An efficient aggregation and overlap removal algorithm for circle maps

  • Christian BeilschmidtEmail author
  • Michael Mattig
  • Thomas Fober
  • Bernhard Seeger


The visualization of spatial data is becoming increasingly important in science, business and many other areas. There are two main reasons for this: First, the amount of spatial data is growing continuously, making it impossible for people to manually process the data in raw form. Secondly, users have very high demands on the interactive processing of big spatial data in visual form. For instance in geography, data often corresponds to a large number of point observations that should be displayed on a constrained screen with limited resolution. This causes two crucial problems: drawing a lot of points is expensive at runtime and leads to a loss of information due to an overloaded and occluded visualization. In this paper we present a new efficient visualization algorithm that avoids these problems by aggregating point data into a set of non-overlapping circles with the following properties: (i) they follow the distribution of the data, (ii) they represent the cardinality of the underlying point subset by the circle area, (iii) they reveal hot spots while simultaneously keeping outliers, and (iv) the number of circles is typically much smaller than the number of points. Based on a quadtree, our algorithm computes the circles in linear time with respect to the number of points. Experimental results confirm its excellent runtime and quality in comparison to competitors.


Point aggregation Spatial visualization Big spatial point data 



This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) under grant no. SE 553/7-2.


  1. 1.
    Madhavan J, Balakrishnan S, Brisbin K, Gonzalez H, Gupta N, Halevy AY, Jacqmin-Adams K, Lam H, Langen A, Lee H (2012) Big data storytelling through interactive maps. IEEE Data Eng Bull 35(2):46Google Scholar
  2. 2.
    Zhang L, Stoffel A, Behrisch M, Mittelstadt S, Schreck T, Pompl R, Weber S, Last H, Keim D (2012) Visual analytics for the big data era - a comparative review of state-of-the-art commercial systems. In: VAST’12: Proceedings of the 2012 IEEE conference on visual analytics science and technology. IEEE Computer Society, Washington, pp 173–182Google Scholar
  3. 3.
    Keim D, Andrienko G, Fekete JD, Görg C, Kohlhammer J, Melançon G (2008). In: Kerren A, Stasko JT, Fekete JD, North C (eds) Information visualization. Springer, Berlin, pp 154–175Google Scholar
  4. 4.
    Diepenbroek M, Glöckner F, Grobe P et al (2014) Towards an integrated biodiversity and ecological research data management and archiving platform: the German federation for the curation of biological data (GFBio). In: GI-Jahrestagung, pp 1711–1721Google Scholar
  5. 5.
    Authmann C, Beilschmidt C, Drönner J, Mattig M, Seeger B (2015) Rethinking spatial processing in data-intensive science. In: BTW 2015: Datenbanksysteme für business, Technologie und Web - Workshopband, vol P242. Gesellschaft für Informatik e.V., Bonn, pp 161–170Google Scholar
  6. 6.
    Beilschmidt C, Drönner J, Mattig M, Schmidt M, Authmann C, Niamir A, Hickler T, Seeger B (2017) Interactive data exploration for geoscience. In: BTW 2017: Datenbanksysteme für Business, Technologie und Web - Workshopband, vol P-266. Gesell-schaft für Informatik e.V., Bonn, pp 117–126Google Scholar
  7. 7.
    Beilschmidt C, Drȯnner J., Mattig M, Seeger B (2017) VAT: a system for data-driven biodiversity research. In: EDBT 2017: Proceedings of the 20th international conference on extending database technology., Konstanz, pp 546–549Google Scholar
  8. 8.
    Beilschmidt C, Fober T, Mattig M, Seeger B (2017) A linear-time algorithm for the aggregation and visualization of big spatial point data. In: SIGSPATIAL ’17: proceedings of the 25th ACM SIGSPATIAL international conference on advances in geographic information systems. ACM, New York, pp 73:1–73:4Google Scholar
  9. 9.
    Jänicke S, Heine C, Scheuermann G (2013) GeoTemCo: comparative visualization of geospatial-temporal data with clutter removal based on dynamic delaunay triangulations. In: VISIGRAPP 2012: proceedings of the 7th international joint conference on computer vision, imaging and computer graphics. Theory and application, vol 359. Springer, Berlin, pp 160–175Google Scholar
  10. 10.
    Beilschmidt C, Fober T, Mattig M, Seeger B (2017) Quality measures for visual point clustering in geospatial mapping. In: W2GIS 2017: proceedings of the 15th international symposium on web and wireless geographical information systems. Springer International Publishing, Cham, pp 153–168Google Scholar
