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Computational Study of the 3D Affine Transformation Part I. 3-point Problem
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| Organization: | Budapest University of Technology and Economics |
| Department: | Photogrammetry and Geoinformatics |
| Organization: | Fordham University |
| Department: | Department of Mathematics |
| Organization: | Budapest University of Technology and Economics |
| Department: | Department of Geodesy and Surveying |
| Organization: | Curtin University of Technology |
| Department: | Spatial Sciences, Division of Resource and Environmental |
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2008-03-10
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In case of considerable nonlinearity i.e. in geodesy, photogrammetry, robotics, it is difficult to find proper initial values to solve the parameter estimation problem of 3D affine transformation with 9 parameters via linearization and/or iteration. In this paper, we developed a symbolic - numeric method to achieve the solution without initial guess. Our method employs explicit analytical expressions developed by computer algebra technique via Dixon resultant for solving 3 -point problem. Numerical illustration is presented with real world geodetical data representing Hungarian Datum.
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9-parameter 3D transformation, solution of polynomial system, symbolic solution, Dixon resultant, early discovery factors, Groebner basis, homotopy, Jenkins-Traub algorithm, global minimization, genetic algorithm
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| 3Daffine_FullPart_1modified08.nb (2 MB) - Mathematica Notebook [for Mathematica 6.0] |
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