Spherical demons: fast surface registration

Pearls and Pitfalls of Adaptive Optics Ophthalmoscopy in Inherited Retinal Diseases

Adaptive optics (AO) retinal imaging enables individual photoreceptors to be visualized in the clinical setting. AO imaging can be a powerful clinical tool for detecting photoreceptor degeneration at a cellular level that might be overlooked through conventional structural assessments, such as spectral-domain optical coherence tomography (SD-OCT). Therefore, AO imaging has gained significant interest in the study of photoreceptor degeneration, one of the most common causes of inherited blindness. Growing evidence supports that AO imaging may be useful for diagnosing early-stage retinal dystrophy before it becomes apparent on fundus examination or conventional retinal imaging. In addition, serial AO imaging may detect structural disease progression in early-stage disease over a shorter period compared to SD-OCT. Although AO imaging is gaining popularity as a structural endpoint in clinical trials, the results should be interpreted with caution due to several pitfalls, including the lack of standardized imaging and image analysis protocols, frequent ocular comorbidities that affect image quality, and significant interindividual variation of normal values. Herein, we summarize the current state-of-the-art AO imaging and review its potential applications, limitations, and pitfalls in patients with inherited retinal diseases.

Surface-Based Spatial Pyramid Matching of Cortical Regions for Analysis of Cognitive Performance

We propose a method to analyze the relationship between the shape of functional regions of the cortex and cognitive measures, such as reading ability and vocabulary knowledge. Functional regions on the cortical surface can vary not only in size and shape but also in topology and position relative to neighboring regions. Standard diffeomorphism-based shape analysis tools do not work well here because diffeomorphisms are unable to capture these topological differences, which include region splitting and merging across subjects. State-of-the-art cortical surface shape analyses compute derived regional properties (scalars), such as regional volume, cortical thickness, curvature, and gyrification index. However, these methods cannot compare the full extent of topological or shape differences in cortical regions. We propose icosahedral spatial pyramid matching (ISPM) of region borders computed on the surface of a sphere to capture this variation in regional topology, position, and shape. We then analyze how this variation corresponds to measures of cognitive performance. We compare our method to other approaches and find that it is indeed informative to consider aspects of shape beyond the standard approaches. Analysis is performed using a subset of 27 test/retest subjects from the Human Connectome Project in order to understand both the effectiveness and reproducibility of this method.

Symplectomorphic registration with phase space regularization by entropy spectrum pathways

PURPOSE

The ability to register image data to a common coordinate system is a critical feature of virtually all imaging studies. However, in spite of the abundance of literature on the subject and the existence of several variants of registration algorithms, their practical utility remains problematic, as commonly acknowledged even by developers of these methods.

METHODS

A new registration method is presented that utilizes a Hamiltonian formalism and constructs registration as a sequence of symplectomorphic maps in conjunction with a novel phase space regularization. For validation of the framework a panel of deformations expressed in analytical form is developed that includes deformations based on known physical processes in MRI and reproduces various distortions and artifacts typically present in images collected using these different MRI modalities.

RESULTS

The method is demonstrated on the three different magnetic resonance imaging (MRI) modalities by mapping between high resolution anatomical (HRA) volumes, medium resolution diffusion weighted MRI (DW-MRI) and HRA volumes, and low resolution functional MRI (fMRI) and HRA volumes.

CONCLUSIONS

The method has shown an excellent performance and the panel of deformations was instrumental to quantify its repeatability and reproducibility in comparison to several available alternative approaches.

Comprehensive evaluation of ten deformable image registration algorithms for contour propagation between CT and cone-beam CT images in adaptive head & neck radiotherapy

Deformable image registration (DIR) is a critical technic in adaptive radiotherapy (ART) for propagating contours between planning computerized tomography (CT) images and treatment CT/cone-beam CT (CBCT) images to account for organ deformation for treatment re-planning. To validate the ability and accuracy of DIR algorithms in organ at risk (OAR) contour mapping, ten intensity-based DIR strategies, which were classified into four categories—optical flow-based, demons-based, level-set-based and spline-based—were tested on planning CT and fractional CBCT images acquired from twenty-one head & neck (H&N) cancer patients who underwent 6~7-week intensity-modulated radiation therapy (IMRT). Three similarity metrics, i.e., the Dice similarity coefficient (DSC), the percentage error (PE) and the Hausdorff distance (HD), were employed to measure the agreement between the propagated contours and the physician-delineated ground truths of four OARs, including the vertebra (VTB), the vertebral foramen (VF), the parotid gland (PG) and the submandibular gland (SMG). It was found that the evaluated DIRs in this work did not necessarily outperform rigid registration. DIR performed better for bony structures than soft-tissue organs, and the DIR performance tended to vary for different ROIs with different degrees of deformation as the treatment proceeded. Generally, the optical flow-based DIR performed best, while the demons-based DIR usually ranked last except for a modified demons-based DISC used for CT-CBCT DIR. These experimental results suggest that the choice of a specific DIR algorithm depends on the image modality, anatomic site, magnitude of deformation and application. Therefore, careful examinations and modifications are required before accepting the auto-propagated contours, especially for automatic re-planning ART systems.

