Registration of 3-D head surfaces using multiple landmarks

A mathematical procedure based on Newton´s method is described that enables surface measurements to be registered, or normalized, with respect to spatial position, orientation, and, optionally, scale in three dimensions. An operator is required to identify homologous landmarks on the computer graphics images of surfaces to be registered. In this application, where the method is used to measure changes in facial shape, these landmarks are restricted to parts of the surface that have remained unchanged between the surfaces to be registered. Error in the registration of landmarks is minimized in a least-squares sense; hence multiple landmarks are favored to minimize the effect of individual errors produced by the measuring system and the operator. Examples are presented using measurements of the head taken with an optical surface scanner and a conventional X-ray computed tomography scanner