Tractometry analysis represents a significant advancement in neuroimaging, offering a detailed examination of the brain's white matter at a micro level. Unlike traditional ROI or voxel-based methods, tractometry precisely reconstructs and characterizes white matter tracts. Using advanced diffusion MRI and tractography algorithms, it maps the trajectory, shape, and connectivity patterns of individual white matter bundles. Accurate alignment of these tracts across different groups is crucial for reliable and reproducible results. Nonlinear registration techniques are essential for achieving this alignment, harmonizing bundle shapes, and improving sensitivity to disease-related changes. However, nonlinear registration is complex, especially with tractography data, which digitally represents the brain's white matter anatomy. Potential structural changes in the bundle's shape during registration can lead to artifacts that obscure critical anatomical details needed for disease identification. We introduce BundleWarp, a streamline-based nonlinear deformable registration method designed specifically for white matter tracts. BundleWarp employs a sophisticated approach to align two white matter bundles while preserving their topological and anatomical features. It is formulated as a probability density estimation problem with motion coherence penalties, ensuring coherent movement of points along streamlines and maintaining the anatomical integrity of tracts through displacement field regularization. Additionally, we introduce a tract morphometry framework utilizing the displacement field generated by BundleWarp to analyze white matter tract shape differences. Our results show that BundleWarp effectively quantifies bundle shape differences and enhances structural harmonization in tractometry analysis for diverse subjects, including those with Alzheimer's and Parkinson's disease. Test-retest experiments further demonstrate that BundleWarp substantially improves subject fingerprinting by increasing within-subject reproducibility of both bundle shape and microstructural profiles (FA, MD, RD, AD). It precisely maps the brain's neuronal pathways, offering a robust tractometry framework with enhanced sensitivity for detecting disease-related structural and microstructural changes in white matter tracts associated with Mild Cognitive Impairment (MCI), dementia, and early-stage Alzheimer's biomarkers, including amyloid-beta plaques and tau neurofibrillary tangles.

Independent and identically distributed (i.i.d.) data is essential to many data analysis and modeling techniques. In the medical domain, collecting data from multiple sites or institutions is a common strategy that guarantees sufficient clinical diversity, determined by the decentralized nature of medical data. However, data from various sites are easily biased by the local environment or facilities, thereby violating the i.i.d. rule. A common strategy is to harmonize the site bias while retaining important biological information. The ComBat is among the most popular harmonization approaches and has recently been extended to handle distributed sites. However, when faced with situations involving newly joined sites in training or evaluating data from unknown/unseen sites, ComBat lacks compatibility and requires retraining with data from all the sites. The retraining leads to significant computational and logistic overhead that is usually prohibitive. In this work, we develop a novel Cluster ComBat harmonization algorithm, which leverages cluster patterns of the data in different sites and greatly advances the usability of ComBat harmonization. We use extensive simulation and real medical imaging data from ADNI to demonstrate the superiority of the proposed approach. Our codes are provided in https://github.com/illidanlab/distributed-cluster-harmonization.

BACKGROUND: Brain volume has been widely studied in the neuroimaging field, since it is an important and heritable trait associated with brain development, aging and various neurological and psychiatric disorders. Genome-wide association studies (GWAS) have successfully identified numerous associations between genetic variants such as single nucleotide polymorphisms and complex traits like brain volume. However, it is unclear how these genetic variations influence regional gene expression levels, which may subsequently lead to phenotypic changes. S-PrediXcan is a tissue-specific transcriptomic data analysis method that can be applied to bridge this gap. In this work, we perform an S-PrediXcan analysis on GWAS summary data from two large imaging genetics initiatives, the UK Biobank and Enhancing Neuroimaging Genetics through Meta Analysis, to identify tissue-specific transcriptomic effects on two closely related brain volume measures: total brain volume (TBV) and intracranial volume (ICV). RESULTS: As a result of the analysis, we identified 10 genes that are highly associated with both TBV and ICV. Nine out of 10 genes were found to be associated with TBV in another study using a different gene-based association analysis. Moreover, most of our discovered genes were also found to be correlated with multiple cognitive and behavioral traits. Further analyses revealed the protein-protein interactions, associated molecular pathways and biological functions that offer insight into how these genes function and interact with others. CONCLUSIONS: These results confirm that S-PrediXcan can identify genes with tissue-specific transcriptomic effects on complex traits. The analysis also suggested novel genes whose expression levels are related to brain volumetric traits. This provides important insights into the genetic mechanisms of the human brain.

There are situations where data relevant to machine learning problems are distributed across multiple locations that cannot share the data due to regulatory, competitiveness, or privacy reasons. Machine learning approaches that require data to be copied to a single location are hampered by the challenges of data sharing. Federated Learning (FL) is a promising approach to learn a joint model over all the available data across silos. In many cases, the sites participating in a federation have different data distributions and computational capabilities. In these heterogeneous environments existing approaches exhibit poor performance: synchronous FL protocols are communication efficient, but have slow learning convergence and high energy cost; conversely, asynchronous FL protocols have faster convergence with lower energy cost, but higher communication. In this work, we introduce a novel energy-efficient Semi-Synchronous Federated Learning protocol that mixes local models periodically with minimal idle time and fast convergence. We show through extensive experiments over established benchmark datasets in the computer-vision domain as well as in real-world biomedical settings that our approach significantly outperforms previous work in data and computationally heterogeneous environments .

Visually identifying effective bio-markers from human brain networks poses non-trivial challenges to the field of data visualization and analysis. Existing methods in the literature and neuroscience practice are generally limited to the study of individual connectivity features in the brain (e.g., the strength of neural connection among brain regions). Pairwise comparisons between contrasting subject groups (e.g., the diseased and the healthy controls) are normally performed. The underlying neuroimaging and brain network construction process is assumed to have 100% fidelity. Yet, real-world user requirements on brain network visual comparison lean against these assumptions. In this work, we present MV^2Net, a visual analytics system that tightly integrates multi-variate multi-view visualization for brain network comparison with an interactive wrangling mechanism to deal with data uncertainty. On the analysis side, the system integrates multiple extraction methods on diffusion and geometric connectivity features of brain networks, an anomaly detection algorithm for data quality assessment, single- and multi-connection feature selection methods for bio-marker detection. On the visualization side, novel designs are introduced which optimize network comparisons among contrasting subject groups and related connectivity features. Our design provides level-of-detail comparisons, from juxtaposed and explicit-coding views for subject group comparisons, to high-order composite view for correlation of network comparisons, and to fiber tract detail view for voxel-level comparisons. The proposed techniques are inspired and evaluated in expert studies, as well as through case analyses on diffusion and geometric bio-markers of certain neurology diseases. Results in these experiments demonstrate the effectiveness and superiority of MV^2Net over state-of-the-art approaches.

