REGISTRATION OF 3-D HEAD SURFACES USING MULTIPLE LANDMARKS

A mathematical procedure based on Newton's method is described that en ables surface measurements to be registered, or normalized, with respe ct to spatial position, orientation, and, optionally, scale in three d imensions. An operator is required to identify homologous landmarks on the computer graphics images of surfaces to be registered. In our app lication, where the method is used to measure changes in facial shape, these landmarks are restricted to parts of the surface that have rema ined unchanged between the surfaces to be registered. Error in the reg istration of landmarks is minimized in a least-squares sense, hence mu ltiple landmarks are favored to minimize the effect of individual erro rs produced by the measuring system and the operator. Examples are pre sented using measurements of the head taken with an optical surface sc anner and a conventional x-ray computed tomography scanner.