Van Leemput K. Encoding probabilistic brain atlases using Bayesian inference. IEEE Trans Med Imaging. 2009;28 (6) :822-37.Abstract
This paper addresses the problem of creating probabilistic brain atlases from manually labeled training data. Probabilistic atlases are typically constructed by counting the relative frequency of occurrence of labels in corresponding locations across the training images. However, such an "averaging" approach generalizes poorly to unseen cases when the number of training images is limited, and provides no principled way of aligning the training datasets using deformable registration. In this paper, we generalize the generative image model implicitly underlying standard "average" atlases, using mesh-based representations endowed with an explicit deformation model. Bayesian inference is used to infer the optimal model parameters from the training data, leading to a simultaneous group-wise registration and atlas estimation scheme that encompasses standard averaging as a special case. We also use Bayesian inference to compare alternative atlas models in light of the training data, and show how this leads to a data compression problem that is intuitive to interpret and computationally feasible. Using this technique, we automatically determine the optimal amount of spatial blurring, the best deformation field flexibility, and the most compact mesh representation. We demonstrate, using 2-D training datasets, that the resulting models are better at capturing the structure in the training data than conventional probabilistic atlases. We also present experiments of the proposed atlas construction technique in 3-D, and show the resulting atlases' potential in fully-automated, pulse sequence-adaptive segmentation of 36 neuroanatomical structures in brain MRI scans.
Raviv TR, Van Leemput K, Wells WM, Golland P. Joint segmentation of image ensembles via latent atlases. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :272-80.Abstract
Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. However, the availability of comprehensive, reliable and suitable manual segmentations for atlas construction is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas. Instead, a latent atlas, initialized by a single manual segmentation, is inferred from the evolving segmentations of the ensemble. The proposed method is based on probabilistic principles but is solved using partial differential equations (PDEs) and energy minimization criteria, We evaluate the method by segmenting 50 brain MR volumes. Segmentation accuracy for cortical and subcortical structures approaches the quality of state-of-the-art atlas-based segmentation results, suggesting that the latent atlas method is a reasonable alternative when existing atlases are not compatible with the data to be processed.
Savadjiev P, Kindlmann G, Bouix S, Shenton ME, Westin C-F. Local white matter geometry indices from diffusion tensor gradients. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :345-52.Abstract
We introduce a framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation makes it possible to define scalar geometrical measures that describe the underlying white matter fibres, directly from the diffusion tensor field and its gradient, without requiring prior tractography. We define two new scalar measures of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in-vivo datasets. Finally, we illustrate their applicability in a group study on schizophrenia.
Gerber S, Tasdizen T, Joshi S, Whitaker R. On the manifold structure of the space of brain images. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :305-12.Abstract
This paper investigates an approach to model the space of brain images through a low-dimensional manifold. A data driven method to learn a manifold from a collections of brain images is proposed. We hypothesize that the space spanned by a set of brain images can be captured, to some approximation, by a low-dimensional manifold, i.e. a parametrization of the set of images. The approach builds on recent advances in manifold learning that allow to uncover nonlinear trends in data. We combine this manifold learning with distance measures between images that capture shape, in order to learn the underlying structure of a database of brain images. The proposed method is generative. New images can be created from the manifold parametrization and existing images can be projected onto the manifold. By measuring projection distance of a held out set of brain images we evaluate the fit of the proposed manifold model to the data and we can compute statistical properties of the data using this manifold structure. We demonstrate this technology on a database of 436 MR brain images.
Niethammer M, Zach C, Melonakos J, Tannenbaum A. Near-tubular fiber bundle segmentation for diffusion weighted imaging: segmentation through frame reorientation. Neuroimage. 2009;45 (1 Suppl) :S123-32.Abstract
This paper proposes a methodology to segment near-tubular fiber bundles from diffusion weighted magnetic resonance images (DW-MRI). Segmentation is simplified by locally reorienting diffusion information based on large-scale fiber bundle geometry. Segmentation is achieved through simple global statistical modeling of diffusion orientation. Utilizing a modification of a recent segmentation approach by Bresson et al. allows for a convex optimization formulation of the segmentation problem, combining orientation statistics and spatial regularization. The approach compares favorably with segmentation by full-brain streamline tractography.
