What Data to Co-register for Computing Atlases

Diffeomorphic registration using geodesic shooting and Gauss-Newton optimisation

This paper presents a nonlinear image registration algorithm based on the setting of Large Deformation Diffeomorphic Metric Mapping (LDDMM), but with a more efficient optimisation scheme — both in terms of memory required and the number of iterations required to reach convergence. Rather than perform a variational optimisation on a series of velocity fields, the algorithm is formulated to use a geodesic shooting procedure, so that only an initial velocity is estimated. A Gauss–Newton optimisation strategy is used to achieve faster convergence. The algorithm was evaluated using freely available manually labelled datasets, and found to compare favourably with other inter-subject registration algorithms evaluated using the same data.

Image-driven population analysis through mixture modeling

We present iCluster, a fast and efficient algorithm that clusters a set of images while co-registering them using a parameterized, nonlinear transformation model. The output of the algorithm is a small number of template images that represent different modes in a population. This is in contrast with traditional, hypothesis-driven computational anatomy approaches that assume a single template to construct an atlas. We derive the algorithm based on a generative model of an image population as a mixture of deformable template images. We validate and explore our method in four experiments. In the first experiment, we use synthetic data to explore the behavior of the algorithm and inform a design choice on parameter settings. In the second experiment, we demonstrate the utility of having multiple atlases for the application of localizing temporal lobe brain structures in a pool of subjects that contains healthy controls and schizophrenia patients. Next, we employ iCluster to partition a data set of 415 whole brain MR volumes of subjects aged 18 through 96 years into three anatomical subgroups. Our analysis suggests that these subgroups mainly correspond to age groups. The templates reveal significant structural differences across these age groups that confirm previous findings in aging research. In the final experiment, we run iCluster on a group of 15 patients with dementia and 15 age-matched healthy controls. The algorithm produces two modes, one of which contains dementia patients only. These results suggest that the algorithm can be used to discover subpopulations that correspond to interesting structural or functional "modes."

Effects of registration regularization and atlas sharpness on segmentation accuracy

In non-rigid registration, the tradeoff between warp regularization and image fidelity is typically determined empirically. In atlas-based segmentation, this leads to a probabilistic atlas of arbitrary sharpness: weak regularization results in well-aligned training images and a sharp atlas; strong regularization yields a "blurry" atlas. In this paper, we employ a generative model for the joint registration and segmentation of images. The atlas construction process arises naturally as estimation of the model parameters. This framework allows the computation of unbiased atlases from manually labeled data at various degrees of "sharpness", as well as the joint registration and segmentation of a novel brain in a consistent manner. We study the effects of the tradeoff of atlas sharpness and warp smoothness in the context of cortical surface parcellation. This is an important question because of the increasingly availability of atlases in public databases, and the development of registration algorithms separate from the atlas construction process. We find that the optimal segmentation (parcellation) corresponds to a unique balance of atlas sharpness and warp regularization, yielding statistically significant improvements over the FreeSurfer parcellation algorithm. Furthermore, we conclude that one can simply use a single atlas computed at an optimal sharpness for the registration-segmentation of a new subject with a pre-determined, fixed, optimal warp constraint. The optimal atlas sharpness and warp smoothness can be determined by probing the segmentation performance on available training data. Our experiments also suggest that segmentation accuracy is tolerant up to a small mismatch between atlas sharpness and warp smoothness.

Spherical demons: fast surface registration

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast - registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces.