Chen GH, Shah D, Golland P. A Latent Source Model for Patch-Based Image Segmentation. Med Image Comput Comput Assist Interv. 2015;9351:140–8.

Despite the popularity and empirical success of patch-based nearest-neighbor and weighted majority voting approaches to medical image segmentation, there has been no theoretical development on when, why, and how well these nonparametric methods work. We bridge this gap by providing a theoretical performance guarantee for nearest-neighbor and weighted majority voting segmentation under a new probabilistic model for patch-based image segmentation. Our analysis relies on a new local property for how similar nearby patches are, and fuses existing lines of work on modeling natural imagery patches and theory for nonparametric classification. We use the model to derive a new patch-based segmentation algorithm that iterates between inferring local label patches and merging these local segmentations to produce a globally consistent image segmentation. Many existing patch-based algorithms arise as special cases of the new algorithm.

Parisot S, Arslan S, Passerat-Palmbach J, Wells WM III, Rueckert D. Tractography-Driven Groupwise Multi-scale Parcellation of the Cortex. Inf Process Med Imaging. 2015;24:600–12.

The analysis of the connectome of the human brain provides key insight into the brain’s organisation and function, and its evolution in disease or ageing. Parcellation of the cortical surface into distinct regions in terms of structural connectivity is an essential step that can enable such analysis. The estimation of a stable connectome across a population of healthy subjects requires the estimation of a groupwise parcellation that can capture the variability of the connectome across the population. This problem has solely been addressed in the literature via averaging of connectivity profiles or finding correspondences between individual parcellations a posteriori. In this paper, we propose a groupwise parcellation method of the cortex based on diffusion MR images (dMRI). We borrow ideas from the area of cosegmentation in computer vision and directly estimate a consistent parcellation across different subjects and scales through a spectral clustering approach. The parcellation is driven by the tractography connectivity profiles, and information between subjects and across scales. Promising qualitative and quantitative results on a sizeable data-set demonstrate the strong potential of the method.

Wachinger C, Golland P. Sampling from Determinantal Point Processes for Scalable Manifold Learning. Inf Process Med Imaging. 2015;24:687–98.

High computational costs of manifold learning prohibit its application for large datasets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire dataset with the Nyström method. The two main challenges that arise are: (i) the landmarks selected in non-Euclidean geometries must result in a low reconstruction error, (ii) the graph constructed from sparsely sampled landmarks must approximate the manifold well. We propose to sample the landmarks from determinantal distributions on non-Euclidean spaces. Since current determinantal sampling algorithms have the same complexity as those for manifold learning, we present an efficient approximation with linear complexity. Further, we recover the local geometry after the sparsification by assigning each landmark a local covariance matrix, estimated from the original point set. The resulting neighborhood selection .based on the Bhattacharyya distance improves the embedding of sparsely sampled manifolds. Our experiments show a significant performance improvement compared to state-of-the-art landmark selection techniques on synthetic and medical data.

Toews M, Wachinger C, Estepar RSJ, Wells WM III. A Feature-Based Approach to Big Data Analysis of Medical Images. Inf Process Med Imaging. 2015;24:339–50.

This paper proposes an inference method well-suited to large sets of medical images. The method is based upon a framework where distinctive 3D scale-invariant features are indexed efficiently to identify approximate nearest-neighbor (NN) feature matches-in O (log N) computational complexity in the number of images N. It thus scales well to large data sets, in contrast to methods based on pair-wise image registration or feature matching requiring O(N) complexity. Our theoretical contribution is a density estimator based on a generative model that generalizes kernel density estimation and K-nearest neighbor (KNN) methods.. The estimator can be used for on-the-fly queries, without requiring explicit parametric models or an off-line training phase. The method is validated on a large multi-site data set of 95,000,000 features extracted from 19,000 lung CT scans. Subject-level classification identifies all images of the same subjects across the entire data set despite deformation due to breathing state, including unintentional duplicate scans. State-of-the-art performance is achieved in predicting chronic pulmonary obstructive disorder (COPD) severity across the 5-category GOLD clinical rating, with an accuracy of 89% if both exact and one-off predictions are considered correct.