Applying tensor-based morphometry to parametric surfaces can improve MRI-based disease diagnosis

Many methods have been proposed for computer-assisted diagnostic classification. Full tensor information and machine learning with 3D maps derived from brain images may help detect subtle differences or classify subjects into different groups. Here we develop a new approach to apply tensor-based morphometry to parametric surface models for diagnostic classification. We use this approach to identify cortical surface features for use in diagnostic classifiers. First, with holomorphic 1-forms, we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so-called slit domain. Next, the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map. To analyze anatomical differences, we then analyze the full Riemannian surface metric tensors, which retain multivariate information on local surface geometry. As the number of voxels in a 3D image is large, sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy. Focusing on vertices with greatest effect sizes, we train a diagnostic classifier using the surface features selected by an L1-norm based sparse learning method. Stability selection is applied to validate the selected feature sets. We tested the algorithm on MRI-derived cortical surfaces from 42 subjects with genetically confirmed Williams syndrome and 40 age-matched controls, multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other TBM-based statistics including analysis of the Jacobian determinant and the largest eigenvalue of the surface metric. Our method also gave reasonable classification results relative to the Jacobian determinant, the pair of eigenvalues of the Jacobian matrix and volume features. This analysis pipeline may boost the power of morphometry studies, and may assist with image-based classification.

Helical mode lung 4D-CT reconstruction using Bayesian model

4D computed tomography (CT) has been widely used for treatment planning of thoracic and abdominal cancer radiotherapy. Current 4D-CT lung image reconstruction methods rely on respiratory gating to rearrange the large number of axial images into different phases, which may be subject to external surrogate errors due to poor reproducibility of breathing cycles. New image-matching-based reconstruction works better for the cine mode of 4D-CT acquisition than the helical mode because the table position of each axial image is different in helical mode and image matching might suffer from bigger errors. In helical mode, not only the phases but also the un-uniform table positions of images need to be considered. We propose a Bayesian method for automated 4D-CT lung image reconstruction in helical mode 4D scans. Each axial image is assigned to a respiratory phase based on the Bayesian framework that ensures spatial and temporal smoothness of surfaces of anatomical structures. Iterative optimization is used to reconstruct a series of 3D-CT images for subjects undergoing 4D scans. In experiments, we compared visually and quantitatively the results of the proposed Bayesian 4D-CT reconstruction algorithm with the respiratory surrogate and the image matching-based method. The results showed that the proposed algorithm yielded better 4D-CT for helical scans.

Conformal metric optimization on surface (CMOS) for deformation and mapping in Laplace-Beltrami embedding space

In this paper we develop a novel technique for surface deformation and mapping in the high-dimensional Laplace-Beltrami embedding space. The key idea of our work is to realize surface deformation in the embedding space via optimization of a conformal metric on the surface. Numerical techniques are developed for computing derivatives of the eigenvalues and eigenfunctions with respect to the conformal metric, which is then applied to compute surface maps in the embedding space by minimizing an energy function. In our experiments, we demonstrate the robustness of our method by applying it to map hippocampal atrophy of multiple sclerosis patients with depression on a data set of 109 subjects. Statistically significant results have been obtained that show excellent correlation with clinical variables. A comparison with the popular SPHARM tool has also been performed to demonstrate that our method achieves more significant results.

Surface-based TBM boosts power to detect disease effects on the brain: an N=804 ADNI study

Computational anatomy methods are now widely used in clinical neuroimaging to map the profile of disease effects on the brain and its clinical correlates. In Alzheimer's disease (AD), many research groups have modeled localized changes in hippocampal and lateral ventricular surfaces, to provide candidate biomarkers of disease progression for drug trials. We combined the power of parametric surface modeling and tensor-based morphometry to study hippocampal differences associated with AD and mild cognitive impairment (MCI) in 490 subjects (97 AD, 245 MCI, 148 controls) and ventricular differences in 804 subjects scanned as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI; 184 AD, 391 MCI, 229 controls). We aimed to show that a new multivariate surface statistic based on multivariate tensor-based morphometry (mTBM) and radial distance provides a more powerful way to detect localized anatomical differences than conventional surface-based analysis. In our experiments, we studied correlations between hippocampal atrophy and ventricular enlargement and clinical measures and cerebrospinal fluid biomarkers. The new multivariate statistics gave better effect sizes for detecting morphometric differences, relative to other statistics including radial distance, analysis of the surface tensor and the Jacobian determinant. In empirical tests using false discovery rate curves, smaller sample sizes were needed to detect associations with diagnosis. The analysis pipeline is generic and automated. It may be applied to analyze other brain subcortical structures including the caudate nucleus and putamen. This publically available software may boost power for morphometric studies of subcortical structures in the brain.

