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Wallace H. Coulter Department of Biomedical Engineering
Wallace H. Coulter Department of Biomedical Engineering
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ItemFiltered Multitensor Tractography(Georgia Institute of Technology, 201009) Malcolm, James G. ; Shenton, Martha E. ; Rathi, YogeshWe describe a technique that uses tractography to drive the local fiber model estimation. Existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by those previous. To do this we perform tractography within a filter framework and use a discrete mixture of Gaussian tensors to model the signal. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Using two and threefiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.

ItemAffine Registration of label maps in Label Space(Georgia Institute of Technology, 201004) Rathi, Yogesh ; Malcolm, James G. ; Bouix, Sylvain ; Tannenbaum, Allen R. ; Shenton, Martha E.Two key aspects of coupled multiobject shape analysis and atlas generation are the choice of representation and subsequent registration methods used to align the sample set. For example, a typical brain image can be labeled into three structures: grey matter, white matter and cerebrospinal fluid. Many manipulations such as interpolation, transformation, smoothing, or registration need to be performed on these images before they can be used in further analysis. Current techniques for such analysis tend to trade off performance between the two tasks, performing well for one task but developing problems when used for the other. This article proposes to use a representation that is both flexible and well suited for both tasks. We propose to map object labels to vertices of a regular simplex, e.g. the unit interval for two labels, a triangle for three labels, a tetrahedron for four labels, etc. This representation, which is routinely used in fuzzy classification, is ideally suited for representing and registering multiple shapes. On closer examination, this representation reveals several desirable properties: algebraic operations may be done directly, label uncertainty is expressed as a weighted mixture of labels (probabilistic interpretation), interpolation is unbiased toward any label or the background, and registration may be performed directly. We demonstrate these properties by using label space in a gradient descent based registration scheme to obtain a probabilistic atlas. While straightforward, this iterative method is very slow, could get stuck in local minima, and depends heavily on the initial conditions. To address these issues, two fast methods are proposed which serve as coarse registration schemes following which the iterative descent method can be used to refine the results. Further, we derive an analytical formulation for direct computation of the “group mean” from the parameters of pairwise registration of all the images in the sample set. We show results on richly labeled 2D and 3D data sets.

ItemDeform PFMT: Particle Filter With Mode Tracker for Tracking Nonaffine Contour Deformations(Georgia Institute of Technology, 201004) Vaswani, Namrata ; Rathi, Yogesh ; Yezzi, Anthony ; Tannenbaum, Allen R.We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deforming, each, or at least most, contour points can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters (PF) for large dimensional problems is impractically expensive. However, in most real problems, at any given time, most of the contour deformation occurs in a small number of dimensions ("effective basis space") while the residual deformation in the rest of the state space ("residual space") is small. This property enables us to apply the particle filtering with mode tracking (PFMT) idea that was proposed for such large dimensional problems in recent work. Since most contour deformation is low spatial frequency, we propose to use the space of deformation at a subsampled set of locations as the effective basis space. The resulting algorithm is called deform PFMT. It requires significant modifications compared to the original PFMT because the space of contours is a nonEuclidean infinite dimensional space.

ItemFiltered Tractography: State estimation in a constrained subspace(Georgia Institute of Technology, 20090924) Malcolm, James G. ; Shenton, Martha E. ; Rathi, YogeshWe describe amethod of deterministic tractography using modelbased estimation that remains constrained to the subspace of valid tensor mixture models. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model.We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a weighted mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Further, we modify the Kalman filter to enforce model constraints, i.e. positive eigenvalues and convex weights, thereby constraining it to a subspace of allowable model parameters. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach significantly improves the angular resolution at crossings and branchings while consistently estimating the mixture weights. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization. We conclude by applying unsupervised clustering to provide sidebyside comparison of the models.

ItemThe Effect of Local Fiber Model On Population Studies(Georgia Institute of Technology, 20090924) Malcolm, James G. ; Kubicki, Marek ; Shenton, Martha E. ; Rathi, YogeshDiffusion tensor imaging has made it possible to evaluate the organization and coherence of white matter fiber tracts. Hence, it has been used in many population studies, most notably, to find abnormalities in schizophrenia. To date, most population studies analyzing fiber tracts have used a single tensor as the local fiber model. While robust, this model is known to be a poor fit in regions of crossing or branching pathways. Nevertheless, the effect of using better alternative models on population studies has not been studied. The goal of this paper is to compare white matter abnormalities as revealed by twotensor and singletensor models. To this end, we compare three different regions of the brain from two populations: schizophrenics and normal controls. Preliminary results demonstrate that regions with significant statistical difference indicated using onetensor model do not necessarily match those using the twotensor model and viceversa. We demonstrate this effect using various tensor measures.

