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Volumetric Transformation of Brain Anatomy
 IEEE TRANSACTIONS ON MEDICAL IMAGING
, 1997
"... This paper presents diffeomorphic transformations of threedimensional (3D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarc ..."
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Cited by 115 (10 self)
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This paper presents diffeomorphic transformations of threedimensional (3D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial lowdimensional registration is accomplished by constraining the transformation to be in a lowdimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The highdimensional large deformations are vector fields generated via the mismatch between the template and targetimage volumes constrained to be the solution of a NavierStokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.
Group Actions, Homeomorphisms, and Matching: A General Framework
, 2001
"... This paper constructs metrics on the space of images I defined as orbits under group actions G. The groups studied include the finite dimensional matrix groups and their products, as well as the infinite dimensional diffeomorphisms examined in Trouvé (1999, Quaterly of Applied Math.) and Dupuis et a ..."
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Cited by 104 (7 self)
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This paper constructs metrics on the space of images I defined as orbits under group actions G. The groups studied include the finite dimensional matrix groups and their products, as well as the infinite dimensional diffeomorphisms examined in Trouvé (1999, Quaterly of Applied Math.) and Dupuis et al. (1998). Quaterly of Applied Math.). Leftinvariant metrics are defined on the product G × I thus allowing the generation of transformations of the background geometry as well as the image values. Examples of the application of such metrics are presented for rigid object matching with and without signature variation, curves and volume matching, and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another.
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 Review of Medical Image Registration
 Interactive imageguided neurosurgery
, 1993
"... Introduction The ever expanding gamut of medical imaging techniques provides the clinician an increasingly multifaceted view of brain function and anatomy. The information provided by the various imaging modalities is often complementary (i.e. provides separate but useful information) and synergist ..."
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Cited by 24 (0 self)
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Introduction The ever expanding gamut of medical imaging techniques provides the clinician an increasingly multifaceted view of brain function and anatomy. The information provided by the various imaging modalities is often complementary (i.e. provides separate but useful information) and synergistic (i.e. the combination of information provides useful extra information). For example, Xray computed tomography (CT) and magnetic resonance (MR) imaging exquisitely demonstrate brain anatomy but provide little functional information. Positron emission tomography (PET) and single photon emission computed tomography (SPECT) scans display aspects of brain function and allow metabolic measurements but poorly delineate anatomy. Furthermore, CT and MR images describe complementary morphologic features. For example, bone and calcifications are best seen on CT images, while softtissue structures are better differentiated by MR imaging. Clinical diagnosis and therapy planning and evaluatio
Bayesian Approach to the Brain Image Matching Problem
, 1995
"... The application of image matching to the problem of localizing structural anatomy in images of the human brain forms the specific aim of our work. The interpretation of such images is a difficult task for human observers because of the many ways in which the identity of a given structure can be obsc ..."
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Cited by 11 (3 self)
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The application of image matching to the problem of localizing structural anatomy in images of the human brain forms the specific aim of our work. The interpretation of such images is a difficult task for human observers because of the many ways in which the identity of a given structure can be obscured. Our approach is based on the assumption that a common topology underlies the anatomy of normal individuals. To the degree that this assumption holds, the localization problem can be solved by determining the mapping from the anatomy of a given individual to some referential atlas of cerebral anatomy. Previous such approaches have in many cases relied on a physical interpretation of this mapping. In this paper, we examine a more general Bayesian formulation of the image matching problem and demonstrate the approach on twodimensional magnetic resonance images.
3D Deformable Registration Using a Statistical Atlas with Applications in Medicine
, 1999
"... Registering medical images of different individuals is difficult due to inherent anatomical variabilities and possible pathologies. This thesis focuses on characterizing nonpathological variations in human brain anatomy, and applying such knowledge to achieve accurate 3D deformable registration. I ..."
