Surface-constrained volumetric brain registration using harmonic mappings

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

A geometric method for automatic extraction of sulcal fundi

Sulcal fundi are 3-D curves that lie in the depths of the cerebral cortex and, in addition to their intrinsic value in brain research, are often used as landmarks for downstream computations in brain imaging. In this paper, we present a geometric algorithm that automatically extracts the sulcal fundi from magnetic resonance images and represents them as spline curves lying on the extracted triangular mesh representing the cortical surface. The input to our algorithm is a triangular mesh representation of an extracted cortical surface as computed by one of several available software packages for performing automated and semi-automated cortical surface extraction. Given this input we first compute a geometric depth measure for each triangle on the cortical surface mesh, and based on this information we extract sulcal regions by checking for connected regions exceeding a depth threshold. We then identify endpoints of each region and delineate the fundus by thinning the connected region while keeping the endpoints fixed. The curves, thus, defined are regularized using weighted splines on the surface mesh to yield high-quality representations of the sulcal fundi. We present the geometric framework and validate it with real data from human brains. Comparisons with expert-labeled sulcal fundi are part of this validation process.     

Coupling dense and landmark-based approaches for nonrigid registration

In this paper, we investigate the introduction of cortical constraints for non rigid intersubject brain registration. We extract sulcal patterns with the active ribbon method, presented by Le Goualher et al. (1997). An energy based registration method (Hellier et al., 2001), which will be called photometric registration method in this paper, makes it possible to incorporate the matching of cortical sulci. The local sparse similarity and the photometric similarity are, thus, expressed in a unified framework. We show the benefits of cortical constraints on a database of 18 subjects, with global and local assessment of the registration. This new registration scheme has also been evaluated on functional magnetoencephalography data. We show that the anatomically constrained registration leads to a substantial reduction of the intersubject functional variability.     

Automatic construction of multiple-object three-dimensional statistical shape models: application to cardiac modeling

A novel method is introduced for the generation of landmarks for three-dimensional (3-D) shapes and the construction of the corresponding 3-D statistical shape models. Automatic landmarking of a set of manual segmentations from a class of shapes is achieved by 1) construction of an atlas of the class, 2) automatic extraction of the landmarks from the atlas, and 3) subsequent propagation of these landmarks to each example shape via a volumetric nonrigid registration technique using multiresolution B-spline deformations. This approach presents some advantages over previously published methods: it can treat multiple-part structures and requires less restrictive assumptions on the structure's topology. In this paper, we address the problem of building a 3-D statistical shape model of the left and right ventricle of the heart from 3-D magnetic resonance images. The average accuracy in landmark propagation is shown to be below 2.2 mm. This application demonstrates the robustness and accuracy of the method in the presence of large shape variability and multiple objects.     

Estimation of mouse organ locations through registration of a statistical mouse atlas with micro-CT images

Micro-CT is widely used in preclinical studies of small animals. Due to the low soft-tissue contrast in typical studies, segmentation of soft tissue organs from noncontrast enhanced micro-CT images is a challenging problem. Here, we propose an atlas-based approach for estimating the major organs in mouse micro-CT images. A statistical atlas of major trunk organs was constructed based on 45 training subjects. The statistical shape model technique was used to include inter-subject anatomical variations. The shape correlations between different organs were described using a conditional Gaussian model. For registration, first the high-contrast organs in micro-CT images were registered by fitting the statistical shape model, while the low-contrast organs were subsequently estimated from the high-contrast organs using the conditional Gaussian model. The registration accuracy was validated based on 23 noncontrast-enhanced and 45 contrast-enhanced micro-CT images. Three different accuracy metrics (Dice coefficient, organ volume recovery coefficient, and surface distance) were used for evaluation. The Dice coefficients vary from 0.45 ± 0.18 for the spleen to 0.90 ± 0.02 for the lungs, the volume recovery coefficients vary from 0.96 ± 0.10 for the liver to 1.30 ± 0.75 for the spleen, the surface distances vary from 0.18 ± 0.01 mm for the lungs to 0.72 ± 0.42 mm for the spleen. The registration accuracy of the statistical atlas was compared with two publicly available single-subject mouse atlases, i.e., the MOBY phantom and the DIGIMOUSE atlas, and the results proved that the statistical atlas is more accurate than the single atlases. To evaluate the influence of the training subject size, different numbers of training subjects were used for atlas construction and registration. The results showed an improvement of the registration accuracy when more training subjects were used for the atlas construction. The statistical atlas-based registration was also compared with the thin-plate spline based deformable registration, commonly used in mouse atlas registration. The results revealed that the statistical atlas has the advantage of improving the estimation of low-contrast organs.     