An effective presymptomatic diagnosis and treatment of Alzheimer's disease (AD) would have enormous public health benefits. Sparse coding (SC) has shown strong potential for longitudinal brain image analysis in preclinical AD research. However, the traditional SC computation is time-consuming and does not explore the feature correlations that are consistent over the time. In addition, longitudinal brain image cohorts usually contain incomplete image data and clinical labels. To address these challenges, we propose a novel two-stage Multi-Resemblance Multi-Target Low-Rank Coding (MMLC) method, which encourages that sparse codes of neighboring longitudinal time points are resemblant to each other, favors sparse code low-rankness to reduce the computational cost and is resilient to both source and target data incompleteness. In stage one, we propose an online multi-resemblant low-rank SC method to utilize the common and task-specific dictionaries in different time points to immune to incomplete source data and capture the longitudinal correlation. In stage two, supported by a rigorous theoretical analysis, we develop a multi-target learning method to address the missing clinical label issue. To solve such a multi-task low-rank sparse optimization problem, we propose multi-task stochastic coordinate coding with a sequence of closed-form update steps which reduces the computational costs guaranteed by a theoretical convergence proof. We apply MMLC on a publicly available neuroimaging cohort to predict two clinical measures and compare it with six other methods. Our experimental results show our proposed method achieves superior results on both computational efficiency and predictive accuracy and has great potential to assist the AD prevention.

Multimodal learning aims at utilizing information from a variety of data modalities to improve the generalization performance. One common approach is to seek the common information that is shared among different modalities for learning, whereas we can also fuse the supplementary information to leverage modality-specific information. Though the supplementary information is often desired, most existing multimodal approaches can only learn from samples with complete modalities, which wastes a considerable amount of data collected. Otherwise, model-based imputation needs to be used to complete the missing values and yet may introduce undesired noise, especially when the sample size is limited. In this paper, we proposed a framework based on knowledge distillation, utilizing the supplementary information from all modalities, and avoiding imputation and noise associated with it. Specifically, we first train models on each modality independently using all the available data. Then the trained models are used as teachers to teach the student model, which is trained with the samples having complete modalities. We demonstrate the effectiveness of the proposed method in extensive empirical studies on both synthetic datasets and real-world datasets.

Brain imaging genomics is an emerging data science field, where integrated analysis of brain imaging and genomics data, often combined with other biomarker, clinical and environmental data, is performed to gain new insights into the phenotypic, genetic and molecular characteristics of the brain as well as their impact on normal and disordered brain function and behavior. It has enormous potential to contribute significantly to biomedical discoveries in brain science. Given the increasingly important role of statistical and machine learning in biomedicine and rapidly growing literature in brain imaging genomics, we provide an up-to-date and comprehensive review of statistical and machine learning methods for brain imaging genomics, as well as a practical discussion on method selection for various biomedical applications.

Genome-wide association studies (GWAS) link full genome data to a handful of traits. However, in neuroimaging studies, there is an almost unlimited number of traits that can be extracted for full image-wide big data analyses. Large populations are needed to achieve the necessary power to detect statistically significant effects, emphasizing the need to pool data across multiple studies. Neuroimaging consortia, e.g., ENIGMA and CHARGE, are now analyzing MRI data from over 30,000 individuals. Distributed processing protocols extract harmonized features at each site, and pool together only the cohort statistics using meta analysis to avoid data sharing. To date, such MRI projects have focused on single measures such as hippocampal volume, yet voxelwise analyses (e.g., tensor-based morphometry; TBM) may help better localize statistical effects. This can lead to $10^{13}$1013 tests for GWAS and become underpowered. We developed an analytical framework for multi-site TBM by performing multi-channel registration to cohort-specific templates. Our results highlight the reliability of the method and the added power over alternative options while preserving single site specificity and opening the doors for well-powered image-wide genome-wide discoveries.

Studies of the human brain network are becoming increasingly popular in the fields of neuroscience, computer science, and neurology. Despite this rapidly growing line of research, gaps remain on the intersection of data analytics, interactive visual representation, and the human intelligence—all needed to advance our understanding of human brain networks. This article tackles this challenge by exploring the design space of visual analytics. We propose an integrated framework to orchestrate computational models with comprehensive data visualizations on the human brain network. The framework targets two fundamental tasks: the visual exploration of multi-label brain networks and the visual comparison among brain networks across different subject groups. During the first task, we propose a novel interactive user interface to visualize sets of labeled brain networks; in our second task, we introduce sparse regression models to select discriminative features from the brain network to facilitate the comparison. Through user studies and quantitative experiments, both methods are shown to greatly improve the visual comparison performance. Finally, real-world case studies with domain experts demonstrate the utility and effectiveness of our framework to analyze reconstructions of human brain connectivity maps. The perceptually optimized visualization design and the feature selection model calibration are shown to be the key to our significant findings.

Alzheimer's disease (AD), one of the most common causes of dementia, is a severe irreversible neurodegenerative disease that results in loss of mental functions. The transitional stage between the expected cognitive decline of normal aging and AD, mild cognitive impairment (MCI), has been widely regarded as a suitable time for possible therapeutic intervention. The challenging task of MCI detection is therefore of great clinical importance, where the key is to effectively fuse predictive information from multiple heterogeneous data sources collected from the patients. In this paper, we propose a framework to fuse multiple data modalities for predictive modeling using deep matrix factorization, which explores the non-linear interactions among the modalities and exploits such interactions to transfer knowledge and enable high performance prediction. Specifically, the proposed collective deep matrix factorization decomposes all modalities simultaneously to capture non-linear structures of the modalities in a supervised manner, and learns a modality specific component for each modality and a modality invariant component across all modalities. The modality invariant component serves as a compact feature representation of patients that has high predictive power. The modality specific components provide an effective means to explore imaging genetics, yielding insights into how imaging and genotype interact with each other non-linearly in the AD pathology. Extensive empirical studies using various data modalities provided by Alzheimer's Disease Neuroimaging Initiative (ADNI) demonstrate the effectiveness of the proposed method for fusing heterogeneous modalities.

BACKGROUND: Global scale brain research collaborations such as the ENIGMA (Enhancing Neuro Imaging Genetics through Meta Analysis) consortium are beginning to collect data in large quantity and to conduct meta-analyses using uniformed protocols. It becomes strategically important that the results can be communicated among brain scientists effectively. Traditional graphs and charts failed to convey the complex shapes of brain structures which are essential to the understanding of the result statistics from the analyses. These problems could be addressed using interactive visualization strategies that can link those statistics with brain structures in order to provide a better interface to understand brain research results. RESULTS: We present ENIGMA-Viewer, an interactive web-based visualization tool for brain scientists to compare statistics such as effect sizes from meta-analysis results on standardized ROIs (regions-of-interest) across multiple studies. The tool incorporates visualization design principles such as focus+context and visual data fusion to enable users to better understand the statistics on brain structures. To demonstrate the usability of the tool, three examples using recent research data are discussed via case studies. CONCLUSIONS: ENIGMA-Viewer supports presentations and communications of brain research results through effective visualization designs. By linking visualizations of both statistics and structures, users can gain more insights into the presented data that are otherwise difficult to obtain. ENIGMA-Viewer is an open-source tool, the source code and sample data are publicly accessible through the NITRC website ( http://www.nitrc.org/projects/enigmaviewer_20 ). The tool can also be directly accessed online ( http://enigma-viewer.org ).

