Abstract. We p r e s e n t an approach to elastic registration of tomographic brain images which is based on thin-plate splines and takes into account landmark errors. The inclusion of error information is important in clinical applications since landmark extraction is always prone to error. In comparison to previous work, our approach can cope with anisotropic errors, which is signi cantly more realistic than dealing only with isotropic errors. In particular, it is now possible to include di erent t ypes of landmarks, e.g., quasi-landmarks at the outer contour of the brain. Also, we introduce an approach to estimate landmark localization uncertainties directly from the image data. Experimental results are presented for the registration of 2D and 3D MR images.
MotivationImage registration is fundamental to computer-assisted neurosurgery. Examples are the registration of tomographic images and the registration of images with digital atlases. In either case, the central aim is to increase the accuracy of localizing anatomical structures in 3D space. One principal approach to registration is based on thin-plate splines and anatomical point landmarks.Previous work on thin-plate spline registration has concentrated on specifying the landmarks manually and on using an interpolating transformation model (e.g., 2], 6], 11]). The approach is e cient and well-suited for user-interaction which w e consider important in clinical scenaria. However, with an interpolation scheme the corresponding landmarks are forced to match exactly. I t i s ( i m p l i citly) assumed that the landmark positions are known exactly, w h i c h, however, is generally not true in practical applications. Therefore, to take i n to account landmark localization errors, we h a ve recently introduced an approximation scheme ( 13]). This scheme is based on a minimizing functional, it uses scalar weights to represent landmark errors, and it has been described for images of arbitrary dimensions. The applicability of our approach has been demonstrated for 2D MR images. Bookstein 3] has proposed a di erent approach to relax the interpolation conditions. His approach, however, has not been related to a minimizing