Medical Image Computing and Computer-Assisted Intervention – MICCAI 2014

Point Distribution Models (PDM) are some of the most popular shape description techniques in medical imaging. However, to create an accurate shape model it is essential to have a representative sample of the underlying population, which is often challenging. This problem is particularly relevant as the dimensionality of the modeled structures increases, and becomes critical when dealing with complex 3D shapes. In this paper, we introduce a new generalized multiresolution hierarchical PDM (GMRH-PDM) able to efficiently address the high-dimension-low-sample-size challenge when modeling complex structures. Unlike previous approaches, our new and general framework extends hierarchical modeling to any type of structure (multi- and single-object shapes) allowing to describe efficiently the shape variability at different levels of resolution. Importantly, the configuration of the algorithm is automatized thanks to the new agglomerative landmark clustering method presented here. Our new and automatic GMRH-PDM framework performed significantly better than classical approaches, and as well as the state-of-the-art with the best manual configuration. Evaluations have been studied for two different cases, the right kidney, and a multi-object case composed of eight subcortical structures.

This paper proposes a novel method for the analysis of anatomical shapes present in biomedical image data. Motivated by the natural organization of population data into multiple groups, this paper presents a novel

hierarchical generative

statistical model on shapes. The proposed method represents shapes using pointsets and defines a joint distribution on the population’s (i) shape variables and (ii) object-boundary data. The proposed method solves for optimal (i) point locations, (ii) correspondences, and (iii) model-parameter values as a

single

optimization problem. The optimization uses expectation maximization relying on a novel Markov-chain Monte-Carlo algorithm for

sampling

in Kendall shape space. Results on clinical brain images demonstrate advantages over the state of the art.

In this paper we propose a new method for shape analysis based on the depth-ordering of shapes. We use this depth-ordering to non-parametrically define depth with respect to a normal control population. This allows us to quantify differences with respect to “normality”. We combine this approach with a permutation test allowing it to test for localized shape differences. The method is evaluated on a synthetically generated striatum dataset as well as on a real caudate dataset.

This paper presents a novel algorithm to obtain landmark-based genus-1 surface registration via a special class of quasi-conformal maps called the Teichmüller maps. Registering shapes with important features is an important process in medical imaging. However, it is challenging to obtain a unique and bijective genus-1 surface matching that satisfies the prescribed landmark constraints. In addition, as suggested by [11], conformal transformation provides the most natural way to describe the deformation or growth of anatomical structures. This motivates us to look for the unique mapping between genus-1 surfaces that matches the features while minimizing the maximal conformality distortion. Existence and uniqueness of such optimal diffeomorphism is theoretically guaranteed and is called the Teichmüller extremal mapping. In this work, we propose an iterative algorithm, called the Quasi-conformal (QC) iteration, to find the Teichmüller extremal mapping between the covering spaces of genus-1 surfaces. By representing the set of diffeomorphisms using Beltrami coefficients (BCs), we look for an optimal BC which corresponds to our desired diffeomorphism that matches prescribed features and satisfies the periodic boundary condition on the covering space. Numerical experiments show that our proposed algorithm is efficient and stable for registering genus-1 surfaces even with large amount of landmarks. We have also applied the algorithm on registering vertebral bones with prescribed feature curves, which demonstrates the usefulness of the proposed algorithm.

The term

prediction

implies expected outcome in the future, often based on a model and statistical inference. Longitudinal imaging studies offer the possibility to model temporal change trajectories of anatomy across populations of subjects. In the spirit of subject-specific analysis, such normative models can then be used to compare data from new subjects to the norm and to study progression of disease or to predict outcome. This paper follows a statistical inference approach and presents a framework for prediction of future observations based on past measurements and population statistics. We describe prediction in the context of nonlinear mixed effects modeling (NLME) where the full reference population’s statistics (estimated fixed effects, variance-covariance of random effects, variance of noise) is used along with the individual’s available observations to predict its trajectory. The proposed methodology is generic in regard to application domains. Here, we demonstrate analysis of early infant brain maturation from longitudinal DTI with up to three time points. Growth as observed in DTI-derived scalar invariants is modeled with a parametric function, its parameters being input to NLME population modeling. Trajectories of new subject’s data are estimated when using no observation, only the first or the first two time points. Leave-one-out experiments result in statistics on differences between actual and predicted observations. We also simulate a clinical scenario of prediction on multiple categories, where trajectories predicted from multiple models are classified based on maximum likelihood criteria.

Introducing

BrainPrint

, a compact and discriminative representation of anatomical structures in the brain.

BrainPrint

captures shape information of an ensemble of cortical and subcortical structures by solving the 2D and 3D Laplace-Beltrami operator on triangular (boundary) and tetrahedral (volumetric) meshes. We derive a robust classifier for this representation that identifies the subject in a new scan, based on a database of brain scans. In an example dataset containing over 3000 MRI scans, we show that

BrainPrint

captures unique information about the subject’s anatomy and permits to correctly classify a scan with an accuracy of over 99.8%. All processing steps for obtaining the compact representation are fully automated making this processing framework particularly attractive for handling large datasets.

Longitudinal imaging studies involve tracking changes in individuals by repeated image acquisition over time. The goal of these studies is to quantify biological shape variability within and across individuals, and also to distinguish between normal and disease populations. However, data variability is influenced by outside sources such as image acquisition, image calibration, human expert judgment, and limited robustness of segmentation and registration algorithms. In this paper, we propose a two-stage method for the statistical analysis of longitudinal shape. In the first stage, we estimate diffeomorphic shape trajectories for each individual that minimize inconsistencies in segmented shapes across time. This is followed by a longitudinal mixed-effects statistical model in the second stage for testing differences in shape trajectories between groups. We apply our method to a longitudinal database from PREDICT-HD and demonstrate our approach reduces unwanted variability for both shape and derived measures, such as volume. This leads to greater statistical power to distinguish differences in shape trajectory between healthy subjects and subjects with a genetic biomarker for Huntington’s disease (HD).