Visually comparing human brain networks from multiple population groups serves as an important task in the field of brain connectomics. The commonly used brain network representation, consisting of nodes and edges, may not be able to reveal the most compelling network differences when the reconstructed networks are dense and homogeneous. In this paper, we leveraged the block information on the Region Of Interest (ROI) based brain networks and studied the problem of blockwise brain network visual comparison. An integrated visual analytics framework was proposed. In the first stage, a two-level ROI block hierarchy was detected by optimizing the anatomical structure and the predictive comparison performance simultaneously. In the second stage, the NodeTrix representation was adopted and customized to visualize the brain network with block information. We conducted controlled user experiments and case studies to evaluate our proposed solution. Results indicated that our visual analytics method outperformed the commonly used node-link graph and adjacency matrix design in the blockwise network comparison tasks. We have shown compelling findings from two real-world brain network data sets, which are consistent with the prior connectomics studies.

Lasso regression is a widely used technique in data mining for model selection and feature extraction. In many applications, it remains challenging to apply the regression model to large-scale problems that have massive data samples with high-dimensional features. One popular and promising strategy is to solve the Lasso problem in parallel. Parallel solvers run multiple cores in parallel on a shared memory system to speedup the computation, while the practical usage is limited by the huge dimension in the feature space. Screening is a promising method to solve the problem of high dimensionality by discarding the inactive features and removing them from optimization. However, when integrating screening methods with parallel solvers, most of solvers cannot guarantee the convergence on the reduced feature matrix. In this paper, we propose a novel parallel framework by parallelizing screening methods and integrating it with our proposed parallel solver. We propose two parallel screening algorithms: Parallel Strong Rule (PSR) and Parallel Dual Polytope Projection (PDPP). For the parallel solver, we proposed an Asynchronous Grouped Coordinate Descent method (AGCD) to optimize the regression problem in parallel on the reduced feature matrix. AGCD is based on a grouped selection strategy to select the coordinate that has the maximum descent for the objective function in a group of candidates. Empirical studies on the real-world datasets demonstrate that the proposed parallel framework has a superior performance compared to the state-of-the-art parallel solvers.

Workflow reuse is a major benefit of workflow systems and shared workflow repositories, but there are barely any studies that quantify the degree of reuse of workflows or the practical barriers that may stand in the way of successful reuse. In our own work, we hypothesize that defining workflow fragments improves reuse, since end-to-end workflows may be very specific and only partially reusable by others. This paper reports on a study of the current use of workflows and workflow fragments in labs that use the LONI Pipeline, a popular workflow system used mainly for neuroimaging research that enables users to define and reuse workflow fragments. We present an overview of the benefits of workflows and workflow fragments reported by users in informal discussions. We also report on a survey of researchers in a lab that has the LONI Pipeline installed, asking them about their experiences with reuse of workflow fragments and the actual benefits they perceive. This leads to quantifiable indicators of the reuse of workflows and workflow fragments in practice. Finally, we discuss barriers to further adoption of workflow fragments and workflow reuse that motivate further work.

Scientific workflows provide the means to define, execute and reproduce computational experiments. However, reusing existing workflows still poses challenges for workflow designers. Workflows are often too large and too specific to reuse in their entirety, so reuse is more likely to happen for fragments of workflows. These fragments may be identified manually by users as sub-workflows, or detected automatically. In this paper we present the FragFlow approach, which detects workflow fragments automatically by analyzing existing workflow corpora with graph mining algorithms. FragFlow detects the most common workflow fragments, links them to the original workflows and visualizes them. We evaluate our approach by comparing FragFlow results against user-defined sub-workflows from three different corpora of the LONI Pipeline system. Based on this evaluation, we discuss how automated workflow fragment detection could facilitate workflow reuse.

We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to model diffusion and cast the ODF segmentation problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and to the concentration parameters, and show its superior performance compared to alternative methods when analyzing complex fiber configurations. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers and white matter fiber tracts of clinical importance.

With the advances and increasing sophistication in data collection techniques, we are facing with large amounts of data collected from multiple heterogeneous sources in many applications. For example, in the study of Alzheimer's Disease (AD), different types of measurements such as neuroimages, gene/protein expression data, genetic data etc. are often collected and analyzed together for improved predictive power. It is believed that a joint learning of multiple data sources is beneficial as different data sources may contain complementary information, and feature-pruning and data source selection are critical for learning interpretable models from high-dimensional data. Very often the collected data comes with block-wise missing entries; for example, a patient without the MRI scan will have no information in the MRI data block, making his/her overall record incomplete. There has been a growing interest in the data mining community on expanding traditional techniques for single-source complete data analysis to the study of multi-source incomplete data. The key challenge is how to effectively integrate information from multiple heterogeneous sources in the presence of block-wise missing data. In this paper we first investigate the situation of complete data and present a unified ``bi-level" learning model for multi-source data. Then we give a natural extension of this model to the more challenging case with incomplete data. Our major contributions are threefold: (1) the proposed models handle both feature-level and source-level analysis in a unified formulation and include several existing feature learning approaches as special cases; (2) the model for incomplete data avoids direct imputation of the missing elements and thus provides superior performances. Moreover, it can be easily generalized to other applications with block-wise missing data sources; (3) efficient optimization algorithms are presented for both the complete and incomplete models. We have performed comprehensive evaluations of the proposed models on the application of AD diagnosis. Our proposed models compare favorably against existing approaches.

Incomplete data present serious problems when integrating largescale brain imaging data sets from different imaging modalities. In the Alzheimer's Disease Neuroimaging Initiative (ADNI), for example, over half of the subjects lack cerebrospinal fluid (CSF) measurements; an independent half of the subjects do not have fluorodeoxyglucose positron emission tomography (FDG-PET) scans; many lack proteomics measurements. Traditionally, subjects with missing measures are discarded, resulting in a severe loss of available information. We address this problem by proposing two novel learning methods where all the samples (with at least one available data source) can be used. In the first method, we divide our samples according to the availability of data sources, and we learn shared sets of features with state-of-the-art sparse learning methods. Our second method learns a base classifier for each data source independently, based on which we represent each source using a single column of prediction scores; we then estimate the missing prediction scores, which, combined with the existing prediction scores, are used to build a multi-source fusion model. To illustrate the proposed approaches, we classify patients from the ADNI study into groups with Alzheimer's disease (AD), mild cognitive impairment (MCI) and normal controls, based on the multi-modality data. At baseline, ADNI's 780 participants (172 AD, 397 MCI, 211 Normal), have at least one of four data types: magnetic resonance imaging (MRI), FDG-PET, CSF and proteomics. These data are used to test our algorithms. Comprehensive experiments show that our proposed methods yield stable and promising results.

The Center for Computational Biology (CCB) is a multidisciplinary program where biomedical scientists, engineers, and clinicians work jointly to combine modern mathematical and computational techniques, to perform phenotypic and genotypic studies of biological structure, function, and physiology in health and disease. CCB has developed a computational framework built around the Manifold Atlas, an integrated biomedical computing environment that enables statistical inference on biological manifolds. These manifolds model biological structures, features, shapes, and flows, and support sophisticated morphometric and statistical analyses. The Manifold Atlas includes tools, workflows, and services for multimodal population-based modeling and analysis of biological manifolds. The broad spectrum of biomedical topics explored by CCB investigators include the study of normal and pathological brain development, maturation and aging, discovery of associations between neuroimaging and genetic biomarkers, and the modeling, analysis, and visualization of biological shape, form, and size. CCB supports a wide range of short-term and long-term collaborations with outside investigators, which drive the center's computational developments and focus the validation and dissemination of CCB resources to new areas and scientific domains.

