Preprint has been published in a journal as an article
DOI of the published article https://doi.org/10.1016/j.ijengsci.2016.02.001
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DOI of the published article https://doi.org/10.1016/j.ijengsci.2016.02.001
Unphysical properties of the rotation tensor estimated by least squares optimization with specific application to biomechanics
DOI:
https://doi.org/10.31224/osf.io/397zyKeywords:
anthropometric scaling, biomechanical motion analysis, factor structure, least squares, polar decomposition, registration of shapes, satellite attitude, soft tissue artifactAbstract
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 vectors Xi (i=1,2,..,n) into another cluster of n vectors xi by a translation and a rotation using a least squares optimization to obtain the rotation tensor Q. The objective of this work is to prove that this rotation tensor Q 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 tensor F, which includes deformations, then the associated rotation tensor R does not exhibit these unphysical properties. An example in biomechanics quantifies the errors of these unphysical properties.Downloads
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Posted
2017-07-21