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Estimation of an unknown cartographic projection and its parameters from the map

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Abstract

This article presents a new off-line method for the detection, analysis and estimation of an unknown cartographic projection and its parameters from a map. Several invariants are used to construct the objective function ϕ that describes the relationship between the 0D, 1D, and 2D entities on the analyzed and reference maps. It is minimized using the Nelder-Mead downhill simplex algorithm. A simplified and computationally cheaper version of the objective function ϕ involving only 0D elements is also presented. The following parameters are estimated: a map projection type, a map projection aspect given by the meta pole K coordinates [φ k , λ k ], a true parallel latitude φ 0, central meridian longitude λ 0, a map scale, and a map rotation. Before the analysis, incorrectly drawn elements on the map can be detected and removed using the IRLS. Also introduced is a new method for computing the L 2 distance between the turning functions Θ1, Θ2 of the corresponding faces using dynamic programming. Our approach may be used to improve early map georeferencing; it can also be utilized in studies of national cartographic heritage or land use applications. The results are presented both for the real cartographic data, representing early maps from the David Rumsay Map Collection, and for the synthetic tests.

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References

  1. Arkin EM, Chew LP, Huttenlocher DP, Kedem K, Mitchell JSB (1991) An efficiently computable metric for comparing polygonal shapes. IEEE J PAMI 13(3):209–216

    Article  Google Scholar 

  2. Bai X, Yang X, Latecki LJ, Liu W, Tu Z (2010) Learning context-sensitive shape similarity by graph transduction. IEEE J PAMI 32(5):861–874

    Article  Google Scholar 

  3. Balletti C, Guerra F, Monti C (2000) Venice: new life in an old map: geometrical analysis and georeferenced visualisation of historic maps. Geoinformatica 3:40–43

    Google Scholar 

  4. Bertram M, Wendrock H (1996) Characterization of planar local arrangement by means of the delaunay neighbourhood. J Microsc 181(1):45–53. doi:10.1046/j.1365-2818.1996.93374.x

    Google Scholar 

  5. Buchar (2009) Assessment of the map projections for world maps. 18th International Cartographic Conference, Olomouc

  6. Bugayevskiy LM, Snyder J (1995) Map projections: a reference manual. CRC Press

  7. Burger G, Embury J, Wilkinson D (1990) The characterization of microstructures using tessellations and their application to deformation processes. Simul Theory Evolving Microstruct 199–209

  8. Chang SH, Cheng FH, Hsu WH, Wu GZ (1997) Fast algorithm for point pattern matching: invariant to translations, rotations and scale changes. Pattern Recogn 30(2):311–320

    Google Scholar 

  9. Craciunescu V, Constantinescu S (2006) Eharta. http://earth.unibuc.ro/articole/eHarta?lang=en

  10. Erle S, Krishnan S, Waters T (2009) World map warp. http://warp.worldmap.harvard.edu/

  11. Esri (2003) Identify an unknown projected coordinate system using arcmap

  12. Esri (2005) Identify an unknown projected coordinate system using arcmap

  13. Fischler MA, Bolles RC (1981) Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun ACM 24(6):381–395. doi:10.1145/358669.358692

    Article  Google Scholar 

  14. Flacke W, Kraus B, Warcup C (2005) Working with projections and datum transformations in ArcGIS: theory and practical examples. Points Verlag. http://books.google.cz/books?id=PfEsAQAAMAAJ

  15. Frank R, Ester M (2006) A quantitative similarity measure for maps. In: Riedl A, Kainz W, Elmes GA (eds) Progress in spatial data handling. Springer, Berlin Heidelberg, pp 435–450

    Chapter  Google Scholar 

  16. Gao F, Han L (2012) Implementing the nelder-mead simplex algorithm with adaptive parameters. Comput Optim Appl 51(1):259–277. doi:10.1007/s10589-010-9329-3

    Article  Google Scholar 

  17. Geography, Division M, Hébert J (1974) Panoramic maps of Anglo-American cities: a checklist of maps in the collections of the Library of Congress, Geography and Map Division, Library of Congress. http://books.google.cz/books?id=eZ7oGwAACAAJ