Neuroimaging biomarkers play a prominent role for disease diagnosis or tracking neurodegenerative processes. Multiple methods have been proposed by the community to extract robust disease specific markers from various imaging modalities. Evaluating the accuracy and robustness of developed methods is difficult due to the lack of a biologically realistic ground truth.

We propose a proof-of-concept method for a patient- and disease-specific brain neurodegeneration simulator. The proposed scheme, based on longitudinal multi-modal data, has been applied to a population of normal controls and patients diagnosed with Alzheimer’s disease or frontotemporal dementia. We simulated follow-up images from baseline scans and compared them to real repeat images. Additionally, simulated maps of volume change are generated, which can be compared to maps estimated from real longitudinal data. The results indicate that the proposed simulator reproduces realistic patient-specific patterns of longitudinal brain change for the given populations.

Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links HyperSPHARM to the diffusion wavelet transform. Specifically, we will show that the HyperSPHARM basis forms a subset of a wavelet-based multi-scale representation of surface-based signals. This wavelet, termed the hyperspherical diffusion wavelet, is a consequence of the equivalence of isotropic heat diffusion smoothing and the diffusion wavelet transform on the hypersphere. Our framework allows for the statistical inference of highly localized anatomical changes, which we demonstrate in the first-ever developmental study on the hyoid bone investigating gender and age effects. We also show that the hyperspherical wavelet successfully picks up group-wise differences that are barely detectable using SPHARM.

We introduce a novel

biologically inspired

feature descriptor, Co-occurrence of Local Anisotropic Gradient Orientations (CoLlAGe), that captures higher order co-occurrence patterns of local gradient tensors at a pixel level to distinguish disease phenotypes that have similar morphologic appearances. A number of pathologies (e.g. subtypes of breast cancer) have different histologic phenotypes but similar radiographic appearances. While texture features have been previously employed for distinguishing subtly different pathologies, they attempt to capture differences in global intensity patterns. In this paper we attempt to model CoLlAGe to identify higher order co-occurrence patterns of gradient tensors at a pixel level. The assumption behind this new feature is that different pathologies, even though they may have very similar overall texture and appearance on imaging, at a local scale, will have different co-occurring patterns with respect to gradient orientations. We demonstrate the utility of CoLlAGe in distinguishing two subtly different types of pathologies on MRI in the context of brain tumors and breast cancer. In the first problem, we look at CoLlAGe for distinguishing radiation effects from recurrent brain tumors over a cohort of 40 studies, and in the second, discriminating different molecular subtypes of breast cancer over a cohort of 73 studies. For both these challenging cohorts, CoLlAGe was found to have significantly improved classification performance, as compared to the traditional texture features such as Haralick, Gabor, local binary patterns, and histogram of gradients.

The entorhinal cortex (ERC) and the perirhinal cortex (PRC) are subregions of the medial temporal lobe (MTL) that play important roles in episodic memory representations, as well as serving as a conduit between other neocortical areas and the hippocampus. They are also the sites where neuronal damage first occurs in Alzheimer’s disease (AD). The ability to automatically quantify the volume and thickness of the ERC and PRC is desirable because these localized measures can potentially serve as better imaging biomarkers for AD and other neurodegenerative diseases. However, large anatomical variation in the PRC makes it a challenging area for analysis. In order to address this problem, we propose an automatic segmentation, clustering, and thickness measurement approach that explicitly accounts for anatomical variation. The approach is targeted to highly anisotropic (0.4x0.4x2.0mm

3

) T2-weighted MRI scans that are preferred by many authors for detailed imaging of the MTL, but which pose challenges for segmentation and shape analysis. After automatically labeling MTL substructures using multi-atlas segmentation, our method clusters subjects into groups based on the shape of the PRC, constructs unbiased population templates for each group, and uses the smooth surface representations obtained during template construction to extract regional thickness measurements in the space of each subject. The proposed thickness measures are evaluated in the context of discrimination between patients with Mild Cognitive Impairment (MCI) and normal controls (NC).

Cortical surface atlases play an increasingly important role for analysis, visualization, and comparison of results across different neuroimaging studies. As the first two years of life is the most dynamic period of postnatal structural and functional development of the highly-folded cerebral cortex, longitudinal (4D) cortical surface atlases for the infant brains during this period is highly desired yet still lacking for early brain development studies. In this paper, we construct the first longitudinal (4D) cortical surface atlases for the dynamic developing infant cortical structures at 1, 3, 6, 9, 12, 18 and 24 months of age, based on 202 serial MRI scans from 35 healthy infants. To ensure longitudinal consistency and unbiasedness of the 4D infant cortical surface atlases, we first compute the within-subject mean cortical folding geometries by groupwise registration of longitudinal surfaces of each infant. Then we establish intersubject cortical correspondences by groupwise registration of the within-subject mean cortical folding geometries of all infants. More importantly, for the first time, we further parcellate the 4D infant surface atlases into developmentally and functionally distinctive regions based solely on the dynamic developmental trajectories of the cortical thickness, by using the spectral clustering method. Specifically, to deal with the problem that each infant has different number of scans, we first compute the within-subject affinity matrix of vertices’ cortical thickness trajectories of each infant, and then we use the averaged affinity matrix of all infants for parcellation. Our constructed 4D infant cortical surface atlases with developmental trajectories based parcellation will greatly facilitate the surface-based analysis of dynamic brain development in infants.

Low-rank image decomposition has the potential to address a broad range of challenges that routinely occur in clinical practice. Its novelty and utility in the context of atlas-based analysis stems from its ability to handle images containing large pathologies and large deformations. Potential applications include atlas-based tissue segmentation and unbiased atlas building from data containing pathologies. In this paper we present atlas-based tissue segmentation of MRI from patients with large pathologies. Specifically, a healthy brain atlas is registered with the low-rank components from the input MRIs, the low-rank components are then re-computed based on those registrations, and the process is then iteratively repeated. Preliminary evaluations are conducted using the brain tumor segmentation challenge data (BRATS ’12).