This paper proposes a novel approach for extracting two intrinsic feature curves on hippocampal (HC) surfaces. The hippocampus is a key target of study in medical imaging, as it degenerates in conditions such as epilepsy and Alzheimer's disease (AD), but its structure is complex. To facilitate HC morphometry, we generate two intrinsic feature curves that describe their global geometries. For example, the separation of them captures thickness changes in HC surfaces, which can be used to effectively measure HC atrophy found in patients with AD. They also separate HC surfaces into upper and lower surface patches where intrinsic shape analysis using conformal modules can be carried out. Based on these curves, we further propose a parameterization of HC surfaces called the eigen-harmonic parameterization (EHP). EHP maps each HC surface onto a parameter domain and imposes longitudinal and azimuthal coordinates on each surface, which follow the gradient and level sets of its first nontrivial Laplace--Beltrami eigenfunction, respectively. Each tubular domain is constructed according to the geometry of an individual HC surface. This gives a parameter domain with much less geometric distortion compared to spherical parameterization. With EHP, all HC surfaces are automatically registered with intrinsic feature curves preserved and geometric distortions minimized. This allows shape analysis on any number of HC surfaces to be performed consistently. We studied geometric changes over time in 138 HC surfaces of patients with AD and normal subjects scanned at two different times. We successfully located areas with significantly different shape changes over time between the two groups.

In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons of anatomy, surface-based registration, and signal processing. Here, we introduce the theories of continuous and discrete surface Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies with user-defined Gaussian curvatures. The resulting conformal parameterizations have no singularities and they are intrinsic and stable. First, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves. Secondly, we conformally parameterize each cortical surface to a parameter domain with a user-designed Gaussian curvature arrangement. In the parameter domain, a shape index based on conformal invariants is computed, and inter-subject cortical surface matching is performed by solving a constrained harmonic map. We illustrate various target curvature arrangements and demonstrate the stability of the method using longitudinal data. To map statistical differences in cortical morphometry, we studied brain asymmetry in 14 healthy control subjects. We used a manifold version of Hotelling's T(2) test, applied to the Jacobian matrices of the surface parameterizations. A permutation test, along with the cumulative distribution of p-values, were used to estimate the overall statistical significance of differences. The results show our algorithm's power to detect subtle group differences in cortical surfaces.

This paper develops an information (inverse-covariance) based method for efficient fusion and distributed estimation of large scale terrain. The output resembles a standard triangulated irregular network (TIN) terrain representation. However the proposed method uses distributed information fusion to estimate the elevations of the mesh vertices. This terrain mapping system is intended to use multiple scanning vehicles for online monitoring of the terrain for automated mining operations or other multi-vehicle field robotics systems. The method is based on a pre-specified regular finite-element mesh to define the set of estimated state variables. The method maintains a joint Gaussian distribution of the mesh vertices' elevations, in the information (inverse-covariance) form. The mesh elevations are estimated jointly given the irregular terrain observations, together with smoothness terms. The smoothness terms enable interpolation into unobserved regions as well as reducing noise. In the information form, the observations and smoothness terms are additive and the information matrix remains sparse in a fixed pattern, enabling constant-memory fusion of observations, efficient distribution among multiple sensing platforms and efficient solving for the estimates and uncertainty. Results show the reduction in data size for the fused observations compared to the raw observations, whilst still obtaining large scale high quality terrain maps. This paper focuses on a hierarchical distributed system in which each node estimates a subset of its parent's region, with the top-level node estimating a terrain map of the whole area. This paper compares two methods for the distributed communication from parent to child: An exact but expensive method, and an approximate fast method. Results compare the communication cost and resulting level of estimation approximation, showing that the marginalised information is expensive and the approximation is acceptable without it. This paper is applied to the estimation of large scale surface terrain from a distributed network of multiple sensors, such as 3D laser scanners, for automated terrain mapping for large scale mining applications.

In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented , where the deformation was regularized by penalizing deviations from a zero rate of strain. In , the terms regularizing the deformation included the covariance of the deformation matrices (Σ) and the vector fields (q) . Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.

Automatic whole-brain extraction from magnetic resonance images (MRI), also known as skull stripping, is a key component in most neuroimage pipelines. As the first element in the chain, its robustness is critical for the overall performance of the system. Many skull stripping methods have been proposed, but the problem is not considered to be completely solved yet. Many systems in the literature have good performance on certain datasets (mostly the datasets they were trained/tuned on), but fail to produce satisfactory results when the acquisition conditions or study populations are different. In this paper we introduce a robust, learning-based brain extraction system (ROBEX). The method combines a discriminative and a generative model to achieve the final result. The discriminative model is a Random Forest classifier trained to detect the brain boundary; the generative model is a point distribution model that ensures that the result is plausible. When a new image is presented to the system, the generative model is explored to find the contour with highest likelihood according to the discriminative model. Because the target shape is in general not perfectly represented by the generative model, the contour is refined using graph cuts to obtain the final segmentation. Both models were trained using 92 scans from a proprietary dataset but they achieve a high degree of robustness on a variety of other datasets. ROBEX was compared with six other popular, publicly available methods (BET, BSE, FreeSurfer, AFNI, BridgeBurner, and GCUT) on three publicly available datasets (IBSR, LPBA40, and OASIS, 137 scans in total) that include a wide range of acquisition hardware and a highly variable population (different age groups, healthy/diseased). The results show that ROBEX provides significantly improved performance measures for almost every method/dataset combination.

Surface registration is widely used in machine vision and medical imaging, where 1-1 correspondences between surfaces are computed to study their variations. Surface maps are usually stored as the 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenience in data transmission and data storage, especially when a large set of surfaces are analyzed. To tackle this problem, we propose a novel representation of surface diffeomorphisms using Beltrami coefficients, which are complex-valued functions defined on surfaces with supreme norm less than 1. Fixing any 3 points on a pair of surfaces, there is a 1-1 correspondence between the set of surface diffeomorphisms between them and the set of Beltrami coefficients on the source domain. Hence, every bijective surface map can be represented by a unique Bel-trami coefficient. Conversely, given a Beltrami coefficient, we can reconstruct the unique surface map associated to it using the Beltrami Holomorphic flow (BHF) method introduced in this paper. Using this representation, 1/3 of the storage space is saved. We can further reduce the storage requirement by 90% by compressing the Beltrami coefficients using Fourier approximations. We test our algorithm on synthetic data, real human brain and hippocampal surfaces. Our results show high accuracy in the reconstructed data, while the amount of storage is greatly reduced. Our approach is compared with the Fourier compression of the coordinate functions using the same amount of data. The latter approach often shows jaggy results and cannot guarantee to preserve diffeomorphisms.

