Properties and applications of the simplified generalized perpendicular bisector
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
An algorithm to decompose n-dimensional rotations into planar rotations
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
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The Helmert transformation is used in geodesy. It transforms a set of points into another by rotation, scaling and translation. When both sets of points are given, then least squares can be used to solve the inverse problem of determining the parameters. In particular, the parameters of the so-called seven-parameter transformation can be obtained by standard methods. In this note, it is shown how a Gauss-Newton method in the rotation parameters alone can easily be implemented to determine the parameters of the nine-parameter transformation (when different scale factors for the variables are needed).