title: A procedure for determining rigid body transformation parameters.
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.
authors.affiliation: Applied Physiology Research Unit, School of Sport and Exercise Sciences, University of Birmingham, Edgbaston, U.K.
authors.forename: J H
authors.initials: JH
authors.lastname: Challis
mesh_terms: D000465:Algorithms; D001696:Biomechanical Phenomena; D001842:Bone and Bones / Q000502:physiology*; D006801:Humans; D015233:Models, Statistical; D009068:Movement; D018482:Muscle, Skeletal / Q000502:physiology*; D013977:Tibia / Q000033:anatomy & histology / Q000502:physiology