In this paper we introduce a new framework for image registration. Our formulation is based on consistent discretization of the optimization problem coupled with a multigrid solution of the linear system which evolve in a Gauss-Newton iteration. We show that our discretization is h-elliptic independent of parameter choice and therefore a simple multigrid implementation can be used. To overcome potential large nonlinearities and to further speed up computation, we use a multilevel continuation technique. We demonstrate the efficiency of our method on a realistic highly nonlinear registration problem.

The position, surface area and visual field representation of human visual areas V1, V2 and V3 were measured using fMRI in 7 subjects (14 hemispheres). Cortical visual field maps of the central 12 deg were measured using rotating wedge and expanding ring stimuli. The boundaries between areas were identified using an automated procedure to fit an atlas of the expected visual field map to the data. All position and surface area measurements were made along the boundary between white matter and gray matter. The representation of the central 2 deg of visual field in areas V1, V2, V3 and hV4 spans about 2100 mm2 and is centered on the lateral-ventral aspect of the occipital lobes at Talairach coordinates -29, -78, -11 and 25, -80, -9. The mean area between the 2-deg and 12-deg eccentricities for the primary visual areas was: V1: 1470 mm2; V2: 1115 mm2; and V3: 819 mm2. The sizes of areas V1, V2 and V3 varied by about a factor of 2.5 across individuals; the sizes of V1 and V2 are significantly correlated within individuals, but there is a very low correlation between V1 and V3. These in vivo measurements of normal human retinotopic visual areas can be used as a reference for comparison to unusual cases involving developmental plasticity, recovery from injury, identifying homology with animal models, or analyzing the computational resources available within the visual pathways.

Abstract.A particular problem in image registration arises for multimodal images taken from different imaging devices and/or modalities. Starting in 1995, mutual information has shown to be a very successful distance measure for multi-modal image registration. However, mutual information has also a number of well-known drawbacks. Its main disadvantage is that it is known to be highly non-convex and has typically many local maxima.This observation motivate us to seek a different image similarity measure which is better suited for optimization but as well capable to handle multi-modal images. In this work we investigate an alternative distance measure which is based on normalized gradients and compare its performance to Mutual Information. We call the new distance measure Normalized Gradient Fields (NGF).

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Diffusion-weighted magnetic resonance imaging is a key investigation technique in modern neuroscience. In clinical settings, diffusion-weighted imaging and its extension to diffusion tensor imaging (DTI) are usually performed applying the technique of echo-planar imaging (EPI). EPI is the commonly available ultrafast acquisition technique for single-shot acquisition with spatial encoding in a Cartesian system. A drawback of these sequences is their high sensitivity against small perturbations of the magnetic field, caused, e.g., by differences in magnetic susceptibility of soft tissue, bone and air. The resulting magnetic field inhomogeneities thus cause geometrical distortions and intensity modulations in diffusion-weighted images. This complicates the fusion with anatomical T1- or T2-weighted MR images obtained with conventional spin- or gradient-echo images and negligible distortion. In order to limit the degradation of diffusion-weighted MR data, we present here a variational approach based on a reference scan pair with reversed polarity of the phase- and frequency-encoding gradients and hence reversed distortion. The key novelty is a tailored nonlinear regularization functional to obtain smooth and diffeomorphic transformations. We incorporate the physical distortion model into a variational image registration framework and derive an accurate and fast correction algorithm. We evaluate the applicability of our approach to distorted DTI brain scans of six healthy volunteers. For all datasets, the automatic correction algorithm considerably reduced the image degradation. We show that, after correction, fusion with T1- or T2-weighted images can be obtained by a simple rigid registration. Furthermore, we demonstrate the improvement due to the novel regularization scheme. Most importantly, we show that it provides meaningful, i.e. diffeomorphic, geometric transformations, independent of the actual choice of the regularization parameters.