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Cited by 10 (0 self)
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Registering medical images of different individuals is difficult due to inherent anatomical variabilities and possible pathologies. This thesis focuses on characterizing nonpathological variations in human brain anatomy, and applying such knowledge to achieve accurate 3D deformable registration. Inherent anatomical variations are automatically extracted by deformably registering training data with an expertsegmented 3D image, a digital brain atlas. Statistical properties of the density and geometric variations in brain anatomy are measured and encoded into the atlas to build a statistical atlas. These statistics can function as prior knowledge to guide the automatic registration process. Compared to an algorithm with no knowledge guidance, registration using the statistical atlas reduces the overall error on 40 test cases by 34%. Automatic registration between the atlas and a subject's data adapts the expert segmentation for the subject, thus reduces the monthslong manual segmentation process to minutes. Accurate and efficient segmentation of medical images enable quantitative study of anatomical differences between populations, as well as detection of abnormal variations indicative of pathologies.
Numerical Methods for HighDimensional Warps
 in Chapter in Brain Warping
, 1998
"... Introduction The fundamental problem in brain warping is to define the class of admissible spatial transformations, which must be sufficiently broad to enable a reference anatomy to fit all subject anatomies, and to develop efficient, automated algorithms for the calculation of the appropriate tran ..."
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Cited by 9 (4 self)
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Introduction The fundamental problem in brain warping is to define the class of admissible spatial transformations, which must be sufficiently broad to enable a reference anatomy to fit all subject anatomies, and to develop efficient, automated algorithms for the calculation of the appropriate transformation. In this chapter, we focus on numerical methods for inferring spatial warps that are very high in dimension in order to accommodate the complex ways in which the neuroanatomy of normal individuals can vary. Specifically, the elastic matching technique described in a previous chapter is implemented. The warps therefore correspond to deformations in the continuum mechanics, and we require methods for solving boundaryvalue problems. Two approaches are standard and each involves a different way of discretizing the problem. The finite difference method , which operates directly on the motion equations, is easy to code and computationally fast, but the fi
Combining anatomical manifold information via diffeomorphic metric mappings for studying cortical thinning of the cingulate gyrus in schizophrenia
, 2007
"... ..."
Towards Automatic Registration of Magnetic Resonance Images of the Brain Using Neural Networks. Part 2
, 1998
"... put of the detector plane of (c) is shown in (e). The entire surface is smoother than (d). The uncorrupted corner and the blurred feature give a less pronounced peak; the position of the corrupted corner cannot be detected with confidence and several likely locations are indicated by the smooth hill ..."
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Cited by 1 (1 self)
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put of the detector plane of (c) is shown in (e). The entire surface is smoother than (d). The uncorrupted corner and the blurred feature give a less pronounced peak; the position of the corrupted corner cannot be detected with confidence and several likely locations are indicated by the smooth hill. Thus, detection and placement can be improved by using sharp feature representations. The aim of this chapter is to develop feature sets with sharp contours. Three amendments to the previously proposed architecture are proposed: the use of spatial competition during training is outlined in x6.2, the selection of a subset of features from a larger set is suggested in x6.3, and the application of thresholdlike, feature postprocessing is discussed in x6.4. First a description of the three methods is given which is followed by an experimental investigation in x6.5. The new feature types of the three methods are given in
Advances in Elastic Matching Theory and its Implementation
, 1997
"... . Computational anatomy via the deformable modeling or elastic matching paradigm is gaining increased prominence in medical imaging research. Our work in atlasbased localization of neuroanatomy has progressed toward statistical approaches that subsume the original elastic matching while retaining i ..."
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Cited by 1 (0 self)
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. Computational anatomy via the deformable modeling or elastic matching paradigm is gaining increased prominence in medical imaging research. Our work in atlasbased localization of neuroanatomy has progressed toward statistical approaches that subsume the original elastic matching while retaining its practical flavor. In view of the complex geometries involved and the sparsity of image features in the localization problem, elastic matching is reformulated using variational principles to facilitate its numerical solution by the finite element method. The variational formulation in addition exposes the means by which Gibbs modeling and, thus, Bayesian analysis can be applied to the problem. In this paper, we review these developments and demonstrate the methods on MRI data, including the computation of interval estimates. 1 Introduction In 1981, Broit in collaboration with Bajcsy introduced a method for the "optimal registration of deformed images" [1], innovating the physicsbased app...