Diffeomorphic sulcal shape analysis for cortical surface registration (original) (raw)
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Cortical sulcal atlas construction using a diffeomorphic mapping approach
2010
We present a geometric approach for constructing shape atlases of sulcal curves on the human cortex. Sulci and gyri are represented as continuous open curves in R 3 , and their shapes are studied as elements of an infinite-dimensional sphere. This shape manifold has some nice properties -it is equipped with a Riemannian L 2 metric on the tangent space and facilitates computational analyses and correspondences between sulcal shapes. Sulcal mapping is achieved by computing geodesics in the quotient space of shapes modulo rigid rotations and reparameterizations. The resulting sulcal shape atlas is shown to preserve important local geometry inherently present in the sample population. This is demonstrated in our experimental results for deep brain sulci, where we integrate the elastic shape model into surface registration framework for a population of 69 healthy young adult subjects.
Diffeomorphic Sulcal Shape Analysis on the Cortex
IEEE Transactions on Medical Imaging, 2000
We present a diffeomorphic approach for constructing intrinsic shape atlases of sulci on the human cortex. Sulci are represented as square-root velocity functions of continuous open curves in , and their shapes are studied as functional representations of an infinite-dimensional sphere. This spherical manifold has some advantageous properties-it is equipped with a Riemannian metric on the tangent space and facilitates computational analyses and correspondences between sulcal shapes. Sulcal shape mapping is achieved by computing geodesics in the quotient space of shapes modulo scales, translations, rigid rotations, and reparameterizations. The resulting sulcal shape atlas preserves important local geometry inherently present in the sample population. The sulcal shape atlas is integrated in a cortical registration framework and exhibits better geometric matching compared to the conventional euclidean method. We demonstrate experimental results for sulcal shape mapping, cortical surface registration, and sulcal classification for two different surface extraction protocols for separate subject populations.
NeuroImage, 2011
This paper introduces a novel large deformation diffeomorphic metric mapping algorithm for whole brain registration where sulcal and gyral curves, cortical surfaces, and intensity images are simultaneously carried from one subject to another through a flow of diffeomorphisms. To the best of our knowledge, this is the first time that the diffeomorphic metric from one brain to another is derived in a shape space of intensity images and point sets (such as curves and surfaces) in a unified manner. We describe the Euler-Lagrange equation associated with this algorithm with respect to momentum, a linear transformation of the velocity vector field of the diffeomorphic flow. The numerical implementation for solving this variational problem, which involves largescale kernel convolution in an irregular grid, is made feasible by introducing a class of computationally friendly kernels. We apply this algorithm to align magnetic resonance brain data. Our whole brain mapping results show that our algorithm outperforms the image-based LDDMM algorithm in terms of the mapping accuracy of gyral/sulcal curves, sulcal regions, and cortical and subcortical segmentation. Moreover, our algorithm provides better whole brain alignment than combined volumetric and surface registration (Postelnicu et al., 2009) and hierarchical attribute matching mechanism for elastic registration (HAMMER) (Shen and Davatzikos, 2002) in terms of cortical and subcortical volume segmentation.
Multi-scale diffeomorphic cortical registration under manifold sulcal constraints
2008
Neuroimaging at the group level requires spatial normalization across individuals. This issue has been receiving considerable attention from multiple research groups. Here we suggest a surface-based geometric approach that consists in matching a set of cortical surfaces through their sulcal imprints. We provide the proof-of-concept of this approach by showing 1) how sulci may be automatically identified and simplified from T1-weighted MRI data series, and 2) how this sulcal information may be considered as landmarks for recent measure-based diffeomorphic deformation approaches. In our framework, the resulting 3D transforms are naturally applied to the entire cortical surface and MRI volumes.
NeuroImage, 2011
In this paper, we deal with a subcortical surface registration problem. Subcortical structures including hippocampi and caudates have a small number of salient features such as heads and tails unlike cortical surfaces. Therefore, it is hard, if not impossible, to perform subcortical surface registration with only such features. It is also non-trivial for neuroanatomical experts to select landmarks consistently for subcortical surfaces of different subjects. We therefore present a landmark-free approach for subcortical surface registration by measuring the amount of mesh distortion between subcortical surfaces assuming that the surfaces are represented by meshes. The input meshes can be constructed using any surface modeling tool available in the public domain since our registration method is independent of a surface modeling process. Given the source and target surfaces together with their representing meshes, the vertex positions of the source mesh are iteratively displaced while preserving the underlying surface shape in order to minimize the distortion to the target mesh. By representing each surface mesh as a point on a high-dimensional Riemannian manifold, we define a distance metric on the manifold that measures the amount of distortion from a given source mesh to the target mesh, based on the notion of isometry while penalizing triangle flipping. Under this metric, we reduce the distortion minimization problem to the problem of constructing a geodesic curve from the moving source point to the fixed target point on the manifold while satisfying the shape-preserving constraint. We adopt a multi-resolution framework to solve the problem for distortion-minimizing mapping between the source and target meshes. We validate our registration scheme through several experiments: distance metric comparison, visual validation using real data, robustness test to mesh variations, feature alignment using anatomic landmarks, consistency with previous clinical findings, and comparison with a surface-based registration method, LDDMM-surface.
