Analyzing functional brain images in a probabilistic atlas: a validation of subvolume thresholding

Identification of a circuit-based endophenotype for familial depression

Frontal and parietal lesions may cause depression, and cortical thinning of the right frontal and parietal lobes has been shown to be a marker of risk for familial major depression. We studied biological offspring within a three-generation cohort, in which risk was defined by the depression status of the first generation, to identify regional volume differences associated with risk for depression throughout the cerebrum. We found reduced frontal and parietal white matter volumes in the high-risk group, including in persons without any personal history of depression, suggesting that hypoplasia of frontal and parietal white matter is an endophenotype for familial depression. In addition, white matter volumes in these regions correlated with current severity of symptoms of depression, inattention, and impulsivity. White matter volumes also correlated strongly with the degree of thinning in the right parietal cortex. These findings support a model of pathogenesis in which hypoplasia within a neural network for attention and emotional processing predisposes to depression.

Surface-based and probabilistic atlases of primate cerebral cortex

Brain atlases play an increasingly important role in neuroimaging, as they are invaluable for analysis, visualization, and comparison of results across studies. For both humans and macaque monkeys, digital brain atlases of many varieties are in widespread use, each having its own strengths and limitations. For studies of cerebral cortex there is particular utility in hybrid atlases that capitalize on the complementary nature of surface and volume representations, are based on a population average rather than an individual brain, and include measures of variation as well as averages. Linking different brain atlases to one another and to online databases containing a growing body of neuroimaging data will enable powerful forms of data mining that accelerate discovery and improve research efficiency.

Combining structural and functional neuroimaging data for studying brain connectivity: a review

Different brain areas are thought to be integrated into large-scale networks to support cognitive function. Recent approaches for investigating structural organization and functional coordination within these networks involve measures of connectivity among brain areas. We review studies combining in vivo structural and functional brain connectivity data, where (a) structural connectivity analysis, mostly based on diffusion tensor imaging is paired with voxel-wise analysis of functional neuroimaging data or (b) the measurement of functional connectivity based on covariance analysis is guided/aided by structural connectivity data. These studies provide insights into the relationships between brain structure and function. Promising trends involve (a) studies where both functional and anatomical connectivity data are collected using high-resolution neuroimaging methods and (b) the development of advanced quantitative models of integration.

Towards multimodal atlases of the human brain

Atlases of the human brain have an important impact on neuroscience. The emergence of ever more sophisticated imaging techniques, brain mapping methods and analytical strategies has the potential to revolutionize the concept of the brain atlas. Atlases can now combine data describing multiple aspects of brain structure or function at different scales from different subjects, yielding a truly integrative and comprehensive description of this organ. These integrative approaches have provided significant impetus for the human brain mapping initiatives, and have important applications in health and disease.

Pixel-based statistical analysis by a 3D clustering approach: application to autoradiographic images

Statistical analysis of medical images in experimental laboratories plays an important role in confirming scientific findings and in guiding potential clinical applications. In experimental neuroscience studies, autoradiographic images taken under differing physiological or pathological conditions from replicate animals are often compared in order to detect any significant change in glucose utilization or blood flow and to localize these changes. For these comparisons to be valid and informative, proper statistical procedures are in order. Conventional methods include statistic parametric mapping (SPM) analysis, non-parametric analysis and cluster-analysis. Each method of comparison has a specific purpose. This paper describes an approach that combines these conventional methods and presents a non-parametric statistical procedure based on cluster-analysis for localizing significant differences in autoradiographic data sets. By thresholding cluster sizes rather than pixel values to reject false positives, this approach enhances statistical power. By re-shuffling the data sets to produce the null distribution of a cluster size statistic, the test makes few assumptions as to the statistical properties of the SPM, and thus it is valid under a broad range of conditions. The designed method was tested on autoradiographic images of rats subjected to moderate traumatic brain injury (TBI). Different methods were also performed on the same data sets. Comparison among these methods shows that this method is suitable for the statistical analysis of autoradiographic images.

A wavelet-based statistical analysis of FMRI data: I. motivation and data distribution modeling

We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the Cauchy, Bessel K Forms, and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlas-based wavelet space representation. In the second part of our investigation, we will apply this technique to analyze a large fMRI dataset involving repeated presentation of sensory-motor response stimuli in young, elderly, and demented subjects.

Three-dimensional average-shape atlas of the honeybee brain and its applications

The anatomical substrates of neural nets are usually composed from reconstructions of neurons that were stained in different preparations. Realistic models of the structural relationships between neurons require a common framework. Here we present 3-D reconstructions of single projection neurons (PN) connecting the antennal lobe (AL) with the mushroom body (MB) and lateral horn, groups of intrinsic mushroom body neurons (type 5 Kenyon cells), and a single mushroom body extrinsic neuron (PE1), aiming to compose components of the olfactory pathway in the honeybee. To do so, we constructed a digital standard atlas of the bee brain. The standard atlas was created as an average-shape atlas of 22 neuropils, calculated from 20 individual immunostained whole-mount bee brains. After correction for global size and positioning differences by repeatedly applying an intensity-based nonrigid registration algorithm, a sequence of average label images was created. The results were qualitatively evaluated by generating average gray-value images corresponding to the average label images and judging the level of detail within the labeled regions. We found that the first affine registration step in the sequence results in a blurred image because of considerable local shape differences. However, already the first nonrigid iteration in the sequence corrected for most of the shape differences among individuals, resulting in images rich in internal detail. A second iteration improved on that somewhat and was selected as the standard. Registering neurons from different preparations into the standard atlas reveals 1) that the m-ACT neuron occupies the entire glomerulus (cortex and core) and overlaps with a local interneuron in the cortical layer; 2) that, in the MB calyces and the lateral horn of the protocerebral lobe, the axon terminals of two identified m-ACT neurons arborize in separate but close areas of the neuropil; and 3) that MB-intrinsic clawed Kenyon cells (type 5), with somata outside the calycal cups, project to the peduncle and lobe output system of the MB and contact (proximate) the dendritic tree of the PE1 neuron at the base of the vertical lobe. Thus the standard atlas and the procedures applied for registration serve the function of creating realistic neuroanatomical models of parts of a neural net. The Honeybee Standard Brain is accessible at www.neurobiologie.fu-berlin.de/beebrain.

Mindboggle: automated brain labeling with multiple atlases

Background

To make inferences about brain structures or activity across multiple individuals, one first needs to determine the structural correspondences across their image data. We have recently developed Mindboggle as a fully automated, feature-matching approach to assign anatomical labels to cortical structures and activity in human brain MRI data. Label assignment is based on structural correspondences between labeled atlases and unlabeled image data, where an atlas consists of a set of labels manually assigned to a single brain image. In the present work, we study the influence of using variable numbers of individual atlases to nonlinearly label human brain image data.

Methods

Each brain image voxel of each of 20 human subjects is assigned a label by each of the remaining 19 atlases using Mindboggle. The most common label is selected and is given a confidence rating based on the number of atlases that assigned that label. The automatically assigned labels for each subject brain are compared with the manual labels for that subject (its atlas). Unlike recent approaches that transform subject data to a labeled, probabilistic atlas space (constructed from a database of atlases), Mindboggle labels a subject by each atlas in a database independently.

Results

When Mindboggle labels a human subject's brain image with at least four atlases, the resulting label agreement with coregistered manual labels is significantly higher than when only a single atlas is used. Different numbers of atlases provide significantly higher label agreements for individual brain regions.

Conclusion

Increasing the number of reference brains used to automatically label a human subject brain improves labeling accuracy with respect to manually assigned labels. Mindboggle software can provide confidence measures for labels based on probabilistic assignment of labels and could be applied to large databases of brain images.

Representative brain selection using a group-specific tissue probability map

PURPOSE

To determine the anatomy of a standard brain reflecting well-defined group characteristics based on probabilistic information from group-specific anatomical variations.

MATERIALS AND METHODS

We constructed a group-specific tissue probabilistic map for 20 subjects and used it to extract voxel-wise probabilistic information for each subject through regional spatial normalization using Automated Image Registration software (AIR 5.2.5). Extracted probabilistic information was then used to determine standard properties of the subjects. For comparison, we employed an empirical scoring function - a measure of entropy - in ordering the data set. A brain with minimum entropy was then selected for a group standard. The evaluation of our proposed method was performed using two different selection schemes: deformation analysis and similarity index measurements.

RESULTS

This method showed highly correlated result with previous method by Kochunov et al., with fewer computational tasks.

CONCLUSION

This method can thus be used to determine an appropriate standard model to compare with disease-affected brains.

Automated brain tissue assessment in the elderly and demented population: construction and validation of a sub-volume probabilistic brain atlas

OBJECTIVES

To develop an automated imaging assessment tool that accommodates the anatomic variability of the elderly and demented population as well as the registration errors occurring during spatial normalization.

METHODS

20 subjects with Alzheimer's disease (AD), mild cognitive impairment, or normal cognition underwent MRI brain imaging and had their 3D volumetric datasets manually partitioned into 68 regions of interest (ROI) termed sub-volumes. Gray matter (GM), white matter (WM), and cerebral spinal fluid (CSF) voxel counts were then made in the subject's native space for comparison against automated volumetric measures within three sub-volume probabilistic atlas (SVPA) models. The three SVPAs were constructed using 12 parameter affine (12 p), 2nd order (2nd), and 6th order (6th) transforms derived from registering the manually partitioned scans into a Talairach compatible AD population-based target. The three SVPA automated measures were compared to the manually derived measures in the 20 subjects' native space with a "jack-knife" procedure in which each subject was assessed by an SVPA they did not contribute toward constructing.

RESULTS

The mean left and right GM ratio (GM ratio = [GM + CSF] / CSF) "r values" for the 3 SVPAs compared to the manually derived ratios across the 68 ROIs were 0.85 for the 12p SVPA, 0.88 for the 2nd SVPA, and 0.89 for the 6th SVPA. The mean left and right WM ratio (WM ratio = [WM + CSF] / CSF) "r values" for the 3 SVPAs being 0.84 for the 12p SVPA, 0.86 for the 2nd SVPA, and 0.88 for the 6th SVPA.

CONCLUSION

We have constructed, from an elderly and demented cohort, an automated brain volumetric tool that has excellent accuracy compared to a manual gold standard and is capable of regional hypothesis testing and individual patient assessment compared to a population.

Region-of-interest-based analysis of clustered BOLD MRI data in experimental arthritis

RATIONALE AND OBJECTIVES

BOLD MRI provides functional information based on minimal changes. Problems inherent in data processing of the very low signal-to-noise-ratio of BOLD experiments have created obstacles for validation of certain techniques using standard strength-field MR scanners. Measures of diagnostic accuracy of clustered data are directly related to the reading parameters used to define regions-of-interest (ROIs). Our primary aim was to determine the combination of ROI-related reading parameters that provides highest accuracy for discrimination of presence or absence of arthritis in acute and subacute stages of the disease using paired comparisons of BOLD MRI data.

MATERIALS AND METHODS

Six male New Zealand white rabbits were injected with albumin into one knee and saline into the contralateral knee, 3 animals had albumin injected into only one of the knees, 2 had saline injected into one of the knees, and 3 animals were not injected. The rabbits' knees underwent BOLD MRI on days 1 and 28 after induction of arthritis, except for the knees of 3 animals (albumin- vs saline-injected knees, n = 2 animals; saline- vs noninjected knees, n = 1 animal) that died before expected and had only the first MRI examination done. Percentage of activated voxels and differences in on-and-off signal intensities were the BOLD MRI methods applied. Data were analyzed using anatomic-driven small ROI, voxel-chaser-driven small ROI and anatomic-driven large ROI techniques.

RESULTS

Diagnostic areas-under-the curve (AUCs) were obtained only for acute arthritis and only when percentage of activated voxels was used. Low threshold, positive voxel activations and small ROIs generated the largest AUCs (AUC +/- SE, .911 +/- .092, P = .014) using either anatomic-driven or voxel-chaser-driven techniques. A sensitivity analysis confirmed the importance of threshold as a parameter for analysis.

CONCLUSION

Low threshold, positive voxel activations and small ROIs constituted the set of reading parameters that provided the most accurate BOLD MRI results.

Discovery and integrative neuroscience

Hypothesis driven research has been shown to be an excellent model for pursuing investigations in neuroscience. The Human Genome Project demonstrated the added value of discovery research, especially in areas where large amounts of data are produced. Neuroscience has become a data rich field, and one that would be enhanced by incorporating the discovery approach. Databases, as well as analytical, modeling and simulation tools, will have to be developed, and they will need to be interoperable and federated. This paper presents an overview of the development of the field of neuroscience databases and associate tools: Neuroinformatics. The primary focus is on the impact of NIH funding of this process. The important issues of data sharing, as viewed from the perspective of the scientist and private and public funding organizations, are discussed. Neuroinformatics will provide more than just a sophisticated array of information technologies to help scientists understand and integrate nervous system data. It will make available powerful models of neural functions and facilitate discovery, hypothesis formulation and electronic collaboration.

Construction and evaluation of an average CT brain image for inter-subject registration

An average CT brain image is constructed to serve as reference frame for inter-subject registration. A set of 96 clinical CT images is used. Registration includes translation, rotation, and anisotropic scaling. A temporary average based on a subset of 32 images is constructed. This image is used as reference for the iterative construction of the average CT image. This approach is computationally efficient and results in a consistent registration of the 96 images. Registration of new images to the average CT is more consistent than registration to a single CT image. The use of the average CT image is illustrated.

Controlling the familywise error rate in functional neuroimaging: a comparative review

Functional neuroimaging data embodies a massive multiple testing problem, where 100,000 correlated test statistics must be assessed. The familywise error rate, the chance of any false positives is the standard measure of Type I errors in multiple testing. In this paper we review and evaluate three approaches to thresholding images of test statistics: Bonferroni, random field and the permutation test. Owing to recent developments, improved Bonferroni procedures, such as Hochberg's methods, are now applicable to dependent data. Continuous random field methods use the smoothness of the image to adapt to the severity of the multiple testing problem. Also, increased computing power has made both permutation and bootstrap methods applicable to functional neuroimaging. We evaluate these approaches on t images using simulations and a collection of real datasets. We find that Bonferroni-related tests offer little improvement over Bonferroni, while the permutation method offers substantial improvement over the random field method for low smoothness and low degrees of freedom. We also show the limitations of trying to find an equivalent number of independent tests for an image of correlated test statistics.

Positron emission tomography imaging of the aging brain

PET imaging provides a vital means to study the human brain in vivo in aging and early disease states. PET studies using selective markers for brain metabolism and neurotransmitter function have uncovered a wealth of information on healthy and pathologic brain aging, and its relationship to behavior and mood states. Recognition of inherent potential confounds in the use of PET in aging studies is essential to the proper interpretation of these data.

Construction of an abdominal probabilistic atlas and its application in segmentation

There have been significant efforts to build a probabilistic atlas of the brain and to use it for many common applications, such as segmentation and registration. Though the work related to brain atlases can be applied to nonbrain organs, less attention has been paid to actually building an atlas for organs other than the brain. Motivated by the automatic identification of normal organs for applications in radiation therapy treatment planning, we present a method to construct a probabilistic atlas of an abdomen consisting of four organs (i.e., liver, kidneys, and spinal cord). Using 32 noncontrast abdominal computed tomography (CT) scans, 31 were mapped onto one individual scan using thin plate spline as the warping transform and mutual information (MI) as the similarity measure. Except for an initial coarse placement of four control points by the operators, the MI-based registration was automatic. Additionally, the four organs in each of the 32 CT data sets were manually segmented. The manual segmentations were warped onto the "standard" patient space using the same transform computed from their gray scale CT data set and a probabilistic atlas was calculated. Then, the atlas was used to aid the segmentation of low-contrast organs in an additional 20 CT data sets not included in the atlas. By incorporating the atlas information into the Bayesian framework, segmentation results clearly showed improvements over a standard unsupervised segmentation method.