  18. Gkalp E, Gngr O, Boz Y (2008) Evaluation of different outlier detection methods for gps networks. Sensors Peterboroug 8(11):7344–7358. http://www.mdpi.com/1424-8220/8/11/7344/

    Article  Google Scholar 

  19. Hekimoglu S, Berber M (2003) Effectiveness of robust methods in heterogeneous linear models. J Geodesy 76(11-12): 706–713. doi:10.1007/s00190-002-0289-y

    Article  Google Scholar 

  20. Huang JF, Lai SH, Cheng CM (2007) Robust fundamental matrix estimation with accurate outlier detection. J Inf Sci Eng 23(4):1213–1225

    Google Scholar 

  21. Huber P (1981) Robust Statistics. Wiley series in probability and mathematical statistics. Probability and mathematical statistics. Wiley. http://books.google.cz/books?id=HQp2BKN-qWoC

  22. Itoh R, Horizoe M, Gotoh K (1995) A method for measuring two-dimensional dispersed state of particles. Adv Powder Technol 6(2):81–89. doi:10.1163/156855295X00086, http://www.sciencedirect.com/science/article/pii/S0921883108605348

    Google Scholar 

  23. Jenny B, Hurni L (2011) Cultural heritage: studying cartographic heritage: analysis and visualization of geometric distortions. Comput Graph 35(2):402–411. doi:10.1016/j.cag.2011.01.005

    Article  Google Scholar 

  24. Kelley CT (1995) Iterative methods for linear and nonlinear equations. No. 16 in Frontiers in Applied Mathematics. SIAM. http://www.siam.org/books/textbooks/fr16_book.pdf

  25. Knight NL, Wang J (2009) A comparison of outlier detection procedures and robust estimation methods in gps positioning. J Navig 62(4):699. http://www.journals.cambridge.org/abstract_S0373463309990142

    Article  Google Scholar 

  26. Kowal KC, P[rbreve]idal P (2012) Online georeferencing for libraries: the british library implementation of georeferencer for spatial metadata enhancement and public engagement. J Map Geogr Libr 8(3):276–289. doi:10.1080/15.4203532012.700914

    Article  Google Scholar 

  27. Krarup T, Juhl JKK (1980) Götterdmmerung over least squares. In: Proceedings of international society for photogrammetry 14th congress ISPRS Commission, vol 3. Hamburg

  28. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the nelder–mead simplex method in low dimensions. SIAM J Optim 9(1):112–147. doi:10.1137/S1052623496303470

    Article  Google Scholar 

  29. Latecki LJ, Lakamper R (2000) Shape similarity measure based on correspondence of visual parts. IEEE J PAMI 22(10):1185–1190

    Article  Google Scholar 

  30. Liu YK, Wang XQ, Bao SZ, Gombosi M, Zalik B (2007) An algorithm for polygon clipping, and for determining polygon intersections and unions. Comput Geosci 33(5):589–598. doi:10.1016/j.cageo.2006.08.008, http://www.sciencedirect.com/science/article/pii/S0098300406001841

    Article  Google Scholar 

  31. Marcelpoil R, Usson Y (1992) Methods for the study of cellular sociology: Voronoi diagrams and parametrization of the spatial relationships. J Theor Biol 154(3):359–369. doi:10.1016/S0022-5193(05)80176-6, http://www.sciencedirect.com/science/article/pii/S0022519305801766

    Article  Google Scholar 

  32. Margalit A, Knott GD (1989) An algorithm for computing the union, intersection or difference of two polygons. Comput Graph 13(2):167–183. doi:10.1016/j.cageo.2008.08, http://www.sciencedirect.com/science/article/pii/0097849389900599

    Article  Google Scholar 

  33. Martnez F, Rueda AJ, Feito FR (2009) A new algorithm for computing boolean operations on polygons. Comput Geosci 35(6):1177–1185. doi:10.1016/j.cageo.2008.08.009, http://www.sciencedirect.com/science/article/pii/S0098300408002793