Surface registration, which transforms different sets of surface data into one common reference space, is an important process which allows us to compare or integrate the surface data effectively. If a nonrigid transformation is required, surface registration is commonly done by parameterizing the surfaces onto a simple parameter domain, such as the unit square or sphere. In this work, we are interested in looking for meaningful registrations between surfaces through parameterizations, using prior features in the form of landmark curves on the surfaces. In particular, we generate optimized conformal parameterizations which match landmark curves exactly with shape-based correspondences between them. We propose a variational method to minimize a compound energy functional that measures the harmonic energy of the parameterization maps and the shape dissimilarity between mapped points on the landmark curves. The novelty is that the computed maps are guaranteed to align the landmark features consistently and give a shape-based diffeomorphism between the landmark curves. We achieve this by intrinsically modeling our search space of maps as flows of smooth vector fields that do not flow across the landmark curves. By using the local surface geometry on the curves to define a shape measure, we compute registrations that ensure consistent correspondences between anatomical features. We test our algorithm on synthetic surface data. An application of our model to medical imaging research is shown, using experiments on brain cortical surfaces, with anatomical (sulcal) landmarks delineated, which show that our computed maps give a shape-based alignment of the sulcal curves without significantly impairing conformality. This ensures correct averaging and comparison of data across subjects.

We compared four automated methods for hippocampal segmentation using different machine learning algorithms: 1) hierarchical AdaBoost, 2) support vector machines (SVM) with manual feature selection, 3) hierarchical SVM with automated feature selection (Ada-SVM), and 4) a publicly available brain segmentation package (FreeSurfer). We trained our approaches using T1-weighted brain MRIs from 30 subjects [10 normal elderly, 10 mild cognitive impairment (MCI), and 10 Alzheimer's disease (AD)], and tested on an independent set of 40 subjects (20 normal, 20 AD). Manually segmented gold standard hippocampal tracings were available for all subjects (training and testing). We assessed each approach's accuracy relative to manual segmentations, and its power to map AD effects. We then converted the segmentations into parametric surfaces to map disease effects on anatomy. After surface reconstruction, we computed significance maps, and overall corrected p-values, for the 3-D profile of shape differences between AD and normal subjects. Our AdaBoost and Ada-SVM segmentations compared favorably with the manual segmentations and detected disease effects as well as FreeSurfer on the data tested. Cumulative p-value plots, in conjunction with the false discovery rate method, were used to examine the power of each method to detect correlations with diagnosis and cognitive scores. We also evaluated how segmentation accuracy depended on the size of the training set, providing practical information for future users of this technique.

In medical shape analysis, a critical problem is reconstructing a smooth surface of correct topology from a binary mask that typically has spurious features due to segmentation artifacts. The challenge is the robust removal of these outliers without affecting the accuracy of other parts of the boundary. In this paper, we propose a novel approach for this problem based on the Laplace-Beltrami (LB) eigen-projection and properly designed boundary deformations. Using the metric distortion during the LB eigen-projection, our method automatically detects the location of outliers and feeds this information to a well-composed and topology-preserving deformation. By iterating between these two steps of outlier detection and boundary deformation, we can robustly filter out the outliers without moving the smooth part of the boundary. The final surface is the eigen-projection of the filtered mask boundary that has the correct topology, desired accuracy and smoothness. In our experiments, we illustrate the robustness of our method on different input masks of the same structure, and compare with the popular SPHARM tool and the topology preserving level set method to show that our method can reconstruct accurate surface representations without introducing artificial oscillations. We also successfully validate our method on a large data set of more than 900 hippocampal masks and demonstrate that the reconstructed surfaces retain volume information accurately.

High angular resolution diffusion imaging has become an important magnetic resonance technique for in vivo imaging. Most current research in this field focuses on developing methods for computing the orientation distribution function (ODF), which is the probability distribution function of water molecule diffusion along any angle on the sphere. In this paper, we present a Riemannian framework to carry out computations on an ODF field. The proposed framework does not require that the ODFs be represented by any fixed parameterization, such as a mixture of von Mises-Fisher distributions or a spherical harmonic expansion. Instead, we use a non-parametric representation of the ODF, and exploit the fact that under the square-root re-parameterization, the space of ODFs forms a Riemannian manifold, namely the unit Hilbert sphere. Specifically, we use Riemannian operations to perform various geometric data processing algorithms, such as interpolation, convolution and linear and nonlinear filtering. We illustrate these concepts with numerical experiments on synthetic and real datasets.

All surfaces can be classified by the conformal equivalence relation. Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used to measure surface deformation. Here we propose to compute a conformal invariant, or shape index, that is associated with the perimeter of the inner concentric circle in the hyperbolic parameter plane. With the surface Ricci flow method, we can conformally map a multiply connected domain to a multi-hole disk and this conformal map can preserve the values of the conformal invariant. Our algorithm provides a stable method to map the values of this shape index in the 2D (hyperbolic space) parameter domain. We also applied this new shape index for analyzing abnormalities in brain morphology in Alzheimer's disease (AD) and Williams syndrome (WS). After cutting along various landmark curves on surface models of the cerebral cortex or hippocampus, we obtained multiple connected domains. We conformally projected the surfaces to hyperbolic plane with surface Ricci flow method, accurately computed the proposed conformal invariant for each selected landmark curve, and assembled these into a feature vector.We also detected group differences in brain structure based on multivariate analysis of the surface deformation tensors induced by these Ricci flow mappings. Experimental results with 3D MRI data from 80 subjects demonstrate that our method powerfully detects brain surface abnormalities when combined with a constrained harmonic map based surface registration method.

In this paper, we propose multivariate tensor-based surface morphometry, a new method for surface analysis, using holomorphic differentials; we also apply it to study brain anatomy. Differential forms provide a natural way to parameterize 3D surfaces, but the multivariate statistics of the resulting surface metrics have not previously been investigated. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We present the canonical holomorphic one-forms with improved numerical accuracy and computational efficiency. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer's Disease (AD; 12 subjects), lateral ventricular surface morphometry in HIV/AIDS (11 subjects) and biomarkers in lateral ventricles in HIV/AIDS (11 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate statistics on the local tensors outperformed other TBM methods including analysis of the Jacobian determinant, the largest eigenvalue, or the pair of eigenvalues, of the surface Jacobian matrix.

Two surfaces are conformally equivalent if there exists a bijective angle-preserving map between them. The Teichmüller space for surfaces with the same topology is a finite-dimensional manifold, where each point represents a conformal equivalence class, and the conformal map is homotopic to the identity map. In this paper, we propose a novel method to apply conformal equivalence based shape index to study brain morphometry. The shape index is defined based on Teichmüller space coordinates. It is intrinsic, and invariant under conformal transformations, rigid motions and scaling. It is also simple to compute; no registration of surfaces is needed. Using the Yamabe flow method, we can conformally map a genus-zero open boundary surface to the Poincaré disk. The shape indices that we compute are the lengths of a special set of geodesics under hyperbolic metric. By computing and studying this shape index and its statistical behavior, we can analyze differences in anatomical morphometry due to disease or development. Study on twin lateral ventricular surface data shows it may help detect generic influence on lateral ventricular shapes. In leave-one-out validation tests, we achieved 100% accurate classification (versus only 68% accuracy for volume measures) in distinguishing 11 HIV/AIDS individuals from 8 healthy control subjects, based on Teichmüller coordinates for lateral ventricular surfaces extracted from their 3D MRI scans.Our conformal invariants, the Teichmüller coordinates, successfully classified all lateral ventricular surfaces, showing their promise for analyzing anatomical surface morphometry.

