A study of three-dimensional curves

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Abstract
In certain abnormalities of spinal shape, the long axis of the spine moves out of the median sagittal plane, producing both an axial torsion and a lateral deviation out of the usual front-back plane. Clinicians need to be able to assess rapidly and accurately whether or not an individual has such an abnormality. In this paper, we examine several case studies. These are analyzed using some simple summary statistics, and the use of these methods to infer abnormality is demonstrated. Using a simple fitted model for the data, an angular estimate of abnormality is obtained. Empirical measures of abnormality based on the eigenvalues of the covariance matrix are also determined. These methods are applied to a number of individuals for whom the surface spinal profiles have been recorded and who have been assessed as normal or abnormal by clinicians.