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A Robust Solution of Similarity Transformation via Dual Quaternions
Author

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Revision date

2014-12-23
Description

A RANSAC type method with a core algorithm based on dual quaternions is presented for similarity transformation. Although dual quaternion technique basically represents rigid transformation (rotation and translation),introducing a simple additional transformation for the scale parameter, one can successfully use it for similarity transformation too, where scaling is also important. For 3-point problem a determined multivariate polynomial system with 7 unknowns can be developed and easily solved by numerical Groebner basis. Since this computation is fast, it can be efficiently integrated it into a RANSAC type method as a core algorithm, where it is solved repeatedly. For n-point problem we employ Gauss-Jacobi method solving the 3-point subsystem simultaneously. This contribution will guide the reader through the different phases of the development of the method step by step illustrated by numerical examples. Finally, example with real world data representing an overdetermined n-point problem is solved. All symbolic and numeric computations have been carried out with Mathematica 10.
Subject

*Applied Mathematics > Numerical Methods
Keywords

similarity transformation, dual quaternions, numerical Groebner basis, RANSAC, Gauss-Jacobi solution
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ETR589XYZGlobal.txt (2.9 KB) - Text file
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HD72xyzLocal.txt (3 KB) - Text file
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DualQuaternion_Application_RANSAC_01.nb (1.2 MB) - Mathematica Notebook