In: Proceedings of the 2005 conference on Genetic and evolutionary computation, GECCO ’05. doi: 10.1137/S1052623401383455ĭas S, Konar A, Chakraborty UK (2005) Two improved differential evolution schemes for faster global search. ĭai YH (2002) Convergence properties of the bfgs algoritm. Advanced Topics in Computer Science Series, McGraw-Hill CompaniesĬrǎciunescu V, Constantinescu S (2006) Eharta.

In: Proceedings of International Conference on Machine Learning and Computing (ICMLC 2009)Ĭorne D, Dorigo M, Glover F (1999) New Ideas in Optimization. doi: 10.1093/imamat/12.3.223Ĭhien CW, Hsu ZR, Lee WP et al (2009) Improving the performance of differential evolution algorithm with modified mutation factor. īroyden CG, DENNIS JE, More JJ (1973) On the local and superlinear convergence of quasi-newton methods. doi: 10.1109/TEVC.2006.872133īroyden CG (1970) The convergence of a class of double rank minimization algorithms: 2.

e-Perimetron 1(1):60–70īrest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. SIAM, Philadelphiaīoutoura C, Livieratos E (2006) Some fundamentals for the study of the geometry of early maps by comparative methods. Lecture Notes in Geoinformation and Cartography, DOI 10.1007/978-4-3_33, (to appear in print)ījörck Å (1996) Numerical Methods for Least Squares Problems. In: Gartner G, Ortag F (eds) Cartography in Central and Eastern Europe. doi: 10.1007/s1070-4īayer T, Potůčková M, Čábelka M (2010) Cartometric Analysis of Old Maps on the Example of Vogt’s Map. e-Perimetron 1(1):32–42īayer T (2014) Estimation of an unknown cartographic projection and its parameters from the map. International Archives of Photogrammetry and Remote Sensing 33(B5/1 PART 5):30–37īalletti C (2006) Georeference in the analysis of the geometric content of early maps. IEEE J PAMI 13 (3):209–216īalletti C (2000) Analytical and quantitative methods for the analysis of the geometrical content of historical cartography. J Oper Res Soc:405–421Īrkin EM, Chew LP, Huttenlocher DP, Kedem K, Mitchell JSB (1991) An efficiently computable metric for comparing polygonal shapes. The proposed algorithms have been implemented in the new version of the detectproj software.Īl-Baali M, Fletcher R (1985) Variational methods for non-linear least-squares. All methods are compared and the results are presented for the synthetic data as well as for 8 early maps from the Map Collection of the Charles University and the David Rumsay Map Collection. The constant values of projection φ k, λ k, φ 1, λ 0, and map constants R,Δ X,Δ Y, α (in relation to which the methods are invariant) are estimated. Due to the non-convexity and discontinuity, its global minimum is determined using the global optimization, represented by the differential evolution.

For the shape similarity approach, the minimized objective function ϕ takes into account the spatial distribution of the features, together with the shapes of the meridians, parallels and other 0D-2D elements. The location similarity approach takes into account the residuals on the corresponding features the minimum is found using the non-linear least squares. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the map projection it could improve their georeference. This article presents three new methods (M5, M6, M7) for the estimation of an unknown map projection and its parameters.

Emory method map projections