Document Open Access Logo

Many-To-Many Polygon Matching à La Jaccard

Authors Alexander Naumann , Annika Bonerath , Jan-Henrik Haunert

PDF
Thumbnail PDF

File

LIPIcs.ESA.2024.90.pdf
  • Filesize: 2 MB
  • 15 pages

Document Identifiers

Author Details

Alexander Naumann
  • University of Bonn, Germany
Annika Bonerath
  • University of Bonn, Germany
Jan-Henrik Haunert
  • University of Bonn, Germany

Funding

  • Naumann, Alexander: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 459420781.
  • Bonerath, Annika: German Research Foundation under Germany’s Excellence Strategy, EXC-2070 - 390732324 - PhenoRob.

Cite AsGet BibTex

Alexander Naumann, Annika Bonerath, and Jan-Henrik Haunert. Many-To-Many Polygon Matching à La Jaccard. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 90:1-90:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.90

Abstract

Integration of spatial data is a major field of research. An important task of data integration is finding correspondences between entities. Here, we focus on combining building footprint data from cadastre and from volunteered geographic information, in particular OpenStreetMap. Previous research on this topic has led to exact 1:1 matching approaches and heuristic m:n matching approaches, most of which are lacking a mathematical problem definition. We introduce a model for many-to-many polygon matching based on the well-established Jaccard index. This is a natural extension to the existing 1:1 matching approaches. We show that the problem is NP-complete and a naive approach via integer programming fails easily. By analyzing the structure of the problem in detail, we can reduce the number of variables significantly. This approach yields an optimal m:n matching even for large real-world instances with appropriate running time. In particular, for the set of all building footprints of the city of Bonn (119,300 / 97,284 polygons) it yielded an optimal solution in approximately 1 hour.

Subject Classification

ACM Subject Classification
  • Information systems → Geographic information systems
  • Theory of computation → Computational geometry
  • Theory of computation → Integer programming
  • Mathematics of computing → Matchings and factors
Keywords
  • polygon matching
  • exact algorithm
  • Jaccard index