Automatic segmentation methods are important tools for quantitative analysis of magnetic resonance images. Recently, patch- based label fusion approaches demonstrated state-of-the-art segmentation accuracy. In this paper, we introduce a new patch-based method using the PatchMatch algorithm to perform segmentation of anatomical structures. Based on an Optimized PAtchMatch Label fusion (OPAL) strategy, the proposed method provides competitive segmentation accuracy in near real time. During our validation on hippocampus segmentation of 80 healthy subjects, OPAL was compared to several state-of-the-art methods. Results show that OPAL obtained the highest median Dice coefficient (89.3%) in less than 1 sec per subject. These results highlight the excellent performance of OPAL in terms of computation time and segmentation accuracy compared to recently published methods.

Connectivity analysis of resting state brain has provided a novel means of investigating brain networks in the study of neurodevelopmental disorders. The study of functional networks, often represented by high dimensional graphs, predicates on the ability of methods in succinctly extracting meaningful representative connectivity information at the subject and population level. This need motivates the development of techniques that can extract underlying network modules that characterize the connectivity in a population, while capturing variations of these modules at the individual level. In this paper, we propose a multi-layer graph clustering technique that fuses the information from a collection of connectivity networks of a population to extract the underlying common network modules that serve as network hubs for the population. These hubs form a functional network atlas. In addition, our technique provides subject-specific factors designed to characterize and quantify the degree of intra- and inter- connectivity between hubs, thereby providing a representation that is amenable to group level statistical analyses. We demonstrate the utility of the technique by creating a population network atlas of connectivity by examining MEG based functional connectivity in typically developing children, and using this to describe the individualized variation in those diagnosed with autism spectrum disorder.

Computing a concise representation of the anatomical variability found in large sets of images is an important first step in many statistical shape analyses. In this paper, we present a generative Bayesian approach for automatic dimensionality reduction of shape variability represented through diffeomorphic mappings. To achieve this, we develop a latent variable model for principal geodesic analysis (PGA) that provides a probabilistic framework for factor analysis on diffeomorphisms. Our key contribution is a Bayesian inference procedure for model parameter estimation and simultaneous detection of the effective dimensionality of the latent space. We evaluate our proposed model for atlas and principal geodesic estimation on the OASIS brain database of magnetic resonance images. We show that the automatically selected latent dimensions from our model are able to reconstruct unseen brain images with lower error than equivalent linear principal components analysis (LPCA) models in the image space, and it also outperforms tangent space PCA (TPCA) models in the diffeomorphism setting.

Magnetic resonance imaging (MRI) is commonly used as a medical diagnosis tool, especially for brain applications. Some limitations affecting image quality include receive field (RF) inhomogeneity and partial volume (PV) effects which arise when a voxel contains two different tissues, introducing blurring. The novel Magnetization-Prepared 2 Rapid Acquisition Gradient Echoes (MP2RAGE) provides an image robust to RF inhomogeneity. However, PV effects are still an issue for automated brain quantification. PV estimation methods have been proposed based on computing the proportion of one tissue with respect to the other using linear interpolation of pure tissue intensity means. We demonstrated that this linear model introduces bias when used with MP2RAGE and we propose two novel solutions. The PV estimation methods were tested on 4 MP2RAGE data sets.

Although much attention has recently been focused on single-subject functional networks, using methods such as resting-state functional MRI, methods for constructing single-subject structural networks are in their infancy. Single-subject cortical networks aim to describe the self-similarity across the cortical structure, possibly signifying convergent developmental pathways. Previous methods for constructing single-subject cortical networks have used patch-based correlations and distance metrics based on curvature and thickness. We present here a method for constructing similarity-based cortical structural networks that utilizes a rotation-invariant representation of structure. The resulting graph metrics are closely linked to age and indicate an increasing degree of closeness throughout development in nearly all brain regions, perhaps corresponding to a more regular structure as the brain matures. The derived graph metrics demonstrate a four-fold increase in power for detecting age as compared to cortical thickness. This proof of concept study indicates that the proposed metric may be useful in identifying biologically relevant cortical patterns.

Quantitative assessment of myelin density in the white matter is an emerging tool for neurodegenerative disease related studies such as multiple sclerosis and Schizophrenia. For the last two decades,

T

2

relaxometry based on multi-exponential fitting to a single slice multi-echo sequence has been the most common MRI technique for myelin water fraction (MWF) mapping, where the short

T

2

is associated with myelin water. However, modeling the spectrum of the relaxations as the sum of large number of impulse functions with unknown amplitudes makes the accuracy and robustness of the estimated MWF’s questionable. In this paper, we introduce a novel model with small number of parameters to simultaneously characterize transverse relaxation rate spectrum and

B

1

inhomogeneity at each voxel. We use mixture of three Wald distributions with unknown mixture weights, mean and shape parameters to represent the distribution of the relative amount of water in between myelin sheets, tissue water, and cerebrospinal fluid. The parameters of the model are estimated using the variable projection method and are used to extract the MWF at each voxel. In addition, we use Extended Phase Graph (EPG) method to compensate for the stimulated echoes caused by

B

1

inhomogeneity. To validate our model, synthetic and real brain experiments were conducted where we have compared our novel algorithm with the non-negative least squares (NNLS) as the state-of-the-art technique in the literature. Our results indicate that we can estimate MWF map with substantially higher accuracy as compared to the NNLS method.

Resting state functional connectivity holds great potential for diagnostic prediction of neurological and psychiatric illness. This paper introduces a compact and information-rich representation of connectivity that is geared directly towards predictive modeling. Our representation does not require a priori identification of localized regions of interest, yet provides a mechanism for interpretation of classifier weights. Experiments confirm increased accuracy associated with our representation and yield interpretations consistent with known physiology.

