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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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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.
Mapping brain maturation
 Trends Neurosci. 2006
"... Human brain maturation is a complex, lifelong process that can now be examined in detail using neuroimaging techniques. Ongoing projects scan subjects longitudinally with structural magnetic resonance imaging (MRI), enabling the timecourse and anatomical sequence of development to be reconstructed ..."
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Cited by 33 (1 self)
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Human brain maturation is a complex, lifelong process that can now be examined in detail using neuroimaging techniques. Ongoing projects scan subjects longitudinally with structural magnetic resonance imaging (MRI), enabling the timecourse and anatomical sequence of development to be reconstructed. Here, we review recent progress on imaging studies of development. We focus on cortical and subcortical changes observed in healthy children, and contrast them with abnormal developmental changes in earlyonset schizophrenia, fetal alcohol syndrome, attentiondeficithyperactivity disorder (ADHD) and Williams syndrome. We relate these structural changes to the cellular processes that underlie them, and to cognitive and behavioral changes occurring throughout childhood and adolescence. Introduction The dynamic course of brain maturation is one of the most fascinating aspects of the human condition. Although brain change and adaptation are part of a lifelong process, the earliest phases of maturation during fetal development and childhood are perhaps the most dramatic and important. Indeed, much of the potential and many of the vulnerabilities of the brain might, in part, depend on the first two decades of life. The cortex and subcortical graymatter nuclei develop during fetal life in a carefully orchestrated sequence of cell proliferation, migration and maturation. This leads to a human brain with w100 billion neurons at birth. However, the brain of a newborn child is only onequarter to onethird of its adult volume, and it continues to grow and specialize according to a precise genetic program, with modifications driven by environmental influences, both positive and negative. With stimulation and experience, the dendritic branching of neurons greatly increases, as do the numbers of synaptic connections. As layers of insulating lipids are laid down on axons through the process of myelination, the conduction speed of fibers that interconnect different brain regions increases w100fold. This exuberant increase in brain connections is followed by an enigmatic process of dendritic 'pruning' and synapse elimination, which leads to a more efficient set of connections that are continuously remodeled throughout life.
Optimization of surface registrations using beltrami holomorphic flow
 J. Sci. Comput
"... In shape analysis, finding an optimal 11 correspondence between surfaces within a large class of admissible bijective mappings is of great importance. Such process is called surface registration. The difficulty lies in the fact that the space of all surface diffeomorphisms is a complicated function ..."
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In shape analysis, finding an optimal 11 correspondence between surfaces within a large class of admissible bijective mappings is of great importance. Such process is called surface registration. The difficulty lies in the fact that the space of all surface diffeomorphisms is a complicated functional space, making exhaustive search for the best mapping challenging. To tackle this problem, we propose a simple representation of bijective surface maps using Beltrami coefficients (BCs), which are complexvalued functions defined on surfaces with supreme norm less than 1. Fixing any 3 points on a pair of surfaces, there is a 11 correspondence between the set of surface diffeomorphisms between them and the set of BCs. Hence, every bijective surface map can be represented by a unique BC. Conversely, given a BC, we can reconstruct the unique surface map associated to it using the Beltrami Holomorphic flow (BHF) method. Using BCs to represent surface maps is advantageous because it is a much simpler functional space, which captures many essential features of a surface map. By adjusting BCs, we equivalently adjust surface diffeomorphisms to obtain the optimal map with desired properties. More specifically, BHF gives us the variation of the associated map under the variation of BC. Using this, a variational problem over the space of surface diffeomorphisms can be easily reformulated into a variational problem over the space of BCs. This makes the minimization procedure much easier. More importantly, the diffeomorphic property is always preserved. We test our method on synthetic examples and real medical applications. Experimental results demonstrate the effectiveness of our proposed algorithm for surface registration. Index Terms Beltrami coefficient, Beltrami holomorphic flow, surface diffeomorphism, surface registration, shape analysis, optimization 1.
Optimized Conformal Surface Registration with Shapebased Landmark Matching ∗
"... Abstract. Surface registration, which transforms different sets of surface data into one common reference space, is an important process which allows us to compare or integrate the surface data effectively. If a nonrigid transformation is required, surface registration is commonly done by parameteri ..."
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Abstract. Surface registration, which transforms different sets of surface data into one common reference space, is an important process which allows us to compare or integrate the surface data effectively. If a nonrigid transformation is required, surface registration is commonly done by parameterizing the surfaces onto a simple parameter domain, such as the unit square or sphere. In this work, we are interested in looking for meaningful registrations between surfaces through parameterizations, using prior features in the form of landmark curves on the surfaces. In particular, we generate optimized conformal parameterizations which match landmark curves exactly with shapebased correspondences between them. We propose a variational method to minimize a compound energy functional that measures the harmonic energy of the parameterization maps and the shape dissimilarity between mapped points on the landmark curves. The novelty is that the computed maps are guaranteed to align the landmark features consistently and give a shapebased diffeomorphism between the landmark curves. We achieve this by intrinsically modeling our search space of maps as flows of smooth vector fields that do not flow across the landmark curves. By using the local surface geometry on the curves to define a shape measure, we compute registrations that ensure consistent correspondences between anatomical features. We test our algorithm on synthetic surface data. An application of our model to medical imaging research is shown, using experiments on brain cortical surfaces, with anatomical (sulcal) landmarks delineated, which show that our computed maps give a shapebased alignment of the sulcal curves without significantly impairing conformality. This ensures correct averaging and comparison of data across subjects.