A primal sketch of the cortex mean curvature: a morphogenesis based approach to study the variability of the folding patterns

In this paper, we propose a new representation of the cortical surface that may be used to study the cortex folding process and to recover some putative stable anatomical landmarks called sulcal roots usually buried in the depth of adult brains. This representation is a primal sketch derived from a scale space computed for the mean curvature of the cortical surface. This scale-space stems from a diffusion equation geodesic to the cortical surface. The primal sketch is made up of objects defined from mean curvature minima and saddle points. The resulting sketch aims first at highlighting significant elementary cortical folds, second at representing the fold merging process during brain growth. The relevance of the framework is illustrated by the study of central sulcus sulcal roots from antenatal to adult age. Some results are proposed for ten different brains. Some preliminary results are also provided for superior temporal sulcus.     

Diffeomorphic brain registration under exhaustive sulcal constraints

The alignment and normalization of individual brain structures is a prerequisite for group-level analyses of structural and functional neuroimaging data. The techniques currently available are either based on volume and/or surface attributes, with limited insight regarding the consistent alignment of anatomical landmarks across individuals. This article details a global, geometric approach that performs the alignment of the exhaustive sulcal imprints (cortical folding patterns) across individuals. This DIffeomorphic Sulcal-based COrtical (DISCO) technique proceeds to the automatic extraction, identification and simplification of sulcal features from T1-weighted Magnetic Resonance Image (MRI) series. These features are then used as control measures for fully-3-D diffeomorphic deformations. Quantitative and qualitative evaluations show that DISCO correctly aligns the sulcal folds and gray and white matter volumes across individuals. The comparison with a recent, iconic diffeomorphic approach (DARTEL) highlights how the absence of explicit cortical landmarks may lead to the misalignment of cortical sulci. We also feature DISCO in the automatic design of an empirical sulcal template from group data. We also demonstrate how DISCO can efficiently be combined with an image-based deformation (DARTEL) to further improve the consistency and accuracy of alignment performances. Finally, we illustrate how the optimized alignment of cortical folds across subjects improves sensitivity in the detection of functional activations in a group-level analysis of neuroimaging data.     

Extracting line representations of sulcal and gyral patterns in MR images of the human brain

This paper describes automatic procedures for extracting sulcal and gyral patterns from magnetic resonance (MR) images of the human brain. Specifically, we present three algorithms for the extraction of gyri, sulci, and sulcal fundi. These algorithms yield highly condensed line representations which can be used to describe the individual properties of the neocortical surface. The algorithms consist of a sequence of image analysis steps applied directly to the volumetric image data without requiring intermediate data representations such as surfaces or three-dimensional renderings. Previous studies have mostly focused on the extraction of surface representations, rather than line representations of cortical structures. We believe that line representations provide a valuable alternative to surface representations.     

Automated extraction and variability analysis of sulcalneuroanatomy

Systematic mapping of the variability in cortical sulcal anatomy is an area of increasing interest which presents numerous methodological challenges. To address these issues, we have implemented sulcal extraction and assisted labeling (SEAL) to automatically extract the two-dimensional (2-D) surface ribbons that represent the median axis of cerebral sulci and to neuroanatomically label these entities. To encode the extracted three-dimensional (3-D) cortical sulcal schematic topography (CSST) we define a relational graph structure composed of two main features: vertices (representing sulci) and arcs (representing the relationships between sulci). Vertices contain a parametric representation of the surface ribbon buried within the sulcus. Points on this surface are expressed in stereotaxic coordinates (i.e., with respect to a standardized brain coordinate system). For each of these vertices, we store length, depth, and orientation as well as anatomical attributes (e.g., hemisphere, lobe, sulcus type, etc.). Each arc stores the 3-D location of the junction between sulci as well as a list of its connecting sulci. Sulcal labeling is performed semiautomatically by selecting a sulcal entity in the CSST and selecting from a menu of candidate sulcus names. In order to help the user in the labeling task, the menu is restricted to the most likely candidates by using priors for the expected sulcal spatial distribution. These priors, i.e., sulcal probabilistic maps, were created from the spatial distribution of 34 sulci traced manually on 36 different subjects. Given these spatial probability maps, the user is provided with the likelihood that the selected entity belongs to a particular sulcus. The cortical structure representation obtained by SEAL is suitable to extract statistical information about both the spatial and the structural composition of the cerebral cortical topography. This methodology allows for the iterative construction of a successively more complete statistical models of the cerebral topography containing spatial distributions of the most important structures, their morphometrics, and their structural components.     

