Partial volume effect modeling for segmentation and tissue classification of brain magnetic resonance images: A review
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paper_title: Automated segmentation and classification of multispectral magnetic resonance images of brain using artificial neural networks

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Presents a fully automated process for segmentation and classification of multispectral magnetic resonance (MR) images. This hybrid neural network method uses a Kohonen self-organizing neural network for segmentation and a multilayer backpropagation neural network for classification. To separate different tissue types, this process uses the standard T1-, T2-, and PD-weighted MR images acquired in clinical examinations. Volumetric measurements of brain structures, relative to intracranial volume, were calculated for an index transverse section in 14 normal subjects (median age 25 years; 7 male, 7 female). This index slice was at the level of the basal ganglia, included both genu and splenium of the corpus callosum, and generally, showed the putamen and lateral ventricle. An intraclass correlation of this automated segmentation and classification of tissues with the accepted standard of radiologist identification for the index slice in the 14 volunteers demonstrated coefficients (r/sub i/) of 0.91, 0.95, and 0.98 for white matter, gray matter, and ventricular cerebrospinal fluid (CSF), respectively. An analysis of variance for estimates of brain parenchyma volumes in 5 volunteers imaged 5 times each demonstrated high intrasubject reproducibility with a significance of at least p<0.05 for white matter, gray matter, and white/gray partial volumes. The population variation, across 14 volunteers, demonstrated little deviation from the averages for gray and white matter, while partial volume classes exhibited a slightly higher degree of variability. This fully automated technique produces reliable and reproducible MR image segmentation and classification while eliminating intra- and interobserver variability.
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paper_title: Comparison and validation of tissue modelization and statistical classification methods in T1-weighted MR brain images

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This paper presents a validation study on statistical nonsupervised brain tissue classification techniques in magnetic resonance (MR) images. Several image models assuming different hypotheses regarding the intensity distribution model, the spatial model and the number of classes are assessed. The methods are tested on simulated data for which the classification ground truth is known. Different noise and intensity nonuniformities are added to simulate real imaging conditions. No enhancement of the image quality is considered either before or during the classification process. This way, the accuracy of the methods and their robustness against image artifacts are tested. Classification is also performed on real data where a quantitative validation compares the methods' results with an estimated ground truth from manual segmentations by experts. Validity of the various classification methods in the labeling of the image as well as in the tissue volume is estimated with different local and global measures. Results demonstrate that methods relying on both intensity and spatial information are more robust to noise and field inhomogeneities. We also demonstrate that partial volume is not perfectly modeled, even though methods that account for mixture classes outperform methods that only consider pure Gaussian classes. Finally, we show that simulated data results can also be extended to real data.
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paper_title: Computerized Brain Tissue Classification of Magnetic Resonance Images: A New Approach to the Problem of Partial Volume Artifact

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Abstract Due to the finite spatial resolution of digital magnetic resonance images of the brain, and the complexity of anatomical interfaces between brain regions of different tissue type, it is inevitable that some voxels will represent a mixture of two or three different tissue types. Outright assignment of such "bipartial" or "tripartial" voxels to one class or another is more problematic and less reliable than assignment of "full-volume" voxels, wholly representative of a single tissue type. We have developed a computerized system for brain tissue classification of dual echo MR data, which uses a polychotomous logistic model for discriminant analysis, combined with a Bayes allocation rule incorporating differential prior probabilities, and spatial connectivity tests, to assign each voxel in the image to one of four possible classes: gray matter, white matter, cerebrospinal fluid, or unclassified. The system supports automated volumetric analysis of segmented images, has low operational overheads, and compares favorably with previous multivariate or "multispectral" approaches to brain MR image segmentation in terms of both validity (bootstrap misclassification rate = 3.3%) and interoperator reliability (intra-class correlation coefficients for all three tissue classes >0.9). We argue that these improvements in performance stem from better methodological management of the related problems of non-Normality of MR signal intensity values and partial volume artifact.
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paper_title: The burden of brain diseases in Europe

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death and years of life lived with disability (YLD). In the present report, data from the GBD 2000 study and from the World Health Report 2001 on brain diseases is extracted for the territory of Europe. This territory corresponds roughly to the membership countries of the European Federation of Neurological Societies. The WHO’s Report has a category called neuropsychiatric diseases, which comprises the majority but not all the brain diseases. In order to gather all brain diseases, stroke, meningitis, half of the burden of injuries and half of the burden of congenital abnormalities are added. Throughout Europe, 23% of the years of healthy life is lost and 50% of YLD are caused by brain diseases. Regarding the key summary measure of lost health, DALY, 35% are because of brain diseases. The fact that approximately one-third of all burden of disease is caused by brain diseases should have an impact on resource allocation to teaching, reasearch, health care and prevention. Although other factors are also of importance, it seems reasonable that one-third of the curriculum at medical school should deal with the brain and that one-third of life science funding should go to basic and clinical neuroscience. In addition, resource allocation to prevention, diagnosis and treatment of brain diseases should be increased to approach, at least, one-third of health care expenditure. With the present data on hand, neurologists, neurosurgeons, psychiatrists, patient organizations and basic neuroscientists have a better possibility to increase the focus on the brain.
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paper_title: A review of MRI findings in schizophrenia

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Abstract After more than 100 years of research, the neuropathology of schizophrenia remains unknown and this is despite the fact that both Kraepelin (1919/1971 : Kraepelin, E., 1919/1971. Dementia praecox. Churchill Livingston Inc., New York) and Bleuler (1911/1950 : Bleuler, E., 1911/1950. Dementia praecox or the group of schizophrenias. International Universities Press, New York), who first described ‘dementia praecox’ and the ‘schizophrenias’, were convinced that schizophrenia would ultimately be linked to an organic brain disorder. Alzheimer (1897 : Alzheimer, A., 1897. Beitrage zur pathologischen anatomie der hirnrinde und zur anatomischen grundlage einiger psychosen. Monatsschrift fur Psychiarie und Neurologie. 2, 82–120) was the first to investigate the neuropathology of schizophrenia, though he went on to study more tractable brain diseases. The results of subsequent neuropathological studies were disappointing because of conflicting findings. Research interest thus waned and did not flourish again until 1976, following the pivotal computer assisted tomography (CT) finding of lateral ventricular enlargement in schizophrenia by Johnstone and colleagues. Since that time significant progress has been made in brain imaging, particularly with the advent of magnetic resonance imaging (MRI), beginning with the first MRI study of schizophrenia by Smith and coworkers in 1984 (Smith, R.C., Calderon, M., Ravichandran, G.K., et al. (1984). Nuclear magnetic resonance in schizophrenia: A preliminary study. Psychiatry Res. 12, 137–147). MR in vivo imaging of the brain now confirms brain abnormalities in schizophrenia. The 193 peer reviewed MRI studies reported in the current review span the period from 1988 to August, 2000. This 12 year period has witnessed a burgeoning of MRI studies and has led to more definitive findings of brain abnormalities in schizophrenia than any other time period in the history of schizophrenia research. Such progress in defining the neuropathology of schizophrenia is largely due to advances in in vivo MRI techniques. These advances have now led to the identification of a number of brain abnormalities in schizophrenia. Some of these abnormalities confirm earlier post-mortem findings, and most are small and subtle, rather than large, thus necessitating more advanced and accurate measurement tools. These findings include ventricular enlargement (80% of studies reviewed) and third ventricle enlargement (73% of studies reviewed). There is also preferential involvement of medial temporal lobe structures (74% of studies reviewed), which include the amygdala, hippocampus, and parahippocampal gyrus, and neocortical temporal lobe regions (superior temporal gyrus) (100% of studies reviewed). When gray and white matter of superior temporal gyrus was combined, 67% of studies reported abnormalities. There was also moderate evidence for frontal lobe abnormalities (59% of studies reviewed), particularly prefrontal gray matter and orbitofrontal regions. Similarly, there was moderate evidence for parietal lobe abnormalities (60% of studies reviewed), particularly of the inferior parietal lobule which includes both supramarginal and angular gyri. Additionally, there was strong to moderate evidence for subcortical abnormalities (i.e. cavum septi pellucidi—92% of studies reviewed, basal ganglia—68% of studies reviewed, corpus callosum—63% of studies reviewed, and thalamus—42% of studies reviewed), but more equivocal evidence for cerebellar abnormalities (31% of studies reviewed). The timing of such abnormalities has not yet been determined, although many are evident when a patient first becomes symptomatic. There is, however, also evidence that a subset of brain abnormalities may change over the course of the illness. The most parsimonious explanation is that some brain abnormalities are neurodevelopmental in origin but unfold later in development, thus setting the stage for the development of the symptoms of schizophrenia. Or there may be additional factors, such as stress or neurotoxicity, that occur during adolescence or early adulthood and are necessary for the development of schizophrenia, and may be associated with neurodegenerative changes. Importantly, as several different brain regions are involved in the neuropathology of schizophrenia, new models need to be developed and tested that explain neural circuitry abnormalities effecting brain regions not necessarily structurally proximal to each other but nonetheless functionally interrelated. Future studies will likely benefit from: (1) studying more homogeneous patient groups so that the relationship between MRI findings and clinical symptoms become more meaningful; (2) studying at risk populations such as family members of patients diagnosed with schizophrenia and subjects diagnosed with schizotypal personality disorder in order to define which abnormalities are specific to schizophrenia spectrum disorders, which are the result of epiphenomena such as medication effects and chronic institutionalization, and which are needed for the development of frank psychosis; (3) examining shape differences not detectable from measuring volume alone; (4) applying newer methods such as diffusion tensor imaging to investigate abnormalities in brain connectivity and white matter fiber tracts; and, (5) using methods that analyze brain function (fMRI) and structure simultaneously.
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paper_title: Voxel-based morphometry—The methods

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At its simplest, voxel-based morphometry (VBM) involves a voxel-wise comparison of the local concentration of gray matter between two groups of subjects. The procedure is relatively straightforward and involves spatially normalizing high-resolution images from all the subjects in the study into the same stereotactic space. This is followed by segmenting the gray matter from the spatially normalized images and smoothing the gray-matter segments. Voxel-wise parametric statistical tests which compare the smoothed gray-matter images from the two groups are performed. Corrections for multiple comparisons are made using the theory of Gaussian random fields. This paper describes the steps involved in VBM, with particular emphasis on segmenting gray matter from MR images with nonuniformity artifact. We provide evaluations of the assumptions that underpin the method, including the accuracy of the segmentation and the assumptions made about the statistical distribution of the data.
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paper_title: The Alzheimer’s Disease Neuroimaging Initiative: A review of papers published since its inception