We present a framework for registering cortical surfaces based on tractography-informed structural connectivity. We define connectivity as a continuous kernel on the product space of the cortex, and develop a method for estimating this kernel from tractography fiber models. Next, we formulate the kernel registration problem, and present a means to non-linearly register two brains’ continuous connectivity profiles. We apply theoretical results from operator theory to develop an algorithm for decomposing the connectome into its shared and individual components. Lastly, we extend two discrete connectivity measures to the continuous case, and apply our framework to 98 Alzheimer’s patients and controls. Our measures show significant differences between the two groups.

Segmentation and parcellation of the thalamus is an important step in providing volumetric assessment of the impact of disease on brain structures. Conventionally, segmentation is carried out on T1-weighted magnetic resonance (MR) images and nuclear parcellation using diffusion weighted MR images. We present the first fully automatic method that incorporates both tissue contrasts and several derived features to first segment and then parcellate the thalamus. We incorporate fractional anisotrophy, fiber orientation from the 5D Knutsson representation of the principal eigenvectors, and connectivity between the thalamus and the cortical lobes, as features. Combining these multiple information sources allows us to identify discriminating dimensions and thus parcellate the thalamic nuclei. A hierarchical random forest framework with a multidimensional feature per voxel, first distinguishes thalamus from background, and then separates each group of thalamic nuclei. Using a leave one out cross-validation on 12 subjects we have a mean Dice score of 0.805 and 0.799 for the left and right thalami, respectively. We also report overlap for the thalamic nuclear groups.

Characterization of disease using stationary resting-state functional connectivity (FC) has provided important hallmarks of abnormal brain activation in many domains. Recent studies of resting-state functional magnetic resonance imaging (fMRI), however, suggest there is a considerable amount of additional knowledge to be gained by investigating the variability in FC over the course of a scan. While a few studies have begun to explore the properties of dynamic FC for characterizing disease, the analysis of dynamic FC over multiple networks at multiple time scales has yet to be fully examined. In this study, we combine dynamic connectivity features in a multi-network, multi-scale approach to evaluate the method’s potential in better classifying childhood autism. Specifically, from a set of group-level intrinsic connectivity networks (ICNs), we use sliding window correlations to compute intra-network connectivity on the subject level. We derive dynamic FC features for all ICNs over a large range of window sizes and then use a multiple kernel support vector machine (MK-SVM) model to combine a subset of these features for classification. We compare the performance our multi-network, dynamic approach to the best results obtained from single-network dynamic FC features and those obtained from both single- and multi-network static FC features. Our experiments show that integrating multiple networks on different dynamic scales has a clear superiority over these existing methods.

The estimation of functional connectivity structure from functional neuroimaging data is an important step toward understanding the mechanisms of various brain diseases and building relevant biomarkers. Yet, such inferences have to deal with the low signal-to-noise ratio and the paucity of the data. With at our disposal a steadily growing volume of publicly available neuroimaging data, it is however possible to improve the estimation procedures involved in connectome mapping. In this work, we propose a novel learning scheme for functional connectivity based on sparse Gaussian graphical models that aims at minimizing the bias induced by the regularization used in the estimation, by carefully separating the estimation of the model support from the coefficients. Moreover, our strategy makes it possible to include new data with a limited computational cost. We illustrate the physiological relevance of the learned prior, that can be identified as a functional connectivity atlas, based on an experiment on 46 subjects of the Human Connectome Dataset.

Functional connectivity using resting-state fMRI has emerged as an important research tool for understanding normal brain function as well as changes occurring during brain development and in various brain disorders. Most prior work has examined changes in pair-wise functional connectivity values using a multi-variate classification approach, such as Support Vector Machines (SVM). While it is powerful, SVMs produce a dense set of high-dimensional weight vectors as output, which are difficult to interpret, and require additional post-processing to relate to known functional networks. In this paper, we propose a joint framework that combines network identification and classification, resulting in a set of networks, or Sparse Connectivity Patterns (SCPs) which are functionally interpretable as well as highly discriminative of the two groups. Applied to a study of normal development classifying children vs. adults, the proposed method provided accuracy of 76%(AUC= 0.85), comparable to SVM (79%,AUC=0.87), but with dramatically fewer number of features (50 features vs. 34716 for the SVM). More importantly, this leads to a tremendous improvement in neuro-scientific interpretability, which is specially advantageous in such a study where the group differences are wide-spread throughout the brain. Highest-ranked discriminative SCPs reflect increases in long-range connectivity in adults between the frontal areas and posterior cingulate regions. In contrast, connectivity between the bilateral parahippocampal gyri was decreased in adults compared to children.

One overarching challenge of clinical magnetic resonance imaging (MRI) is to quantify tissue structure at the cellular scale of micrometers, based on an MRI acquisition with a millimeter resolution. Diffusion MRI (dMRI) provides the strongest sensitivity to the cellular structure. However, interpreting dMRI measurements has remained a highly ill-posed inverse problem. Here we propose a framework that resolves the above challenge for human white matter fibers, by unifying intra-voxel mesoscopic modeling with global fiber tractography. Our algorithm is based on a Simulated Annealing approach which simultaneously optimizes diffusion parameters and fiber locations. Each fiber carries its individual set of diffusion parameters which allows to link them by their structural relationships.

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

We present a novel approach to determine a local q-space metric that is optimal from an information theoretic perspective with respect to the expected signal statistics. It should be noted that the approach does not attempt to optimize the quality of a pre-defined mathematical representation, the estimator. In contrast, our suggestion aims at obtaining the maximum amount of information without enforcing a particular feature representation.