A new method to measure cortical growth in the developing brain

Folding of the cerebral cortex is a critical phase of brain development in higher mammals but the biomechanics of folding remain incompletely understood. During folding, the growth of the cortical surface is heterogeneous and anisotropic. We developed and applied a new technique to measure spatial and directional variations in surface growth from longitudinal magnetic resonance imaging (MRI) studies of a single animal or human subject. MRI provides high resolution 3D image volumes of the brain at different stages of development. Surface representations of the cerebral cortex are obtained by segmentation of these volumes. Estimation of local surface growth between two times requires establishment of a point-to-point correspondence ("registration") between surfaces measured at those times. Here we present a novel approach for the registration of two surfaces in which an energy function is minimized by solving a partial differential equation on a spherical surface. The energy function includes a strain-energy term due to distortion and an "error energy" term due to mismatch between surface features. This algorithm, implemented with the finite element method, brings surface features into approximate alignment while minimizing deformation in regions without explicit matching criteria. The method was validated by application to three simulated test cases and applied to characterize growth of the ferret cortex during folding. Cortical surfaces were created from MRI data acquired in vivo at 14 days, 21 days, and 28 days of life. Deformation gradient and Lagrangian strain tensors describe the kinematics of growth over this interval. These quantitative results illuminate the spatial, temporal, and directional patterns of growth during cortical folding.

Robust surface reconstruction via Laplace-Beltrami eigen-projection and boundary deformation

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

Setting priors and enforcing constraints on matches for nonlinear registration of meshes

We show that a simple probabilistic modelling of the registration problem for surfaces allows to solve it by using standard clustering techniques. In this framework, point-to-point correspondences are hypothesized between the two free-form surfaces, and we show how to specify priors and to enforce global constraints on these matches with only minor changes to the optimisation algorithm. The purpose of these two modifications is to increase its capture range and to obtain more realistic geometrical transformations between the surfaces. We conclude with some validation experiments and results on synthetic and real data.

A combined surface and volumetric registration (SAVOR) framework to study cortical biomarkers and volumetric imaging data

Constructing a one to one correspondence between whole brain MR image scans is a problem of critical importance in neuroimaging analyses. We present a framework to combine the strength of both surface-based and volumetric-based analyses for consistent, bijective data transfer between brain coordinate systems.

A computational model of cerebral cortex folding

The geometric complexity and variability of the human cerebral cortex have long intrigued the scientific community. As a result, quantitative description of cortical folding patterns and the understanding of underlying folding mechanisms have emerged as important research goals. This paper presents a computational 3D geometric model of cerebral cortex folding initialized by MRI data of a human fetal brain and deformed under the governance of a partial differential equation modeling cortical growth. By applying different simulation parameters, our model is able to generate folding convolutions and shape dynamics of the cerebral cortex. The simulations of this 3D geometric model provide computational experimental support to the following hypotheses: (1) Mechanical constraints of the skull regulate the cortical folding process. (2) The cortical folding pattern is dependent on the global cell growth rate of the whole cortex. (3) The cortical folding pattern is dependent on relative rates of cell growth in different cortical areas. (4) The cortical folding pattern is dependent on the initial geometry of the cortex.

A local fast marching-based diffusion tensor image registration algorithm by simultaneously considering spatial deformation and tensor orientation

It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration.

Spherical demons: fast diffeomorphic landmark-free surface registration

We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a Xeon 3.2 GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmark-free surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1) parcellation of in vivo cortical surfaces and 2) Brodmann area localization in ex vivo cortical surfaces.

Inverse-consistent surface mapping with Laplace-Beltrami eigen-features

We propose in this work a novel variational method for computing maps between surfaces by combining informative geometric features and regularizing forces including inverse consistency and harmonic energy. To tackle the ambiguity in defining homologous points on smooth surfaces, we design feature functions in the data term based on the Reeb graph of the Laplace-Beltrami eigenfunctions to quantitatively describe the global geometry of elongated anatomical structures. For inverse consistency and robustness, our method computes simultaneously the forward and backward map by iteratively solving partial differential equations (PDEs) on the surfaces. In our experiments, we successfully mapped 890 hippocampal surfaces and report statistically significant maps of atrophy rates between normal controls and patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD).

Task-optimal registration cost functions

In this paper, we propose a framework for learning the parameters of registration cost functions--such as the tradeoff between the regularization and image similiarity term--with respect to a specific task. Assuming the existence of labeled training data, we specialize the framework for the task of localizing hidden labels via image registration. We learn the parameters of the weighted sum of squared differences (wSSD) image similarity term that are optimal for the localization of Brodmann areas (BAs) in a new subject based on cortical geometry. We demonstrate state-of-the-art localization of V1, V2, BA44 and BA45.

A framework for brain registration via simultaneous surface and volume flow

Volumetric registration of brain MR images presents a challenging problem due to the wide variety of sulcal folding patterns. We present a novel volumetric registration method based on an intermediate parameter space in which the shape differences are normalized. First, we generate a 3D harmonic map of each brain volume to unit ball which is used as an intermediate space. Cortical surface features and volumetric intensity are then used to find a simultaneous surface and volume registration. We present a finite element method for the registration by using a tetrahedral volumetric mesh for registering the interior volumetric information and the corresponding triangulated mesh at the surface points. This framework aligns the convoluted sulcal folding patterns as well as the subcortical structures by allowing simultaneous flow of surface and volumes for registration. We describe the methodology and FEM implementation and then evaluate the method in terms of the overlap between segmented structures in coregistered brains.