ItemFiltered Tractography: Validation on a Physical Phantom(Georgia Institute of Technology, 20090924) Malcolm, James G. ; Shenton, Martha E. ; Rathi, YogeshThis note summarizes a technique that uses tractography to drive the local fiber model estimation. Existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we perform tractography within a filter framework and use a discrete mixture of Gaussian tensors to model the signal. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. We applied this technique to a phantom simulating several complex pathway interactions and highlight tracts passing through several prescribed seed positions.

ItemNeural Tractography Using An Unscented Kalman Filter(Georgia Institute of Technology, 2009) Malcolm, James G. ; Shenton, Martha E. ; Rathi, YogeshWe describe a technique to simultaneously estimate a local neural fiber model and trace out its path. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization.

ItemLabel Space: A Coupled Multishape Representation(Georgia Institute of Technology, 200809) Malcolm, James G. ; Rathi, Yogesh ; Shenton, Martha E. ; Tannenbaum, Allen R.Richly labeled images representing several substructures of an organ occur quite frequently in medical images. For example, a typical brain image can be labeled into grey matter, white matter or cerebrospinal fluid, each of which may be subdivided further. Many manipulations such as interpolation, transformation, smoothing, or registration need to be performed on these images before they can be used in further analysis. In this work, we present a novel multishape representation and compare it with the existing representations to demonstrate certain advantages of using the proposed scheme. Specifically, we propose label space, a representation that is both flexible and well suited for coupled multishape analysis. Under this framework, object labels are mapped to vertices of a regular simplex, e.g. the unit interval for two labels, a triangle for three labels, a tetrahedron for four labels, etc. This forms the basis of a convex linear structure with the property that all labels are equally spaced. We will demonstrate that this representation has several desirable properties: algebraic operations may be performed directly, label uncertainty is expressed equivalently as a weighted mixture of labels or in a probabilistic manner, and interpolation is unbiased toward any label or the background. In order to demonstrate these properties, we compare label space to signed distance maps as well as other implicit representations in tasks such as smoothing, interpolation, registration, and principal component analysis.

ItemA Framework for Image Segmentation Using Shape Models and Kernel Space Shape Priors(Georgia Institute of Technology, 200808) Dambreville, Samuel ; Rathi, Yogesh ; Tannenbaum, Allen R.Segmentation involves separating an object from the background in a given image. The use of image information alone often leads to poor segmentation results due to the presence of noise, clutter or occlusion. The introduction of shape priors in the geometric active contour (GAC) framework has proved to be an effective way to ameliorate some of these problems. In this work, we propose a novel segmentation method combining image information with prior shape knowledge, using levelsets. Following the work of Leventon et al., we propose to revisit the use of PCA to introduce prior knowledge about shapes in a more robust manner. We utilize kernel PCA (KPCA) and show that this method outperforms linear PCA by allowing only those shapes that are close enough to the training data. In our segmentation framework, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description permits to fully take advantage of the Kernel PCA methodology and leads to promising segmentation results. In particular, our shapedriven segmentation technique allows for the simultaneous encoding of multiple types of shapes, and offers a convincing level of robustness with respect to noise, occlusions, or smearing.

ItemSegmenting Images Analytically in Shape Space(Georgia Institute of Technology, 200802) Rathi, Yogesh ; Dambreville, Samuel ; Niethammer, Marc ; Malcolm, James G. ; Levitt, James ; Tannenbaum, Allen R.This paper presents a novel analytic technique to perform shapedriven segmentation. In our approach, shapes are represented using binary maps, and linear PCA is utilized to provide shape priors for segmentation. Intensity based probability distributions are then employed to convert a given test volume into a binary map representation, and a novel energy functional is proposed whose minimum can be analytically computed to obtain the desired segmentation in the shape space. We compare the proposed method with the loglikelihood based energy to elucidate some key differences. Our algorithm is applied to the segmentation of brain caudate nucleus and hippocampus from MRI data, which is of interest in the study of schizophrenia and Alzheimer's disease. Our validation (we compute the Hausdorff distance and the DICE coefficient between the automatic segmentation and groundtruth) shows that the proposed algorithm is very fast, requires no initialization and outperforms the loglikelihood based energy.