Localized Components Analysis (LoCA) is a new method for describing surface shape variation in an ensemble of objects using a linear subspace of spatially localized shape components. In contrast to earlier methods, LoCA optimizes explicitly for localized components and allows a flexible trade-off between localized and concise representations, and the formulation of locality is flexible enough to incorporate properties such as symmetry. This paper demonstrates that LoCA can provide intuitive presentations of shape differences associated with sex, disease state, and species in a broad range of biomedical specimens, including human brain regions and monkey crania.

Neuroimaging data, such as 3-D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3-D space. We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a p-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects.

In this paper, we propose an automated approach for the joint detection of major sulci on cortical surfaces. By representing sulci as nodes in a graphical model, we incorporate Markovian relations between sulci and formulate their detection as a maximum a posteriori (MAP) estimation problem over the joint space of major sulci. To make the inference tractable, a sample space with a finite number of candidate curves is automatically generated at each node based on the Hamilton-Jacobi skeleton of sulcal regions. Using the AdaBoost algorithm, we learn both individual and pairwise shape priors of sulcal curves from training data, which are then used to define potential functions in the graphical model based on the connection between AdaBoost and logistic regression. Finally belief propagation is used to perform the MAP inference and select the joint detection results from the sample spaces of candidate curves. In our experiments, we quantitatively validate our algorithm with manually traced curves and demonstrate the automatically detected curves can capture the main body of sulci very accurately. A comparison with independently detected results is also conducted to illustrate the advantage of the joint detection approach.

Diffusion weighted magnetic resonance (MR) imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of 6 directions, second-order tensors can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve crossing fiber tracts. A number of high-angular resolution schemes with greater than 6 gradient directions have been employed to address this issue. In this paper, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF once this optimal TDF is determined, the diffusion orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function.

Automatically segmenting subcortical structures in brain im ages has the potential to greatly accelerate drug trials and population studies of disease. Here we propose an automatic subcortical segmentation algorithm using the auto context model. Unlike many segmentation algorithms that separately compute a shape prior and an image appearance model, we develop a framework based on machine learning to learn a unified appearance and context model. We trained our algorithm to segment the hippocampus and tested it on 83 brain MRIs (of 35 Alzheimer's disease patients, 22 with mild cognitive impairment, and 26 normal healthy controls). Using standard distance and overlap metrics, the auto context model method significantly outperformed simpler learning-based algorithms (using AdaBoost alone) and the FreeSurfer system. In tests on a public domain dataset designed to validate segmentation [1], our new algorithm also greatly improved upon a recently-proposed hybrid discriminative/generative approach [2], which was among the top three that performed comparably in a recent head-to-head competition.

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or J-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the J-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

In this paper, we propose a new method to construct graphical representations of cortical folding patterns by computing skeletons on triangulated cortical surfaces. In our approach, a cortical surface is first partitioned into sulcal and gyral regions via the solution of a variational problem using graph cuts, which can guarantee global optimality. After that, we extend the method of Hamilton-Jacobi skeleton [1] to subsets of triangulated surfaces, together with a geometrically intuitive pruning process that can trade off between skeleton complexity and the completeness of representing folding patterns. Compared with previous work that uses skeletons of 3-D volumes to represent sulcal patterns, the skeletons on cortical surfaces can be easily decomposed into branches and provide a simpler way to construct graphical representations of cortical morphometry. In our experiments, we demonstrate our method on two different cortical surface models, its ability of capturing major sulcal patterns and its application to compute skeletons of gyral regions.

In this paper, a hybrid discriminative/generative model for brain anatomical structure segmentation is proposed. The learning aspect of the approach is emphasized. In the discriminative appearance models, various cues such as intensity and curvatures are combined to locally capture the complex appearances of different anatomical structures. A probabilistic boosting tree (PBT) framework is adopted to learn multiclass discriminative models that combine hundreds of features across different scales. On the generative model side, both global and local shape models are used to capture the shape information about each anatomical structure. The parameters to combine the discriminative appearance and generative shape models are also automatically learned. Thus, low-level and high-level information is learned and integrated in a hybrid model. Segmentations are obtained by minimizing an energy function associated with the proposed hybrid model. Finally, a grid-face structure is designed to explicitly represent the 3-D region topology. This representation handles an arbitrary number of regions and facilitates fast surface evolution. Our system was trained and tested on a set of 3-D magnetic resonance imaging (MRI) volumes and the results obtained are encouraging.

In this paper, we present a novel framework for constructing large deformation log-unbiased image registration models that generate theoretically and intuitively correct deformation maps. Such registration models do not rely on regridding and are inherently topology preserving. We apply information theory to quantify the magnitude of deformations and examine the statistical distributions of Jacobian maps in the logarithmic space. To demonstrate the power of the proposed framework, we generalize the well known viscous fluid registration model to compute log-unbiased deformations. We tested the proposed method using a pair of binary corpus callosum images, a pair of two-dimensional serial MRI images, and a set of three-dimensional serial MRI brain images. We compared our results to those computed using the viscous fluid registration method, and demonstrated that the proposed method is advantageous when recovering voxel-wise maps of local tissue change.

In [8], the authors proposed the large deformation log-unbiased diffeomorphic nonlinear image registration model which has been successfully used to obtain theoretically and intuitively correct deformation maps. In this paper, we extend this idea to simultaneously registering and tracking deforming objects in a sequence of two or more images. We generalize a level set based Chan-Vese multiphase segmentation model to consider Jacobian fields while segmenting regions of growth and shrinkage in deformations. Deforming objects are thus classified based on magnitude of homogeneous deformation. Numerical experiments demonstrating our results include a pair of two-dimensional synthetic images and pairs of two-dimensional and three-dimensional serial MRI images.

The 16 papers in this special issue focus on the growing field of computational neuroanatomy. Some of the topics covered include: new work on deformable geometry and surface-based anatomical modeling; analysis of anatomical shape, with applications to disease classification and computer-aided diagnosis; new types of statistical analyses of structural brain images; and image registration.

In order to compare anatomical and functional brain imaging data across subjects, the images must first be registered to a common coordinate system in which anatomical features are aligned. Intensity-based volume registration methods can align subcortical structures well, but the variability in sulcal folding patterns typically results in misalignment of the cortical surface. Conversely, surface-based registration using sulcal features can produce excellent cortical alignment but the mapping between brains is restricted to the cortical surface. Here we describe a method for volumetric registration that also produces an accurate one-to-one point correspondence between cortical surfaces. This is achieved by first parameterizing and aligning the cortical surfaces using sulcal landmarks. We then use a constrained harmonic mapping to extend this surface correspondence to the entire cortical volume. Finally, this mapping is refined using an intensity-based warp. We demonstrate the utility of the method by applying it to T1-weighted magnetic resonance images (MRIs). We evaluate the performance of our proposed method relative to existing methods that use only intensity information; for this comparison we compute the intersubject alignment of expert-labeled subcortical structures after registration.

Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on the Jacobian map, which estimates local tissue gain or loss. Here, we provide rigorous mathematical analyses of the Jacobian maps, and use themto motivate a new numerical method to construct unbiased nonlinear image registration. First, we argue that logarithmic transformation is crucial for analyzing Jacobian values representing morphometric differences. We then examine the statistical distributions of log-Jacobian maps by defining the Kullback-Leibler (KL) distance on material density functions arising in continuum-mechanical models. With this framework, unbiased image registration can be constructed by quantifying the symmetric KL-distance between the identity map and the resulting deformation. Implementation details, addressing the proposed unbiased registration as well as the minimization of symmetric image matching functionals, are then discussed and shown to be applicable to other registration methods, such as inverse consistent registration. In the results section, we test the proposed framework, as well as present an illustrative application mapping detailed 3-D brain changes in sequential magnetic resonance imaging scans of a patient diagnosed with semantic dementia. Using permutation tests, we show that the symmetrization of image registration statistically reduces skewness in the log-Jacobian map.

It is important to detect and extract the major cortical sulci from brain images, but manually annotating these sulci is a time-consuming task and requires the labeler to follow complex protocols. This paper proposes a learning-based algorithm for automated extraction of the major cortical sulci from magnetic resonance imaging (MRI) volumes and cortical surfaces. Unlike alternative methods for detecting the major cortical sulci, which use a small number of predefined rules based on properties of the cortical surface such as the mean curvature, our approach learns a discriminative model using the probabilistic boosting tree algorithm (PBT). PBT is a supervised learning approach which selects and combines hundreds of features at different scales, such as curvatures, gradients and shape index. Our method can be applied to either MRI volumes or cortical surfaces. It first outputs a probability map which indicates how likely each voxel lies on a major sulcal curve. Next, it applies dynamic programming to extract the best curve based on the probability map and a shape prior. The algorithm has almost no parameters to tune for extracting different major sulci. It is very fast (it runs in under 1 min per sulcus including the time to compute the discriminative models) due to efficient implementation of the features (e.g., using the integral volume to rapidly compute the responses of 3-D Haar filters). Because the algorithm can be applied to MRI volumes directly, there is no need to perform preprocessing such as tissue segmentation or mapping to a canonical space. The learning aspect of our approach makes the system very flexible and general. For illustration, we use volumes of the right hemisphere with several major cortical sulci manually labeled. The algorithm is tested on two groups of data, including some brains from patients with Williams Syndrome, and the results are very encouraging.

In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks.

Anatomical features on cortical surfaces are usually represented by landmark curves, called sulci/gyri curves. These landmark curves are important information for neuroscientists to study brain diseases and to match different cortical surfaces. Manual labelling of these landmark curves is time-consuming, especially when there is a large set of data. In this paper, we proposed to trace the landmark curves on cortical surfaces automatically based on the principal directions. Suppose we are given the global conformal parametrization of a cortical surface, By fixing two endpoints, the anchor points, we propose to trace the landmark curves iteratively on the spherical/rectangular parameter domain along the principal direction. Consequently, the landmark curves can be mapped onto the cortical surface. To speed up the iterative scheme, a good initial guess of the landmark curve is necessary. We proposed a method to get a good initialization by extracting the high curvature region on the cortical surface using the Chan-Vese segmentation. This involves solving a PDE on the manifold using our global conformal parametrization technique. Experimental results show that the landmark curves detected by our algorithm closely resemble to those manually labelled curves. As an application, we used these automatically labelled landmark curves to build average cortical surfaces with an optimized brain conformal mapping method. Experimental results show our method can help automatically matching brain cortical surfaces.

We propose a novel adaptive approach based on the Reproducing Kernel Particle Method (RKPM) to extract the cortical surfaces of the brain from three-dimensional (3-D) magnetic resonance images (MRIs). To formulate the discrete equations of the deformable model, a flexible particle shape function is employed in the Galerkin approximation of the weak form of the equilibrium equations. The proposed support generation method ensures that support of all particles cover the entire computational domains. The deformable model is adaptively adjusted by dilating the shape function and by inserting or merging particles in the high curvature regions or regions stopped by the target boundary. The shape function of the particle with a dilation parameter is adaptively constructed in response to particle insertion or merging. The proposed method offers flexibility in representing highly convolved structures and in refining the deformable models. Self-intersection of the surface, during evolution, is prevented by tracing backward along gradient descent direction from the crest interface of the distance field, which is computed by fast marching. These operations involve a significant computational cost. The initial model for the deformable surface is simple and requires no prior knowledge of the segmented structure. No specific template is required, e.g., an average cortical surface obtained from many subjects. The extracted cortical surface efficiently localizes the depths of the cerebral sulci, unlike some other active surface approaches that penalize regions of high curvature. Comparisons with manually segmented landmark data are provided to demonstrate the high accuracy of the proposed method. We also compare the proposed method to the finite element method, and to a commonly used cortical surface extraction approach, the CRUISE method. We also show that the independence of the shape functions of the RKPM from the underlying mesh enhances the convergence speed of the deformable model.

Face recognition and many medical imaging applications require the computation of dense correspondence vector fields that match one surface with another. In brain imaging, surface-based registration is useful for tracking brain change, and for creating statistical shape models of anatomy. Based on surface correspondences, metrics can also be designed to measure differences in facial geometry and expressions. To avoid the need for a large set of manually-defined landmarks to constrain these surface correspondences, we developed an algorithm to automate the matching of surface features. It extends the mutual information method to automatically match general 3D surfaces (including surfaces with a branching topology). We use diffeomorphic flows to optimally align the Riemann surface structures of two surfaces. First, we use holomorphic I-forms to induce consistent conformal grids on both surfaces. High genus surfaces are mapped to a set of rectangles in the Euclidean plane and closed genus-zero surfaces are mapped to the sphere. Next, we compute stable geometric features (mean curvature and conformal factor) and pull them back as scalar fields onto the 2D parameter domains. Mutual information is used as a cost functional to drive a fluid flow in the parameter domain that optimally aligns these surface features. A diffeomorphic surface-to-surface mapping is then recovered that matches surfaces in 3D. Lastly, we present a spectral method that ensures that the grids induced on the target surface remain conformal when pulled through the correspondence field. Using the chain rule, we express the gradient of the mutual information between surfaces in the conformal basis of the source surface. This finite-dimensional linear space generates all conformal reparameterizations of the surface. Illustrative experiments apply the method to face recognition and to the registration of brain structures, such as the hippocampus in 3D MRI scans, a key step in understanding brain shape alterations in Alzheimer's disease and schizophrenia.

We propose a general method that parameterizes general surfaces with complex (possible branching) topology using Riemann surface structure. Rather than evolve the surface geometry to a plane or sphere, we instead use the fact that all orientable surfaces are Riemann surfaces and admit conformal structures, which induce special curvilinear coordinate systems on the surfaces. We can then automatically partition the surface using a critical graph that connects zero points in the global conformal structure on the surface. The trajectories of iso-parametric curves canonically partition a surface into patches. Each of these patches is either a topological disk or a cylinder and can be conformally mapped to a parallelogram by integrating a holomorphic I-form defined on the surface. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. For surfaces with similar topology and geometry, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other using constrained harmonic maps. The surface similarity can be measured by direct computation of distance between each pair of corresponding points on two surfaces. To illustrate the technique, we computed conformal structures for anatomical surfaces in MRI scans of the brain and human face surfaces. We found that the resulting parameterizations were consistent across subjects, even for branching structures such as the ventricles, which are otherwise difficult to parameterize. Our method provides a surface-based framework for statistical comparison of surfaces and for generating grids on surfaces for PDE-based signal processing.

