Results 1  10
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18
Mapping cortical change in Alzheimer’s disease, brain development, and schizophrenia
, 2004
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Computational anatomy: Shape, growth, and atrophy comparison via diffeomorphisms
 NeuroImage
, 2004
"... Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa I. The observable images are the output of medical imaging devices. There are three components that CA examine ..."
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Cited by 62 (2 self)
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Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g a G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(d) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.
An Extension of the ICP Algorithm for Modeling Nonrigid Objects with Mobile Robots
"... The iterative closest point (ICP) algorithm [2] is a popular method for modeling 3D objects from range data. The classical ICP algorithm rests on a rigid surface assumption. Building on recent work on nonrigid object models [5, 16, 9] , this paper presents an ICP algorithm capable of modeling nonrig ..."
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Cited by 46 (6 self)
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The iterative closest point (ICP) algorithm [2] is a popular method for modeling 3D objects from range data. The classical ICP algorithm rests on a rigid surface assumption. Building on recent work on nonrigid object models [5, 16, 9] , this paper presents an ICP algorithm capable of modeling nonrigid objects, where individual scans may be subject to local deformations. We describe an integrated mathematical framework for simultaneously registering scans and recovering the surface configuration. To tackle the resulting...
The role of image registration in brain mapping
, 2001
"... Image registration is a key step in a great variety of biomedical imaging applications. It provides the ability to geometrically align one dataset with another, and is a prerequisite for all imaging applications that compare datasets across subjects, imaging modalities, or across time. Registration ..."
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Cited by 38 (0 self)
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Image registration is a key step in a great variety of biomedical imaging applications. It provides the ability to geometrically align one dataset with another, and is a prerequisite for all imaging applications that compare datasets across subjects, imaging modalities, or across time. Registration algorithms also enable the pooling and comparison of experimental findings across laboratories, the construction of populationbased brain atlases, and the creation of systems to detect group patterns in structural and functional imaging data. We review the major types of registration approaches used in brain imaging today. We focus on their conceptual basis, the underlying mathematics, and their strengths and weaknesses in different contexts. We describe the major goals of registration, including data fusion, quantification of change, automated image segmentation and labeling, shape measurement, and pathology detection. We indicate that registration algorithms have great potential when used in conjunction with a digital brain atlas, which acts as a reference system in which brain images can be compared for statistical analysis. The resulting armory of registration approaches is fundamental to medical image analysis, and in a brain mapping context provides a means to elucidate clinical, demographic, or functional trends in the anatomy or physiology of the brain.
Large Deformation Diffeomorphic Metric Curve Mapping
 INT J COMPUT VIS
, 2008
"... We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space R d. Curves are first represented as vectorvalued measures, which incorporate bot ..."
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Cited by 29 (3 self)
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We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space R d. Curves are first represented as vectorvalued measures, which incorporate both location and the first order geometric structure of the curves. Then, a Hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves. We describe a discretized version of this, in which discrete sequences of points along the curve are represented by vectorvalued functionals. This gives a convenient and practical way to define a matching functional for curves. We derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in R 2 and R 3. Behaviors of the curve mapping are discussed using 2D curves. The applications to shape classification is shown and
Spherical Demons: Fast Diffeomorphic LandmarkFree Surface Registration
 IEEE TRANSACTIONS ON MEDICAL IMAGING. 29(3):650–668, 2010
, 2010
"... 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. B ..."
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Cited by 25 (5 self)
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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 160k nodes requires less than 5 minutes when warping the atlas and less than 3 minutes when warping the subject on a Xeon 3.2GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmarkfree 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 invivo cortical surfaces and (2) Brodmann area localization in exvivo cortical surfaces.
Validating cortical surface analysis of medial prefrontal cortex,”
 NeuroImage,
, 2001
"... This paper describes cortical analysis of 19 high resolution MRI subvolumes of medial prefrontal cortex (MPFC), a region that has been implicated in major depressive disorder. An automated Bayesian segmentation is used to delineate the MRI subvolumes into cerebrospinal fluid (CSF), gray matter (GM) ..."
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Cited by 13 (4 self)
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This paper describes cortical analysis of 19 high resolution MRI subvolumes of medial prefrontal cortex (MPFC), a region that has been implicated in major depressive disorder. An automated Bayesian segmentation is used to delineate the MRI subvolumes into cerebrospinal fluid (CSF), gray matter (GM), white matter (WM), and partial volumes of either CSF/GM or GM/WM. The intensity value at which there is equal probability of GM and GM/WM partial volume is used to reconstruct MPFC cortical surfaces based on a 3D isocontouring algorithm. The segmented data and the generated surfaces are validated by comparison with hand segmented data and semiautomated contours, respectively. The L 1 distances between Bayesian and hand segmented data are 0.050.10 (n ؍ 5). Fifty percent of the voxels of the reconstructed surface lie within 0.120.28 mm (n ؍ 14) from the semiautomated contours. Cortical thickness metrics are generated in the form of frequency of occurrence histograms for GM and WM labelled voxels as a function of their position from the cortical surface. An algorithm to compute the surface area of the GM/WM interface of the MPFC subvolume is described. These methods represent a novel approach to morphometric chacterization of regional cortex features which may be important in the study of psychiatric disorders such as major depression.
Surface fluid registration of conformal representation: Application to detect disease . . .
 NEUROIMAGE
, 2013
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An Optimal Control Approach for Deformable Registration
"... This paper addresses largedisplacementdiffeomorphic mapping registration from an optimal control perspective. This viewpoint leads to two complementary formulations. One approach requires the explicit computation of coordinate maps, whereas the other is formulated strictly in the image domain (thu ..."
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Cited by 3 (1 self)
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This paper addresses largedisplacementdiffeomorphic mapping registration from an optimal control perspective. This viewpoint leads to two complementary formulations. One approach requires the explicit computation of coordinate maps, whereas the other is formulated strictly in the image domain (thus making it also applicable to manifolds which require multiple coordinate charts). We discuss their intrinsic relation as well as the advantages and disadvantages of the two approaches. Further, we propose a novel formulation for unbiased image registration, which naturally extends to the case of timeseries of images. We discuss numerical implementation details and carefully evaluate the properties of the alternative algorithms. 1.
Brain Mapping with the Ricci Flow Conformal Parameterization and Multivariate Statistics on Deformation Tensors
"... Abstract. By solving the Yamabe equation with the discrete surface Ricci flow method, we can conformally parameterize a multiple boundary surface by a multihole disk. The resulting parameterizations do not have any singularities and they are intrinsic and stable. For applications in brain mapping r ..."
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Cited by 3 (1 self)
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Abstract. By solving the Yamabe equation with the discrete surface Ricci flow method, we can conformally parameterize a multiple boundary surface by a multihole disk. The resulting parameterizations do not have any singularities and they are intrinsic and stable. For applications in brain mapping research, first, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves. Secondly, we conformally parameterize each cortical surface using a multihole disk. Intersubject cortical surface matching is performed by solving a constrained harmonic map in the canonical parameter domain. To map group differences in cortical morphometry, we then compute a manifold version of Hotelling’s T 2 test on the Jacobian matrices. Permutation testing was used to estimate statistical significance. We studied brain morphology in 21 patients with Williams Syndrome (WE) and 21 matched healthy control subjects with the proposed method. The results demonstrate our algorithm’s potential power to effectively detect group differences on cortical surfaces. 1