Sabuncu MR, Yeo TBT, Van Leemput K, Vercauteren T, Golland P. Asymmetric image-template registration. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :565-73.Abstract
A natural requirement in pairwise image registration is that the resulting deformation is independent of the order of the images. This constraint is typically achieved via a symmetric cost function and has been shown to reduce the effects of local optima. Consequently, symmetric registration has been successfully applied to pairwise image registration as well as the spatial alignment of individual images with a template. However, recent work has shown that the relationship between an image and a template is fundamentally asymmetric. In this paper, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.
Poynton C, Jenkinson M, Wells III WM. Atlas-based Improved Prediction of Magnetic Field Inhomogeneity for Distortion Correction of EPI Data. Med Image Comput Comput Assist Interv. 2009;12 (Pt 2) :951-9.Abstract

We describe a method for atlas-based segmentation of structural MRI for calculation of magnetic fieldmaps. CT data sets are used to construct a probabilistic atlas of the head and corresponding MR is used to train a classifier that segments soft tissue, air, and bone. Subject-specific fieldmaps are computed from the segmentations using a perturbation field model. Previous work has shown that distortion in echo-planar images can be corrected using predicted fieldmaps. We obtain results that agree well with acquired fieldmaps: 90% of voxel shifts from predicted fieldmaps show subvoxel disagreement with those computed from acquired fieldmaps. In addition, our fieldmap predictions show statistically significant improvement following inclusion of the atlas.

Tristán-Vega A, Westin C-F, Aja-Fernández S. Bias of least squares approaches for diffusion tensor estimation from array coils in DT-MRI. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :919-26.Abstract
Least Squares (LS) and its weighted version are standard techniques to estimate the Diffusion Tensor (DT) from Diffusion Weighted Images (DWI). They require to linearize the problem by computing the logarithm of the DWI. For the single-coil Rician noise model it has been shown that this model does not introduce a significant bias, but for multiple array coils and parallel imaging, the noise cannot longer be modeled as Rician. As a result the validity of LS approaches is not assured. An analytical study of noise statistics for a multiple coil system is carried out, together with the Weighted LS formulation and noise analysis for this model. Results show that the bias in the computation of the components of the DT may be comparable to their variance in many cases, stressing the importance of unbiased filtering previous to DT estimation.
Ziyan U, Sabuncu MR, Grimson EWL, Westin C-F. Consistency Clustering: A Robust Algorithm for Group-wise Registration, Segmentation and Automatic Atlas Construction in Diffusion MRI. Int J Comput Vis. 2009;85 (3) :279-290.Abstract
We propose an integrated registration and clustering algorithm, called "consistency clustering", that automatically constructs a probabilistic white-matter atlas from a set of multi-subject diffusion weighted MR images. We formulate the atlas creation as a maximum likelihood problem which the proposed method solves using a generalized Expectation Maximization (EM) framework. Additionally, the algorithm employs an outlier rejection and denoising strategy to produce sharp probabilistic maps of certain bundles of interest. We test this algorithm on synthetic and real data, and evaluate its stability against initialization. We demonstrate labeling a novel subject using the resulting spatial atlas and evaluate the accuracy of this labeling. Consistency clustering is a viable tool for completely automatic white-matter atlas construction for sub-populations and the resulting atlas is potentially useful for making diffusion measurements in a common coordinate system to identify pathology related changes or developmental trends.
Toews M, Wells WM, Collins LD, Arbel T. Feature-based morphometry. Med Image Comput Comput Assist Interv. 2009;12 (Pt 2) :109-16.Abstract
This paper presents feature-based morphometry (FBM), a new, fully data-driven technique for identifying group-related differences in volumetric imagery. In contrast to most morphometry methods which assume one-to-one correspondence between all subjects, FBM models images as a collage of distinct, localized image features which may not be present in all subjects. FBM thus explicitly accounts for the case where the same anatomical tissue cannot be reliably identified in all subjects due to disease or anatomical variability. A probabilistic model describes features in terms of their appearance, geometry, and relationship to subgroups of a population, and is automatically learned from a set of subject images and group labels. Features identified indicate group-related anatomical structure that can potentially be used as disease biomarkers or as a basis for computer-aided diagnosis. Scale-invariant image features are used, which reflect generic, salient patterns in the image. Experiments validate FBM clinically in the analysis of normal (NC) and Alzheimer's (AD) brain images using the freely available OASIS database. FBM automatically identifies known structural differences between NC and AD subjects in a fully data-driven fashion, and obtains an equal error classification rate of 0.78 on new subjects.