Quantitative comparison and analysis of brain image registration using frequency-adaptive wavelet shrinkage

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.

Mapping genetic influences on human brain structure

Recent advances in brain imaging and genetics have empowered the mapping of genetic and environmental influences on the human brain. These techniques shed light on the 'nature/nurture' debate, revealing how genes determine individual differences in intelligence quotient (IQ) or risk for disease. They visualize which aspects of brain structure and function are heritable, and to what degree, linking these features with behavioral or cognitive traits or disease phenotypes. In genetically transmitted disorders such as schizophrenia, patterns of brain structure can be associated with increased disease liability, and sites can be mapped where non-genetic triggers may initiate disease. We recently developed a large-scale computational brain atlas, including data components from the Finnish Twin registry, to store information on individual variations in brain structure and their heritability. Algorithms from random field theory, anatomical modeling, and population genetics were combined to detect a genetic continuum in which brain structure is heavily genetically determined in some areas but not others. These algorithmic advances motivate studies of disease in which the normative atlas acts as a quantitative reference for the heritability of structural differences and deficits in patient populations. The resulting genetic brain maps isolate biological markers for inherited traits and disease susceptibility, which may serve as targets for genetic linkage and association studies. Computational methods from brain imaging and genetics can be fruitfully merged, to shed light on the inheritance of personality differences and behavioral traits, and the genetic transmission of diseases that affect the human brain.

A probabilistic atlas and reference system for the human brain: International Consortium for Brain Mapping (ICBM)

Motivated by the vast amount of information that is rapidly accumulating about the human brain in digital form, we embarked upon a program in 1992 to develop a four-dimensional probabilistic atlas and reference system for the human brain. Through an International Consortium for Brain Mapping (ICBM) a dataset is being collected that includes 7000 subjects between the ages of eighteen and ninety years and including 342 mono- and dizygotic twins. Data on each subject includes detailed demographic, clinical, behavioural and imaging information. DNA has been collected for genotyping from 5800 subjects. A component of the programme uses post-mortem tissue to determine the probabilistic distribution of microscopic cyto- and chemoarchitectural regions in the human brain. This, combined with macroscopic information about structure and function derived from subjects in vivo, provides the first large scale opportunity to gain meaningful insights into the concordance or discordance in micro- and macroscopic structure and function. The philosophy, strategy, algorithm development, data acquisition techniques and validation methods are described in this report along with database structures. Examples of results are described for the normal adult human brain as well as examples in patients with Alzheimer's disease and multiple sclerosis. The ability to quantify the variance of the human brain as a function of age in a large population of subjects for whom data is also available about their genetic composition and behaviour will allow for the first assessment of cerebral genotype-phenotype-behavioural correlations in humans to take place in a population this large. This approach and its application should provide new insights and opportunities for investigators interested in basic neuroscience, clinical diagnostics and the evaluation of neuropsychiatric disorders in patients.

Detecting disease-specific patterns of brain structure using cortical pattern matching and a population-based probabilistic brain atlas

The rapid creation of comprehensive brain image databases mandates the development of mathematical algorithms to uncover disease specific patterns of brain structure and function in human populations. We describe our construction of probabilistic atlases that store detailed information on how the brain varies across age and gender, across time, in health and disease, and in large human populations. Specifically, we introduce a mathematical framework based on covariant partial differential equations (PDEs), pull-backs of mappings under harmonic flows, and high-dimensional random tensor fields to encode variations in cortical patterning, asymmetry and tissue distribution in a population-based brain image database (N =94 scans). We use this information to detect disease-specific abnormalities in Alzheimer's disease and schizophrenia, including dynamic changes over time. Illustrative examples are chosen to show how group patterns of cortical organization, asymmetry, and disease-specific trends can be resolved that are not apparent in individual brain images. Finally, we create four-dimensional (4D) maps that store probabilistic information on the dynamics of brain change in development and disease. Digital atlases that generate these maps show considerable promise in identifying general patterns of structural and functional variation in diseased populations, and revealing how these features depend on demographic, genetic, clinical and therapeutic parameters.