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The Alzheimer's Disease Neuroimaging Initiative (ADNI) is an ongoing, longitudinal, multicenter study designed to develop clinical, imaging, genetic, and biochemical biomarkers for the early detection and tracking of Alzheimer's disease (AD). The study aimed to enroll 400 subjects with early mild cognitive impairment (MCI), 200 subjects with early AD, and 200 normal control subjects; $67 million funding was provided by both the public and private sectors, including the National Institute on Aging, 13 pharmaceutical companies, and 2 foundations that provided support through the Foundation for the National Institutes of Health. This article reviews all papers published since the inception of the initiative and summarizes the results as of February 2011. The major accomplishments of ADNI have been as follows: (1) the development of standardized methods for clinical tests, magnetic resonance imaging (MRI), positron emission tomography (PET), and cerebrospinal fluid (CSF) biomarkers in a multicenter setting; (2) elucidation of the patterns and rates of change of imaging and CSF biomarker measurements in control subjects, MCI patients, and AD patients. CSF biomarkers are consistent with disease trajectories predicted by β-amyloid cascade (Hardy, J Alzheimers Dis 2006;9(Suppl 3):151-3) and tau-mediated neurodegeneration hypotheses for AD, whereas brain atrophy and hypometabolism levels show predicted patterns but exhibit differing rates of change depending on region and disease severity; (3) the assessment of alternative methods of diagnostic categorization. Currently, the best classifiers combine optimum features from multiple modalities, including MRI, [(18)F]-fluorodeoxyglucose-PET, CSF biomarkers, and clinical tests; (4) the development of methods for the early detection of AD. CSF biomarkers, β-amyloid 42 and tau, as well as amyloid PET may reflect the earliest steps in AD pathology in mildly symptomatic or even nonsymptomatic subjects, and are leading candidates for the detection of AD in its preclinical stages; (5) the improvement of clinical trial efficiency through the identification of subjects most likely to undergo imminent future clinical decline and the use of more sensitive outcome measures to reduce sample sizes. Baseline cognitive and/or MRI measures generally predicted future decline better than other modalities, whereas MRI measures of change were shown to be the most efficient outcome measures; (6) the confirmation of the AD risk loci CLU, CR1, and PICALM and the identification of novel candidate risk loci; (7) worldwide impact through the establishment of ADNI-like programs in Europe, Asia, and Australia; (8) understanding the biology and pathobiology of normal aging, MCI, and AD through integration of ADNI biomarker data with clinical data from ADNI to stimulate research that will resolve controversies about competing hypotheses on the etiopathogenesis of AD, thereby advancing efforts to find disease-modifying drugs for AD; and (9) the establishment of infrastructure to allow sharing of all raw and processed data without embargo to interested scientific investigators throughout the world. The ADNI study was extended by a 2-year Grand Opportunities grant in 2009 and a renewal of ADNI (ADNI-2) in October 2010 through to 2016, with enrollment of an additional 550 participants.
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paper_title: Measuring the thickness of the human cerebral cortex from magnetic resonance images

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Accurate and automated methods for measuring the thickness of human cerebral cortex could provide powerful tools for diagnosing and studying a variety of neurodegenerative and psychiatric disorders. Manual methods for estimating cortical thickness from neuroimaging data are labor intensive, requiring several days of effort by a trained anatomist. Furthermore, the highly folded nature of the cortex is problematic for manual techniques, frequently resulting in measurement errors in regions in which the cortical surface is not perpendicular to any of the cardinal axes. As a consequence, it has been impractical to obtain accurate thickness estimates for the entire cortex in individual subjects, or group statistics for patient or control populations. Here, we present an automated method for accurately measuring the thickness of the cerebral cortex across the entire brain and for generating cross-subject statistics in a coordinate system based on cortical anatomy. The intersubject standard deviation of the thickness measures is shown to be less than 0.5 mm, implying the ability to detect focal atrophy in small populations or even individual subjects. The reliability and accuracy of this new method are assessed by within-subject test–retest studies, as well as by comparison of cross-subject regional thickness measures with published values.
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paper_title: Estimation of the partial volume effect in MRI

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The partial volume effect (PVE) arises in volumetric images when more than one tissue type occurs in a voxel. In such cases, the voxel intensity depends not only on the imaging sequence and tissue properties, but also on the proportions of each tissue type present in the voxel. We have demonstrated in previous work that ignoring this effect by establishing binary voxel-based segmentations introduces significant errors in quantitative measurements, such as estimations of the volumes of brain structures. In this paper, we provide a statistical estimation framework to quantify PVE and to propagate voxel-based estimates in order to compute global magnitudes, such as volume, with associated estimates of uncertainty. Validation is performed on ground truth synthetic images and MRI phantoms, and a clinical study is reported. Results show that the method allows for robust morphometric studies and provides resolution unattainable to date.
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paper_title: The clinical use of structural MRI in Alzheimer disease

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Structural imaging based on magnetic resonance is an integral part of the clinical assessment of patients with suspected Alzheimer dementia. Prospective data on the natural history of change in structural markers from preclinical to overt stages of Alzheimer disease are radically changing how the disease is conceptualized, and will influence its future diagnosis and treatment. Atrophy of medial temporal structures is now considered to be a valid diagnostic marker at the mild cognitive impairment stage. Structural imaging is also included in diagnostic criteria for the most prevalent non-Alzheimer dementias, reflecting its value in differential diagnosis. In addition, rates of whole-brain and hippocampal atrophy are sensitive markers of neurodegeneration, and are increasingly used as outcome measures in trials of potentially disease-modifying therapies. Large multicenter studies are currently investigating the value of other imaging and nonimaging markers as adjuncts to clinical assessment in diagnosis and monitoring of progression. The utility of structural imaging and other markers will be increased by standardization of acquisition and analysis methods, and by development of robust algorithms for automated assessment.
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paper_title: Segmentation and measurement of brain structures in MRI including confidence bounds

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Abstract The advent of new and improved imaging devices has allowed an impressive increase in the accuracy and precision of MRI acquisitions. However, the volumetric nature of the image formation process implies an inherent uncertainty, known as the partial volume effect, which can be further affected by artifacts such as magnetic inhomogeneities and noise. These degradations seriously challenge the application to MRI of any segmentation method, especially on data sets where the size of the object or effect to be studied is small relative to the voxel size, as is the case in multiple sclerosis and schizophrenia. We develop an approach to this problem by estimating a set of bounds on the spatial location of each organ to be segmented. First, we describe a method for 3D segmentation from voxel data which combines statistical classification and geometry-driven segmentation; then we discuss how the partial volume effect is estimated and object measurements are obtained. A comprehensive validation study and a set of results on clinical applications are also described.
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paper_title: Brain tissue classification of magnetic resonance images using partial volume modeling

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This paper presents a fully automatic three-dimensional classification of brain tissues for Magnetic Resonance (MR) images. An MR image volume may be composed of a mixture of several tissue types due to partial volume effects. Therefore, we consider that in a brain dataset there are not only the three main types of brain tissue: gray matter, white matter, and cerebro spinal fluid, called pure classes, but also mixtures, called mixclasses. A statistical model of the mixtures is proposed and studied by means of simulations. It is shown that it can be approximated by a Gaussian function under some conditions. The D'Agostino-Pearson normality test is used to assess the risk alpha of the approximation. In order to classify a brain into three types of brain tissue and deal with the problem of partial volume effects, the proposed algorithm uses two steps: 1) segmentation of the brain into pure and mixclasses using the mixture model; 2) reclassification of the mixclasses into the pure classes using knowledge about the obtained pure classes. Both steps use Markov random field (MRF) models. The multifractal dimension, describing the topology of the brain, is added to the MRFs to improve discrimination of the mixclasses. The algorithm is evaluated using both simulated images and real MR images with different T1-weighted acquisition sequences.
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paper_title: Brain MRI Tissue Classification Based on Local Markov Random Fields

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A new method for tissue classification of brain magnetic resonance images (MRI) of the brain is proposed. The method is based on local image models where each models the image content in a subset of the image domain. With this local modeling approach, the assumption that tissue types have the same characteristics over the brain needs not to be evoked. This is important because tissue type characteristics, such as T1 and T2 relaxation times and proton density, vary across the individual brain and the proposed method offers improved protection against intensity non-uniformity artifacts that can hamper automatic tissue classification methods in brain MRI. A framework in which local models for tissue intensities and Markov Random Field priors are combined into a global probabilistic image model is introduced. This global model will be an inhomogeneous Markov Random Field and it can be solved by standard algorithms such as iterative conditional modes. The division of the whole image domain into local brain regions possibly having different intensity statistics is realized via sub-volume probabilistic atlases. Finally, the parameters for the local intensity models are obtained without supervision by maximizing the weighted likelihood of a certain finite mixture model. For the maximization task, a novel genetic algorithm almost free of initialization dependency is applied. The algorithm is tested on both simulated and real brain MR images. The experiments confirm that the new method offers a useful improvement of the tissue classification accuracy when the basic tissue characteristics vary across the brain and the noise level of the images is reasonable. The method also offers better protection against intensity non-uniformity artifact than the corresponding method based on a global (whole image) modeling scheme.
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paper_title: Online Resource for Validation of Brain Segmentation Methods

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Abstract One key issue that must be addressed during the development of image segmentation algorithms is the accuracy of the results they produce. Algorithm developers require this so they can see where methods need to be improved and see how new developments compare with existing ones. Users of algorithms also need to understand the characteristics of algorithms when they select and apply them to their neuroimaging analysis applications. Many metrics have been proposed to characterize error and success rates in segmentation, and several datasets have also been made public for evaluation. Still, the methodologies used in analyzing and reporting these results vary from study to study, so even when studies use the same metrics their numerical results may not necessarily be directly comparable. To address this problem, we developed a web-based resource for evaluating the performance of skull-stripping in T1-weighted MRI. The resource provides both the data to be segmented and an online application that performs a validation study on the data. Users may download the test dataset, segment it using whichever method they wish to assess, and upload their segmentation results to the server. The server computes a series of metrics, displays a detailed report of the validation results, and archives these for future browsing and analysis. We applied this framework to the evaluation of 3 popular skull-stripping algorithms — the Brain Extraction Tool [Smith, S.M., 2002. Fast robust automated brain extraction. Hum. Brain Mapp. 17 (3),143–155 (Nov)], the Hybrid Watershed Algorithm [Segonne, F., Dale, A.M., Busa, E., Glessner, M., Salat, D., Hahn, H.K., Fischl, B., 2004. A hybrid approach to the skull stripping problem in MRI. NeuroImage 22 (3), 1060–1075 (Jul)], and the Brain Surface Extractor [Shattuck, D.W., Sandor-Leahy, S.R., Schaper, K.A., Rottenberg, D.A., Leahy, R.M., 2001. Magnetic resonance image tissue classification using a partial volume model. NeuroImage 13 (5), 856–876 (May) under several different program settings. Our results show that with proper parameter selection, all 3 algorithms can achieve satisfactory skull-stripping on the test data.
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paper_title: A Review of Methods for Correction of Intensity Inhomogeneity in MRI

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Medical image acquisition devices provide a vast amount of anatomical and functional information, which facilitate and improve diagnosis and patient treatment, especially when supported by modern quantitative image analysis methods. However, modality specific image artifacts, such as the phenomena of intensity inhomogeneity in magnetic resonance images (MRI), are still prominent and can adversely affect quantitative image analysis. In this paper, numerous methods that have been developed to reduce or eliminate intensity inhomogeneities in MRI are reviewed. First, the methods are classified according to the inhomogeneity correction strategy. Next, different qualitative and quantitative evaluation approaches are reviewed. Third, 60 relevant publications are categorized according to several features and analyzed so as to reveal major trends, popularity, evaluation strategies and applications. Finally, key evaluation issues and future development of the inhomogeneity correction field, supported by the results of the analysis, are discussed
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paper_title: Quantification of MR brain images by mixture density and partial volume modeling.

