Spatial Normalization

We describe a comprehensive framework for performing rapid and automatic non-label based nonlinear spatial normalizations. The approach adopted minimizes the residual squared diierence between an image and a template of the same modality. In order to reduce the number of parameters to be tted, the nonlinear warps are described by a linear combination of low spatial frequency basis functions. The objective is to determine the optimum coeecients for each of the bases by minimizing the sum of squared diierences between the image and template, while simultaneously maximizing the smoothness of the transformation using a maximum a posteriori (MAP) approach. Most MAP approaches assume that the variance associated with each voxel is already known and that there is no covariance between neighboring voxels. The approach described here attempts to estimate this variance from the data, and also corrects for the correlations between neighboring voxels. This makes the same approach suitable for the spatial normalization of both high quality MR images, and low resolution noisy PET images. A fast algorithm has been developed that utilizes Taylor's Theorem and the separable nature of the basis functions, meaning that most of the nonlinear spatial variability between images can be automatically corrected within a few minutes. 1 Background This paper concerns the problem of nonlinear spatial normalization: Namely how to map a single subject's brain image into a standard space. The solution of this problem allows for a wide range of voxel-based analyses and facilitates the comparison of diierent subjects and databases. The problem of spatial normalization is not a trivial one; indeed at some anatomical scales it is not clear that a solution even exists. A fundamental advantage of using spatially normalized images is that activations can be reported according to a set of meaningful Euclidian coordinates within a standard space (Fox, 1995). New results can be readily incorporated into ongoing brain atlas and database projects such as that being developed by the International Consortium for Human Brain Mapping (ICBM) (Mazziotta et al., 1995). The most commonly adopted coordinate system within the brain imaging community is that described by the atlas of Talairach & Tournoux (1988). When whole brain structural images (typically high resolution MRI) of the subject are available in addition to the functional images, the images can be co-registered using any one of a number of methods for inter-modality registration (Pelizzari et al. the spatial transformations that warp the images to the …