    Article  Google Scholar 

  34. Mckinnon KIM (1996) Convergence of the nelder-mead simplex method to a non-stationary point. Tech rep. SIAM J Optim

  35. MetaCarta (2009) Labs: Map rectifier. http://labs.metacarta.com/rectifier/

  36. Mount DM, Netanyahu NS, Le Moigne J (1998) Improved algorithms for robust point pattern matching and applications to image registration. In: Proceedings of the fourteenth annual symposium on Computational geometry, SCG ’98, pp 155–164. ACM, New York. doi:10.1145/276884.276902

  37. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313. doi:10.1093/comjnl/7.4.308, http://comjnl.oxfordjournals.org/content/7/4/308.abstract

    Google Scholar 

  38. Okabe A, Boots B, Sugihara K, Chiu DSN, Chiu SN (2000) Spatial tessellations: concepts and applications of voronoi diagrams Wiley series in probability and statistics. Wiley

  39. Okabe A, Sugihara K (2012) Spatial analysis along networks: statistical and computational methods. Statistics in practice. Wiley. http://books.google.cz/books?id=k738tgAACAAJ

  40. Pham N, Wilamowski BM (2011) Improved nelder meads simplex method and applications. Electrical and Computer Engineering, Auburn University, Alabama

  41. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical Recipes 3rd edn. The Art of Scientific Computing, 3 edn. Cambridge University Press, New York

  42. Pridal P (2011) Georeferencer. http://www.georeferencer.org

  43. Pun CM, Li C (2009) Shape classification using simplification and tangent function. In: Proceedings of the 8th WSEAS international conference on circuits, systems, electronics, control & signal processing, CSECS’09. World Scientific and Engineering Academy and Society (WSEAS), Stevens Point, Wisconsin. pp 261–266. http://dl.acm.org/citation.cfm?id=1.736282.1736330

  44. Reps J (1998) Bird’s eye views: historic lithographs of North American cities. Princeton Architectural Press. http://books.google.cz/books?id=bPTFQgAACAAJ

  45. Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York

    Book  Google Scholar 

  46. Snyder JP (1987) Map projections–a working manual. Tech. Rep. 1395, U.S. Geological Survey. http://pubs.er.usgs.gov/usgspubs/pp/pp1395

  47. Subbarao R, Meer P (2006) Beyond ransac: user independent robust regression. In: Proceedings of the 2006 conference on computer vision and pattern recognition workshop, CVPRW ’06, p 101. IEEE Computer Society, Washington DC. doi:10.1109/CVPRW.2006.43

  48. Veltkamp RC, Hagedoorn M (1999) State-of-the-art in shape matching. Tech. rep., Principles of visual information retrieval

  49. Volotao CFDS, Santos RDCD, Erthal GJ, Dutra LV (2010) Shape characterization with turning functions. In: Proceedings of the 17th international conference on systems, signals and image processing. Editora da Universidade Federal Fluminense vol 1, pp 554–557. http://urlib.net/dpi.inpe.br/plutao/2010/11.11.17.36.41

  50. Walters FHLRJr, Morgan SL, Deming SN (1991) Sequential Simplex Optimization: a Technique for Improving Quality and Productivity in Research, Development, and Manufacturing Chemometrics series. CRC. http://www.worldcat.org/isbn/0849358949

  51. Wamelen PBV, Li Z, Iyengar SS (1999) A fast algorithm for the point pattern matching problem

  52. Wieser A, Brunner FK (2000) An extended weight model for GPS phase observations, earth, planets, and space 53:777–882

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Acknowledgments

This article was supported by a grant from the Ministry of Culture of the Czech Republic, No. DF11P01OVV003 “TEMAP - Technology for Access to Czech Map Collections: Methodology and Software for the Protection and Re-use of the National Cartographic Heritage”.

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  1. Department of Applied Geoinformatics and Cartography, Faculty of Sciences, Charles University in Prague, Celetná 597/13, 116 36, Prague 1, Czech Republic

    Tomas Bayer

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Bayer, T. Estimation of an unknown cartographic projection and its parameters from the map. Geoinformatica 18, 621–669 (2014). https://doi.org/10.1007/s10707-013-0200-4

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