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The problem of automatic quantification of brain tissue by utilizing single-valued (single echo) magnetic resonance imaging (MRI) brain scans is addressed. It is shown that this problem can be solved without classification or segmentation, a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap. The general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues. The quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture. This problem is solved by tree annealing with and without partial volume utilized, the results compared, and the sensitivity of the tree annealing algorithm to various parameters is exhibited. The actual quantification is performed by two methods: a classification-based method called Bayes quantification, and parameter estimation. Results from each method are presented for synthetic and actual data.
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paper_title: Partial volume tissue classification of multichannel magnetic resonance images-a mixel model

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A single volume element (voxel) in a medical image may be composed of a mixture of multiple tissue types. The authors call voxels which contain multiple tissue classes mixels. A statistical mixel image model based on Markov random field (MRF) theory and an algorithm for the classification of mixels are presented. The authors concentrate on the classification of multichannel magnetic resonance (MR) images of the brain although the algorithm has other applications. The authors also present a method for compensating for the gray-level variation of MR images between different slices, which is primarily caused by the inhomogeneity of the RF field produced by the imaging coil. >
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paper_title: Statistical models of partial volume effect

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Statistical models of partial volume effect for systems with various types of noise or pixel value distributions are developed and probability density functions are derived. The models assume either Gaussian system sampling noise or intrinsic material variances with Gaussian or Poisson statistics. In particular, a material can be viewed as having a distinct value that has been corrupted by additive noise either before or after partial volume mixing, or the material could have nondistinct values with a Poisson distribution as might be the case in nuclear medicine images. General forms of the probability density functions are presented for the N material cases and particular forms for two- and three-material cases are derived. These models are incorporated into finite mixture densities in order to more accurately model the distribution of image pixel values. Examples are presented using simulated histograms to demonstrate the efficacy of the models for quantification. Modeling of partial volume effect is shown to be useful when one of the materials is present in images mainly as a pixel component. >
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paper_title: Partial volume segmentation of brain magnetic resonance images based on maximum a posteriori probability.

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Noise, partial volume (PV) effect and image-intensity inhomogeneity render a challenging task for segmentation of brain magnetic resonance (MR) images. Most of the current MR image segmentation methods focus on only one or two of the effects listed above. The objective of this paper is to propose a unified framework, based on the maximum a posteriori probability principle, by taking all these effects into account simultaneously in order to improve image segmentation performance. Instead of labeling each image voxel with a unique tissue type, the percentage of each voxel belonging to different tissues, which we call a mixture, is considered to address the PV effect. A Markov random field model is used to describe the noise effect by considering the nearby spatial information of the tissue mixture. The inhomogeneity effect is modeled as a bias field characterized by a zero mean Gaussian prior probability. The well-known fuzzy C-mean model is extended to define the likelihood function of the observed image. This framework reduces theoretically, under some assumptions, to the adaptive fuzzy C-mean (AFCM) algorithm proposed by Pham and Prince. Digital phantom and real clinical MR images were used to test the proposed framework. Improved performance over the AFCM algorithm was observed in a clinical environment where the inhomogeneity, noise level and PV effect are commonly encountered.
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paper_title: On the statistical analysis of dirty pictures

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may 7th, 1986, Professor A. F. M. Smith in the Chair] SUMMARY A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular "colour" belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a nondegenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics. The method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field. Some complications, including parameter estimation, are discussed. Potential applications are mentioned briefly.
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paper_title: Partial volume tissue classification of multichannel magnetic resonance images-a mixel model

paper_content:

A single volume element (voxel) in a medical image may be composed of a mixture of multiple tissue types. The authors call voxels which contain multiple tissue classes mixels. A statistical mixel image model based on Markov random field (MRF) theory and an algorithm for the classification of mixels are presented. The authors concentrate on the classification of multichannel magnetic resonance (MR) images of the brain although the algorithm has other applications. The authors also present a method for compensating for the gray-level variation of MR images between different slices, which is primarily caused by the inhomogeneity of the RF field produced by the imaging coil. >
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paper_title: Magnetic resonance image tissue classification using a partial volume model

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Abstract We describe a sequence of low-level operations to isolate and classify brain tissue within T1-weighted magnetic resonance images (MRI). Our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering, edge detection, and mathematical morphology. We compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic B-spline gain field to local estimates of the image nonuniformity spaced throughout the MRI volume. The local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point. The measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit. Voxels in the intensity-normalized image are then classified into six tissue types using a maximum a posteriori classifier. This classifier combines the partial volume tissue measurement model with a Gibbs prior that models the spatial properties of the brain. We validate each stage of our algorithm on real and phantom data. Using data from the 20 normal MRI brain data sets of the Internet Brain Segmentation Repository, our method achieved average κ indices of κ = 0.746 ± 0.114 for gray matter (GM) and κ = 0.798 ± 0.089 for white matter (WM) compared to expert labeled data. Our method achieved average κ indices κ = 0.893 ± 0.041 for GM and κ = 0.928 ± 0.039 for WM compared to the ground truth labeling on 12 volumes from the Montreal Neurological Institute's BrainWeb phantom.
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paper_title: Improved estimates of partial volume coefficients from noisy brain MRI using spatial context

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This paper addresses the problem of accurate voxel-level estimation of tissue proportions in the human brain magnetic resonance imaging (MRI). Due to the finite resolution of acquisition systems, MRI voxels can contain contributions from more than a single tissue type. The voxel-level estimation of this fractional content is known as partial volume coefficient estimation. In the present work, two new methods to calculate the partial volume coefficients under noisy conditions are introduced and compared with current similar methods. Concretely, a novel Markov Random Field model allowing sharp transitions between partial volume coefficients of neighbouring voxels and an advanced non-local means filtering technique are proposed to reduce the errors due to random noise in the partial volume coefficient estimation. In addition, a comparison was made to find out how the different methodologies affect the measurement of the brain tissue type volumes. Based on the obtained results, the main conclusions are that (1) both Markov Random Field modelling and non-local means filtering improved the partial volume coefficient estimation results, and (2) non-local means filtering was the better of the two strategies for partial volume coefficient estimation.
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paper_title: Segmentation of MRI brain scans using non-uniform partial volume densities

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Abstract We present an algorithm that provides a partial volume segmentation of a T1-weighted image of the brain into gray matter, white matter and cerebrospinal fluid. The algorithm incorporates a non-uniform partial volume density that takes the curved nature of the cortex into account. The pure gray and white matter intensities are estimated from the image, using scanner noise and cortical partial volume effects. Expected tissue fractions are subsequently computed in each voxel. The algorithm has been tested for reliability, correct estimation of the pure tissue intensities on both real (repeated) MRI data and on simulated (brain) images. Intra-class correlation coefficients (ICCs) were above 0.93 for all volumes of the three tissue types for repeated scans from the same scanner, as well as for scans with different voxel sizes from different scanners with different field strengths. The implementation of our non-uniform partial volume density provided more reliable volumes and tissue fractions, compared to a uniform partial volume density. Applying the algorithm to simulated images showed that the pure tissue intensities were estimated accurately. Variations in cortical thickness did not influence the accuracy of the volume estimates, which is a valuable property when studying (possible) group differences. In conclusion, we have presented a new partial volume segmentation algorithm that allows for comparisons over scanners and voxel sizes.
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paper_title: Quantification of MR brain images by mixture density and partial volume modeling.

paper_content:

The problem of automatic quantification of brain tissue by utilizing single-valued (single echo) magnetic resonance imaging (MRI) brain scans is addressed. It is shown that this problem can be solved without classification or segmentation, a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap. The general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues. The quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture. This problem is solved by tree annealing with and without partial volume utilized, the results compared, and the sensitivity of the tree annealing algorithm to various parameters is exhibited. The actual quantification is performed by two methods: a classification-based method called Bayes quantification, and parameter estimation. Results from each method are presented for synthetic and actual data.
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paper_title: Partial volume tissue classification of multichannel magnetic resonance images-a mixel model

paper_content:

A single volume element (voxel) in a medical image may be composed of a mixture of multiple tissue types. The authors call voxels which contain multiple tissue classes mixels. A statistical mixel image model based on Markov random field (MRF) theory and an algorithm for the classification of mixels are presented. The authors concentrate on the classification of multichannel magnetic resonance (MR) images of the brain although the algorithm has other applications. The authors also present a method for compensating for the gray-level variation of MR images between different slices, which is primarily caused by the inhomogeneity of the RF field produced by the imaging coil. >
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paper_title: Statistical models of partial volume effect

paper_content:

Statistical models of partial volume effect for systems with various types of noise or pixel value distributions are developed and probability density functions are derived. The models assume either Gaussian system sampling noise or intrinsic material variances with Gaussian or Poisson statistics. In particular, a material can be viewed as having a distinct value that has been corrupted by additive noise either before or after partial volume mixing, or the material could have nondistinct values with a Poisson distribution as might be the case in nuclear medicine images. General forms of the probability density functions are presented for the N material cases and particular forms for two- and three-material cases are derived. These models are incorporated into finite mixture densities in order to more accurately model the distribution of image pixel values. Examples are presented using simulated histograms to demonstrate the efficacy of the models for quantification. Modeling of partial volume effect is shown to be useful when one of the materials is present in images mainly as a pixel component. >
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paper_title: Multivariate Tissue Classification of MRI Images for 3-D Volume Reconstruction - A Statistical Approach

paper_content:

One of the major problems in 3-D volume reconstruction from magnetic resonance imaging (MRI) is the difficulty in automating the classification of soft tissues. Because of the complicated soft tissue structures revealed by MRI, it is not easy to segment the images with simple algorithms. MRI can obtain multiple images from the same anatomical section with different pulse sequences, with each image having different response characteristics for each soft tissue. Using the gray level distributions of soft tissues, we have developed two statistical classifiers that utilize the image context information based on the Markov Random Field (MRF) image model. One of the classifiers classifies each voxel to a specific tissue type and the other estimates the partial volume of each tissue within each voxel. Since the voxel sizes of tomographic images are finite and the measurements from tissue boundaries represent the mixture of multiple tissue types, it is preferable that the classifier should not classify each voxel in all-or-none fashion; rather, it should be able to tell the percentage volume of each class in each voxel for the better visualization of the prepared 3-D dataset. The paper presents the theoretical basis of the algorithms and experimental evaluation results of the classifiers in terms of classification accuracy, as compared to the conventional maximum likelihood classifier.
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paper_title: Fast and robust parameter estimation for statistical partial volume models in brain MRI

paper_content:

Due to the finite spatial resolution of imaging devices, a single voxel in a medical image may be composed of mixture of tissue types, an effect known as partial volume effect (PVE). Partial volume estimation, that is, the estimation of the amount of each tissue type within each voxel, has received considerable interest in recent years. Much of this work has been focused on the mixel model, a statistical model of PVE. We propose a novel trimmed minimum covariance determinant (TMCD) method for the estimation of the parameters of the mixel PVE model. In this method, each voxel is first labeled according to the most dominant tissue type. Voxels that are prone to PVE are removed from this labeled set, following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class. Comparisons between different methods for parameter estimation based on classified images as well as expectation--maximization-like (EM-like) procedure for simultaneous parameter and partial volume estimation are reported. The robust estimators based on a pruned classification as presented here are shown to perform well even if the initial classification is of poor quality. The results obtained are comparable to those obtained using the EM-like procedure, but require considerably less computation time. Segmentation results of real data based on partial volume estimation are also reported. In addition to considering the parameter estimation problem, we discuss differences between different approximations to the complete mixel model. In summary, the proposed TMCD method allows for the accurate, robust, and efficient estimation of partial volume model parameters, which is crucial to a variety of brain MRI data analysis procedures such as the accurate estimation of tissue volumes and the accurate delineation of the cortical surface.
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paper_title: Estimation of the partial volume effect in MRI

paper_content:

The partial volume effect (PVE) arises in volumetric images when more than one tissue type occurs in a voxel. In such cases, the voxel intensity depends not only on the imaging sequence and tissue properties, but also on the proportions of each tissue type present in the voxel. We have demonstrated in previous work that ignoring this effect by establishing binary voxel-based segmentations introduces significant errors in quantitative measurements, such as estimations of the volumes of brain structures. In this paper, we provide a statistical estimation framework to quantify PVE and to propagate voxel-based estimates in order to compute global magnitudes, such as volume, with associated estimates of uncertainty. Validation is performed on ground truth synthetic images and MRI phantoms, and a clinical study is reported. Results show that the method allows for robust morphometric studies and provides resolution unattainable to date.
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paper_title: Magnetic resonance image tissue classification using a partial volume model

paper_content:

Abstract We describe a sequence of low-level operations to isolate and classify brain tissue within T1-weighted magnetic resonance images (MRI). Our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering, edge detection, and mathematical morphology. We compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic B-spline gain field to local estimates of the image nonuniformity spaced throughout the MRI volume. The local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point. The measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit. Voxels in the intensity-normalized image are then classified into six tissue types using a maximum a posteriori classifier. This classifier combines the partial volume tissue measurement model with a Gibbs prior that models the spatial properties of the brain. We validate each stage of our algorithm on real and phantom data. Using data from the 20 normal MRI brain data sets of the Internet Brain Segmentation Repository, our method achieved average κ indices of κ = 0.746 ± 0.114 for gray matter (GM) and κ = 0.798 ± 0.089 for white matter (WM) compared to expert labeled data. Our method achieved average κ indices κ = 0.893 ± 0.041 for GM and κ = 0.928 ± 0.039 for WM compared to the ground truth labeling on 12 volumes from the Montreal Neurological Institute's BrainWeb phantom.
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paper_title: Unifying framework for multimodal brain MRI segmentation based on Hidden Markov Chains

paper_content:

Abstract In the frame of 3D medical imaging, accurate segmentation of multimodal brain MR images is of interest for many brain disorders. However, due to several factors such as noise, imaging artifacts, intrinsic tissue variation and partial volume effects, tissue classification remains a challenging task. In this paper, we present a unifying framework for unsupervised segmentation of multimodal brain MR images including partial volume effect, bias field correction, and information given by a probabilistic atlas. Here-proposed method takes into account neighborhood information using a Hidden Markov Chain (HMC) model. Due to the limited resolution of imaging devices, voxels may be composed of a mixture of different tissue types, this partial volume effect is included to achieve an accurate segmentation of brain tissues. Instead of assigning each voxel to a single tissue class (i.e., hard classification), we compute the relative amount of each pure tissue class in each voxel (mixture estimation). Further, a bias field estimation step is added to the proposed algorithm to correct intensity inhomogeneities. Furthermore, atlas priors were incorporated using probabilistic brain atlas containing prior expectations about the spatial localization of different tissue classes. This atlas is considered as a complementary sensor and the proposed method is extended to multimodal brain MRI without any user-tunable parameter (unsupervised algorithm). To validate this new unifying framework, we present experimental results on both synthetic and real brain images, for which the ground truth is available. Comparison with other often used techniques demonstrates the accuracy and the robustness of this new Markovian segmentation scheme.
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paper_title: Fuzzy Markovian Segmentation in Application of Magnetic Resonance Images

paper_content:

In this paper, we present a fuzzy Markovian method for brain tissue segmentation from magnetic resonance images. Generally, there are three main brain tissues in a brain dataset: gray matter, white matter, and cerebrospinal fluid. However, due to the limited resolution of the acquisition system, many voxels may be composed of multiple tissue types (partial volume effects). The proposed method aims at calculating a fuzzy membership in each voxel to indicate the partial volume degree, which is statistically modeled. Since our method is unsupervised, it first estimates the parameters of the fuzzy Markovian random field model using a stochastic gradient algorithm. The fuzzy Markovian segmentation is then performed automatically. The accuracy of the proposed method is quantitatively assessed on a digital phantom using an absolute average error and qualitatively tested on real MRI brain data. A comparison with the widely used fuzzy C-means algorithm is carried out to show numerous advantages of our method.
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paper_title: A unifying framework for partial volume segmentation of brain MR images

paper_content:

Accurate brain tissue segmentation by intensity-based voxel classification of magnetic resonance (MR) images is complicated by partial volume (PV) voxels that contain a mixture of two or more tissue types. In this paper, we present a statistical framework for PV segmentation that encompasses and extends existing techniques. We start from a commonly used parametric statistical image model in which each voxel belongs to one single tissue type, and introduce an additional downsampling step that causes partial voluming along the borders between tissues. An expectation-maximization approach is used to simultaneously estimate the parameters of the resulting model and perform a PV classification. We present results on well-chosen simulated images and on real MR images of the brain, and demonstrate that the use of appropriate spatial prior knowledge not only improves the classifications, but is often indispensable for robust parameter estimation as well. We conclude that general robust PV segmentation of MR brain images requires statistical models that describe the spatial distribution of brain tissues more accurately than currently available models.
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paper_title: Partial Volume Segmentation of Cerebral MRI Scans with Mixture Model Clustering

paper_content:

A mixture model clustering algorithm is presented for robust MRI brain image segmentation in the presence of partial volume averaging. The method uses additional classes to represent partial volume voxels of mixed tissue type in the data with their probability distributions modeled accordingly. The image model also allows for tissue-dependent variance values and voxel neighborhood information is taken into account in the clustering formulation. The final result is the estimated fractional amount of each tissue type present within a voxel in addition to the label assigned to the voxel. A multi-threaded implementation of the method is evaluated using both synthetic and real MRI data.
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paper_title: Magnetic resonance image tissue classification using a partial volume model

paper_content:

Abstract We describe a sequence of low-level operations to isolate and classify brain tissue within T1-weighted magnetic resonance images (MRI). Our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering, edge detection, and mathematical morphology. We compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic B-spline gain field to local estimates of the image nonuniformity spaced throughout the MRI volume. The local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point. The measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit. Voxels in the intensity-normalized image are then classified into six tissue types using a maximum a posteriori classifier. This classifier combines the partial volume tissue measurement model with a Gibbs prior that models the spatial properties of the brain. We validate each stage of our algorithm on real and phantom data. Using data from the 20 normal MRI brain data sets of the Internet Brain Segmentation Repository, our method achieved average κ indices of κ = 0.746 ± 0.114 for gray matter (GM) and κ = 0.798 ± 0.089 for white matter (WM) compared to expert labeled data. Our method achieved average κ indices κ = 0.893 ± 0.041 for GM and κ = 0.928 ± 0.039 for WM compared to the ground truth labeling on 12 volumes from the Montreal Neurological Institute's BrainWeb phantom.
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paper_title: Quantification of MR brain images by mixture density and partial volume modeling.

paper_content:

The problem of automatic quantification of brain tissue by utilizing single-valued (single echo) magnetic resonance imaging (MRI) brain scans is addressed. It is shown that this problem can be solved without classification or segmentation, a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap. The general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues. The quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture. This problem is solved by tree annealing with and without partial volume utilized, the results compared, and the sensitivity of the tree annealing algorithm to various parameters is exhibited. The actual quantification is performed by two methods: a classification-based method called Bayes quantification, and parameter estimation. Results from each method are presented for synthetic and actual data.
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paper_title: MR image-based measurement of rates of change in volumes of brain structures. Part I: method and validation.

paper_content:

A detailed analysis procedure is described for evaluating rates of volumetric change in brain structures based on structural magnetic resonance (MR) images. In this procedure, a series of image processing tools have been employed to address the problems encountered in measuring rates of change based on structural MR images. These tools include an algorithm for intensity non-uniformity correction, a robust algorithm for three-dimensional image registration with sub-voxel precision and an algorithm for brain tissue segmentation. However, a unique feature in the procedure is the use of a fractional volume model that has been developed to provide a quantitative measure for the partial volume effect. With this model, the fractional constituent tissue volumes are evaluated for voxels at the tissue boundary that manifest partial volume effect, thus allowing tissue boundaries be defined at a sub-voxel level and in an automated fashion. Validation studies are presented on key algorithms including segmentation and registration. An overall assessment of the method is provided through the evaluation of the rates of brain atrophy in a group of normal elderly subjects for which the rate of brain atrophy due to normal aging is predictably small. An application of the method is given in Part II where the rates of brain atrophy in various brain regions are studied in relation to normal aging and Alzheimer's disease.
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paper_title: Fast and robust parameter estimation for statistical partial volume models in brain MRI

paper_content:

Due to the finite spatial resolution of imaging devices, a single voxel in a medical image may be composed of mixture of tissue types, an effect known as partial volume effect (PVE). Partial volume estimation, that is, the estimation of the amount of each tissue type within each voxel, has received considerable interest in recent years. Much of this work has been focused on the mixel model, a statistical model of PVE. We propose a novel trimmed minimum covariance determinant (TMCD) method for the estimation of the parameters of the mixel PVE model. In this method, each voxel is first labeled according to the most dominant tissue type. Voxels that are prone to PVE are removed from this labeled set, following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class. Comparisons between different methods for parameter estimation based on classified images as well as expectation--maximization-like (EM-like) procedure for simultaneous parameter and partial volume estimation are reported. The robust estimators based on a pruned classification as presented here are shown to perform well even if the initial classification is of poor quality. The results obtained are comparable to those obtained using the EM-like procedure, but require considerably less computation time. Segmentation results of real data based on partial volume estimation are also reported. In addition to considering the parameter estimation problem, we discuss differences between different approximations to the complete mixel model. In summary, the proposed TMCD method allows for the accurate, robust, and efficient estimation of partial volume model parameters, which is crucial to a variety of brain MRI data analysis procedures such as the accurate estimation of tissue volumes and the accurate delineation of the cortical surface.
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paper_title: A segmentation-based and partial volume compensated method for accurate measurement of lateral ventricular volumes on TI-weighted magnetic resonance images

paper_content:

Lateral ventricular volumes based on segmented brain MR images can be significantly underestimated if partial volume effects are not considered. This is because a group of voxels in the neighborhood of lateral ventricles is often mis-classified as gray matter voxels due to partial volume effects. This group of voxels is actually a mixture of ventricular cerebro-spinal fluid and the white matter and therefore, a portion of it should be included as part of the lateral ventricular structure. In this note, we describe an automated method for the measurement of lateral ventricular volumes on segmented brain MR images. Image segmentation was carried in combination of intensity correction and thresholding. The method is featured with a procedure for addressing mis-classified voxels in the surrounding of lateral ventricles. A detailed analysis showed that lateral ventricular volumes could be underestimated by 10 to 30% depending upon the size of the lateral ventricular structure, if mis-classified voxels were not included. Validation of the method was done through comparison with the averaged manually traced volumes. Finally, the merit of the method is demonstrated in the evaluation of the rate of lateral ventricular enlargement.
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paper_title: Genetic Algorithms for Finite Mixture Model Based Voxel Classification in Neuroimaging

paper_content:

Finite mixture models (FMMs) are an indispensable tool for unsupervised classification in brain imaging. Fitting an FMM to the data leads to a complex optimization problem. This optimization problem is difficult to solve by standard local optimization methods, such as the expectation-maximization (EM) algorithm, if a principled initialization is not available. In this paper, we propose a new global optimization algorithm for the FMM parameter estimation problem, which is based on real coded genetic algorithms. Our specific contributions are two-fold: 1) we propose to use blended crossover in order to reduce the premature convergence problem to its minimum and 2) we introduce a completely new permutation operator specifically meant for the FMM parameter estimation. In addition to improving the optimization results, the permutation operator allows for imposing biologically meaningful constraints to the FMM parameter values. We also introduce a hybrid of the genetic algorithm and the EM algorithm for efficient solution of multidimensional FMM fitting problems. We compare our algorithm to the self-annealing EM-algorithm and a standard real coded genetic algorithm with the voxel classification tasks within the brain imaging. The algorithms are tested on synthetic data as well as real three-dimensional image data from human magnetic resonance imaging, positron emission tomography, and mouse brain MRI. The tissue classification results by our method are shown to be consistently more reliable and accurate than with the competing parameter estimation methods
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paper_title: Unifying framework for multimodal brain MRI segmentation based on Hidden Markov Chains

paper_content:

Abstract In the frame of 3D medical imaging, accurate segmentation of multimodal brain MR images is of interest for many brain disorders. However, due to several factors such as noise, imaging artifacts, intrinsic tissue variation and partial volume effects, tissue classification remains a challenging task. In this paper, we present a unifying framework for unsupervised segmentation of multimodal brain MR images including partial volume effect, bias field correction, and information given by a probabilistic atlas. Here-proposed method takes into account neighborhood information using a Hidden Markov Chain (HMC) model. Due to the limited resolution of imaging devices, voxels may be composed of a mixture of different tissue types, this partial volume effect is included to achieve an accurate segmentation of brain tissues. Instead of assigning each voxel to a single tissue class (i.e., hard classification), we compute the relative amount of each pure tissue class in each voxel (mixture estimation). Further, a bias field estimation step is added to the proposed algorithm to correct intensity inhomogeneities. Furthermore, atlas priors were incorporated using probabilistic brain atlas containing prior expectations about the spatial localization of different tissue classes. This atlas is considered as a complementary sensor and the proposed method is extended to multimodal brain MRI without any user-tunable parameter (unsupervised algorithm). To validate this new unifying framework, we present experimental results on both synthetic and real brain images, for which the ground truth is available. Comparison with other often used techniques demonstrates the accuracy and the robustness of this new Markovian segmentation scheme.
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paper_title: A unifying framework for partial volume segmentation of brain MR images

paper_content:

Accurate brain tissue segmentation by intensity-based voxel classification of magnetic resonance (MR) images is complicated by partial volume (PV) voxels that contain a mixture of two or more tissue types. In this paper, we present a statistical framework for PV segmentation that encompasses and extends existing techniques. We start from a commonly used parametric statistical image model in which each voxel belongs to one single tissue type, and introduce an additional downsampling step that causes partial voluming along the borders between tissues. An expectation-maximization approach is used to simultaneously estimate the parameters of the resulting model and perform a PV classification. We present results on well-chosen simulated images and on real MR images of the brain, and demonstrate that the use of appropriate spatial prior knowledge not only improves the classifications, but is often indispensable for robust parameter estimation as well. We conclude that general robust PV segmentation of MR brain images requires statistical models that describe the spatial distribution of brain tissues more accurately than currently available models.
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paper_title: A modified fuzzy clustering algorithm for operator independent brain tissue classification of dual echo MR images

paper_content:

Methods for brain tissue classification or segmentation of structural magnetic resonance imaging (MRI) data should ideally be independent of human operators for reasons of reliability and tractability. An algorithm is described for fully automated segmentation of dual echo, fast spin-echo MRI data. The method is used to assign fuzzy-membership values for each of four tissue classes (gray matter, white matter, cerebrospinal fluid and dura) to each voxel based on partition of a two dimensional feature space. Fuzzy clustering is modified for this application in two ways. First, a two component normal mixture model is initially fitted to the thresholded feature space to identify exemplary gray and white matter voxels. These exemplary data protect subsequently estimated cluster means against the tendency of unmodified fuzzy clustering to equalize the number of voxels in each class. Second, fuzzy clustering is implemented in a moving window scheme that accommodates reduced image contrast at the axial extremes of the transmitting/receiving coil. MRI data acquired from 5 normal volunteers were used to identify stable values for three arbitrary parameters of the algorithm: feature space threshold, relative weight of exemplary gray and white matter voxels, and moving window size. The modified algorithm incorporating these parameter values was then used to classify data from simulated images of the brain, validating the use of fuzzy-membership values as estimates of partial volume. Gray:white matter ratios were estimated from 20 twenty normal volunteers (mean age 32.8 years). Processing time for each three-dimensional image was approximately 30 min on a 170 MHz workstation. Mean cerebral gray and white matter volumes estimated from these automatically segmented images were very similar to comparable results previously obtained by operator dependent methods, but without their inherent unreliability.
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paper_title: Segmentation of Brain MRI Using SOM-FCM-Based Method and 3D Statistical Descriptors

paper_content:

Current medical imaging systems provide excellent spatial resolution, high tissue contrast, and up to 65535 intensity levels. Thus, image processing techniques which aim to exploit the information contained in the images are necessary for using these images in computer-aided diagnosis (CAD) systems. Image segmentation may be defined as the process of parcelling the image to delimit different neuroanatomical tissues present on the brain. In this paper we propose a segmentation technique using 3D statistical features extracted from the volume image. In addition, the presented method is based on unsupervised vector quantization and fuzzy clustering techniques and does not use any a priori information. The resulting fuzzy segmentation method addresses the problem of partial volume effect (PVE) and has been assessed using real brain images from the Internet Brain Image Repository (IBSR).
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paper_title: Adaptable fuzzy C-Means for improved classification as a preprocessing procedure of brain parcellation

paper_content:

Parcellation, one of several brain analysis methods, is a procedure popular for subdividing the regions identified by segmentation into smaller topographically defined units. The fuzzy clustering algorithm is mainly used to preprocess parcellation into several segmentation methods, because it is very appropriate for the characteristics of magnetic resonance imaging (MRI), such as partial volume effect and intensity inhomogeneity. However, some gray matter, such as basal ganglia and thalamus, may be misclassified into the white matter class using the conventional fuzzy C-Means (FCM) algorithm. Parcellation has been nearly achieved through manual drawing, but it is a tedious and time-consuming process. We propose improved classification using successive fuzzy clustering and implementing the parcellation module with the modified graphic user interface (GUI) for the convenience of users.
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paper_title: Improved estimates of partial volume coefficients from noisy brain MRI using spatial context

paper_content:

This paper addresses the problem of accurate voxel-level estimation of tissue proportions in the human brain magnetic resonance imaging (MRI). Due to the finite resolution of acquisition systems, MRI voxels can contain contributions from more than a single tissue type. The voxel-level estimation of this fractional content is known as partial volume coefficient estimation. In the present work, two new methods to calculate the partial volume coefficients under noisy conditions are introduced and compared with current similar methods. Concretely, a novel Markov Random Field model allowing sharp transitions between partial volume coefficients of neighbouring voxels and an advanced non-local means filtering technique are proposed to reduce the errors due to random noise in the partial volume coefficient estimation. In addition, a comparison was made to find out how the different methodologies affect the measurement of the brain tissue type volumes. Based on the obtained results, the main conclusions are that (1) both Markov Random Field modelling and non-local means filtering improved the partial volume coefficient estimation results, and (2) non-local means filtering was the better of the two strategies for partial volume coefficient estimation.
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paper_title: Brain MRI Tissue Classification Based on Local Markov Random Fields

paper_content:

A new method for tissue classification of brain magnetic resonance images (MRI) of the brain is proposed. The method is based on local image models where each models the image content in a subset of the image domain. With this local modeling approach, the assumption that tissue types have the same characteristics over the brain needs not to be evoked. This is important because tissue type characteristics, such as T1 and T2 relaxation times and proton density, vary across the individual brain and the proposed method offers improved protection against intensity non-uniformity artifacts that can hamper automatic tissue classification methods in brain MRI. A framework in which local models for tissue intensities and Markov Random Field priors are combined into a global probabilistic image model is introduced. This global model will be an inhomogeneous Markov Random Field and it can be solved by standard algorithms such as iterative conditional modes. The division of the whole image domain into local brain regions possibly having different intensity statistics is realized via sub-volume probabilistic atlases. Finally, the parameters for the local intensity models are obtained without supervision by maximizing the weighted likelihood of a certain finite mixture model. For the maximization task, a novel genetic algorithm almost free of initialization dependency is applied. The algorithm is tested on both simulated and real brain MR images. The experiments confirm that the new method offers a useful improvement of the tissue classification accuracy when the basic tissue characteristics vary across the brain and the noise level of the images is reasonable. The method also offers better protection against intensity non-uniformity artifact than the corresponding method based on a global (whole image) modeling scheme.
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paper_title: Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm

paper_content:

The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation--no spatial information is taken into account. This causes the FM model to work only on well-defined images with low levels of noise; unfortunately, this is often not the the case due to artifacts such as partial volume effect and bias field distortion. Under these conditions, FM model-based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites. Although MRF modeling has been employed in MR image segmentation by other researchers, most reported methods are limited to using MRF as a general prior in an FM model-based approach. To fit the HMRF model, an EM algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into a HMRF-EM framework, an accurate and robust segmentation can be achieved. More importantly, the HMRF-EM framework can easily be combined with other techniques. As an example, we show how the bias field correction algorithm of Guillemaud and Brady (1997) can be incorporated into this framework to achieve a three-dimensional fully automated approach for brain MR image segmentation.
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paper_title: Automated model-based tissue classification of MR images of the brain

paper_content:

Describes a fully automated method for model-based tissue classification of magnetic resonance (MR) images of the brain. The method interleaves classification with estimation of the model parameters, improving the classification at each iteration. The algorithm is able to segment single- and multi-spectral MR images, corrects for MR signal inhomogeneities, and incorporates contextual information by means of Markov random Fields (MRF's). A digital brain atlas containing prior expectations about the spatial location of tissue classes is used to initialize the algorithm. This makes the method fully automated and therefore it provides objective and reproducible segmentations. The authors have validated the technique on simulated as well as on real MR images of the brain.
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paper_title: Voxel-based morphometry—The methods

paper_content:

At its simplest, voxel-based morphometry (VBM) involves a voxel-wise comparison of the local concentration of gray matter between two groups of subjects. The procedure is relatively straightforward and involves spatially normalizing high-resolution images from all the subjects in the study into the same stereotactic space. This is followed by segmenting the gray matter from the spatially normalized images and smoothing the gray-matter segments. Voxel-wise parametric statistical tests which compare the smoothed gray-matter images from the two groups are performed. Corrections for multiple comparisons are made using the theory of Gaussian random fields. This paper describes the steps involved in VBM, with particular emphasis on segmenting gray matter from MR images with nonuniformity artifact. We provide evaluations of the assumptions that underpin the method, including the accuracy of the segmentation and the assumptions made about the statistical distribution of the data.
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paper_title: Cerebral atrophy and its relation to cognitive impairment in Parkinson disease

paper_content:

Objective:Voxel-based morphometry was used to compare the amounts of gray matter in the brains of patients with Parkinson disease (PD) and normal control subjects (NCs) and to identify the specific regions responsible for cognitive dysfunction in PD. Methods:Patients were classified into nondemented (ND) and demented (D) groups according to the criteria of the Diagnostic and Statistical Manual of Mental Disorders (4th ed.), and a group comparison was performed. In the ND patients, a correlation was also performed between local gray matter density and the score on Raven Colored Progressive Matrices (RCPM), a test of executive and visuospatial function. Results:In patients with advanced ND-PD vs NCs, atrophic changes were observed in the limbic/paralimbic areas and the prefrontal cortex. In D vs ND patients, atrophic change was observed widely in the limbic/paralimbic system, including the anterior cingulate gyrus and hippocampus as well as the temporal lobe, dorsolateral prefrontal cortex, thalamus, and caudate nucleus. The RCPM score was positively correlated with the gray matter density in the dorsolateral prefrontal cortex and the parahippocampal gyrus. Conclusions:In patients with Parkinson disease (PD), atrophic changes occur mainly in the limbic/paralimbic and prefrontal areas. These atrophic changes may be related to the development of dementia in PD.
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paper_title: Cerebral asymmetry and the effects of sex and handedness on brain structure: A voxel-based morphometric analysis of 465 normal adult human brains

paper_content:

