Abstract
This paper examines the multiple atlas random diffeomorphic orbit model in Computational Anatomy (CA) for parameter estimation and segmentation of subcortical and ventricular neuroanatomy in magnetic resonance imagery. We assume that there exist multiple magnetic resonance image (MRI) atlases, each atlas containing a collection of locally-defined charts in the brain generated via manual delineation of the structures of interest. We focus on maximum a posteriori estimation of high dimensional segmentations of MR within the class of generative models representing the observed MRI as a conditionally Gaussian random field, conditioned on the atlas charts and the diffeomorphic change of coordinates of each chart that generates it. The charts and their diffeomorphic correspondences are unknown and viewed as latent or hidden variables. We demonstrate that the expectation-maximization (EM) algorithm arises naturally, yielding the likelihood-fusion equation which the a posteriori estimator of the segmentation labels maximizes. The likelihoods being fused are modeled as conditionally Gaussian random fields with mean fields a function of each atlas chart under its diffeomorphic change of coordinates onto the target. The conditional-mean in the EM algorithm specifies the convex weights with which the chart-specific likelihoods are fused. The multiple atlases with the associated convex weights imply that the posterior distribution is a multi-modal representation of the measured MRI. Segmentation results for subcortical and ventricular structures of subjects, within populations of demented subjects, are demonstrated, including the use of multiple atlases across multiple diseased groups.
Highlights
The advent of high-resolution T1-weighted magnetic resonance (MR) neuroimaging technologies facilitates a detailed exploration into human brain anatomy
The problem focused on in this paper is to extend the generative random diffeomorphic orbit model that has been used in single atlas approaches [30,31,35,39] to the multiple atlas model, in which are the diffeomorphic changes in coordinates unknown and jointly measurable parameters are unknown such as those arising in: (1) atlas labeling corresponding to disease inference, (2) structure parameters such as volumes, or (3) dense label field estimation associated with segmenting the target image into anatomically defined regions
We explored the efficacy of adding neighboring tissue labels around the structures of interest in the atlas
Summary
The advent of high-resolution T1-weighted magnetic resonance (MR) neuroimaging technologies facilitates a detailed exploration into human brain anatomy. There exists a large research community supported by universally deployed software packages [1,2,3,4,5] applying automated methods for reconstruction of the human brain structures, which often rely on pre-defined brain atlases These atlases represent structural and functional information of the brain associated to single-subject, population-averaged, or multiple brain atlas coordinate systems including whole brain based coordinate systems [6,7,8,9,10,11], white matter based coordinate systems [12,13,14,15,16,17], and surface based coordinate systems [18,19,20,21]; see [22] for an excellent review. In these global deformable template methods [40], the parameters to be estimated are not ‘‘isolated’’ from the simultaneous acquisition of the global shape phenotype, which is encoded via the structure of the template and the associated deformation
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