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Deformable medical image registration: A survey
 IEEE TRANSACTIONS ON MEDICAL IMAGING
, 2013
"... Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multimodality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudin ..."
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Cited by 35 (1 self)
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Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multimodality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudinal studies, where temporal structural or anatomical changes are investigated; and iii) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.
Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal
"... Abstract. We propose a new methodology to analyze the anatomical variability of a set of longitudinal data (population scanned at several ages). This method accounts not only for the usual 3D anatomical variability (geometry of structures), but also for possible changes in the dynamics of evolution ..."
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Cited by 34 (18 self)
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Abstract. We propose a new methodology to analyze the anatomical variability of a set of longitudinal data (population scanned at several ages). This method accounts not only for the usual 3D anatomical variability (geometry of structures), but also for possible changes in the dynamics of evolution of the structures. It does not require that subjects are scanned the same number of times or at the same ages. First a regression model infers a continuous evolution of shapes from a set of observations of the same subject. Second, spatiotemporal registrations deform jointly (1) the geometry of the evolving structure via 3D deformations and (2) the dynamics of evolution via time change functions. Third, we infer from a population a prototype scenario of evolution and its 4D variability. Our method is used to analyze the morphological evolution of 2D profiles of hominids skulls and to analyze brain growth from amygdala of autistics, developmental delay and control children. 1 Methodology for Statistics on Longitudinal Data
Time sequence diffeomorphic metric mapping and parallel transport track . . .
 NEUROIMAGE 45 (2009) S51–S60
, 2009
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A Continuum Mechanical Approach to Geodesics in Shape Space
"... In this paper concepts from continuum mechanics are used to define geodesic paths in the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation. A geodesic path is defined ..."
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Cited by 11 (5 self)
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In this paper concepts from continuum mechanics are used to define geodesic paths in the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation. A geodesic path is defined as the family of shapes such that the total amount of viscous dissipation caused by an optimal material transport along the path is minimized. The approach can easily be generalized to shapes given as segment contours of multilabeled images and to geodesic paths between partially occluded objects. The proposed computational framework for finding such a minimizer is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 11 correspondence along the induced flow in shape space. When decreasing the time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the underlying shape space. If the constraint of pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional, one obtains for decreasing time step size an optical flow term controlling the transport of the shape by the underlying motion field. The method is implemented via a level set representation of shapes, and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations. The numerical relaxation of the energy is performed via an efficient multiscale procedure in space and time. Various examples for 2D and 3D shapes underline the effectiveness and robustness of the proposed approach. 1
Constructing reparametrization invariant metrics on spaces of plane curves
, 2012
"... on spaces of plane curves ..."
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A New Riemannian Setting for Surface Registration
, 2011
"... Abstract. We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic matching framework. In the latte ..."
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Cited by 8 (7 self)
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Abstract. We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic matching framework. In the latter approach a deformation is prescribed on the ambient space, which then drags along an embedded surface. In contrast our metric is defined directly on the deformation vector field and can therefore be called an inner metric. We also show how to discretize the corresponding geodesic equation and compute the gradient of the cost functional using finite elements.
Sectional Curvature in terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
"... statistics of the infinite dimensional shape manifolds). MM would like to thank Andrea Bertozzi of UCLA for her continuous advice and and support. This paper deals with the computation of sectional curvature for the manifolds of N landmarks (or feature points) in D dimensions, endowed with the Riema ..."
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Cited by 6 (5 self)
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statistics of the infinite dimensional shape manifolds). MM would like to thank Andrea Bertozzi of UCLA for her continuous advice and and support. This paper deals with the computation of sectional curvature for the manifolds of N landmarks (or feature points) in D dimensions, endowed with the Riemannian metric induced by the group action of diffeomorphisms. The inverse of the metric tensor for these manifolds (i.e. the cometric), when written in coordinates, is such that each of its elements depends on at most 2D of the ND coordinates. This makes the matrices of partial derivatives of the cometric very sparse in nature, thus suggesting solving the highly nontrivial problem of developing a formula that expresses sectional curvature in terms of the cometric and its first and second partial derivatives (we call this Mario’s formula). We apply such formula to the manifolds of landmarks and in particular we fully explore the case of geodesics on which only two points have nonzero momenta and compute the sectional curvatures of 2planes spanned by the tangents to such geodesics. The latter example gives insight to the geometry of the full manifolds of landmarks. 1
Matrixvalued Kernels for Shape Deformation Analysis
, 2013
"... The main purpose of this paper is providing a systematic study and classification of nonscalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an ..."
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Cited by 2 (0 self)
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The main purpose of this paper is providing a systematic study and classification of nonscalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an introduction to matrixvalued kernels and their relevant differential properties, we explore extensively those, that we call TRI kernels, that induce a metric on the corresponding Hilbert spaces of vector fields that is both translation and rotationinvariant. These are analyzed in an effective manner in the Fourier domain, where the characterization of RKHS of curlfree and divergencefree vector fields is particularly natural. A simple technique for constructing generic matrixvalued kernels from scalar kernels is also developed. We accompany the exposition of the theory with several examples, and provide numerical results that show the dynamics induced by different choices of TRI kernels on the manifold of labeled landmark points.
Geometry of image registration: The diffeomorphism group and momentum maps
, 2013
"... Abstract These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.1 1 ..."
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Abstract These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.1 1
R.: An invariant shape representation using the anisotropic Helmholtz equation
 MICCAI
, 2012
"... Abstract. Analyzing geometry of sulcal curves on the human cortical surface requires a shape representation invariant to Euclidean motion. We present a novel shape representation that characterizes the shape of a curve in terms of a coordinate system based on the eigensystem of the anisotropic Helmh ..."
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Abstract. Analyzing geometry of sulcal curves on the human cortical surface requires a shape representation invariant to Euclidean motion. We present a novel shape representation that characterizes the shape of a curve in terms of a coordinate system based on the eigensystem of the anisotropic Helmholtz equation. This representation has many desirable properties: stability, uniqueness and invariance to scaling and isometric transformation. Under this representation, we can find a pointwise shape distance between curves as well as a bijective smooth pointtopoint correspondence. When the curves are sampled irregularly, we also present a fast and accurate computational method for solving the eigensystem using a finite element formulation. This shape representation is used to find symmetries between corresponding sulcal shapes between cortical hemispheres. For this purpose, we automatically generate 26 sulcal curves for 24 subject brains and then compute their invariant shape representation. Leftright sulcal shape symmetry as measured by the shape representation’s metric demonstrates the utility of the presented invariant representation for shape analysis of the cortical folding pattern. 1