We used voxel-based morphometry (VBM) to examine human brain asymmetry and the effects of sex and handedness on brain structure in 465 normal adults. We observed significant asymmetry of cerebral grey and white matter in the occipital, frontal, and temporal lobes (petalia), including Heschl's gyrus, planum temporale (PT) and the hippocampal formation. Males demonstrated increased leftward asymmetry within Heschl's gyrus and PT compared to females. There was no significant interaction between asymmetry and handedness and no main effect of handedness. There was a significant main effect of sex on brain morphology, even after accounting for the larger global volumes of grey and white matter in males. Females had increased grey matter volume adjacent to the depths of both central sulci and the left superior temporal sulcus, in right Heschl's gyrus and PT, in right inferior frontal and frontomarginal gyri and in the cingulate gyrus. Females had significantly increased grey matter concentration extensively and relatively symmetrically in the cortical mantle, parahippocampal gyri, and in the banks of the cingulate and calcarine sulci. Males had increased grey matter volume bilaterally in the mesial temporal lobes, entorhinal and perirhinal cortex, and in the anterior lobes of the cerebellum, but no regions of increased grey matter concentration.
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paper_title: Regional impact of field strength on voxel‐based morphometry results

paper_content:

The objective of this study was to characterize the sensitivity of voxel-based morphometry (VBM) results to choice field strength. We chose to investigate the two most widespread acquisition sequences for VBM, FLASH and MP-RAGE, at 1.5 and 3 T. We first evaluated image quality of the four acquisition protocols in terms of SNR and image uniformity. We then performed a VBM study on eight subjects scanned twice using the four protocols to evaluate differences in grey matter (GM) density and corresponding scan-rescan variability, and a power analysis for each protocol in the context a longitudinal and cross-sectional VBM study. As expected, the SNR increased significantly at 3 T for both FLASH and MP-RAGE. Image non-uniformity increased as well, in particular for MP-RAGE. The differences in CNR and contrast non-uniformity cause regional biases between protocols in the VBM results, in particular between sequences at 3 T. The power analysis results show an overall decrease in the number of subjects required in a longitudinal study to detect a difference in GM density at 3 T for MP-RAGE, but an increase for FLASH. The number of subjects required in a cross-sectional VBM study is higher at 3 T for both sequences. Our results show that each protocol has a distinct regional sensitivity pattern to morphometric change, which goes against the classical view of VBM as an unbiased whole brain analysis technique, complicates the combination of data within a VBM study and the direct comparison of VBM studies based on different protocols. Hum Brain Mapp, 2010. © 2009 Wiley-Liss, Inc.
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paper_title: Measurement of cortical thickness from MRI by minimum line integrals on soft‐classified tissue

paper_content:

Estimating the thickness of the cerebral cortex is a key step in many brain imaging studies, revealing valuable information on development or disease progression. In this work, we present a framework for measuring the cortical thickness, based on minimizing line integrals over the probability map of the gray matter in the MRI volume. We first prepare a probability map that contains the probability of each voxel belonging to the gray matter. Then, the thickness is basically defined for each voxel as the minimum line integral of the probability map on line segments centered at the point of interest. In contrast to our approach, previous methods often perform a binary-valued hard segmentation of the gray matter before measuring the cortical thickness. Due to image noise and partial volume effects, such a hard classification ignores the underlying tissue class probabilities assigned to each voxel, discarding potentially useful information. We describe our proposed method and demonstrate its performance on both artificial volumes and real 3D brain MRI data from subjects with Alzheimer’s disease and healthy individuals.
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paper_title: Automated 3-D extraction and evaluation of the inner and outer cortical surfaces using a Laplacian map and partial volume effect classification

paper_content:

Accurate reconstruction of the inner and outer cortical surfaces of the human cerebrum is a critical objective for a wide variety of neuroimaging analysis purposes, including visualization, morphometry, and brain mapping. The Anatomic Segmentation using Proximity (ASP) algorithm, previously developed by our group, provides a topology-preserving cortical surface deformation method that has been extensively used for the aforementioned purposes. However, constraints in the algorithm to ensure topology preservation occasionally produce incorrect thickness measurements due to a restriction in the range of allowable distances between the gray and white matter surfaces. This problem is particularly prominent in pediatric brain images with tightly folded gyri. This paper presents a novel method for improving the conventional ASP algorithm by making use of partial volume information through probabilistic classification in order to allow for topology preservation across a less restricted range of cortical thickness values. The new algorithm also corrects the classification of the insular cortex by masking out subcortical tissues. For 70 pediatric brains, validation experiments for the modified algorithm, Constrained Laplacian ASP (CLASP), were performed by three methods: (i) volume matching between surface-masked gray matter (GM) and conventional tissue-classified GM, (ii) surface matching between simulated and CLASP-extracted surfaces, and (iii) repeatability of the surface reconstruction among 16 MRI scans of the same subject. In the volume-based evaluation, the volume enclosed by the CLASP WM and GM surfaces matched the classified GM volume 13% more accurately than using conventional ASP. In the surface-based evaluation, using synthesized thick cortex, the average difference between simulated and extracted surfaces was 4.6 T 1.4 mm for conventional ASP and 0.5 T 0.4 mm for CLASP. In a repeatability study, CLASP produced a 30% lower RMS error for the GM surface and a 8% lower RMS error for the
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paper_title: Voxel-based cortical thickness measurements in MRI

paper_content:

The thickness of the cerebral cortex can provide valuable information about normal and abnormal neuroanatomy. High resolution MRI together with powerful image processing techniques has made it possible to perform these measurements automatically over the whole brain. Here we present a method for automatically generating voxel-based cortical thickness (VBCT) maps. This technique results in maps where each voxel in the grey matter is assigned a thickness value. Sub-voxel measurements of thickness are possible using sub-sampling and interpolation of the image information. The method is applied to repeated MRI scans of a single subject from two MRI scanners to demonstrate its robustness and reproducibility. A simulated data set is used to show that small focal differences in thickness between two groups of subjects can be detected. We propose that the analysis of VBCT maps can provide results that are complementary to other anatomical analyses such as voxel-based morphometry.
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paper_title: Cortical thickness analysis examined through power analysis and a population simulation

paper_content:

We have previously developed a procedure for measuring the thickness of cerebral cortex over the whole brain using 3-D MRI data and a fully automated surface-extraction (ASP) algorithm. This paper examines the precision of this algorithm, its optimal performance parameters, and the sensitivity of the method to subtle, focal changes in cortical thickness. The precision of cortical thickness measurements was studied using a simulated population study and single subject reproducibility metrics. Cortical thickness was shown to be a reliable method, reaching a sensitivity (probability of a true-positive) of 0.93. Six different cortical thickness metrics were compared. The simplest and most precise method measures the distance between corresponding vertices from the white matter to the gray matter surface. Given two groups of 25 subjects, a 0.6-mm (15%) change in thickness can be recovered after blurring with a 3-D Gaussian kernel (full-width half max = 30 mm). Smoothing across the 2-D surface manifold also improves precision; in this experiment, the optimal kernel size was 30 mm.
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paper_title: Automated voxel-based 3D cortical thickness measurement in a combined Lagrangian–Eulerian PDE approach using partial volume maps

paper_content:

Accurate cortical thickness estimation is important for the study of many neurodegenerative diseases. Many approaches have been previously proposed, which can be broadly categorised as mesh-based and voxel-based. While the mesh-based approaches can potentially achieve subvoxel resolution, they usually lack the computational efficiency needed for clinical applications and large database studies. In contrast, voxel-based approaches, are computationally efficient, but lack accuracy. The aim of this paper is to propose a novel voxel-based method based upon the Laplacian definition of thickness that is both accurate and computationally efficient. A framework was developed to estimate and integrate the partial volume information within the thickness estimation process. Firstly, in a Lagrangian step, the boundaries are initialized using the partial volume information. Subsequently, in an Eulerian step, a pair of partial differential equations are solved on the remaining voxels to finally compute the thickness. Using partial volume information significantly improved the accuracy of the thickness estimation on synthetic phantoms, and improved reproducibility on real data. Significant differences in the hippocampus and temporal lobe between healthy controls (NC), mild cognitive impaired (MCI) and Alzheimer’s disease (AD) patients were found on clinical data from the ADNI database. We compared our method in terms of precision, computational speed and statistical power against the Eulerian approach. With a slight increase in computation time, accuracy and precision were greatly improved. Power analysis demonstrated the ability of our method to yield statistically significant results when comparing AD and NC. Overall, with our method the number of samples is reduced by 25% to find significant differences between the two groups.
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paper_title: Fast and robust parameter estimation for statistical partial volume models in brain MRI

paper_content:

Due to the finite spatial resolution of imaging devices, a single voxel in a medical image may be composed of mixture of tissue types, an effect known as partial volume effect (PVE). Partial volume estimation, that is, the estimation of the amount of each tissue type within each voxel, has received considerable interest in recent years. Much of this work has been focused on the mixel model, a statistical model of PVE. We propose a novel trimmed minimum covariance determinant (TMCD) method for the estimation of the parameters of the mixel PVE model. In this method, each voxel is first labeled according to the most dominant tissue type. Voxels that are prone to PVE are removed from this labeled set, following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class. Comparisons between different methods for parameter estimation based on classified images as well as expectation--maximization-like (EM-like) procedure for simultaneous parameter and partial volume estimation are reported. The robust estimators based on a pruned classification as presented here are shown to perform well even if the initial classification is of poor quality. The results obtained are comparable to those obtained using the EM-like procedure, but require considerably less computation time. Segmentation results of real data based on partial volume estimation are also reported. In addition to considering the parameter estimation problem, we discuss differences between different approximations to the complete mixel model. In summary, the proposed TMCD method allows for the accurate, robust, and efficient estimation of partial volume model parameters, which is crucial to a variety of brain MRI data analysis procedures such as the accurate estimation of tissue volumes and the accurate delineation of the cortical surface.
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paper_title: Measuring the thickness of the human cerebral cortex from magnetic resonance images

paper_content:

Accurate and automated methods for measuring the thickness of human cerebral cortex could provide powerful tools for diagnosing and studying a variety of neurodegenerative and psychiatric disorders. Manual methods for estimating cortical thickness from neuroimaging data are labor intensive, requiring several days of effort by a trained anatomist. Furthermore, the highly folded nature of the cortex is problematic for manual techniques, frequently resulting in measurement errors in regions in which the cortical surface is not perpendicular to any of the cardinal axes. As a consequence, it has been impractical to obtain accurate thickness estimates for the entire cortex in individual subjects, or group statistics for patient or control populations. Here, we present an automated method for accurately measuring the thickness of the cerebral cortex across the entire brain and for generating cross-subject statistics in a coordinate system based on cortical anatomy. The intersubject standard deviation of the thickness measures is shown to be less than 0.5 mm, implying the ability to detect focal atrophy in small populations or even individual subjects. The reliability and accuracy of this new method are assessed by within-subject test–retest studies, as well as by comparison of cross-subject regional thickness measures with published values.
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paper_title: Automated 3-D Extraction of Inner and Outer Surfaces of Cerebral Cortex from MRI

paper_content:

Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented here, with two novel features. First, explicit prevention of self-intersecting surface geometries is provided, unlike conventional deformable models, which use regularization constraints to discourage but not necessarily prevent such behavior. Second, deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model-based constraints such as expected thickness of an anatomic surface. These two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human MR images, accurately locating the depths of the sulci, even where noise and partial volume artifacts in the image obscure the visibility of sulci. The extracted surfaces are enforced to be simple two-dimensional manifolds (having the topology of a sphere), even though the data may have topological holes. This automatic 3-D cortex segmentation technique has been applied to 150 normal subjects, simultaneously extracting both the gray/white and gray/cerebrospinal fluid interface from each individual. The collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter. Three alternative criteria for defining cortical thickness at each cortical location were developed and compared. These results are shown to corroborate published postmortem and in vivo measurements of cortical thickness.
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paper_title: Atlas-Free Surface Reconstruction of the Cortical Grey-White Interface in Infants

paper_content:

Background ::: The segmentation of the cortical interface between grey and white matter in magnetic resonance images (MRI) is highly challenging during the first post-natal year. First, the heterogeneous brain maturation creates important intensity fluctuations across regions. Second, the cortical ribbon is highly folded creating complex shapes. Finally, the low tissue contrast and partial volume effects hamper cortex edge detection in parts of the brain. ::: Methods and Findings ::: We present an atlas-free method for segmenting the grey-white matter interface of infant brains in T2-weighted (T2w) images. We used a broad characterization of tissue using features based not only on local contrast but also on geometric properties. Furthermore, inaccuracies in localization were reduced by the convergence of two evolving surfaces located on each side of the inner cortical surface. Our method has been applied to eleven brains of one- to four-month-old infants. Both quantitative validations against manual segmentations and sulcal landmarks demonstrated good performance for infants younger than two months old. Inaccuracies in surface reconstruction increased with age in specific brain regions where the tissue contrast decreased with maturation, such as in the central region. ::: Conclusions ::: We presented a new segmentation method which achieved good to very good performance at the grey-white matter interface depending on the infant age. This method should reduce manual intervention and could be applied to pathological brains since it does not require any brain atlas.
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paper_title: Automated segmentation of multiple sclerosis lesion subtypes with multichannel MRI

paper_content:

PURPOSE ::: To automatically segment multiple sclerosis (MS) lesions into three subtypes (i.e., enhancing lesions, T1 "black holes", T2 hyperintense lesions). ::: ::: ::: MATERIALS AND METHODS ::: Proton density-, T2- and contrast-enhanced T1-weighted brain images of 12 MR scans were pre-processed through intracranial cavity (IC) extraction, inhomogeneity correction and intensity normalization. Intensity-based statistical k-nearest neighbor (k-NN) classification was combined with template-driven segmentation and partial volume artifact correction (TDS+) for segmentation of MS lesions subtypes and brain tissue compartments. Operator-supervised tissue sampling and parameter calibration were performed on 2 randomly selected scans and were applied automatically to the remaining 10 scans. Results from this three-channel TDS+ (3ch-TDS+) were compared to those from a previously validated two-channel TDS+ (2ch-TDS+) method. The results of both the 3ch-TDS+ and 2ch-TDS+ were also compared to manual segmentation performed by experts. ::: ::: ::: RESULTS ::: Intra-class correlation coefficients (ICC) of 3ch-TDS+ for all three subtypes of lesions were higher (ICC between 0.95 and 0.96) than that of 2ch-TDS+ for T2 lesions (ICC = 0.82). The 3ch-TDS+ also identified the three lesion subtypes with high specificity (98.7-99.9%) and accuracy (98.5-99.9%). Sensitivity of 3ch-TDS+ for T2 lesions was 16% higher than with 2ch-TDS+. Enhancing lesions were segmented with the best sensitivity (81.9%). "Black holes" were segmented with the least sensitivity (62.3%). ::: ::: ::: CONCLUSION ::: 3ch-TDS+ is a promising method for automated segmentation of MS lesion subtypes.
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paper_title: Automatic segmentation and reconstruction of the cortex from neonatal MRI

paper_content:

Abstract Segmentation and reconstruction of cortical surfaces from magnetic resonance (MR) images are more challenging for developing neonates than adults. This is mainly due to the dynamic changes in the contrast between gray matter (GM) and white matter (WM) in both T1- and T2-weighted images (T1w and T2w) during brain maturation. In particular in neonatal T2w images WM typically has higher signal intensity than GM. This causes mislabeled voxels during cortical segmentation, especially in the cortical regions of the brain and in particular at the interface between GM and cerebrospinal fluid (CSF). We propose an automatic segmentation algorithm detecting these mislabeled voxels and correcting errors caused by partial volume effects. Our results show that the proposed algorithm corrects errors in the segmentation of both GM and WM compared to the classic expectation maximization (EM) scheme. Quantitative validation against manual segmentation demonstrates good performance (the mean Dice value: 0.758 ± 0.037 for GM and 0.794 ± 0.078 for WM). The inner, central and outer cortical surfaces are then reconstructed using implicit surface evolution. A landmark study is performed to verify the accuracy of the reconstructed cortex (the mean surface reconstruction error: 0.73 mm for inner surface and 0.63 mm for the outer). Both segmentation and reconstruction have been tested on 25 neonates with the gestational ages ranging from ∼ 27 to 45 weeks. This preliminary analysis confirms previous findings that cortical surface area and curvature increase with age, and that surface area scales to cerebral volume according to a power law, while cortical thickness is not related to age or brain growth.
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paper_title: Time-series analysis of MRI intensity patterns in multiple sclerosis

paper_content:

Abstract In progressive neurological disorders, such as multiple sclerosis (MS), magnetic resonance imaging (MRI) follow-up is used to monitor disease activity and progression and to understand the underlying pathogenic mechanisms. This article presents image postprocessing methods and validation for integrating multiple serial MRI scans into a spatiotemporal volume for direct quantitative evaluation of the temporal intensity profiles. This temporal intensity signal and its dynamics have thus far not been exploited in the study of MS pathogenesis and the search for MRI surrogates of disease activity and progression. The integration into a four-dimensional data set comprises stages of tissue classification, followed by spatial and intensity normalization and partial volume filtering. Spatial normalization corrects for variations in head positioning and distortion artifacts via fully automated intensity-based registration algorithms, both rigid and nonrigid. Intensity normalization includes separate stages of correcting intra- and interscan variations based on the prior tissue class segmentation. Different approaches to image registration, partial volume correction, and intensity normalization were validated and compared. Validation included a scan–rescan experiment as well as a natural-history study on MS patients, imaged in weekly to monthly intervals over a 1-year follow-up. Significant error reduction was observed by applying tissue-specific intensity normalization and partial volume filtering. Example temporal profiles within evolving multiple sclerosis lesions are presented. An overall residual signal variance of 1.4% ± 0.5% was observed across multiple subjects and time points, indicating an overall sensitivity of 3% (for axial dual echo images with 3-mm slice thickness) for longitudinal study of signal dynamics from serial brain MRI.
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paper_title: Automatic statistical shape analysis of cerebral asymmetry in 3D T1-weighted magnetic resonance images at vertex-level: application to neuroleptic-naïve schizophrenia.

paper_content:

The study of the structural asymmetries in the human brain can assist the early diagnosis and progression of various neuropsychiatric disorders, and give insights into the biological bases of several cognitive deficits. The high inter-subject variability in cortical morphology complicates the detection of abnormal asymmetries especially if only small samples are available. This work introduces a novel automatic method for the local (vertex-level) statistical shape analysis of gross cerebral hemispheric surface asymmetries which is robust to the individual cortical variations. After segmentation of the cerebral hemispheric volumes from three-dimensional (3D) T1-weighted magnetic resonance images (MRI) and their spatial normalization to a common space, the right hemispheric masks were reflected to match with the left ones. Cerebral hemispheric surfaces were extracted using a deformable model-based algorithm which extracted the salient morphological features while establishing the point correspondence between the surfaces. The interhemispheric asymmetry, quantified by customized measures of asymmetry, was evaluated in a few thousands of corresponding surface vertices and tested for statistical significance. The developed method was tested on scans obtained from a small sample of healthy volunteers and first-episode neuroleptic-naïve schizophrenics. A significant main effect of the disease on the local interhemispheric asymmetry was observed, both in females and males, at the frontal and temporal lobes, the latter being often linked to the cognitive, auditory, and memory deficits in schizophrenia. The findings of this study, although need further testing in larger samples, partially replicate previous studies supporting the hypothesis of schizophrenia as a neurodevelopmental disorder.
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paper_title: Quantitative analysis of MRI signal abnormalities of brain white matter with high reproducibility and accuracy.

paper_content:

PURPOSE ::: To assess the reproducibility and accuracy compared to radiologists of three automated segmentation pipelines for quantitative magnetic resonance imaging (MRI) measurement of brain white matter signal abnormalities (WMSA). ::: ::: ::: MATERIALS AND METHODS ::: WMSA segmentation was performed on pairs of whole brain scans from 20 patients with multiple sclerosis (MS) and 10 older subjects who were positioned and imaged twice within 30 minutes. Radiologist outlines of WMSA on 20 sections from 16 patients were compared with the corresponding results of each segmentation method. ::: ::: ::: RESULTS ::: The segmentation method combining expectation-maximization (EM) tissue segmentation, template-driven segmentation (TDS), and partial volume effect correction (PVEC) demonstrated the highest accuracy (the absolute value of the Z-score was 0.99 for both groups of subjects), as well as high interscan reproducibility (repeatability coefficient was 0.68 mL in MS patients and 1.49 mL in aging subjects). ::: ::: ::: CONCLUSION ::: The addition of TDS to the EM segmentation and PVEC algorithms significantly improved the accuracy of WMSA volume measurements, while also improving measurement reproducibility.
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paper_title: A Modified Probabilistic Neural Network for Partial Volume Segmentation in Brain MR Image

paper_content:

A modified probabilistic neural network (PNN) for brain tissue segmentation with magnetic resonance imaging (MRI) is proposed. In this approach, covariance matrices are used to replace the singular smoothing factor in the PNN's kernel function, and weighting factors are added in the pattern of summation layer. This weighted probabilistic neural network (WPNN) classifier can account for partial volume effects, which exist commonly in MRI, not only in the final result stage, but also in the modeling process. It adopts the self-organizing map (SOM) neural network to overly segment the input MR image, and yield reference vectors necessary for probabilistic density function (pdf) estimation. A supervised "soft" labeling mechanism based on Bayesian rule is developed, so that weighting factors can be generated along with corresponding SOM reference vectors. Tissue classification results from various algorithms are compared, and the effectiveness and robustness of the proposed approach are demonstrated.
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paper_title: Automatic cerebral and cerebellar hemisphere segmentation in 3D MRI: Adaptive disconnection algorithm

paper_content:

This paper describes the automatic Adaptive Disconnection method to segment cerebral and cerebellar hemispheres of human brain in three-dimensional magnetic resonance imaging (MRI). Using the partial differential equations based shape bottlenecks algorithm cooperating with an information potential value clustering process, it detects and cuts, first, the compartmental connections between the cerebrum, the cerebellum and the brainstem in the white matter domain, and then, the interhemispheric connections of the extracted cerebrum and cerebellum volumes. As long as the subject orientation in the scanner is given, the variations in subject location and normal brain morphology in different images are accommodated automatically, thus no stereotaxic image registration is required. The modeling of partial volume effect is used to locate cerebrum, cerebellum and brainstem boundaries, and make the interhemispheric connections detectable. The Adaptive Disconnection method was tested with 10 simulated images from the BrainWeb database and 39 clinical images from the LONI Probabilistic Brain Atlas database. It obtained lower error rates than a traditional shape bottlenecks algorithm based segmentation technique (BrainVisa) and linear and nonlinear registration based brain hemisphere segmentation methods. Segmentation accuracies were evaluated against manual segmentations. The Adaptive Disconnection method was also confirmed not to be sensitive to the noise and intensity non-uniformity in the images. We also applied the Adaptive Disconnection method to clinical images of 22 healthy controls and 18 patients with schizophrenia. A preliminary cerebral volumetric asymmetry analysis based on these images demonstrated that the Adaptive Disconnection method is applicable to study abnormal brain asymmetry in schizophrenia.
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paper_title: Rapid Communication Robust unsupervised segmentation of infarct lesion from diffusion tensor MR images using multiscale statistical classification and partial volume voxel reclassification

paper_content:

