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22
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 50 (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.
A Framework For Computational Anatomy
, 2002
"... The rapid collection of brain images from healthy and diseased subjects has stimulated the development of powerful mathematical algorithms to compare, pool and average brain data across whole populations. Brain structure is so complex and variable that new approaches in computer vision, partial diff ..."
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Cited by 36 (15 self)
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The rapid collection of brain images from healthy and diseased subjects has stimulated the development of powerful mathematical algorithms to compare, pool and average brain data across whole populations. Brain structure is so complex and variable that new approaches in computer vision, partial differential equations, and statistical field theory are being formulated to detect and visualize diseasespecific patterns. We present some novel mathematical strategies for computational anatomy, focusing on the creation of populationbased brain atlases. These atlases describe how the brain varies with age, gender, genetics, and over time. We review applications in Alzheimer's disease, schizophrenia and brain development, outlining some current challenges in the field.
Large deformation diffeomorphic metric mapping of vector fields
 IEEE Trans. Med. Imag
, 2005
"... This paper proposes a method to match diffusion tensor magnetic resonance images (DTMRI) through the large deformation diffeomorphic metric mapping of vector fields, focusing on the fiber orientations, considered as unit vector fields on the image volume. We study a suitable action of diffeomorphis ..."
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Cited by 25 (9 self)
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This paper proposes a method to match diffusion tensor magnetic resonance images (DTMRI) through the large deformation diffeomorphic metric mapping of vector fields, focusing on the fiber orientations, considered as unit vector fields on the image volume. We study a suitable action of diffeomorphisms on such vector fields, and provide an extension of the Large Deformation Diffeomorphic Metric Mapping framework to this type of dataset, resulting in optimizing for geodesics on the space of diffeomorphisms connecting two images. Two different distance function of vector fields are considered. Existence of the minimizers under smoothness assumptions on the compared vector fields is proved, and coarse to fine hierarchical strategies are detailed, to reduce both ambiguities and computation load. This is illustrated by numerical experiments on DTMRI heart and brain images. 1.
Spatial Normalization and Averaging of Diffusion Tensor MRI Data Sets
, 2002
"... Diffusion tensor magnetic resonance imaging (DTMRI) is unique in providing information about both the structural integrity and the orientation of white matter fibers in vivo and, through “tractography”, revealing the trajectories of white matter tracts. DTMRI is therefore a promising technique for ..."
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Cited by 20 (1 self)
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Diffusion tensor magnetic resonance imaging (DTMRI) is unique in providing information about both the structural integrity and the orientation of white matter fibers in vivo and, through “tractography”, revealing the trajectories of white matter tracts. DTMRI is therefore a promising technique for detecting differences in white matter architecture between different subject populations. However, while studies involving analyses of group averages of scalar quantities derived from DTMRI data have been performed, as yet there have been no similar studies involving the whole tensor. Here we present the first step towards realizing such a study, i.e., the spatial normalization of whole tensor data sets. The approach is illustrated by spatial normalization of 10 DTMRI data sets to a standard
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 15 (1 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
Similarity Measures for Matching Diffusion Tensor Images
 In Proceedings of the British Machine Vision Conference (BMVC
, 1999
"... In this paper, we discuss matching of diffusion tensor (DT) MRIs of the human brain. Issues concerned with matching and transforming these complex images are discussed. A number of similarity measures are proposed, based on indices derived from the DT, the DT itself and the DT deviatoric. Each m ..."
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Cited by 14 (1 self)
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In this paper, we discuss matching of diffusion tensor (DT) MRIs of the human brain. Issues concerned with matching and transforming these complex images are discussed. A number of similarity measures are proposed, based on indices derived from the DT, the DT itself and the DT deviatoric. Each measure is used to drive an elastic matching algorithm applied to the task of registration of 3D images of the human brain. The performance of the various similarity measures is compared empirically by use of several quality of match measures computed over a pair of matched images. Results indicate that the best matches are obtained from a Euclidean difference measure using the full DT. 1 Introduction Diffusion tensor (DT) imaging is a recent innovation in magnetic resonance imaging (MRI), [1]. In DT imaging, the measurement acquired at each voxel in an image volume is a symmetric second order tensor, which describes the local water diffusion properties of the material being imaged. Th...
Statistical Morphometry in Neuroanatomy
, 2001
"... The scientific aim of computational neuroanatomy using magnetic resonance imaging (MRI) is to quantify inter and intrasubject morphological variabilities. A unified statistical frame work for analyzing temporally varying brain morphology is presented. Based on the math ematical framework of diff ..."
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Cited by 8 (1 self)
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The scientific aim of computational neuroanatomy using magnetic resonance imaging (MRI) is to quantify inter and intrasubject morphological variabilities. A unified statistical frame work for analyzing temporally varying brain morphology is presented. Based on the math ematical framework of differential geometry, the deformation of the brain is modeled and key morphological descriptors such as length, area, volume dilatation and curvature change are computed. To increase the signaltonoise ratio, Gaussian kernel smoothing is applied to 3D images. For 2D curved cortical surface, diffusion smoothing, which generalizes Gaus sian kernel smoothing, has been developed. Afterwards, statistical inference is based on the excursion probability of random fields defined on manifolds.
DiffusionTensor Image Registration
"... In this chapter, we introduce the problem of registering diffusion tensor magnetic resonance (DTMR) images. The registration task for these images is made challenging by the orientational information they contain, which is affected by the registration transformation. This information about orient ..."
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Cited by 4 (1 self)
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In this chapter, we introduce the problem of registering diffusion tensor magnetic resonance (DTMR) images. The registration task for these images is made challenging by the orientational information they contain, which is affected by the registration transformation. This information about orientation and other aspects of the diffusion tensor are exploited in the development of similarity measures with which to guide DTMR image registration, and the current stateoftheart is reviewed. The chapter concludes with a discussion of some outstanding issues and future avenues for research in diffusion tensor registration.
A New Algorithm for Generating Quadrilateral Meshes and Its Application to FEBased Image Registration
 In Proceedings of the 12th International Meshing Roundtable
, 2003
"... The use of finite element (FE) analysis in the simulation of physical phenomena over the human body has necessitated the construction of meshes from images. Despite the availability of several tools for generating meshes for FEbased applications, most cannot deal directly with the raw pixelwise re ..."
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Cited by 3 (2 self)
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The use of finite element (FE) analysis in the simulation of physical phenomena over the human body has necessitated the construction of meshes from images. Despite the availability of several tools for generating meshes for FEbased applications, most cannot deal directly with the raw pixelwise representation of image data. Additionally, some are optimized for the construction of much simpler shapes than those encountered within the human body. In this work, we introduce a new algorithm to obtain strictly convex quadrilateral meshes of bounded size from triangulations of polygonal regions with or without polygonal holes. We present an approach to construct quadrilateral meshes from segmented images using the aforementioned algorithm, and a quantitative analysis of the quality of the meshes generated by our algorithm with respect to the performance of a FEbased image registration method that takes image meshes as input.