Geometric Surface and Brain Warping via Geodesic Minimizing Lipschitz Extensions
 MATHEMATICAL FOUNDATIONS OF COMPUTATIONAL ANATOMY (MFCA'06)
, 2006
"... Based on the notion of Minimizing Lipschitz Extensions and its connection with the infinity Laplacian, a theoretical and computational framework for geometric nonrigid surface warping, and in particular the nonlinear registration of brain imaging data, is presented in this paper. The basic concept i ..."
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Cited by 3 (1 self)
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Based on the notion of Minimizing Lipschitz Extensions and its connection with the infinity Laplacian, a theoretical and computational framework for geometric nonrigid surface warping, and in particular the nonlinear registration of brain imaging data, is presented in this paper. The basic concept is to compute a map between surfaces that minimizes a distortion measure based on geodesic distances while respecting the provided boundary conditions. In particular, the global Lipschitz constant of the map is minimized. This framework allows generic boundary conditions to be applied and direct surfacetosurface warping. It avoids the need for intermediate maps that flatten the surface onto the plane or sphere, as is commonly done in the literature on surfacebased nonrigid registration. The presentation of the framework is complemented with examples on synthetic geometric phantoms and cortical surfaces extracted from human brain MRI scans.
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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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
3D SURFACE MATCHING WITH MUTUAL INFORMATION AND RIEMANN SURFACE STRUCTURES
"... Many medical imaging applications require the computation of dense correspondence vector fields that match one surface with another. Surfacebased registration is useful for tracking brain change, registering functional imaging data from multiple subjects, and for creating statistical shape models o ..."
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Many medical imaging applications require the computation of dense correspondence vector fields that match one surface with another. Surfacebased registration is useful for tracking brain change, registering functional imaging data from multiple subjects, and for creating statistical shape models of anatomy. To avoid the need for a large set of manuallydefined landmarks to constrain these surface correspondences, we developed an algorithm to automate the matching of surface features. It extends the mutual information method to automatically match general 3D surfaces (including surfaces with a branching topology). We use diffeomorphic flows to optimally align the Riemann surface structures of two surfaces. First, we use holomorphic 1forms to induce consistent conformal grids on both surfaces. High genus surfaces are mapped to a set of rectangles in the Euclidean plane, and closed genuszero surfaces are mapped to the sphere. Next, we compute stable geometric features (mean curvature and the conformal factor) and pull them back as scalar fields onto the 2D parameter domains. Mutual information is used as a cost functional to drive a fluid flow in the parameter domain that optimally aligns these surface features. A diffeomorphic surfacetosurface mapping is then recovered that matches anatomy in 3D. Lastly, we present a spectral method that ensures that the grids induced on the target surface remain conformal when pulled through the correspondence field. Using the chain rule, we express the gradient of the mutual information between surfaces in the conformal basis of the source surface. This finitedimensional linear space generates all conformal reparameterizations of the surface. Illustrative experiments show the method applied to hippocampal surface registration, a key step in subcortical shape analysis in Alzheimer’s disease and schizophrenia.
Combination of Brain Conformal Mapping and Landmarks: A Variational Approach,” Computer Graphics and Imaging 2005
"... To compare and integrate brain data, data from multiple subjects are typically mapped into a canonical space. One method to do this is to conformally map cortical surfaces to the sphere. It is well known that any genus zero Riemann surface can be mapped conformally to a sphere. Since the cortical su ..."
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To compare and integrate brain data, data from multiple subjects are typically mapped into a canonical space. One method to do this is to conformally map cortical surfaces to the sphere. It is well known that any genus zero Riemann surface can be mapped conformally to a sphere. Since the cortical surface of the brain is a genus zero surface, conformal mapping offers a convenient method to parameterize cortical surfaces without angular distortion, generating an orthogonal grid on the cortex that locally preserves the metric. To compare cortical surfaces more effectively, it is advantageous to adjust the conformal parameterizations to match consistent anatomical features across subjects. This matching of cortical patterns improves the alignment of data across subjects, although it is more challenging to create a consistent conformal (orthogonal) parameterization of anatomy across subjects when landmarks are constrained to lie at specific locations in the spherical parameter space. Here we propose a new method, based on a new energy functional, to optimize the conformal parameterization of cortical surfaces by using landmarks. Experimental results on a dataset of 40 brain hemispheres showed that the landmark mismatch energy can be significant reduced while effectively preserving conformality. The key advantage of this conformal parameterization approach is that any local adjustments of the mapping to match landmarks do not affect the conformality of the mapping significantly. We also examined how the parameterization changes with different weighting factors. As expected, the landmark matching error can be reduced if it is more heavily penalized, but conformality is progressively reduced.
Hierarchical Framework for Shape Correspondence
, 2013
"... Detecting similarity between nonrigid shapes is one of the fundamental problems in computer vision. In order to measure the similarity the shapes must first be aligned. As opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations, reflections and ..."
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Cited by 1 (1 self)
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Detecting similarity between nonrigid shapes is one of the fundamental problems in computer vision. In order to measure the similarity the shapes must first be aligned. As opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations, reflections and translations, nonrigid alignment is not easily parameterized. Majority of the methods addressing this problem boil down to a minimization of a certain distortion measure. The complexity of a matching process is exponential by nature, but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth twomanifolds. Here we model the shapes using both local and global structures, employ these to construct a quadratic dissimilarity measure, and provide a hierarchical framework for minimizing it to obtain sparse set of corresponding points. These correspondences may serve as an initialization for dense linear correspondence search.