Tensor-based morphometry (TBM) is widely used in computational anatomy as a means to understand shape variation between MR structural brain images. A 3D nonlinear registration technique is used to align all brain images to a common neuroanatomical template, and the deformation fields are analyzed statistically to identify group differences in anatomy in TBM. Differences between images are usually computed solely from the determinants of the Jacobian matrices J that are associated with the deformation fields computed by the registration procedure. The determinants give the local volume increases and reductions of the image from the registration. However, only the magnitude of the expansions or contractions is examined, while the directional components of the changes are ignored. We propose an approach which remedies this problem, by computing both shape and volume change statistics using the deformation tensors, defined as (J^T J)^1/2. Furthermore, detection power depends on several factors, and key among these is the quality of the non-linear registration, which depends both on the registration algorithm and on the common target to which all images are mapped. We designed a new fluid registration code which penalizes deviations from zero deformation tensors. To reduce dependence on the choice of individual template, we average deformation tensors from multiple registrations to individual reference images. The registration and statistics in the proposed approach can both be extended in a straightforward way to the analysis of diffusion tensor images.
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