Ou W, Raij T, Lin F-H, Golland P, Hämäläinen M. Modeling adaptation effects in fMRI analysis. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :1009-17.Abstract
The standard general linear model (GLM) for rapid event-related fMRI design protocols typically ignores reduction in hemodynamic responses in successive stimuli in a train due to incomplete recovery from the preceding stimuli. To capture this adaptation effect, we incorporate a region-specific adaptation model into GLM. The model quantifies the rate of adaptation across brain regions, which is of interest in neuroscience. Empirical evaluation of the proposed model demonstrates its potential to improve detection sensitivity. In the fMRI experiments using visual and auditory stimuli, we observed that the adaptation effect is significantly stronger in the visual area than in the auditory area, suggesting that we must account for this effect to avoid bias in fMRI detection.
Sabuncu MR, Yeo TBT, Van Leemput K, Fischl B, Golland P. Supervised nonparametric image parcellation. Med Image Comput Comput Assist Interv. 2009;12 (Pt 2) :1075-83.Abstract
Segmentation of medical images is commonly formulated as a supervised learning problem, where manually labeled training data are summarized using a parametric atlas. Summarizing the data alleviates the computational burden at the expense of possibly losing valuable information on inter-subject variability. This paper presents a novel framework for Supervised Nonparametric Image Parcellation (SNIP). SNIP models the intensity and label images as samples of a joint distribution estimated from the training data in a non-parametric fashion. By capitalizing on recently developed fast and robust pairwise image alignment tools, SNIP employs the entire training data to segment a new image via Expectation Maximization. The use of multiple registrations increases robustness to occasional registration failures. We report experiments on 39 volumetric brain MRI scans with manual labels for the white matter, cortex and subcortical structures. SNIP yields better segmentation than state-of-the-art algorithms in multiple regions of interest.
Yeo TBT, Sabuncu M, Golland P, Fischl B. Task-optimal registration cost functions. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :598-606.Abstract
In this paper, we propose a framework for learning the parameters of registration cost functions--such as the tradeoff between the regularization and image similiarity term--with respect to a specific task. Assuming the existence of labeled training data, we specialize the framework for the task of localizing hidden labels via image registration. We learn the parameters of the weighted sum of squared differences (wSSD) image similarity term that are optimal for the localization of Brodmann areas (BAs) in a new subject based on cortical geometry. We demonstrate state-of-the-art localization of V1, V2, BA44 and BA45.
Malcolm JG, Shenton ME, Rathi Y. Two-Tensor Tractography using a Constrained Filter. Med Image Comput Comput Assist Interv. 2009;12 (Pt 1) :894-902.Abstract
We describe a technique to simultaneously estimate a weighted, positive-definite multi-tensor fiber model and perform tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a weighted mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Further, we modify the Kalman filter to enforce model constraints, i.e. positive eigenvalues and convex weights. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach significantly improves the angular resolution at crossings and branchings while consistently estimating the mixture weights. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization.
Ur Rehman T, Haber E, Pryor G, Melonakos J, Tannenbaum A. 3D nonrigid registration via optimal mass transport on the GPU. Med Image Anal. 2009;13 (6) :931-40.Abstract
In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for optimal mass transport (OMT) with applications to non-rigid 3D image registration. The approach utilizes all of the gray-scale data in both images, and the optimal mapping from image A to image B is the inverse of the optimal mapping from B to A. Further, no landmarks need to be specified, and the minimizer of the distance functional involved is unique. Our implementation also employs multigrid, and parallel methodologies on a consumer graphics processing unit (GPU) for fast computation. Although computing the optimal map has been shown to be computationally expensive in the past, we show that our approach is orders of magnitude faster then previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the accuracy of registration). We give results where the algorithm was used to compute non-rigid registrations of 3D synthetic data as well as intra-patient pre-operative and post-operative 3D brain MRI datasets.