Results for three significantly different average propagator distributions are presented. The results show that the optimal q-space metric has a strong dependence on the assumed distribution in the targeted tissue. In many practical cases educated guesses can be made regarding the average propagator distribution present. In such cases the presented analysis can produce a metric that is optimal with respect to this distribution. The metric will be different at different q-space locations and is defined by the amount of additional information that is obtained when adding a second sample at a given offset from a first sample. The intention is to use the obtained metric as a guide for the generation of specific efficient q-space sample distributions for the targeted tissue.

This paper introduces image quality transfer. The aim is to learn the fine structural detail of medical images from high quality data sets acquired with long acquisition times or from bespoke devices and transfer that information to enhance lower quality data sets from standard acquisitions. We propose a framework for solving this problem using random forest regression to relate patches in the low-quality data set to voxel values in the high quality data set. Two examples in diffusion MRI demonstrate the idea. In both cases, we learn from the Human Connectome Project (HCP) data set, which uses an hour of acquisition time per subject, just for diffusion imaging, using custom built scanner hardware and rapid imaging techniques. The first example, super-resolution of diffusion tensor images (DTIs), enhances spatial resolution of standard data sets with information from the high-resolution HCP data. The second, parameter mapping, constructs neurite orientation density and dispersion imaging (NODDI) parameter maps, which usually require specialist data sets with two

b

-values, from standard single-shell high angular resolution diffusion imaging (HARDI) data sets with

b

 = 1000 s mm

− 2

. Experiments quantify the improvement against alternative image reconstructions in comparison to ground truth from the HCP data set in both examples and demonstrate efficacy on a standard data set.

Invariants play a crucial role in Diffusion MRI. In DTI (2

nd

order tensors), invariant scalars (FA, MD) have been successfully used in clinical applications. But DTI has limitations and HARDI models (e.g. 4

th

order tensors) have been proposed instead. These, however, lack invariant features and computing them systematically is challenging.

We present a simple and systematic method to compute a

functionally complete set

of invariants of a non-negative 3D 4

th

order tensor with respect to

SO

3

. Intuitively, this transforms the tensor’s non-unique ternary quartic (TQ) decomposition (from Hilbert’s theorem) to a unique canonical representation independent of orientation – the invariants.

The method consists of two steps. In the first, we reduce the 18 degrees-of-freedom (DOF) of a TQ representation by 3-DOFs via an orthogonal transformation. This transformation is designed to enhance a rotation-invariant property of choice of the 3D 4

th

order tensor. In the second, we further reduce 3-DOFs via a 3D rotation transformation of coordinates to arrive at a canonical set of invariants to

SO

3

of the tensor.

The resulting invariants are, by construction, (i) functionally

complete

, (ii) functionally

irreducible

(if desired), (iii) computationally

efficient

and (iv)

reversible

(mappable to the TQ coefficients or shape); which is the novelty of our contribution in comparison to prior work.

Results from synthetic and real data experiments validate the method and indicate its importance.

We present a technique for mapping dispersion anisotropy of neurites in the human brain

in vivo

. Neurites are the structural substrate of the brain that support its function. Measures of their morphology from histology provide the gold standard for diagnosing various brain disorders. Some of these measures, e.g. neurite density and orientation dispersion, can now be mapped

in vivo

using diffusion MRI, enabling their use in clinical applications. However,

in vivo

methods for estimating more sophisticated measures, such as dispersion anisotropy, have yet to be demonstrated. Dispersion anisotropy allows more refined characterisation of the complex neurite configurations such as fanning or bending axons; its quantification

in vivo

can offer new imaging markers. The aim of this work is to develop a method to estimate dispersion anisotropy

in vivo

. Our approach builds on the Neurite Orientation Dispersion and Density Imaging (NODDI), an existing clinically feasible diffusion MRI technique. The estimation of dispersion anisotropy is achieved by incorporating Bingham distribution as the neurite orientation distribution function, with no additional acquisition requirements. We show the first

in vivo

maps of dispersion anisotropy and demonstrate that it can be estimated accurately with a clinically feasible protocol. We additionally show that the original NODDI is robust to the effects of dispersion anisotropy, when the the new parameter is not of interest.

Advanced diffusion weighted MR imaging allows non-invasive study on the structural connectivity of human brains. Fiber orientation distributions (FODs) reconstructed from diffusion data are a popular model to represent crossing fibers. For this sophisticated image representation of connectivity, classical image operations such as smoothing must be redefined. In this paper, we propose a novel rotation-induced Riemannian metric for FODs, and introduce a weighted diffusion process for FODs regarding this Riemannian manifold. We show how this Riemannian manifold can be used for smoothing, interpolation and building image-pyramids, yielding more accurate or intuitively more reasonable results than the linear or the unit hyper-sphere manifold.

The residence time

τ

i

of water inside axons is an important biomarker for white matter pathologies of the human central nervous system, as myelin damage is hypothesised to increase axonal permeability, and thus reduce

τ

i

. Diffusion-weighted (DW) MRI is potentially able to measure

τ

i

as it is sensitive to the average displacement of water molecules in tissue. However, previous work addressing this has been hampered by a lack of both sensitive data and accurate mathematical models. We address the latter problem by constructing a computational model using Monte Carlo simulations and machine learning in order to learn a mapping between features derived from DW MR signals and ground truth microstructure parameters. We test our method using simulated and in vivo human brain data. Simulation results show that our approach provides a marked improvement over the most widely used mathematical model. The trained model also predicts sensible microstructure parameters from in vivo human brain data, matching values of

τ

i

found in the literature.

Tractography in diffusion tensor imaging estimates connectivity in the brain through observations of local diffusivity. These observations are noisy and of low resolution and, as a consequence, connections cannot be found with high precision. We use probabilistic numerics to estimate connectivity between regions of interest and contribute a Gaussian Process tractography algorithm which allows for both quantification and visualization of its posterior uncertainty. We use the uncertainty both in visualization of individual tracts as well as in heat maps of tract locations. Finally, we provide a quantitative evaluation of different metrics and algorithms showing that the adjoint metric [8] combined with our algorithm produces paths which agree most often with experts.

