Determining the movements of the skeleton using well-configured markers

Abstract

The problem of determining skeletal movements in three dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of the landmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.