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Computational Study of the 3D Affine Transformation Part I. 3-point Problem
Authors

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Robert H. Lewis
Organization: Fordham University
Department: Department of Mathematics
Piroska Zaletnyik
Organization: Budapest University of Technology and Economics
Department: Department of Geodesy and Surveying
Joseph Awange
Organization: Curtin University of Technology
Department: Spatial Sciences, Division of Resource and Environmental
Revision date

2008-03-10
Description

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.
Subjects

*Applied Mathematics
*Social Science > Geography and Cartography
Keywords

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]