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A procedure for determining rigid body transformation parameters.

J H Challis
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Abstract

For many biomechanical applications it is necessary to determine the parameters which describe the transformation of a rigid body from one reference frame to another. These parameters are a scaling factor, an attitude matrix, and a translation vector. The paper presents a new procedure for the determination of these parameters incorporating the work of Arun et al. [IEEE Trans. Pattern Anal. Machine Intell, 9, 698-700 (1987)] but expanding their analysis to allow for the determination of a scale factor, the scalar weighting of the least-squares problem, and the problem of obtaining the incorrect determinant when determining the attitude matrix. The procedure, which requires the coordinates of three or more non-collinear points, is based around the singular value decomposition, and provides a least-squares estimate of the rigid body transformation parameters. Examples are presented of the use of this procedure for determining the attitude of a rigid body, and for osteometric scaling. When used for osteometric scaling mirror transformations are possible, therefore a right-hand specimen can be scaled to the left-hand side of another specimen.

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AlgorithmsBiomechanical PhenomenaBone and BonesHumansModels, StatisticalMovementMuscle, SkeletalTibiaJournal Article

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BibTeXRIS

J H Challis. 1995. A procedure for determining rigid body transformation parameters.. https://doi.org/10.1016/0021-9290(94)00116-l

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