As noted earlier, because of pronounced anatomic variability between individual human brains, any atlas or clinical diagnostic system based on a single subject's anatomy cannot succeed fully. A deformable brain atlas counteracts some of the limitations of a fixed atlas by using mathematically flexible transformations. Nonetheless, its success is still based on the premise that brains resemble a prototypical template of anatomy and can be produced by continuously deforming it.
Atlasing considerations suggest that a statistical confidence limit, rather than an absolute representation of neuroanatomy, may be more appropriate for representing particular subpopulations. Methods to create probabilistic brain atlases currently fall into three major categories, each differing slightly in its conceptual foundations. The three methods are density-based, label-based, and deformation-based approaches.
(1) Density-Based Approaches. Initial approaches to population-based atlasing concentrated on generating average representations of anatomy by intensity averaging of multiple MRI scans [1,31]. The average that results has large areas, especially at the cortex, where individual structures are blurred because of spatial variability in the population. Although this blurring limits their usefulness as a quantitative tool, the templates can be used as targets for the automated registration and mapping of MR and coregistered functional data into stereotaxic space .
(2) Label-Based Approaches. In label-based approaches (; also known as SPAM approaches, short for statistical/probabilistic anatomy maps), large ensembles of brain data are manually labeled, or "segmented," into subvolumes, after registration into stereotaxic space. A probability map is then constructed for each segmented structure, by determining the proportion of subjects assigned a given anatomic label at each voxel position [32,74,76]. The information these probability maps provide on the location of various tissue classes in stereotaxic space has been useful in designing automated tissue classifiers and approaches to correct radio-frequency and intensity inhomogeneities in MR scans . In our laboratory, we have also used SPAM probabilistic maps to constrain the search space for significant activations in PET and SPECT imaging experiments [25,65].
(3) Deformation-Based Approaches. As noted earlier, when applied to two different 3D brain scans, a nonlinear registration calculates a deformation map (Figs 5, 6) that matches brain structures in one scan with their counterparts in the other. In probabilistic atlases based on deformation maps [109,110,112], statistical properties of these deformation maps are encoded locally to determine the magnitude and directional biases of anatomic variation. Encoding of local variation can then be used to assess the severity of structural variants outside of the normal range, which may be a sign of disease . A major goal in designing this type of pathology detection system is to recognize that both the magnitude and local directional biases of structural variability in the brain may be different at every single anatomic point . In contrast to the intensity averaging of other current approaches [1,31], an anisotropic random vector field framework is introduced to encode directional biases in anatomic variability and map out abnormalities in new subjects .
The three major approaches for probabilistic atlas construction differ only in the attribute whose statistical distribution is modeled and analyzed. Random vector fields (i.e., vector distributions of deformation vectors at each point in space) are analyzed in approaches based on deformation maps, while random scalar fields are used to model MR intensity statistics in the density-based approach, and to model the incidence of binary labels in space in the label-based approach.
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