 45256–45265. https://doi.org/10.1109/ACCESS.2022.3169177</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Shili H. Clustering in big data analytics: a systematic review and comparative analysis (review article). Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2023. V. 23. N 5. P. 967–979. https://doi.org/10.17586/2226-1494-2023-23-5-967-979</mixed-citation><mixed-citation xml:lang="en">Shili H. Clustering in big data analytics: a systematic review and comparative analysis (review article). Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2023, vol. 23, no. 5, pp. 967–979. https://doi.org/10.17586/2226-1494-2023-23-5-967-979</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Ikotun A.M., Ezugwu A.E., Abualigah L., Abuhaija B., Heming J. K-means clustering algorithms: a comprehensive review, variants analysis, and advances in the era of big data // Information Sciences. 2023. V. 622. P. 178–210. https://doi.org/10.1016/j.ins.2022.11.139</mixed-citation><mixed-citation xml:lang="en">Ikotun A.M., Ezugwu A.E., Abualigah L., Abuhaija B., Heming J. K-means clustering algorithms: a comprehensive review, variants analysis, and advances in the era of big data. Information Sciences, 2023, vol. 622, pp. 178–210. https://doi.org/10.1016/j.ins.2022.11.139</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Ester M., Kriegel H.-P., Sander J., Xu X. A density-based algorithm for discovering clusters in large spatial databases with noise // Proc. of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96). 1996. P. 226–231.</mixed-citation><mixed-citation xml:lang="en">Ester M., Kriegel H.-P., Sander J., Xu X. A density-based algorithm for discovering clusters in large spatial databases with noise. Proc. of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96), 1996, pp. 226–231.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Jang J.H., Hong K.S. Fast line segment grouping method for finding globally more favorable line segments // Pattern Recognition. 2002. V. 35. N 10. P. 2235–2247. https://doi.org/10.1016/S0031-3203(01)00175-3</mixed-citation><mixed-citation xml:lang="en">Jang J.H., Hong K.S. Fast line segment grouping method for finding globally more favorable line segments. Pattern Recognition, 2002, vol. 35, no. 10, pp. 2235–2247. https://doi.org/10.1016/S0031-3203(01)00175-3</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Gao J., Langberg M., Schulman L.J. Clustering lines in highdimensional space: Classification of incomplete data // ACM Transactions on Algorithms. 2010. V. 7. N 1. P. 8. https://doi.org/10.1145/1868237.1868246</mixed-citation><mixed-citation xml:lang="en">Gao J., Langberg M., Schulman L.J. Clustering lines in highdimensional space: Classification of incomplete data. ACM Transactions on Algorithms, 2010, vol. 7, no. 1, pp. 8. https://doi.org/10.1145/1868237.1868246</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Айдагулов Р.Р., Главацкий С.Т., Михалёв А.В. Модели кластеризации // Фундаментальная и прикладная математика. 2020. Т. 23. № 2. С. 17–36.</mixed-citation><mixed-citation xml:lang="en">Aidagulov R.R., Glavatsky S.T., Mikhalev A.V. Clustering models. Journal of Mathematical Sciences, 2022, vol. 262, no. 5. pp. 603–616. (in Russian). https://doi.org/10.1007/s10958-022-05841-9</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Kang Y., Wu K., Gao S., Ng I., Rao J., Ye S., Zhang F., Fei T. STICC: a multivariate spatial clustering method for repeated geographic pattern discovery with consideration of spatial contiguity // International Journal of Geographical Information Science. 2022. V. 36. N 8. P. 1518–1549. https://doi.org/10.1080/13658816.2022.2053980</mixed-citation><mixed-citation xml:lang="en">Kang Y., Wu K., Gao S., Ng I., Rao J., Ye S., Zhang F., Fei T. STICC: a multivariate spatial clustering method for repeated geographic pattern discovery with consideration of spatial contiguity. International Journal of Geographical Information Science, 2022, vol. 36, no. 8, pp. 1518–1549. https://doi.org/10.1080/13658816.2022.2053980</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Alomari H.W., Al-Badarneh A.F., Al-Alaj A., Khamaiseh S.Y. Enhanced approach for agglomerative clustering using topological relations // IEEE Access. 2023. V. 11. P. 21945–21967. https://doi.org/10.1109/access.2023.3252374</mixed-citation><mixed-citation xml:lang="en">Alomari H.W., Al-Badarneh A.F., Al-Alaj A., Khamaiseh S.Y. Enhanced approach for agglomerative clustering using topological relations. IEEE Access, 2023, vol. 11, pp. 21945–21967. https://doi.org/10.1109/access.2023.3252374</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Edelsbrunner H., Letscher H., Zomorodian A. Topological persistence and simplification // Discrete &amp; Computational Geometry. 2002. V. 28. N 4. P. 511–533. https://doi.org/10.1007/s00454-002-2885-2</mixed-citation><mixed-citation xml:lang="en">Edelsbrunner H., Letscher H., Zomorodian A. Topological persistence and simplification. Discrete &amp; Computational Geometry, 2002, vol. 28, no. 4, pp. 511–533. https://doi.org/10.1007/s00454-002-2885-2</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Абакумов А.В., Еремеев С.В. Оценка возможности применения метода декомпозиции изображений по топологическим признакам для уменьшения энтропии при их сжатии // Научно-технический вестник информационных технологий, механики и оптики. 2023. Т. 23. № 6. С. 1152–1161. https://doi:10.17586/2226-1494-2023-23-6-1152-1161</mixed-citation><mixed-citation xml:lang="en">Abakumov A.V., Eremeev S.V. Assessing the possibility of using the method of image decomposition based on topological features to reduce entropy during their compression. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2023, vol. 23, no. 6, pp. 1152–1161. (in Russian). https://doi.org/10.17586/2226-1494-2023-23-6-1152-1161</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Xu F., Beard K. A unifying framework for analysis of spatial-temporal event sequence similarity and its applications // ISPRS International Journal of Geo-Information. 2021. V. 10. N 9. P. 594. https://doi.org/10.3390/ijgi10090594</mixed-citation><mixed-citation xml:lang="en">Xu F., Beard K. A unifying framework for analysis of spatial-temporal event sequence similarity and its applications. ISPRS International Journal of Geo-Information, 2021, vol. 10, no. 9, pp. 594. https://doi.org/10.3390/ijgi10090594</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Rykov A., De Amorim R.C., Makarenkov V., Mirkin B. Inertia-based indices to determine the number of clusters in K-Means: an experimental evaluation // IEEE Access. 2024. V. 12. P. 11761–11773. https://doi.org/10.1109/ACCESS.2024.3350791</mixed-citation><mixed-citation xml:lang="en">Rykov A., De Amorim R.C., Makarenkov V., Mirkin B. Inertia-based indices to determine the number of clusters in K-Means: an experimental evaluation. IEEE Access, 2024, vol. 12, pp. 11761–11773. https://doi.org/10.1109/ACCESS.2024.3350791</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