Maps of the brain

We review recent developments in brain mapping and computational anatomy that have greatly expanded our ability to analyze brain structure and function. The enormous diversity of brain maps and imaging methods has spurred the development of population-based digital brain atlases. These atlases store information on how the brain varies across age and gender, across time, in health and disease, and in large human populations. We describe how brain atlases, and the computational tools that align new datasets with them, facilitate comparison of brain data across experiments, laboratories, and from different imaging devices. The major methods are presented for the construction of probabilistic atlases, which store information on anatomic and functional variability in a population. Algorithms are reviewed that create composite brain maps and atlases based on multiple subjects. We show that group patterns of cortical organization, asymmetry, and disease-specific trends can be resolved that may not be apparent in individual brain maps. Finally, we describe the creation of four-dimensional (4D) maps that store information on the dynamics of brain change in development and disease. Digital atlases that correlate these maps show considerable promise in identifying general patterns of structural and functional variation in human populations, and how these features depend on demographic, genetic, cognitive, and clinical parameters.

Cortical change in Alzheimer's disease detected with a disease-specific population-based brain atlas

We report the first detailed population-based maps of cortical gray matter loss in Alzheimer's disease (AD), revealing prominent features of early structural change. New computational approaches were used to: (i) distinguish variations in gray matter distribution from variations in gyral patterns; (ii) encode these variations in a brain atlas (n = 46); (iii) create detailed maps localizing gray matter differences across groups. High resolution 3D magnetic resonance imaging (MRI) volumes were acquired from 26 subjects with mild to moderate AD (age 75.8+/-1.7 years, MMSE score 20.0+/-0.9) and 20 normal elderly controls (72.4+/-1.3 years) matched for age, sex, handedness and educational level. Image data were aligned into a standardized coordinate space specifically developed for an elderly population. Eighty-four anatomical models per brain, based on parametric surface meshes, were created for all 46 subjects. Structures modeled included: cortical surfaces, all major superficial and deep cortical sulci, callosal and hippocampal surfaces, 14 ventricular regions and 36 gyral boundaries. An elastic warping approach, driven by anatomical features, was then used to measure gyral pattern variations. Measures of gray matter distribution were made in corresponding regions of cortex across all 46 subjects. Statistical variations in cortical patterning, asymmetry, gray matter distribution and average gray matter loss were then encoded locally across the cortex. Maps of group differences were generated. Average maps revealed complex profiles of gray matter loss in disease. Greatest deficits (20-30% loss, P<0.001-0.0001) were mapped in the temporo-parietal cortices. The sensorimotor and occipital cortices were comparatively spared (0-5% loss, P>0.05). Gray matter loss was greater in the left hemisphere, with different patterns in the heteromodal and idiotypic cortex. Gyral pattern variability also differed in cortical regions appearing at different embryonic phases. 3D mapping revealed profiles of structural deficits consistent with the cognitive, metabolic and histological changes in early AD. These deficits can therefore be (i) charted in a living population and (ii) compared across individuals and groups, facilitating longitudinal, genetic and interventional studies of dementia.

The role of image registration in brain mapping

Image registration is a key step in a great variety of biomedical imaging applications. It provides the ability to geometrically align one dataset with another, and is a prerequisite for all imaging applications that compare datasets across subjects, imaging modalities, or across time. Registration algorithms also enable the pooling and comparison of experimental findings across laboratories, the construction of population-based brain atlases, and the creation of systems to detect group patterns in structural and functional imaging data. We review the major types of registration approaches used in brain imaging today. We focus on their conceptual basis, the underlying mathematics, and their strengths and weaknesses in different contexts. We describe the major goals of registration, including data fusion, quantification of change, automated image segmentation and labeling, shape measurement, and pathology detection. We indicate that registration algorithms have great potential when used in conjunction with a digital brain atlas, which acts as a reference system in which brain images can be compared for statistical analysis. The resulting armory of registration approaches is fundamental to medical image analysis, and in a brain mapping context provides a means to elucidate clinical, demographic, or functional trends in the anatomy or physiology of the brain.