Pujol S, Wells WM III, Pierpaoli C, Brun C, Gee J, Cheng G, Vemuri B, Commowick O, Prima S, Stamm A, Goubran M, Khan A, Peters T, Neher P, Maier-Hein KH, Shi Y, Tristan-Vega A, Veni G, Whitaker R, Styner M, Westin CF, Gouttard S, Norton I, Chauvin L, Mamata H, Gerig G, Nabavi A, Golby A, Kikinis R. The DTI Challenge: Toward Standardized Evaluation of Diffusion Tensor Imaging Tractography for Neurosurgery. J Neuroimaging. 2015;25(6):875–82.

BACKGROUND AND PURPOSE: Diffusion tensor imaging (DTI) tractography reconstruction of white matter pathways can help guide brain tumor resection. However, DTI tracts are complex mathematical objects and the validity of tractography-derived information in clinical settings has yet to be fully established. To address this issue, we initiated the DTI Challenge, an international working group of clinicians and scientists whose goal was to provide standardized evaluation of tractography methods for neurosurgery. The purpose of this empirical study was to evaluate different tractography techniques in the first DTI Challenge workshop. METHODS: Eight international teams from leading institutions reconstructed the pyramidal tract in four neurosurgical cases presenting with a glioma near the motor cortex. Tractography methods included deterministic, probabilistic, filtered, and global approaches. Standardized evaluation of the tracts consisted in the qualitative review of the pyramidal pathways by a panel of neurosurgeons and DTI experts and the quantitative evaluation of the degree of agreement among methods. RESULTS: The evaluation of tractography reconstructions showed a great interalgorithm variability. Although most methods found projections of the pyramidal tract from the medial portion of the motor strip, only a few algorithms could trace the lateral projections from the hand, face, and tongue area. In addition, the structure of disagreement among methods was similar across hemispheres despite the anatomical distortions caused by pathological tissues. CONCLUSIONS: The DTI Challenge provides a benchmark for the standardized evaluation of tractography methods on neurosurgical data. This study suggests that there are still limitations to the clinical use of tractography for neurosurgical decision making.

Ohtani T, Bouix S, Lyall AE, Hosokawa T, Saito Y, Melonakos E, Westin CF, Seidman LJ, Goldstein J, Mesholam-Gately R, Petryshen T, Wojcik J, Kubicki M. Abnormal White Matter Connections between Medial Frontal Regions Predict Symptoms in Patients with First Episode Schizophrenia. Cortex. 2015;71:264–76.

INTRODUCTION: The medial orbitofrontal cortex (mOFC) and rostral part of anterior cingulate cortex (rACC) have been suggested to be involved in the neural network of salience and emotional processing, and associated with specific clinical symptoms in schizophrenia. Considering the schizophrenia dysconnectivity hypothesis, the connectivity abnormalities between mOFC and rACC might be associated with clinical characteristics in first episode schizophrenia patients (FESZ). METHODS: After parcellating mOFC into the anterior and posterior part, diffusion properties of the mOFC-rACC white matter connections for 21 patients with FESZ and 21 healthy controls (HCs) were examined using stochastic tractography, one of the most effective Diffusion Tensor Imaging (DTI) methods for examining tracts between adjacent gray matter (GM) regions. RESULTS: Fractional anisotropy (FA) reductions were observed in bilateral posterior, but not anterior mOFC-rACC connections (left: p < .0001; right: p < .0001) in FESZ compared to HCs. In addition, reduced FA in the left posterior mOFC-rACC connection was associated with more severe anhedonia-asociality (rho = -.633, p = .006) and total score (rho = -.520, p = .032) in the Scale for the Assessment of Negative Symptoms (SANS); reduced FA in the right posterior mOFC-rACC connection was associated with more severe affective flattening (rho = -.644, p = .005), total score (rho = -.535, p = .027) in SANS, hallucinations (rho = -.551, p = .018), delusions (rho = -.632, p = .005) and total score (rho = -.721, p = .001) in the Scale for the Assessment of Positive Symptoms (SAPS) in FESZ. CONCLUSIONS: The observed white matter abnormalities within the connections between mOFC and rACC might be associated with the psychopathology of the early stage of schizophrenia.

Ning L, Setsompop K, Michailovich O, Makris N, Westin CF, Rathi Y. A Compressed-Sensing Approach for Super-Resolution Reconstruction of Diffusion MRI. Inf Process Med Imaging. 2015;24:57–68.