Mapping the neuronal wiring diagrams in the brain at multiple spatial scales has been one of the major brain mapping objectives. Macro-scale medical imaging modalities such as diffusion tensor imaging (DTI) and meso-scale biological imaging such as serial two-photon tomography have emerged as the prominent tools to reveal structural connectivity patterns at multiple scales. However, a significant gap that whether/how DTI data and microscopic data are correlated with each other for the same species of mammalian brains, e.g., mouse brains, has been rarely explored. To bridge this knowledge gap, this work aims to construct multi-modal mouse brain connectomes via joint modeling of macro-scale DTI data and meso-scale neuronal tracing data. Specifically, the high-resolution DTI data and its streamline tractography result are mapped to the Allen Mouse Brain Atlas, in which the high-density axonal projections were already mapped by microscopic serial two-photon tomography. Then, multi-modal connectomes were constructed and the multi-view spectral clustering method is employed to assess consistent and discrepant connectivity patterns across the multi-scale multi-modal connectomes. Experimental results demonstrated the importance of fusing multimodal, multi-scale imaging modalities for structural connectivity and connectome mapping.

In diffusion MRI (dMRI), determining an appropriate sampling scheme is crucial for acquiring the maximal amount of information for data reconstruction and analysis using the minimal amount of time. For single-shell acquisition, uniform sampling without directional preference is usually favored. To achieve this, a commonly used approach is the Electrostatic Energy Minimization (EEM) method introduced in dMRI by Jones et al. However, the electrostatic energy formulation in EEM is not

directly

related to the goal of optimal sampling-scheme design, i.e., achieving large angular separation between sampling points. A mathematically more natural approach is to consider the Spherical Code (SC) formulation, which aims to achieve uniform sampling by maximizing the minimal angular difference between sampling points on the unit sphere. Although SC is well studied in the mathematical literature, its current formulation is limited to a single shell and is not applicable to multiple shells. Moreover, SC, or more precisely continuous SC (CSC), currently can only be applied on the

continuous

unit sphere and hence cannot be used in situations where one or several subsets of sampling points need to be determined from an existing sampling scheme. In this case, discrete SC (DSC) is required. In this paper, we propose novel DSC and CSC methods for designing uniform single-/multi-shell sampling schemes. The DSC and CSC formulations are solved respectively by Mixed Integer Linear Programming (MILP) and a gradient descent approach. A fast greedy incremental solution is also provided for both DSC and CSC. To our knowledge, this is the first work to use SC formulation for designing sampling schemes in dMRI. Experimental results indicate that our methods obtain larger angular separation and better rotational invariance than the generalized EEM (gEEM) method currently used in the Human Connectome Project (HCP).

Quantitative and qualitative analysis of white matter fibers resulting from tractography algorithms is made difficult by their huge number. To this end, we propose an

approximation scheme

which gives as result a more concise but at the same time exhaustive representation of a fiber bundle. It is based on a novel computational model for fibers, called

weighted currents

, characterised by a metric that considers both the pathway and the anatomical locations of the endpoints of the fibers. Similarity has therefore a twofold connotation: geometrical and related to the connectivity. The core idea is to use this metric for approximating a fiber bundle with a set of weighted prototypes, chosen among the fibers, which represent ensembles of similar fibers. The weights are related to the number of fibers represented by the prototypes. The algorithm is divided into two steps. First, the main modes of the fiber bundle are detected using a

modularity based clustering

algorithm. Second, a

prototype fiber selection

process is carried on in each cluster separately. This permits to explain the main patterns of the fiber bundle in a fast and accurate way.

Recent studies have found that the modular structure of functional brain network is disrupted during the progress of Alzheimer’s disease. The modular structure of network is the most basic topological invariant in determining the shape of network in the view of algebraic topology. In this study, we propose a new method to find another higher order topological invariant, hole, based on persistent homology. If a hole exists in the network, the information can be inefficiently delivered between regions. If we can localize the hole in the network, we can infer the reason of network inefficiency. We propose to detect the persistent hole using the spectrum of

k

 −Laplacian, which is the generalized version of graph Laplacian. The method is applied to the metabolic network based on FDG-PET data of Alzheimer disease (AD), mild cognitive impairment (MCI) and normal control (NC) groups. The experiments show that the persistence of hole can be used as a biological marker of disease progression to AD. The localized hole may help understand the brain network abnormality in AD, revealing that the limbic-temporo-parietal association regions disturb direct connections between other regions.

Combining multi-modality brain data for disease diagnosis commonly leads to improved performance. A challenge in using multi-modality data is that the data are commonly incomplete; namely, some modality might be missing for some subjects. In this work, we proposed a deep learning based framework for estimating multi-modality imaging data. Our method takes the form of convolutional neural networks, where the input and output are two volumetric modalities. The network contains a large number of trainable parameters that capture the relationship between input and output modalities. When trained on subjects with all modalities, the network can estimate the output modality given the input modality. We evaluated our method on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database, where the input and output modalities are MRI and PET images, respectively. Results showed that our method significantly outperformed prior methods.

Many recent scientific efforts have been devoted to constructing the human connectome using Diffusion Tensor Imaging (DTI) data for understanding the large-scale brain networks that underlie higher-level cognition in human. However, suitable computational network analysis tools are still lacking in human connectome research. To address this problem, we propose a novel multi-graph min-max cut model to detect the consistent network modules from the brain connectivity networks of all studied subjects. A new multi-graph MinMax cut model is introduced to solve this challenging computational neuroscience problem and the efficient optimization algorithm is derived. In the identified connectome module patterns, each network module shows similar connectivity patterns in all subjects, which potentially associate to specific brain functions shared by all subjects. We validate our method by analyzing the weighted fiber connectivity networks. The promising empirical results demonstrate the effectiveness of our method.

