Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentation
<div class="abstract"><div class="abstract_item"><em>Modern techniques for the map analysis allow for the creation of full or partial geometric reconstruction of its content. The projection is described by the set of estimated constant values: transformed pole p...
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| Format: | Article |
| Language: | English |
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Czech Technical University in Prague
2017-03-01
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| Series: | Geoinformatics FCE CTU |
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| Online Access: | https://ojs.cvut.cz/ojs/index.php/gi/article/view/4095 |
| _version_ | 1818927890223333376 |
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| author | Tomáš Bayer |
| author_facet | Tomáš Bayer |
| author_sort | Tomáš Bayer |
| collection | DOAJ |
| description | <div class="abstract"><div class="abstract_item"><em>Modern techniques for the map analysis allow for the creation of full or partial geometric reconstruction of its content. The projection is described by the set of estimated constant values: transformed pole position, standard parallel latitude, longitude of the central meridian, and a constant parameter. Analogously the analyzed map is represented by its constant values: auxiliary sphere radius, origin shifts, and angle of rotation. Several new methods denoted as M6-M9 for the estimation of an unknown map projection and its parameters differing in the number of determined parameters, reliability, robustness, and convergence have been developed. However, their computational demands are similar. Instead of directly measuring the dissimilarity of two projections, the analyzed map in an unknown projection and the image of the sphere in the well-known (i.e., analyzed) projection are compared. Several distance functions for the similarity measurements based on the location as well as shape similarity approaches are proposed. An unconstrained global optimization problem poorly scaled, with large residuals, for the vector of unknown parameters is solved by the hybrid BFGS method. To avoid a slower convergence rate for small residual problems, it has the ability to switch between first- and second-order methods. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the projection. Its importance is primarily referred to refinement of spatial georeference for the medium- and small-scale maps, analysis of the knowledge about the former world, analysis of the incorrectly/inaccurately drawn regions, and appropriate cataloging of maps. The proposed algorithms have been implemented in the new version of the <span style="font-family: monospace;">detectproj</span> software.</em></div></div> |
| first_indexed | 2024-12-20T03:20:12Z |
| format | Article |
| id | doaj.art-9fe8dc15ca974bdba0264c8e4f96b5bd |
| institution | Directory Open Access Journal |
| issn | 1802-2669 |
| language | English |
| last_indexed | 2024-12-20T03:20:12Z |
| publishDate | 2017-03-01 |
| publisher | Czech Technical University in Prague |
| record_format | Article |
| series | Geoinformatics FCE CTU |
| spelling | doaj.art-9fe8dc15ca974bdba0264c8e4f96b5bd2022-12-21T19:55:15ZengCzech Technical University in PragueGeoinformatics FCE CTU1802-26692017-03-01161175210.14311/gi.16.1.23599Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentationTomáš Bayer0Department of Geomatics, Faculty of Civil Engineering, Czech Technical University in Prague<div class="abstract"><div class="abstract_item"><em>Modern techniques for the map analysis allow for the creation of full or partial geometric reconstruction of its content. The projection is described by the set of estimated constant values: transformed pole position, standard parallel latitude, longitude of the central meridian, and a constant parameter. Analogously the analyzed map is represented by its constant values: auxiliary sphere radius, origin shifts, and angle of rotation. Several new methods denoted as M6-M9 for the estimation of an unknown map projection and its parameters differing in the number of determined parameters, reliability, robustness, and convergence have been developed. However, their computational demands are similar. Instead of directly measuring the dissimilarity of two projections, the analyzed map in an unknown projection and the image of the sphere in the well-known (i.e., analyzed) projection are compared. Several distance functions for the similarity measurements based on the location as well as shape similarity approaches are proposed. An unconstrained global optimization problem poorly scaled, with large residuals, for the vector of unknown parameters is solved by the hybrid BFGS method. To avoid a slower convergence rate for small residual problems, it has the ability to switch between first- and second-order methods. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the projection. Its importance is primarily referred to refinement of spatial georeference for the medium- and small-scale maps, analysis of the knowledge about the former world, analysis of the incorrectly/inaccurately drawn regions, and appropriate cataloging of maps. The proposed algorithms have been implemented in the new version of the <span style="font-family: monospace;">detectproj</span> software.</em></div></div>https://ojs.cvut.cz/ojs/index.php/gi/article/view/4095Map projectionanalysisdetectionearly mapslocation similarityoptimizationnon-linear least squaresBFGSgeoreferenceM-estimatorsHuber function |
| spellingShingle | Tomáš Bayer Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentation Geoinformatics FCE CTU Map projection analysis detection early maps location similarity optimization non-linear least squares BFGS georeference M-estimators Huber function |
| title | Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentation |
| title_full | Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentation |
| title_fullStr | Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentation |
| title_full_unstemmed | Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentation |
| title_short | Estimation of the Cartographic Projection and~its Application in Geoinformatics-habilitation thesis presentation |
| title_sort | estimation of the cartographic projection and its application in geoinformatics habilitation thesis presentation |
| topic | Map projection analysis detection early maps location similarity optimization non-linear least squares BFGS georeference M-estimators Huber function |
| url | https://ojs.cvut.cz/ojs/index.php/gi/article/view/4095 |
| work_keys_str_mv | AT tomasbayer estimationofthecartographicprojectionanditsapplicationingeoinformaticshabilitationthesispresentation |