Generalized mathematical representation of the soft tissue artefact

Abstract

While reconstructing skeletal movement using stereophotogrammetry, the relative movement between a skin marker and the underlying bone is regarded as an artefact (soft tissue artefact: STA). Similarly, the consequent pose, size and shape variations that affect a cluster of markers associated with a bony segment, or any arbitrary change of configuration in the marker local positions as representative of the skin envelope shape variation, may also be looked upon as an STA. Bone pose estimators able to compensate for these artefacts must embed relevant a priori knowledge in the form of an STA mathematical model. Prior to tackling this modeling exercise, an appropriate definition and mathematical representation of the STA time histories must be accomplished. Relevant appropriateness is based on the degree of approximation of the STA reconstruction and on the number of parameters involved. The objective of this study was to propose a generalized mathematical representation of the STA which would be applicable for most plausible definitions of it. To this purpose, a modal approach was used that, most importantly, allows for the splitting of a given STA into additive components (modes). For each STA definition, these modes may be ranked according to the contribution that each of them gives to the reconstruction of the STA. In this way, the STA definition leading to the minimum number of modes, and, therefore, of parameters, that provides an adequate approximation for further purposes can be selected, allowing a trade-off between complexity and effectiveness of the STA model. Using information available in the literature and data provided by an ex-vivo experiment, it is shown that the modes corresponding to the different STA definitions (individual marker displacements, marker-cluster geometrical transformations, and skin envelope shape variations) can be ranked and selected leading, respectively, to a large, moderate or low number of parameters embedded in the STA mathematical representation.

Keywords: Deformation energy; Marker-cluster geometrical transformation; STA mathematical model; Skin envelope shape variations; Skin marker displacement.