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Articles

Simplification of polylines by segment collapse: minimizing areal displacement while preserving area

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Pages 22-46 | Received 30 Sep 2018, Accepted 22 May 2019, Published online: 30 Jul 2019

References

  • Attneave, F. (1954). Some informational aspects of visual perception. Psychological Review, 61, 183–193. doi: 10.1037/h0054663
  • de Berg, M., van Kreveld, M., Overmars, M., & Schwarzkopf, O. (2000). Computational geometry: Algorithms and applications (2nd ed.). Berlin: Springer.
  • Bose, P., Cabello, S., Cheong, O., Gudmundsson, J., van Kreveld, M., & Speckman, B. (2006). Area-preserving approximations of polygonal paths. Journal of Discrete Algorithms, 4(4), 554–566. doi: 10.1016/j.jda.2005.06.008
  • Braden, B. (1986). The surveyor’s area formula. The College Mathematics Journal, 17(4), 326–337. doi:10.2307/2686282 doi: 10.1080/07468342.1986.11972974
  • Buttenfield, B. P. (1985). Treatment of the cartographic line. Cartographica: The International Journal for Geographic Information and Geovisualization, 22(2), 1–26. doi: 10.3138/FWV8-3802-2282-6U47
  • Cromley, R. G. (1992). Principal axis line simplification. Computers & Geosciences, 18(8), 1003–1011. doi: 10.1016/0098-3004(92)90017-L
  • Douglas, D. H., & Peucker, T. K. (1973). Algorithms for the reduction of the number of points required to represent a digitised line or its caricature. Cartographica: The International Journal for Geographic Information and Geovisualization, 10(2), 112–122. doi: 10.3138/FM57-6770-U75U-7727
  • Eppstein, D. (1994). Approximating the minimum weight Steiner triangulation. Discrete & Computational Geometry, 11(2), 163–191. doi:10.1007/BF02574002.
  • Gary, R. H., Wilson, Z. D., Archuleta, C. M., Thompson, F. E., & Vrabel, J. (2010). Production of a national 1:1,000,000-scale hydrography dataset for the United States: Feature selection, simplification, and refinement. Washington D.C.: U.S. Geological survey Scientific Invertigations Report 2009-5202 (revised 2010).
  • Gökgöz, T., Sen, A., Memduhoglu, A., & Hacar, M. (2015). A new algorithm for cartographic simplification of streams and lakes using deviation angles and error Bands. ISPRS International Journal of Geo-Information, 4, 2185–2204. doi:10.3390/ijgi4042185.
  • Hangouët, J. F. (1995). Computation of the Hausdorff distance between plane vector polylines. Auto-Carto XII: Proceedings of the International Symposium on Computer-Assisted Cartography, Charlotte, North Carolina.
  • Kulik, L., Duckham, M., & Egenhofer, E. (2005). Ontology-driven map generalization. Journal of Visual Languages & Computing, 16(3), 245–267. doi: 10.1016/j.jvlc.2005.02.001
  • Lee, D., & Hardy, P. (2005). Automating generalization – tools and models. Proceedings of XXII International Cartographic Congress (ICC 2005), A Coruña, Spain.
  • Li, Z. (2006). Algorithmic foundations of multi-scale spatial representation. Boca Raton: CRC Press.
  • Li, Z. (2007). Digital map generalization at the age of the enlightenment: A review of the first forty years. The Cartographic Journal, 44(1), 80–93. doi: 10.1179/000870407X173913
  • Li, Z., & Openshaw, S. (1992). Algorithms for automated line generalization based on a natural principle of objective generalization. International Journal of Geographical Information Systems, 6(5), 373–389. doi: 10.1080/02693799208901921
  • MacEachren, A. M. (1985). Compactness of geographic shape: Comparison and evaluation of measures. Geografiska Annaler: Series B, Human Geography, 67(1), 53–67. doi: 10.1080/04353684.1985.11879515
  • McMaster, R. B. (1986). A statistical analysis of mathematical measures for linear simplification. The American Cartographer, 13(2), 103–116. doi: 10.1559/152304086783900059
  • McMaster, R. B., & Shea, K. S. (1992). Generalization in digital cartography. Washington, DC: Association of American Geographers.
  • Meulemans, W., van Renssen, A., & Speckmann, B. (2010). Area-preserving subdivision schematization. In S. I. Fabrikant, T. Reichenbacher, M. van Kreveld, & C. Schlieder (Eds.), Proceedings, GIScience 2010, LCNS 6292 (pp. 160–174). Berlin: Springer-Verlag.
  • Mustiere, S. (2005). Cartographic generalization of roads in a local adaptive approach: A knowledge acquisition problem. International Journal of Geographical Information Science, 19(8–9), 937–955. doi: 10.1080/13658810509161245