Rubin DL, Talos I-F, Halle M, Musen MA, Kikinis R. Computational neuroanatomy: ontology-based representation of neural components and connectivity. BMC Bioinformatics. 2009;10 Suppl 2 :S3.Abstract
BACKGROUND: A critical challenge in neuroscience is organizing, managing, and accessing the explosion in neuroscientific knowledge, particularly anatomic knowledge. We believe that explicit knowledge-based approaches to make neuroscientific knowledge computationally accessible will be helpful in tackling this challenge and will enable a variety of applications exploiting this knowledge, such as surgical planning. RESULTS: We developed ontology-based models of neuroanatomy to enable symbolic lookup, logical inference and mathematical modeling of neural systems. We built a prototype model of the motor system that integrates descriptive anatomic and qualitative functional neuroanatomical knowledge. In addition to modeling normal neuroanatomy, our approach provides an explicit representation of abnormal neural connectivity in disease states, such as common movement disorders. The ontology-based representation encodes both structural and functional aspects of neuroanatomy. The ontology-based models can be evaluated computationally, enabling development of automated computer reasoning applications. CONCLUSION: Neuroanatomical knowledge can be represented in machine-accessible format using ontologies. Computational neuroanatomical approaches such as described in this work could become a key tool in translational informatics, leading to decision support applications that inform and guide surgical planning and personalized care for neurological disease in the future.
Rathi Y, Michailovich O, Shenton ME, Bouix S. Directional functions for orientation distribution estimation. Med Image Anal. 2009;13 (3) :432-44.Abstract
Computing the orientation distribution function (ODF) from high angular resolution diffusion imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation. Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a "hybrid" framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between two ODF's.
Venkataraman A, Van Dijk KRA, Buckner RL, Golland P. Exploring Functional Connectivity in fMRI via Clustering. Proc IEEE Int Conf Acoust Speech Signal Process. 2009;2009 :441-4.Abstract
In this paper we investigate the use of data driven clustering methods for functional connectivity analysis in fMRI. In particular, we consider the K-Means and Spectral Clustering algorithms as alternatives to the commonly used Seed-Based Analysis. To enable clustering of the entire brain volume, we use the Nyström Method to approximate the necessary spectral decompositions. We apply K-Means, Spectral Clustering and Seed-Based Analysis to resting-state fMRI data collected from 45 healthy young adults. Without placing any a priori constraints, both clustering methods yield partitions that are associated with brain systems previously identified via Seed-Based Analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.
Sabuncu MR, Balci SK, Shenton ME, Golland P. Image-driven population analysis through mixture modeling. IEEE Trans Med Imaging. 2009;28 (9) :1473-87.Abstract
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."
Goodman AA, Rosolowsky EW, Borkin MA, Foster JB, Halle M, Kauffmann J, Pineda JE. A role for self-gravity at multiple length scales in the process of star formation. Nature. 2009;457 (7225) :63-6.Abstract
Self-gravity plays a decisive role in the final stages of star formation, where dense cores (size approximately 0.1 parsecs) inside molecular clouds collapse to form star-plus-disk systems. But self-gravity's role at earlier times (and on larger length scales, such as approximately 1 parsec) is unclear; some molecular cloud simulations that do not include self-gravity suggest that 'turbulent fragmentation' alone is sufficient to create a mass distribution of dense cores that resembles, and sets, the stellar initial mass function. Here we report a 'dendrogram' (hierarchical tree-diagram) analysis that reveals that self-gravity plays a significant role over the full range of possible scales traced by (13)CO observations in the L1448 molecular cloud, but not everywhere in the observed region. In particular, more than 90 per cent of the compact 'pre-stellar cores' traced by peaks of dust emission are projected on the sky within one of the dendrogram's self-gravitating 'leaves'. As these peaks mark the locations of already-forming stars, or of those probably about to form, a self-gravitating cocoon seems a critical condition for their existence. Turbulent fragmentation simulations without self-gravity-even of unmagnetized isothermal material-can yield mass and velocity power spectra very similar to what is observed in clouds like L1448. But a dendrogram of such a simulation shows that nearly all the gas in it (much more than in the observations) appears to be self-gravitating. A potentially significant role for gravity in 'non-self-gravitating' simulations suggests inconsistency in simulation assumptions and output, and that it is necessary to include self-gravity in any realistic simulation of the star-formation process on subparsec scales.