3D Brain surface matching based on geodesics and local geometry
Computer Vision and Image Understanding, 2003
The non-rigid registration of surfaces is a complex and difficult task for which there are many important applications, such as comparing shape between deformable objects and comparing associated function. This paper presents a new approach for brain surface matching by determining the correspondence of 3D point sets between pairs of surfaces. The algorithm is based on shape using a combination of geodesic distance and surface curvature. There are two major procedures involved. An initial sparse set of corresponding points is first generated by matching local geometrical features. Geodesic distance interpolation is then employed hierarchically in order to capture the complex surface. By this scheme, surface correspondence and triangulation are computed simultaneously. Experiments applied to human cerebral cortical surfaces are shown to evaluate the approach. It is shown that the proposed method performs well for both surface matching and surface shape recovery.
Diffeomorphic brain registration under exhaustive sulcal constraints
Medical Imaging, …, 2011
Group-level analysis of structural and functional neuroimaging data requires the spatial coregistration and normalization of individual brain structures. The highly-variable topography and topology of the cortical surface across individuals makes it a geometrical object of paramount complexity to align. Most existing registration approaches focus either on volume or surface attributes, with limited appraisal of and/or constraints on the consistent inter-individual alignment of anatomical landmarks. We propose a global, geometric approach that performs an explicit, diffeomorphic registration of individual folding patterns (the so-called, sulcal imprints). This DIffeomorphic Sulcal-based COrtical (DISCO) technique proceeds to a quasi-exhaustive automatic extraction, identification and simplification of sulcal features from T1-weighted Magnetic Resonance Image (MRI) series. These features then serve as control measures of subsequent, full 3D diffeomorphic deformations. We show quantitative and qualitative evaluations that indicate that DISCO correctly aligns both 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 critical misalignments of sulci. We feature DISCO in the automatic design of an empirical sulcal template from group data. We also show how deformation constraints can be pooled from the global cortical folding information extracted from all individuals in the group. Finally, we illustrate how a better alignment of folds across subjects enhances sensitivity in the detection of functional activations in a group-level analysis of neuroimaging data.
Registration of cortical surfaces using sulcal landmarks for group analysis of MEG data
International Congress Series, 2007
We present a method to register individual cortical surfaces to a surface-based brain atlas or canonical template using labeled sulcal curves as landmark constraints. To map one cortex smoothly onto another, we minimize a thin-plate spline energy defined on the surface by solving the associated partial differential equations (PDEs). By using covariant derivatives in solving these PDEs, we compute the bending energy with respect to the intrinsic geometry of the 3D surface rather than evaluating it in the flattened metric of the 2D parameter space. This covariant approach greatly reduces the confounding effects of the surface parameterization on the resulting registration.
Proceedings - Society of Photo-Optical Instrumentation Engineers, 2013
In this work, we present a novel cortical correspondence method with application to the macaque brain. The correspondence method is based on sulcal curve constraints on a spherical deformable registration using spherical harmonics to parameterize the spherical deformation. Starting from structural MR images, we first apply existing preprocessing steps: brain tissue segmentation using the Automatic Brain Classification tool (ABC), as well as cortical surface reconstruction and spherical parametrization of the cortical surface via Constrained Laplacian-based Automated Segmentation with Proximities (CLASP). Then, initial correspondence between two cortical surfaces is automatically determined by a curve labeling method using sulcal landmarks extracted along sulcal fundic regions. Since the initial correspondence is limited to sulcal regions, we use spherical harmonics to extrapolate and regularize this correspondence to the entire cortical surface. To further improve the correspondence...
Multi-manifold diffeomorphic metric mapping for aligning cortical hemispheric surfaces
Neuroimage, 2010
Cortical surface-based analysis has been widely used in anatomical and functional studies because it is geometrically appropriate for the cortex. One of the main challenges in the cortical surface-based analysis is to optimize the alignment of the cortical hemispheric surfaces across individuals. In this paper, we introduce a multi-manifold large deformation diffeomorphic metric mapping (MM-LDDMM) algorithm that allows simultaneously carrying the cortical hemispheric surface and its sulcal curves from one to the other through a flow of diffeomorphisms. We present an algorithm based on recent derivation of a law of momentum conservation for the geodesics of diffeomorphic flow. Once a template is fixed, the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point on curves and surfaces along the geodesic is completely determined by the momentum at the origin. We solve for trajectories (geodesics) of the kinetic energy by computing its variation with respect to the initial momentum and by applying a gradient descent scheme. The MM-LDDMM algorithm optimizes the initial momenta encoding the anatomical variation of each individual relative to a common coordinate system in a linear space, which provides a natural scheme for shape deformation average and template (or atlas) generation. We applied the MM-LDDMM algorithm for constructing the templates for the cortical surface and 14 sulcal curves of each hemisphere using a group of 40 subjects. The estimated template shape reflects regions which are highly variable across these subjects. Compared with existing single-manifold LDDMM algorithms, such as the LDDMM-curve mapping and the LDDMM-surface mapping, the MM-LDDMM mapping provides better results in terms of surface to surface distances in five predefined regions.