Recently, neuroimaging data have been increasingly used to study the causal relationship among brain regions for the understanding and diagnosis of brain diseases. Recent work on sparse Gaussian Bayesian network (SGBN) has shown it as an efficient tool to learn large scale directional brain networks from neuroimaging data. In this paper, we propose a learning approach to constructing SGBNs that are both representative and discriminative for groups in comparison. A max-margin criterion built directly upon the SGBN models is proposed to effectively optimize the classification performance of the SGBNs. The proposed method shows significant improvements over the state-of-the-art works in the discriminative power of SGBNs.

Brain imaging genetics is an emergent research field where the association between genetic variations such as single nucleotide polymorphisms (SNPs) and neuroimaging quantitative traits (QTs) is evaluated. Sparse canonical correlation analysis (SCCA) is a bi-multivariate analysis method that has the potential to reveal complex multi-SNP-multi-QT associations. Most existing SCCA algorithms are designed using the soft threshold strategy, which assumes that the features in the data are independent from each other. This independence assumption usually does not hold in imaging genetic data, and thus inevitably limits the capability of yielding optimal solutions. We propose a novel structure-aware SCCA (denoted as S2CCA) algorithm to not only eliminate the independence assumption for the input data, but also incorporate group-like structure in the model. Empirical comparison with a widely used SCCA implementation, on both simulated and real imaging genetic data, demonstrated that S2CCA could yield improved prediction performance and biologically meaningful findings.

We propose a method for fast, accurate and robust localization of several organs in medical images. We generalize global-to-local cascades of regression forests [1] to multiple organs. A first regressor encodes global relationships between organs. Subsequent regressors refine the localization of each organ locally and independently for improved accuracy. We introduce

confidence maps

, which incorporate information about both the regression vote distribution and the organ shape through probabilistic atlases. They are used within the cascade itself, to better select the test voxels for the second set of regressors, and to provide richer information than the classical bounding boxes thanks to the shape prior. We demonstrate the robustness and accuracy of our approach through a quantitative evaluation on a large database of 130 CT volumes.

Feature encoding plays an important role for medical image classification. Intra-cluster features such as bag of visual words have been widely used for feature encoding, which are based on the statistical information within each clusters of local features and therefore fail to capture the inter-cluster statistics, such as how the visual words co-occur in images. This paper proposes a new method to choose a subset of cluster pairs based on the idea of Latent Semantic Analysis (LSA) and proposes a new inter-cluster statistics which capture richer information than the traditional co-occurrence information. Since the cluster pairs are selected based on image patches rather than the whole images, the final representation also captures the local structures present in images. Experiments on medical datasets show that explicitly encoding inter-cluster statistics in addition to intra-cluster statistics significantly improves the classification performance, and adding the rich inter-cluster statistics performs better than the frequency based inter-cluster statistics.

Discriminative supervised learning algorithms, such as Support Vector Machines, are becoming increasingly popular in biomedical image computing. One of their main uses is to construct image-based prediction models, e.g., for computer aided diagnosis or “mind reading.” A major challenge in these applications is the biological interpretation of the machine learning models, which can be arbitrarily complex functions of the input features (e.g., as induced by kernel-based methods). Recent work has proposed several strategies for deriving maps that highlight regions relevant for accurate prediction. Yet most of these methods either rely on strong assumptions about the prediction model (e.g., linearity, sparsity) and/or data (e.g., Gaussianity), or fail to exploit the covariance structure in the data. In this work, we propose a computationally efficient and universal framework for quantifying associations captured by black box machine learning models. Furthermore, our theoretical perspective reveals that examining associations with predictions, in the absence of ground truth labels, can be very informative. We apply the proposed method to machine learning models trained to predict cognitive impairment from structural neuroimaging data. We demonstrate that our approach yields biologically meaningful maps of association.

The quantitative assessment of surgical outcomes using personalized anatomical models is an essential task for the treatment of spinal deformities such as adolescent idiopathic scoliosis. However an accurate 3D reconstruction of the spine from postoperative X-ray images remains challenging due to presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. In this paper, we formulate the reconstruction problem as an optimization over a manifold of articulated spine shapes learned from pathological training data. The manifold itself is represented using a novel data structure, a multi-level manifold ensemble, which contains links between nodes in a single hierarchical structure, as well as links between different hierarchies, representing overlapping partitions. We show that this data structure allows both efficient localization and navigation on the manifold, for on-the-fly building of local nonlinear models (manifold charting). Our reconstruction framework was tested on pre- and postoperative X-ray datasets from patients who underwent spinal surgery. Compared to manual ground-truth, our method achieves a 3D reconstruction accuracy of 2.37 ±0.85mm for postoperative spine models and can deal with severe cases of scoliosis.

Training an effective and scalable system for medical image analysis usually requires a large amount of labeled data, which incurs a tremendous annotation burden for pathologists. Recent progress in active learning can alleviate this issue, leading to a great reduction on the labeling cost without sacrificing the predicting accuracy too much. However, most existing active learning methods disregard the “structured information” that may exist in medical images (

e.g.

, data from individual patients), and make a simplifying assumption that unlabeled data is independently and identically distributed. Both may not be suitable for real-world medical images. In this paper, we propose a novel batch-mode active learning method which explores and leverages such structured information in annotations of medical images to enforce diversity among the selected data, therefore maximizing the information gain. We formulate the active learning problem as an adaptive submodular function maximization problem subject to a partition matroid constraint, and further present an efficient greedy algorithm to achieve a good solution with a theoretically proven bound. We demonstrate the efficacy of our algorithm on thousands of histopathological images of breast microscopic tissues.

