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62
Unified segmentation
, 2005
"... A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and ..."
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Cited by 324 (12 self)
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A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps. A strategy for optimising the model parameters is described, along with the requisite partial derivatives of the objective function.
Population shape regression from random design data
- IN: PROC. OF ICCV 2007
, 2007
"... Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, and in particular it is applicable to the study of anatomical growth and shape change. When the underlying process can be modeled by parameters in a Euclidean s ..."
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Cited by 79 (15 self)
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Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, and in particular it is applicable to the study of anatomical growth and shape change. When the underlying process can be modeled by parameters in a Euclidean space, classical regression techniques [13, 34] are applicable and have been studied extensively. However, recent work suggests that attempts to describe anatomical shapes using flat Euclidean spaces undermines our ability to represent natural biological variability [9, 11]. In this paper we develop a method for regression analysis of general, manifold-valued data. Specifically, we extend Nadaraya-Watson kernel regression by recasting the regression problem in terms of Fréchet expectation. Although this method is quite general, our driving problem is the study anatomical shape change as a function of age from random design image data. We demonstrate our method by analyzing shape change in the brain from a random design dataset of MR images of 89 healthy adults ranging in age from 22 to 79 years. To study the small scale changes in anatomy, we use the infinite dimensional manifold of diffeomorphic transformations, with an associated metric. We regress a representative anatomical shape, as a function of age, from this population.
Mapping cortical change in Alzheimer’s disease, brain development, and schizophrenia
, 2004
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Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors
"... Abstract—This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical temp ..."
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Cited by 44 (10 self)
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Abstract—This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling’s 2 test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry. Index Terms—Brain, image analysis, Lie groups, magnetic resonance imaging (MRI), statistics. I.
Large deformation diffeomorphism and momentum based hippocampal shape discrimination in dementia of the Alzheimer type
- IEEE TRANS. MED. IMAG
, 2007
"... In large-deformation diffeomorphic metric mapping (LDDMM), the diffeomorphic matching of images are modeled as evolution in time, or a flow, of an associated smooth velocity vector field controlling the evolution. The initial momentum parameterizes the whole geodesic and encodes the shape and form o ..."
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Cited by 25 (1 self)
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In large-deformation diffeomorphic metric mapping (LDDMM), the diffeomorphic matching of images are modeled as evolution in time, or a flow, of an associated smooth velocity vector field controlling the evolution. The initial momentum parameterizes the whole geodesic and encodes the shape and form of the target image. Thus, methods such as principal component analysis (PCA) of the initial momentum leads to analysis of anatomical shape and form in target images without being restricted to smalldeformation assumption in the analysis of linear displacements. We apply this approach to a study of dementia of the Alzheimer type (DAT). The left hippocampus in the DAT group shows significant shape abnormality while the right hippocampus shows similar pattern of abnormality. Further, PCA of the initial momentum leads to correct classification of 12 out of 18 DAT subjects and 22 out of 26 control subjects.
Fluid registration of diffusion tensor images using information theory
- IEEE Trans. Med. Imaging
, 2008
"... Abstract—We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density funct ..."
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Cited by 22 (3 self)
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Abstract—We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data. Index Terms—Diffusion tensor imaging (DTI), fluid registration, high angular resolution diffusion imaging (HARDI), Kullback-Leibler divergence. I.
Statistical properties of Jacobian maps and the realization of unbiased large-deformation nonlinear image registration
- IEEE Trans. Med. Imaging
"... Abstract—Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on ..."
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Cited by 19 (5 self)
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Abstract—Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on the Jacobian map, which estimates local tissue gain or loss. Here, we provide rigorous mathematical analyses of the Jacobian maps, and use themto motivate a new numerical method to construct unbiased nonlinear image registration. First, we argue that log-arithmic transformation is crucial for analyzing Jacobian values representing morphometric differences. We then examine the statistical distributions of log-Jacobian maps by defining the Kullback–Leibler (KL) distance on material density functions arising in continuum-mechanical models. With this framework, unbiased image registration can be constructed by quantifying
Topology preserving log-unbiased nonlinear image registration: Theory and implementation
- IEEE Conference on Computer Vision and Pattern Recognition
, 2007
"... In this paper, we present a novel framework for constructing large deformation log-unbiased image registration models that generate theoretically and intuitively correct deformation maps. Such registration models do not rely on regridding and are inherently topology preserving. We apply information ..."
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Cited by 16 (5 self)
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In this paper, we present a novel framework for constructing large deformation log-unbiased image registration models that generate theoretically and intuitively correct deformation maps. Such registration models do not rely on regridding and are inherently topology preserving. We apply information theory to quantify the magnitude of deformations and examine the statistical distributions of Jacobian maps in the logarithmic space. To demonstrate the power of the proposed framework, we generalize the well known viscous fluid registration model to compute logunbiased deformations. We tested the proposed method using a pair of binary corpus callosum images, a pair of two-dimensional serial MRI images, and a set of threedimensional serial MRI brain images. We compared our results to those computed using the viscous fluid registration method, and demonstrated that the proposed method is advantageous when recovering voxel-wise maps of local tissue change. 1.
Computational models for image guided, robot-assisted and simulated medical interventions
- Proceedings of the IEEE
, 2006
"... Abstract — Medical Image Analysis plays a crucial role in the diagnosis, planning, control and follow-up of therapy. To be combined efficiently with medical robotics, Medical Image Analysis can be supported by the development of specific computational models of the human body operating at various le ..."
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Cited by 8 (5 self)
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Abstract — Medical Image Analysis plays a crucial role in the diagnosis, planning, control and follow-up of therapy. To be combined efficiently with medical robotics, Medical Image Analysis can be supported by the development of specific computational models of the human body operating at various levels. We describe in this article a hierarchy of these computational models, including the geometrical, physical and physiological levels, and illustrate their potential use in a number of advanced medical applications including image guided, robot-assisted and simulated medical interventions. We conclude this article with scientific perspectives.
SharpMean: groupwise registration guided by sharp mean image and tree-based registration
- NeuroImage
, 2011
"... Groupwise registration has become more and more popular due to its attractiveness for unbiased analysis of population data. One of the most popular approaches for groupwise registration is to iteratively calculate the group mean image and then register all subject images towards the latest estimated ..."
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Cited by 8 (3 self)
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Groupwise registration has become more and more popular due to its attractiveness for unbiased analysis of population data. One of the most popular approaches for groupwise registration is to iteratively calculate the group mean image and then register all subject images towards the latest estimated group mean image. However, its performance might be undermined by the fuzzy mean image estimated in the very beginning of groupwise registration procedure, because all subject images are far from being well-aligned at that moment. In this paper, we first point out the significance of always keeping the group mean image sharp and clear throughout the entire groupwise registration procedure, which is intuitively important but has not been explored in the literature yet. To achieve this, we resort to developing the robust mean-image estimator by the adaptive weighting strategy, where the weights are adaptive across not only the individual subject images but also all spatial locations in the image domain. On the other hand, we notice that some subjects might have large anatomical variations from the group mean image, which challenges most of the state-of-the-art registration algorithms. To ensure good registration results in each iteration, we explore the manifold of subject images and build a minimal spanning tree (MST) with the group mean image as the root of the MST. Therefore, each
