4.2 Dependence of Error

The errors in registration are calculated as the difference in the registration translations and rotations produced from a clinical (based on ILM) and nominal technique (based on the use of the external fiducials on real scans or a priori knowledge in simulation). The errors in a registration with the ILM technique are dependent on the number of point pairs used, m, the correspondence or homology error between corresponding points in each volume, and the configuration of the point sets. The homology error which describes the perturbation between corresponding configurations may be characterised by the full width at half maximum, , of the frequency distribution resulting from the repeated selection of the same point in an image. A distribution is effected because of the resolution limits of the sensor and the interpretive faculties of the operator selecting the points. The error in registration will be dependent on the dimension or radius of the point sets' configurations because of the greater lever introduced at larger radii by the same rotation about a centroid. For a configuration described by the radial dispersion of the point pairs, r, and the same m, a distribution of translation and rotation errors results from N registrations where the same point pairs were chosen N times because of the finite . The distribution of the errors may be characterised by their standard deviation, , and used to quantify the registration errors. With the assumption of a Gaussian probability distribution of the errors, the probability for the likelihood of a certain magnitude of error in the translational, , and rotational, , components of the affine transformation may also be specified. That the probability distribution is reasonably Gaussian is estimated by calculating the reduced statistic, , where for the number of degrees of freedom [Bev69] (please refer to the appendix).