Validation of Point Fiducial Based Registration and Cross Validation Using External Fiducial Gold Standards

One of the most basic methods of rigid-body registration is to have someone with anatomic expertise pick pairs of homo logous points in the two images. Ideally, three points would suffice to compute the correct registration parameters in three dimensions. However, the selection of points is certain to have some inaccuracy, so many points are typically chosen and registration is performed in a way that minimizes the summed squared distance between homologous points after registration. The translational component of this minimization problem is solved easily by aligning the centroid of the points in one image with the centroid of the homologous set of points in the other image. An easy way to do this is to redefine the origin of the coordinate system in each image so that it is located at the centroid position. The rotational component is then derived using a method known as the Procrustes algorithm, which provides an exact noniterative solution [3]. The residual RMS error after registration with this algorithm is termed the fiducial registration error (FRE) by Fitzpatrick et al. [1]. This error can be used to estimate the slightly larger error in localization of each individual fiducial point using the equation

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