Manual region tracing method for segmentation of infarction lesions in images from diffusion tensor magnetic resonance imaging (DT-MRI) is usually used in clinical works, but it is time consuming. A new unsupervised method has been developed, which is a multistage procedure, involving image preprocessing, calculation of tensor field and measurement of diffusion anisotropy, segmentation of infarction volume based on adaptive multiscale statistical classification (MSSC), and partial volume voxel reclassification (PVVR). The method accounts for random noise, intensity overlapping, partial volume effect (PVE), and intensity shading artifacts, which always appear in DT-MR images. The proposed method was applied to 20 patients with clinically diagnosed brain infarction by DT-MRI scans. The accuracy and reproducibility in terms of identifying the infarction lesion have been confirmed by clinical experts. This automatic segmentation method is promising not only in detecting the location and the size of infarction lesion in stroke patient but also in quantitatively analyzing diffusion
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paper_title: Anisotropic partial volume CSF modeling for EEG source localization

paper_content:

Abstract Electromagnetic source localization (ESL) provides non-invasive evaluation of brain electrical activity for neurology research and clinical evaluation of neurological disorders such as epilepsy. Accurate ESL results are dependent upon the use of patient specific models of bioelectric conductivity. While the effects of anisotropic conductivities in the skull and white matter have been previously studied, little attention has been paid to the accurate modeling of the highly conductive cerebrospinal fluid (CSF) region. This study examines the effect that partial volume errors in CSF segmentations have upon the ESL bioelectric model. These errors arise when segmenting sulcal channels whose widths are similar to the resolution of the magnetic resonance (MR) images used for segmentation, as some voxels containing both CSF and gray matter cannot be definitively assigned a single label. These problems, particularly prevalent in pediatric populations, make voxelwise segmentation of CSF compartments a difficult problem. Given the high conductivity of CSF, errors in modeling this region may result in large errors in the bioelectric model. We introduce here a new approach for using estimates of partial volume fractions in the construction of patient specific bioelectric models. In regions where partial volume errors are expected, we use a layered gray matter-CSF model to construct equivalent anisotropic conductivity tensors. This allows us to account for the inhomogeneity of the tissue within each voxel. Using this approach, we are able to reduce the error in the resulting bioelectric models, as evaluated against a known high resolution model. Additionally, this model permits us to evaluate the effects of sulci modeling errors and quantify the mean error as a function of the change in sulci width. Our results suggest that both under and over-estimation of the CSF region leads to significant errors in the bioelectric model. While a model with fixed partial volume fraction is able to reduce this error, we see the largest improvement when using voxel specific partial volume estimates. Our cross-model analyses suggest that an approximately linear relationship exists between sulci error and the error in the resulting bioelectric model. Given the difficulty of accurately segmenting narrow sulcal channels, this suggests that our approach may be capable of improving the accuracy of patient specific bioelectric models by several percent, while introducing only minimal additional computational requirements.
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paper_title: Robust White Matter Lesion Segmentation in FLAIR MRI

paper_content:

This paper discusses a white matter lesion (WML) segmentation scheme for fluid attenuation inversion recovery (FLAIR) MRI. The method computes the volume of lesions with subvoxel precision by accounting for the partial volume averaging (PVA) artifact. As WMLs are related to stroke and carotid disease, accurate volume measurements are most important. Manual volume computation is laborious, subjective, time consuming, and error prone. Automated methods are a nice alternative since they quantify WML volumes in an objective, efficient, and reliable manner. PVA is initially modeled with a localized edge strength measure since PVA resides in the boundaries between tissues. This map is computed in 3-D and is transformed to a global representation to increase robustness to noise. Significant edges correspond to PVA voxels, which are used to find the PVA fraction α (amount of each tissue present in mixture voxels). Results on simulated and real FLAIR images show high WML segmentation performance compared to ground truth (98.9% and 83% overlap, respectively), which outperforms other methods. Lesion load studies are included that automatically analyze WML volumes for each brain hemisphere separately. This technique does not require any distributional assumptions/parameters or training samples and is applied on a single MR modality, which is a major advantage compared to the traditional methods.
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paper_title: Adaptive neonate brain segmentation.

paper_content:

Babies born prematurely are at increased risk of adverse neurodevelopmental outcomes. Recent advances suggest that measurement of brain volumes can help in defining biomarkers for neurodevelopmental outcome. These techniques rely on an accurate segmentation of the MRI data. However, due to lack of contrast, partial volume (PV) effect, the existence of both hypo- and hyper-intensities and significant natural and pathological anatomical variability, the segmentation of neonatal brain MRI is challenging. We propose a pipeline for image segmentation that uses a novel multi-model Maximum a posteriori Expectation Maximisation (MAP-EM) segmentation algorithm with a prior over both intensities and the tissue proportions, a B0 inhomogeneity correction, and a spatial homogeneity term through the use of a Markov Random Field. This robust and adaptive technique enables the segmentation of images with high anatomical disparity from a normal population. Furthermore, the proposed method implicitly models Partial Volume, mitigating the problem of neonatal white/grey matter intensity inversion. Experiments performed on a clinical cohort show expected statistically significant correlations with gestational age at birth and birthweight. Furthermore, the proposed method obtains statistically significant improvements in Dice scores when compared to the a Maximum Likelihood EM algorithm.
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paper_title: Novel whole brain segmentation and volume estimation using quantitative MRI

paper_content:

OBJECTIVES ::: Brain segmentation and volume estimation of grey matter (GM), white matter (WM) and cerebro-spinal fluid (CSF) are important for many neurological applications. Volumetric changes are observed in multiple sclerosis (MS), Alzheimer's disease and dementia, and in normal aging. A novel method is presented to segment brain tissue based on quantitative magnetic resonance imaging (qMRI) of the longitudinal relaxation rate R(1), the transverse relaxation rate R(2) and the proton density, PD. ::: ::: ::: METHODS ::: Previously reported qMRI values for WM, GM and CSF were used to define tissues and a Bloch simulation performed to investigate R(1), R(2) and PD for tissue mixtures in the presence of noise. Based on the simulations a lookup grid was constructed to relate tissue partial volume to the R(1)-R(2)-PD space. The method was validated in 10 healthy subjects. MRI data were acquired using six resolutions and three geometries. ::: ::: ::: RESULTS ::: Repeatability for different resolutions was 3.2% for WM, 3.2% for GM, 1.0% for CSF and 2.2% for total brain volume. Repeatability for different geometries was 8.5% for WM, 9.4% for GM, 2.4% for CSF and 2.4% for total brain volume. ::: ::: ::: CONCLUSION ::: We propose a new robust qMRI-based approach which we demonstrate in a patient with MS. ::: ::: ::: KEY POINTS ::: • A method for segmenting the brain and estimating tissue volume is presented • This method measures white matter, grey matter, cerebrospinal fluid and remaining tissue • The method calculates tissue fractions in voxel, thus accounting for partial volume • Repeatability was 2.2% for total brain volume with imaging resolution <2.0 mm.
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paper_title: Automatic brain segmentation using fractional signal modeling of a multiple flip angle, spoiled gradient-recalled echo acquisition

paper_content:

Object ::: The aim of this study was to demonstrate a new automatic brain segmentation method in magnetic resonance imaging (MRI).
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paper_title: Automated Segmentation of Hippocampal Subfields From Ultra-High Resolution In Vivo MRI

paper_content:

Recent developments in MRI data acquisition technology are starting to yield images that show anatomical features of the hippo- campal formation at an unprecedented level of detail, providing the ba- sis for hippocampal subfield measurement. However, a fundamental bottleneck in MRI studies of the hippocampus at the subfield level is that they currently depend on manual segmentation, a laborious process that severely limits the amount of data that can be analyzed. In this article, we present a computational method for segmenting the hippo- campal subfields in ultra-high resolution MRI data in a fully automated fashion. Using Bayesian inference, we use a statistical model of image formation around the hippocampal area to obtain automated segmenta- tions. We validate the proposed technique by comparing its segmenta- tions to corresponding manual delineations in ultra-high resolution MRI scans of 10 individuals, and show that automated volume measurements of the larger subfields correlate well with manual volume estimates. Unlike manual segmentations, our automated technique is fully repro- ducible, and fast enough to enable routine analysis of the hippocampal subfields in large imaging studies. V C 2009 Wiley-Liss, Inc.
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paper_title: The future of ultra-high field MRI and fMRI for study of the human brain

paper_content:

Abstract MRI and fMRI have been used for about three and two decades respectively and much has changed over this time period, both in the quality of the data and in the range of applications for studying the brain. Apart from resolution improvements from around 4 mm in the early days to below 0.5 mm with modern technology, novel uses of contrast have led to the ability to sensitize images to some of the brain's structural properties at the cellular scale as well as study the localization and organization of brain function at the level of cortical columns. These developments have in part been facilitated by a continuing drive to increase the magnetic field strength. Will the next few decades see similar improvements? Here we will discuss current state of high field MRI, expected further increases in field strength, and improvements expected with these increases.
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Title: Partial Volume Effect Modeling for Segmentation and Tissue Classification of Brain Magnetic Resonance Images: A Review

Section 1: Introduction
Description 1: Provide an overview of the importance and challenges of analyzing brain MR images, including the phenomena of partial volume effects (PVE) and its impact on tissue classification and brain structure quantification.

Section 2: Image Pre-processing
Description 2: Discuss the necessary image pre-processing steps required prior to partial volume estimation, including intensity non-uniformity correction, brain extraction, and registration to stereotactic space.

Section 3: Definition and Approximations
Description 3: Define the partial volume effect and the mixel model used to statistically represent it, including necessary notations and assumptions about the tissue types and image intensities.

Section 4: Direct Solution via Penalized Least Squares
Description 4: Explain the direct solution approach for PVCs using penalized least squares, including constraints and regularization techniques to handle noise and variability.

Section 5: Two-step Algorithms
Description 5: Describe the two-step algorithms for partial volume estimation, detailing the initial classification of tissue configurations followed by the restricted PVC estimation.

Section 6: Discretization Approaches
Description 6: Introduce discretization methods for solving the PVC problem, explaining how these methods restrict PVC values to discrete sets and use MRF approaches for spatial modeling.

Section 7: Parameter Estimation
Description 7: Discuss the methods for estimating model parameters, such as mean intensities and covariances, which are crucial for accurate partial volume estimation.

Section 8: Fuzzy C-means
Description 8: Explore the fuzzy C-means algorithm and its modifications as applied to tissue classification, comparing its outcomes with those from the mixel model.

Section 9: Bayesian Tissue Classifiers
Description 9: Review Bayesian decision theory-based classifiers for tissue classification, emphasizing their use of posterior probability maps and prior information.

Section 10: Voxel-based Morphometry
Description 10: Discuss the application of partial volume estimation in voxel-based morphometry (VBM) for comparing gray matter densities between subject groups.

Section 11: Cortical Thickness
Description 11: Detail the measurement of cortical thickness using both mesh-based and voxel-based techniques, highlighting how PVE impacts these measurements.

Section 12: Other Applications
Description 12: Present additional applications of PVE modeling in brain MRI, such as neonatal brain segmentation, hemisphere segmentation, EEG source localization, and lesion load computations.

Section 13: Future Perspectives
Description 13: Outline potential future directions in PVE modeling and its applications, including the use of quantitative tissue mapping and high-field MRI for improved segmentation accuracy.