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FIGURE 7 3D image warping measures patterns of anatomic differences. T1-weighted MR sagittal brain slice images from (left, a) a normal elderly subject's scan; (b) a "target" anatomy, from a patient with clinically determined Alzheimer's disease; and (c) result of warping the reference anatomy into structural correspondence with the target. Note the precise nonlinear registration of the cortical boundaries, the desired reconfiguration of the major sulci, and the contraction of the ventricular space and cerebellum. The complexity of the recovered deformation field is shown by applying the two in-slice components of the 3D volumetric transformation to a regular grid in the reference coordinate system. This visualization technique (d) highlights the especially large contraction in the cerebellar region, and the complexity of the warping field in the posterior frontal and cingulate areas, corresponding to subtle local variations in anatomy between the two subjects. To monitor the smooth transition to the surrounding anatomy of the deformation fields initially defined on the surface systems, the magnitude of the warping field is visualized (e) on models of the surface anatomy of the target brain, as well as on an orthogonal plane slicing through many of these surfaces at the same level as the anatomic sections. The warping field extends smoothly from the complex anatomic surfaces into the surrounding brain architecture, and severe deformations are highlighted in the pre-marginal cortex, ventricular, and cerebellar areas. See also Plate 84.

FIGURE 8 Cortical Surface Extraction. Prior to matching cortical surfaces across subjects, a high-resolution surface representation of the cortex is obtained with a semi-automatic 3D active surface extraction algorithm [73, 74]. A spherical mesh surface (top left) is governed by a system of partial differential equations, which allow it to be continuously deformed to match a target boundary defined by a threshold value in the continuous 3D MR image intensity field. The algorithm operates in a multiscale fashion, so that progressively finer surface detail is extracted at finer scale representations of the data. The initial surface, composed of 8192 polygons, is extracted rapidly, but expresses only the gross shape of the cortex (top right). After several finer scale steps, the final model of the cortex (lower left) consists of a high-resolution mesh consisting of 100,000-150,000 discrete triangular elements that tile the surface (lower right). See also Plate 85.

FIGURE 8 Cortical Surface Extraction. Prior to matching cortical surfaces across subjects, a high-resolution surface representation of the cortex is obtained with a semi-automatic 3D active surface extraction algorithm [73, 74]. A spherical mesh surface (top left) is governed by a system of partial differential equations, which allow it to be continuously deformed to match a target boundary defined by a threshold value in the continuous 3D MR image intensity field. The algorithm operates in a multiscale fashion, so that progressively finer surface detail is extracted at finer scale representations of the data. The initial surface, composed of 8192 polygons, is extracted rapidly, but expresses only the gross shape of the cortex (top right). After several finer scale steps, the final model of the cortex (lower left) consists of a high-resolution mesh consisting of 100,000-150,000 discrete triangular elements that tile the surface (lower right). See also Plate 85.

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