clear from a brief inspection of the MR and CT head images in Fig. 1 or the CT and PET images in Fig. 2. Types of correlation have, however, been used for intermodality medical image registration since the earliest days of this field. Maguire ef aZ. [2] proposed an algorithm for registration of CT and PET images of the head using a transformation that could be represented by a second-order 2D (for two single slices) or 3D (for volumes) polynomial calculated from landmarks that were interactively identified and refined by local cross correlation. Apicella ef aZ. [3] proposed the use of Fourier invariants to provide fast cross-correlation of MR and PET images. A few years later, van den Elsen ef aZ. [4] used an intensity remapping algorithm to make cross-correlation applicable to MR-CT registration. None of these methods became widely used. The favorite intermodality image registration techniques in the late 1980s and early 1990s used point landmarks [5-7] or surfaces [8-10], and implementations of these approaches were in use in several centers. The first intermodality intensity-based registration algorithm that became widely used was the variance of intensity ratios proposed by Roger Woods for the registration of MR and PET brain images [11]. This algorithm involved an apparently trivial change to the source code of his previously published PET-PET registration technique [12], but transformed its functionality. This algorithm makes an idealized assumption that "all pixels with a particular MR pixel value represent the same tissue type so that values of corresponding PET pixels should also be similar to each other". The algorithm therefore minimizes the normalized standard deviation of PET voxel values for each of 256 MR intensity partitions. For reliable use, it was found to be necessary to remove dura, skull, and scalp from the MR images prior to registration.

For registration of the images A and B, the variance of intensity ratios (VTR) can be calculated in two ways, either as the sum of the normalized standard deviation of voxel values in B for each intensity a in A(VTRB), or as the sum of the normalized standard deviation of voxel values in A for each intensity b in B(V7PA):



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