  11. 11.
    Jȧnicke S, Heine C, Stockmann R, Scheuermann G (2012) Comparative visualization of geospatial-temporal data. In: GRAPP & IVAPP 2012 proceedings of the international conference on computer graphics theory and applications and international conference on information visualization theory and application. SciTePress, Setu̇bal, pp 613–625Google Scholar
  12. 12.
    Slocum T, McMaster R, Kessler F, Howard H (2009) Thematic cartography and geovisualization. Prentice Hall, Upper Saddle RiverGoogle Scholar
  13. 13.
    Pickering S (2017) A new way to proxy levels of infrastructure development research and politics, 4(1)Google Scholar
  14. 14.
    Forrest D, Castner HW (1985) The design and perception of point symbols for tourist maps. Cartogr J 22(1):11CrossRefGoogle Scholar
  15. 15.
    de Berg M, Cheong O, van Kreveld MJ, Overmars MH (2008) Computational geometry: algorithms and applications, 3rd edn. Springer, BerlinCrossRefGoogle Scholar
  16. 16.
    Bereuter P, Weibel R (2013) Real-time generalization of point data in mobile and web mapping using quadtrees. Cartogr Geogr Inf Sci 40(4):271CrossRefGoogle Scholar
  17. 17.
    Samet H (2006) Foundations of multidimensional and metric data structures. Morgan Kaufmann, San FranciscoGoogle Scholar
  18. 18.
    Aggarwal CC, Reddy CK (2014) Data clustering: algorithms and applications. CRC Press, Boca RatonCrossRefGoogle Scholar
  19. 19.
    Park Y, Cafarella MJ, Mozafari B (2016) Visualization-aware sampling for very large databases. In: Proceedings of the IEEE 32nd international conference on data engineering (ICDE). IEEE Computer Society, Washington, pp 755–766Google Scholar
  20. 20.
    Wang L, Christensen R, Li F, Yi K (2015) Spatial Online Sampling and Aggregation. Proc VLDB Endow 9(3):84CrossRefGoogle Scholar
  21. 21.
    Sarma AD, Lee H, Gonzalez H, Madhavan J, Halevy AY (2012) Efficient spatial sampling of large geographical tables. In: SIGMOD ’12: proceedings of the 2012 ACM SIGMOD international conference on management of data. ACM, New York, pp 193–204Google Scholar
  22. 22.
    Grȯbe M, Burghardt D (2017) Micro diagrams: a multi-scale approach for mapping large categorised point datasets. In: Proceedings of AGILE 2017: the 20th AGILE international conference on geographic information scienceGoogle Scholar
  23. 23.
    Liu Z, Jiang B, Heer J (2013) imMens: real-time visual querying of big data. Comput Graph Forum 32(3):421CrossRefGoogle Scholar
  24. 24.
    Zhang L, Rooney C, Nachmanson L, Wong BLW, Kwon BC, Stoffel F, Hund M, Qazi N, Singh U, Keim DA (2016) Spherical similarity explorer for comparative case analysis. In: Proceedings of the IS&T international symposium on electronic imaging 2016 visualization and data analysis. Ingenta, Oxford, pp 1–10Google Scholar
  25. 25.
    Ghanem TM, Magdy A, Musleh M, Ghani S, Mokbel MF (2014) VisCAT: spatio-temporal visualization and aggregation of categorical attributes in twitter data. In: SIGSPATIAL ’14: proceedings of the 22th ACM SIGSPATIAL international conference on advances in geographic information systems. ACM, New York, pp 537–540Google Scholar
  26. 26.
    Ellis G, Dix A (2007) A taxonomy of clutter reduction for information visualisation. IEEE Trans Vis Comput Graph 13(6):1216CrossRefGoogle Scholar
  27. 27.
    Samet H (1990) The design and analysis of spatial data structures. Addison-Wesley, ReadingGoogle Scholar
  28. 28.
    Konheim AG (2010) Hashing in computer science: fifty years of slicing and dicing. Wiley, HobokenCrossRefGoogle Scholar
  29. 29.
    Bader M (2013) Space-filling curves - an introduction with applications in scientific computing. Springer, BerlinGoogle Scholar
  30. 30.
    Lipowski A, Lipowska D (2012) Roulette-wheel selection via stochastic acceptance. Physica A: Statist Mech Appl 391(6):2193CrossRefGoogle Scholar
  31. 31.
    Liu Z, Heer J (2014) The effects of interactive latency on exploratory visual analysis. IEEE Trans Vis Comput Graph 20(12):2122CrossRefGoogle Scholar
  32. 32.
    Corder GW, Foreman DI (2014) Nonparametric statistics: a step-by-step approach. Wiley, HobokenGoogle Scholar
  33. 33.
    Grbiċ R, Grahovac D, Scitovski R (2016) A method for solving the multiple ellipses detection problem. Pattern Recogn 60:824CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Christian Beilschmidt
    • 1
    Email author
  • Michael Mattig
    • 1
  • Thomas Fober
    • 1
  • Bernhard Seeger
    • 1
  1. 1.University of MarburgMarburgGermany

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