We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on magnetic resonance imaging (MRI) data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

Level set methods offer highly robust and accurate methods for detecting interfaces of complex structures. Efficient techniques are required to transform an interface to a globally defined level set function. In this paper, a novel level set method based on an adaptive triangular mesh is proposed for segmentation of medical images. Special attention is paid to an adaptive mesh refinement and redistancing technique for level set propagation, in order to achieve higher resolution at the interface with minimum expense. First, a narrow band around the interface is built in an upwind fashion. An active square technique is used to determine the shortest distance correspondence (SDC) for each grid vertex. Simultaneously, we also give an efficient approach for signing the distance field. Then, an adaptive improvement algorithm is proposed, which essentially combines two basic techniques: a long-edge-based vertex insertion strategy, and a local improvement. These guarantee that the refined triangulation is related to features along the front and has elements with appropriate size and shape, which fit the front well. We propose a short-edge elimination scheme to coarsen the refined triangular mesh, in order to reduce the extra storage. Finally, we reformulate the general evolution equation by updating 1) the velocities and 2) the gradient of level sets on the triangulated mesh. We give an approach for tracing contours from the level set on the triangulated mesh. Given a two-dimensional image with N grids along a side, the proposed algorithms run in O(kN) time at each iteration. Quantitative analysis shows that our algorithm is of first order accuracy; and when the interface-fitted property is involved in the mesh refinement, both the convergence speed and numerical accuracy are greatly improved. We also analyze the effect of redistancing frequency upon convergence speed and accuracy. Numerical examples include the extraction of inner and outer surfaces of the cerebral cortex from magnetic resonance imaging brain images.

In the field of template-based medical image analysis, image registration and normalization are frequently used to evaluate and interpret data in a standard template or reference atlas space. Despite the large number of image-registration (warping) techniques developed recently in the literature, only a few studies have been undertaken to numerically characterize and compare various alignment methods. In this paper, we introduce a new approach for analyzing image registration based on a selective-wavelet reconstruction technique using a frequency-adaptive wavelet shrinkage. We study four polynomial-based and two higher complexity nonaffine warping methods applied to groups of stereotaxic human brain structural (magnetic resonance imaging) and functional (positron emission tomography) data. Depending upon the aim of the image registration, we present several warp classification schemes. Our method uses a concise representation of the native and resliced (pre- and post-warp) data in compressed wavelet space to assess quality of registration. This technique is computationally inexpensive and utilizes the image compression, image enhancement, and denoising characteristics of the wavelet-based function representation, as well as the optimality properties of frequency-dependent wavelet shrinkage.

This paper presents a fully automated segmentation method for medical images. The goal is to localize and parameterize a variety of types of structure in these images for subsequent quantitative analysis. We propose a new hybrid strategy that combines a general elastic template matching approach and an evolutionary heuristic. The evolutionary algorithm uses prior statistical information about the shape of the target structure to control the behavior of a number of deformable templates. Each template, modeled in the form of a B-spline, is warped in a potential field which is itself dynamically adapted. Such a hybrid scheme proves to be promising: by maintaining a population of templates, we cover a large domain of the solution space under the global guidance of the evolutionary heuristic, and thoroughly explore interesting areas. We address key issues of automated image segmentation systems. The potential fields are initially designed based on the spatial features of the edges in the input image, and are subjected to spatially adaptive diffusion to guarantee the deformation of the template. This also improves its global consistency and convergence speed. The deformation algorithm can modify the internal structure of the templates to allow a better match. We investigate in detail the preprocessing phase that the images undergo before they can be used more effectively in the iterative elastic matching procedure: a texture classifier, trained via linear discriminant analysis of a learning set, is used to enhance the contrast of the target structure with respect to surrounding tissues. We show how these techniques interact within a statistically driven evolutionary scheme to achieve a better tradeoff between template flexibility and sensitivity to noise and outliers. We focus on understanding the features of template matching that are most beneficial in terms of the achieved match. Examples from simulated and real image data are discussed, with considerations of algorithmic efficiency.

The authors describe the development of a four-dimensional atlas and reference system that includes both macroscopic and microscopic information on structure and function of the human brain in persons between the ages of 18 and 90 years. Given the presumed large but previously unquantified degree of structural and functional variance among normal persons in the human population, the basis for this atlas and reference system is probabilistic. Through the efforts of the International Consortium for Brain Mapping (ICBM), 7,000 subjects will be included in the initial phase of database and atlas development. For each subject, detailed demographic, clinical, behavioral, and imaging information is being collected. In addition, 5,800 subjects will contribute DNA for the purpose of determining genotype- phenotype-behavioral correlations. The process of developing the strategies, algorithms, data collection methods, validation approaches, database structures, and distribution of results is described in this report. Examples of applications of the approach are described for the normal brain in both adults and children as well as in patients with schizophrenia. This project should provide new insights into the relationship between microscopic and macroscopic structure and function in the human brain and should have important implications in basic neuroscience, clinical diagnostics, and cerebral disorders.

The authors have devised, implemented, and tested a fast, spatially accurate technique for calculating the high-dimensional deformation field relating the brain anatomies of an arbitrary pair of subjects. The resulting three-dimensional (3-D) deformation map can be used to quantify anatomic differences between subjects or within the same subject over time and to transfer functional information between subjects or integrate that information on a single anatomic template. The new procedure is based on developmental processes responsible for variations in normal human anatomy and is applicable to 3-D brain images in general, regardless of modality. Hybrid surface models known as Chen surfaces (based on superquadrics and spherical harmonics) are used to efficiently initialize 3-D active surfaces, and these then extract from both scans the developmentally fundamental surfaces of the ventricles and cortex. The construction of extremely complex surface deformation maps on the internal cortex is made easier by building a generic surface structure to model it. Connected systems of parametric meshes model several deep sulci whose trajectories represent critical functional boundaries. These sulci are sufficiently extended inside the brain to reflect subtle and distributed variations in neuroanatomy between subjects. The algorithm then calculates the high-dimensional volumetric warp (typically with 3842x256x3 approximately 0.1 billion degrees of freedom) deforming one 3-D scan into structural correspondence with the other. Integral distortion functions are used to extend the deformation field required to elastically transform nested surfaces to their counterparts in the target scan. The algorithm's accuracy is tested, by warping 3-D magnetic resonance imaging (MRI) volumes from normal subjects and Alzheimer's patients, and by warping full-color 1024(3 ) digital cryosection volumes of the human head onto MRI volumes. Applications are discussed, including the transfer of multisubject 3-D functional, vascular, and histologic maps onto a single anatomic template; the mapping of 3-D brain atlases onto the scans of new subjects; and the rapid detection, quantification, and mapping of local shape changes in 3-D medical images in disease and during normal or abnormal growth and development.