Unphysical properties of the rotation tensor estimated by least squares optimization with specific application to biomechanics. (June 2016) - Rubin, M.B.; Solav, D.
Abstract: Analysis of the transformation of one data set into another is a ubiquitous problem in many fields of science. Many works approximate the transformation of a reference cluster of n vectorsX i ( i = 1, 2, …, n ) into another cluster of n vectorsx i by a translation and a rotation using a least squares optimization to obtain the rotation tensorQ . The objective of this work is to prove that this rotation tensorQ exhibits unphysical dependence on the shape and orientation of the reference cluster. In contrast, when the transformation is approximated by a translation and a general non-singular tensorF, which includes deformations, then the associated rotation tensorR does not exhibit these unphysical properties. An example in biomechanics quantifies the errors of these unphysical properties.