The probabilistic atlas described above is defined by the connectivity of its tetrahedral mesh, its reference position xr, and the probabilities of label occurrences α. Using the techniques developed in (Van Leemput, (in press) ), we automatically learn these properties from a set of example segmentations. The learning involves maximizing the probability with which the atlas model would generate the example segmentations, or, equivalently, minimizing the number of bits needed to encode them. As shown in (Van Leemput, (in press) ), this procedure automatically yields sparse atlas representations that explicitly avoid overfitting to the training data, and that are therefore better at predicting the neuroanatomy in new subjects than conventional probabilistic atlases.
The segmentations we use for atlas computation are based on manual delineations of the hippocampal subfields in ultra-high resolution T1-weighted MRI scans of a number of different subjects. These delineations include the fimbria, presubiculum, subiculum, CA1, CA2/3, and CA4/DG fields, as well as choroid plexus, hippocampal fissure, and inferior lateral ventricle, as shown in Figure 1. Because the hippocampal formation covers only a small part of the images, we define a cuboid region of interest (ROI) encompassing all the structures of interest in all subjects after affine registration, and model the segmentations within this ROI only. (More details about the manual segmentation protocol and the definition of the ROI are given below.) Prior to atlas computation, voxels inside the ROI not belonging to one of the manually delineated subregions are automatically labeled as white matter, gray matter, or CSF using a brain MRI tissue classification algorithm (Van Leemput et al., 1999b ), as these tissues provide useful additional information about the global anatomy in and around the hippocampal formation.
An example of the prior, learned from hippocampal labels in nine subjects, is shown in Figure 2.