We present an innovative framework for reconstructing high-spatial-resolution diffusion magnetic resonance imaging (dMRI) from multiple low-resolution (LR) images. Our approach combines the twin concepts of compressed sensing (CS) and classical super-resolution to reduce acquisition time while increasing spatial resolution. We use subpixel-shifted LR images with down-sampled and non-overlapping diffusion directions to reduce acquisition time. The diffusion signal in the high resolution (HR) image is represented in a sparsifying basis of spherical ridgelets to model complex fiber orientations with reduced number of measurements. The HR image is obtained as the solution of a convex optimization problem which can be solved using the proposed algorithm based on the alternating direction method of multipliers (ADMM). We qualitatively and quantitatively evaluate the performance of our method on two sets of in-vivo human brain data and show its effectiveness in accurately recovering very high resolution diffusion images.

We introduce a nuclear magnetic resonance method for quantifying the shape of axially symmetric microscopic diffusion tensors in terms of a new diffusion anisotropy metric, DΔ, which has unique values for oblate, spherical, and prolate tensor shapes. The pulse sequence includes a series of equal-amplitude magnetic field gradient pulse pairs, the directions of which are tailored to give an axially symmetric diffusion-encoding tensor b with variable anisotropy bΔ. Averaging of data acquired for a range of orientations of the symmetry axis of the tensor b renders the method insensitive to the orientation distribution function of the microscopic diffusion tensors. Proof-of-principle experiments are performed on water in polydomain lyotropic liquid crystals with geometries that give rise to microscopic diffusion tensors with oblate, spherical, and prolate shapes. The method could be useful for characterizing the geometry of fluid-filled compartments in porous solids, soft matter, and biological tissues.

Ning L, Westin CF, Rathi Y. Estimating diffusion propagator and its moments using directional radial basis functions. IEEE Trans Med Imaging. 2015;34(10):2058–78.

The ensemble average diffusion propagator (EAP) obtained from diffusion MRI (dMRI) data captures important structural properties of the underlying tissue. As such, it is imperative to derive an accurate estimate of the EAP from the acquired diffusion data. In this work, we propose a novel method for estimating the EAP by representing the diffusion signal as a linear combination of directional radial basis functions scattered in q-space. In particular, we focus on a special case of anisotropic Gaussian basis functions and derive analytical expressions for the diffusion orientation distribution function (ODF), the return-to-origin probability (RTOP), and mean-squared-displacement (MSD). A significant advantage of the proposed method is that the second and the fourth order moment tensors of the EAP can be computed explicitly. This allows for computing several novel scalar indices (from the moment tensors) such as mean-fourth-order-displacement (MFD) and generalized kurtosis (GK)-which is a generalization of the mean kurtosis measure used in diffusion kurtosis imaging. Additionally, we also propose novel scalar indices computed from the signal in q-space, called the q-space mean-squared-displacement (QMSD) and the q-space mean-fourth-order-displacement (QMFD), which are sensitive to short diffusion time scales. We validate our method extensively on data obtained from a physical phantom with known crossing angle as well as on in-vivo human brain data. Our experiments demonstrate the robustness of our method for different combinations of b-values and number of gradient directions.

Batmanghelich NK, Saeedi A, Cho M, Estepar RSJ, Golland P. Generative Method to Discover Genetically Driven Image Biomarkers. Inf Process Med Imaging. 2015;24:30–42.

We present a generative probabilistic approach to discovery of disease subtypes determined by the genetic variants. In many diseases, multiple types of pathology may present simultaneously in a patient, making quantification of the disease challenging. Our method seeks common co-occurring image and genetic patterns in a population as a way to model these two different data types jointly. We assume that each patient is a mixture of multiple disease subtypes and use the joint generative model of image and genetic markers to identify disease subtypes guided by known genetic influences. Our model is based on a variant of the so-called topic models that uncover the latent structure in a collection of data. We derive an efficient variational inference algorithm to extract patterns of co-occurrence and to quantify the presence of heterogeneous disease processes in each patient. We evaluate the method on simulated data and illustrate its use in the context of Chronic Obstructive Pulmonary Disease (COPD) to characterize the relationship between image and genetic signatures of COPD subtypes in a large patient cohort.