  • Nakos, B., Gaffuri, J., & Mustiere, S. (2008). A transition from simplification to generalisation of natural occurring lines. Proceedings 11th ICA Workshop on Generaliszation and Multiple Representations, Montpelier, France.
  • Nutanong, S., Jacox, E. H., & Samet, H. (2011). An incremental Hausdorff distance calculation algorithm. 37th International Conference on Very Large Data Bases, Seattle, Washington.
  • Ramer, U. (1972). An iterative procedure for the polygonal approximation of plane curves. Computer Graphics and Image Processing, 1(3), 244–256. doi: 10.1016/S0146-664X(72)80017-0
  • Raposo, P. (2013). Scale-specific automated line simplification by vertex clustering on a hexagonal tessellation. Cartography and Geographic Information Science, 40(5), 427–443. doi: 10.1080/15230406.2013.803707
  • Rucklidge, W. (1996). Efficient visual recognition using the Hausdorff distance. Berlin: Springer-Verlag. 186 pp. Lecture Notes in Computer Science (1173).
  • Saalfeld, A. (1999). Topologically consistent line simplification with the Douglas-Peucker algorithm. Cartography and Geographic Information Science, 26(1), 7–18. Doi: 10.1559/15230409978242901 doi: 10.1559/152304099782424901
  • Samsonov, T. E., & Yakimova, O. P. (2017). Shape-adaptive geometric simplification of heterogeneous line datasets. International Journal of Geographical Information Science, 31(8), 1485–1520. doi: 10.1080/13658816.2017.1306864
  • Shahriari, N., & Tao, V. (2002). Minimising positional errors in line simplification using adaptive tolerance values. Proceedings, 34th symposium on geospatial theory, processing and applications, Ottawa, Canada. Retrieved from http://www.isprs.org/proceedings/XXXIV/part4/pdfpapers/063.pdf.
  • Shen, Y., Ai, T., & He, Y. (2018). A new approach to line simplification based on image processing: A case study of water area boundaries. International Journal of Geo-Information, 7–41. doi:10.3390/ijgi7020041.
  • Shi, W., & Cheung, C. (2006). Performance evaluation of line simplification algorithms for vector generalization. The Cartographic Journal, 43(1), 27–44. doi: 10.1179/000870406X93490
  • Stanislawski, L. V. (2009). Feature pruning by upstream drainage area to support automated generalization of the United States National Hydrography dataset. Computers, Environment and Urban Systems, 33(5), 325–333. doi: 10.1016/j.compenvurbsys.2009.07.004
  • Stanislawski, L. V., Buttenfield, B. P., Bereuter, P., Savino, S., & Brewer, C. A. (2014). Generalization operators. In D. Burghardt, C. Duchêne, & W. A. Mackaness (Eds.), Abstracting information in a data rich world: Methodologies and applications of map generalization (pp. 157–195). Berlin: Springer Lecture Notes in Geoinformation and Cartography. doi: 10.1007/978-3-319-00203-3
  • Stanislawski, L. V., Falgout, J., & Buttenfield, B. P. (2015). Automated extraction of natural drainage density patterns for the conterminous united states through high-performance computing. The Cartographic Journal, 52(2), 185–192. doi: 10.1080/00087041.2015.1119466
  • Stanislawski, L. V., Liu, Y., Buttenfield, B. P., Survila, K., Wendel, J., & Okok, A. (2016). High performance computing to support multiscale representation of hydrography in the conterminous United States. Proceedings, 19th ICA workshop on generalization and multiple representation, June 14, 2016, Helsinki, Finland, 10 p.
  • Töpfer, F., & Pillewizer, W. (1966). The principles of selection. The Cartographic Journal, 3(1), 10–16. doi: 10.1179/caj.1966.3.1.10
  • Tutić, D., & Lapaine, M. (2009). Area preserving cartographic line generalization. Journal of the Croatian Cartographic Society, 8(11), 84–100.
  • U.S. Bureau of the Budget. (1947). United States National Map accuracy standards, June 17.
  • U.S. Geological Survey. (2017). The National Hydrography dataset. Production dates 2002-2017. Retrieved from https://nhd.usgs.gov/data.html, Last visited 03/17/2017.
  • Visvalingam, M., & Whyatt, J. D. (1992). Line generalisation by repeated elimination of the smallest area. Discussion paper 10, Cartographic Information Systems Research Group (CISRG), The University of Hull.
  • Wang, Z., & Müller, J.-C. (1998). Line generalization based on analysis of shape characteristics. Cartography and Geographic Information Systems, 25(1), 3–15. doi: 10.1559/152304098782441750
  • Zhou, S., & Jones, C. B. (2005). Shape-aware line generalisation with weighted effective area. In P. F. Fisher (Ed.), Developments in Spatial Handling 11th International Symposium on Spatial Handling (pp. 369–380). Berlin: Springer-Verlag.

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