We propose a novel unstained cell detection algorithm based on unsupervised learning. The algorithm utilizes the scale invariant feature transform (SIFT), a self-labeling algorithm, and two clustering steps in order to achieve high performance in terms of time and detection accuracy. Unstained cell imaging is dominated by phase contrast and bright field microscopy. Therefore, the algorithm was assessed on images acquired using these two modalities. Five cell lines having in total 37 images and 7250 cells were considered for the evaluation: CHO, L929, Sf21, HeLa, and Bovine cells. The obtained F-measures were between 85.1 and 89.5. Compared to the state-of-the-art, the algorithm achieves very close F-measure to the supervised approaches in much less time.

This paper presents Group-sparse Nonnegative supervised Canonical Correlation Analysis (GNCCA), a novel methodology for identifying discriminative features from multiple feature views. Existing correlation-based methods do not guarantee positive correlations of the selected features and often need a pre-feature selection step to reduce redundant features on each feature view. The new GNCCA approach attempts to overcome these issues by incorporating (1) a nonnegativity constraint that guarantees positive correlations in the reduced representation and (2) a group-sparsity constraint that allows for simultaneous between- and within- view feature selection. In particular, GNCCA is designed to emphasize correlations between feature views and class labels such that the selected features guarantee better class separability. In this work, GNCCA was evaluated on three prostate cancer (CaP) prognosis tasks: (i) identifying 40 CaP patients with and without 5-year biochemical recurrence following radical prostatectomy by fusing quantitative features extracted from digitized pathology and proteomics, (ii) predicting

in vivo

prostate cancer grade for 16 CaP patients by fusing T2w and DCE MRI, and (iii) localizing CaP/benign regions on MR spectroscopy and MRI for 36 patients. For the three tasks, GNCCA identifies a feature subset comprising 2%, 1% and 22%, respectively, of the original extracted features. These selected features achieve improved or comparable results compared to using all features with the same Support Vector Machine (SVM) classifier. In addition, GNCCA consistently outperforms 5 state-of-the-art feature selection methods across all three datasets.

In this work, we formulate a clustering-induced multi-task learning method for feature selection in Alzheimer’s Disease (AD) or Mild Cognitive Impairment (MCI) diagnosis. Unlike the previous methods that often assumed a unimodal data distribution, we take into account the underlying multipeak distribution of classes. The rationale for our approach is that it is likely for neuroimaging data to have multiple peaks or modes in distribution due to the inter-subject variability. In this regard, we use a clustering method to discover the multipeak distributional characteristics and define subclasses based on the clustering results, in which each cluster covers a peak. We then encode the respective subclasses,

i.e.

, clusters, with their unique codes by imposing the subclasses of the same original class close to each other and those of different original classes distinct from each other. We finally formulate a multi-task learning problem in an ℓ

2,1

-penalized regression framework by taking the codes as new label vectors of our training samples, through which we select features for classification. In our experimental results on the ADNI dataset, we validated the effectiveness of the proposed method by achieving the maximal classification accuracies of 95.18% (AD/Normal Control: NC), 79.52% (MCI/NC), and 72.02% (MCI converter/MCI non-converter), outperforming the competing single-task learning method.

In this paper, we consider the joint regression and classification in Alzheimer’s disease diagnosis and propose a novel multi-relation regularization method that exploits the relational information inherent in the observations and then combines it with an ℓ

2,1

-norm within a least square regression framework for feature selection. Specifically, we use three kinds of relationships: feature-feature relation, response-response relation, and sample-sample relation. By imposing these three relational characteristics along with the ℓ

2,1

-norm on the weight coefficients, we formulate a new objective function. After feature selection based on the optimal weight coefficients, we train two support vector regression models to predict the clinical scores of Alzheimer’s Disease Assessment Scale-Cognitive subscale (ADAS-Cog) and Mini-Mental State Examination (MMSE), respectively, and a support vector classification model to identify the clinical label. We conducted clinical score prediction and disease status identification jointly on the Alzheimer’s Disease Neuroimaging Initiative dataset. The experimental results showed that the proposed regularization method outperforms the state-of-the-art methods, in the metrics of correlation coefficient and root mean squared error in regression and classification accuracy, sensitivity, specificity, and area under the receiver operating characteristic curve in classification.

As minimally invasive surgery becomes increasingly popular, the volume of recorded laparoscopic videos will increase rapidly. Invaluable information for teaching, assistance during difficult cases, and quality evaluation can be accessed from these videos through a video search engine. Typically, video search engines give a list of the most relevant videos pertaining to a keyword. However, instead of a whole video, one is often only interested in a fraction of the video (e.g. intestine stitching in bypass surgeries). In addition, video search requires semantic tags, yet the large amount of data typically generated hinders the feasibility of manual annotation. To tackle these problems, we propose a coarse-to-fine video indexing approach that looks for the time boundaries of a task in a laparoscopic video based on a video snippet query. We combine our search approach with the Fisher kernel (FK) encoding and show that similarity measures on this encoding are better suited for this problem than traditional similarities, such as dynamic time warping (DTW). Despite visual challenges, such as the presence of smoke, motion blur, and lens impurity, our approach performs very well in finding 3 tasks in 49 bypass videos, 1 task in 23 hernia videos, and also 1 cross-surgery task between 49 bypass and 7 sleeve gastrectomy videos.

We propose a novel framework for exploring patterns of respiratory pathophysiology from paired breath-hold CT scans. This is designed to enable analysis of large datasets with the view of determining relationships between functional measures, disease state and the likelihood of disease progression. The framework is based on the local distribution of image features at various anatomical scales. Principal Component Analysis is used to visualise and quantify the multi-scale anatomical variation of features, whilst the distribution subspace can be exploited within a classification setting. This framework enables hypothesis testing related to the different phenotypes implicated in Chronic Obstructive Pulmonary Disease (COPD). We illustrate the potential of our method on initial results from a subset of patients from the COPDGene study, who are exacerbation susceptible and non-susceptible.