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

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

Automated extraction of the cortical sulci based on a supervised learning approach

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

Automatic construction of 3-D statistical deformation models of the brain using nonrigid registration

In this paper, we show how the concept of statistical deformation models (SDMs) can be used for the construction of average models of the anatomy and their variability. SDMs are built by performing a statistical analysis of the deformations required to map anatomical features in one subject into the corresponding features in another subject. The concept of SDMs is similar to statistical shape models (SSMs) which capture statistical information about shapes across a population, but offers several advantages over SSMs. First, SDMs can be constructed directly from images such as three-dimensional (3-D) magnetic resonance (MR) or computer tomography volumes without the need for segmentation which is usually a prerequisite for the construction of SSMs. Instead, a nonrigid registration algorithm based on free-form deformations and normalized mutual information is used to compute the deformations required to establish dense correspondences between the reference subject and the subjects in the population class under investigation. Second, SDMs allow the construction of an atlas of the average anatomy as well as its variability across a population of subjects. Finally, SDMs take the 3-D nature of the underlying anatomy into account by analysing dense 3-D deformation fields rather than only information about the surface shape of anatomical structures. We show results for the construction of anatomical models of the brain from the MR images of 25 different subjects. The correspondences obtained by the nonrigid registration are evaluated using anatomical landmark locations and show an average error of 1.40 mm at these anatomical landmark positions. We also demonstrate that SDMs can be constructed so as to minimize the bias toward the chosen reference subject.     

Improved labeling of subcortical brain structures in atlas-based segmentation of magnetic resonance images

Precise labeling of subcortical structures plays a key role in functional neurosurgical applications. Labels from an atlas image are propagated to a patient image using atlas-based segmentation. Atlas-based segmentation is highly dependent on the registration framework used to guide the atlas label propagation. This paper focuses on atlas-based segmentation of subcortical brain structures and the effect of different registration methods on the generated subcortical labels. A single-step and three two-step registration methods appearing in the literature based on affine and deformable registration algorithms in the ANTS and FSL algorithms are considered. Experiments are carried out with two atlas databases of IBSR and LPBA40. Six segmentation metrics consisting of Dice overlap, relative volume error, false positive, false negative, surface distance, and spatial extent are used for evaluation. Segmentation results are reported individually and as averages for nine subcortical brain structures. Based on two statistical tests, the results are ranked. In general, among four different registration strategies investigated in this paper, a two-step registration consisting of an initial affine registration followed by a deformable registration applied to subcortical structures provides superior segmentation outcomes. This method can be used to provide an improved labeling of the subcortical brain structures in MRIs for different applications.     

Joint Sulcal Detection on Cortical Surfaces With Graphical Models and Boosted Priors

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

Automatic matching of homologous histological sections

The role of neuroanatomical atlases is undergoing a significant redefinition as digital atlases become available. These have the potential to serve as more than passive guides and to hold the role of directing segmentation and multimodal fusion of experimental data. Key elements needed to support these new tasks are registration algorithms. For images derived from histological procedures, the need is for techniques to map the two-dimensional (2-D) images of the sectional material into the reference atlas which may be a full three-dimensional (3-D) data set or one consisting of a series of 2-D images. A variety of 2-D-2-D registration methods are available to align experimental images with the atlas once the corresponding plane of section through the atlas has been identified. Methods to automate the identification of the homologous plane, however, have not been previously reported. Here, the authors use the external section contour to drive the identification and registration procedure. For this purpose, the authors model the contours by B-splines because of their attractive properties the most important of which are: (1) smoothness and continuity; (2) local controllability which implies that local changes in shape are confined to the B-spline parameters local to that change; (3) shape invariance under affine transformation, which means that the affine transformed curve is still a B-spline whose control points are related to the object control points through the transformation. The authors present a fast algorithm for estimating the control points of the B-spline which is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure that depends directly on the parameters of the B-spline. Performance tests are reported using histological material from rat brains     

Hamilton-Jacobi skeleton on cortical surfaces

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

A Geometry-Driven Optical Flow Warping for Spatial Normalization of Cortical Surfaces

Spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences, thereby allowing for group analysis to be carried out. The work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold. The geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework. A multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain, creating the desired normalization. The partial differential equation that carries out the warping is implemented in a Euclidean framework in order to facilitate a multiresolution strategy, thereby permitting large deformations between the two surfaces. The technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces. A quantitative comparison between our proposed surface-based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface-based spatial normalization performs better in matching homologous cortical anatomies.      

Brain surface conformal parameterization using Riemann surface structure

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