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Supplementary Materials

References

  1. Alex Bewley, Zongyuan Ge, Lionel Ott, Fabio Ramos, and Ben Upcroft. Simple online and realtime tracking. In 2016 IEEE International Conference on Image Processing (ICIP), pages 3464-3468, 2016. URL: https://doi.org/10.1109/ICIP.2016.7533003.
  2. Bezirksregierung Köln. ALKIS (Amtliches Liegenschaftskatasterinformationssystem). Data accessed from ALKIS via https://www.opengeodata.nrw.de/produkte/geobasis/lk/akt/gru_xml/, 2023. Accessed: 01.03.2024.
  3. Stefan Canzar, Khaled Elbassioni, Gunnar Klau, and Julián Mestre. On tree-constrained matchings and generalizations. Algorithmica, 71:98-109, July 2011. URL: https://doi.org/10.1007/978-3-642-22006-7_9.
  4. Muhammed Fatih Demirci. Many-to-many feature matching for structural pattern recognition. PhD thesis, Drexel University, USA, 2005. AAI3194363. Google Scholar
  5. Hongchao Fan, Alexander Zipf, Qing Fu, and Pascal Neis. Quality assessment for building footprints data on openstreetmap. International Journal of Geographical Information Science, 28(4):700-719, 2014. URL: https://doi.org/10.1080/13658816.2013.867495.
  6. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2023. URL: https://www.gurobi.com.
  7. Robert Hecht, Carola Kunze, and Stefan Hahmann. Measuring completeness of building footprints in openstreetmap over space and time. ISPRS International Journal of Geo-Information, 2(4):1066-1091, 2013. URL: https://doi.org/10.3390/ijgi2041066.
  8. Shahab Jozdani and Dongmei Chen. On the versatility of popular and recently proposed supervised evaluation metrics for segmentation quality of remotely sensed images: An experimental case study of building extraction. ISPRS Journal of Photogrammetry and Remote Sensing, 160:275-290, 2020. URL: https://doi.org/10.1016/j.isprsjprs.2020.01.002.
  9. Richard Karp. Reducibility among combinatorial problems. Complexity of Computer Computations, 40:85-103, January 1972. URL: https://doi.org/10.1007/978-3-540-68279-0_8.
  10. Jung Ok Kim, Kiyun Yu, Joon Heo, and Won Hee Lee. A new method for matching objects in two different geospatial datasets based on the geographic context. Computers & Geosciences, 36(9):1115-1122, 2010. URL: https://doi.org/10.1016/j.cageo.2010.04.003.
  11. Lingjia Liu, Xinyan Zhu, Daoye Zhu, and Ding Xiaohui. M:n object matching on multiscale datasets based on mbr combinatorial optimization algorithm and spatial district. Transactions in GIS, 22, November 2018. URL: https://doi.org/10.1111/tgis.12488.
  12. Fabian Müller, Ionuț Iosifescu, and Lorenz Hurni. Assessment and visualization of osm building footprint quality. In Proceedings of the 27th International Cartographic Conference (ICC 2015), Rio de Janeiro, Brazil, August 2015. Google Scholar
  13. Samuel Murray. Real-Time Multiple Object Tracking - A Study on the Importance of Speed. Degree project, KTH Royal institute of technology school of computer science and communication, Stockholm, Sweden, September 2017. Google Scholar
  14. Meghana Nasre, Prajakta Nimbhorkar, Keshav Ranjan, and Ankita Sarkar. Popular critical matchings in the many-to-many setting. Theoretical Computer Science, 982:114281, 2024. URL: https://doi.org/10.1016/j.tcs.2023.114281.
  15. OpenStreetMap Contributors. OpenStreetMap. https://www.openstreetmap.org, 2004-present. Accessed: 01.03.2024.
  16. QGIS Development Team. QGIS Geographic Information System. QGIS Association, %Y. URL: https://www.qgis.org.
  17. Juan J. Ruiz-Lendínez, Manuel A. Ureña-Cámara, and Francisco J. Ariza-López. A polygon and point-based approach to matching geospatial features. ISPRS International Journal of Geo-Information, 6(12), 2017. URL: https://doi.org/10.3390/ijgi6120399.
  18. Ali Shokoufandeh, Yakov Keselman, Fatih Demirci, Diego Macrini, and Sven Dickinson. Many-to-Many Feature Matching in Object Recognition, pages 107-125. Springer Berlin Heidelberg, Berlin, Heidelberg, 2006. URL: https://doi.org/10.1007/11414353_8.
  19. The CGAL Project. CGAL User and Reference Manual. CGAL Editorial Board, 5.6 edition, 2023. URL: https://doc.cgal.org/5.6/Manual/packages.html.
  20. Matthias P. Wagner and Natascha Oppelt. Extracting agricultural fields from remote sensing imagery using graph-based growing contours. Remote Sensing, 12(7), 2020. URL: https://doi.org/10.3390/rs12071205.
  21. Volker Walter. Matching of spatial data - on the example of the datamodels ATKIS and GDF. Phd thesis, German Geodetic Commission, Munich, Germany, 1997. Google Scholar
  22. Volker Walter and Dieter Fritsch. Matching spatial data sets: a statistical approach. International Journal of Geographical Information Science, 13(5):445-473, 1999. URL: https://doi.org/10.1080/136588199241157.
  23. Xiaofang Wang, Yu Zang, Yiping Chen, Cheng Wang, and Jonathan Li. Rural road networks matching via extending line. In IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium, pages 7419-7422, 2018. URL: https://doi.org/10.1109/IGARSS.2018.8519400.
  24. Kiyun Yu Yong Huh, Jiyoung Kim and Sunghwan Cho. M:n object matching between image and map object data sets by means of latent semantic analysis. International Journal of Remote Sensing, 35(18):6799-6814, 2014. URL: https://doi.org/10.1080/01431161.2014.965286.
  25. Mikhail Zaslavskiy, Francis Bach, and Jean-Philippe Vert. Many-to-many graph matching: A continuous relaxation approach. In Machine Learning and Knowledge Discovery in Databases, pages 515-530, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact