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Richard M Leahy - One of the best experts on this subject based on the ideXlab platform.

  • Geodesic Curvature flow on surfaces for automatic sulcal delineation
    International Symposium on Biomedical Imaging, 2012
    Co-Authors: Anand A Joshi, David W Shattuck, Hanna Damasio, Richard M Leahy
    Abstract:

    Sulcal folds (sulci) on the cortical surface are important landmarks of interest for investigating brain development and disease. Accurate and automatic delineation of the sulci is a challenging problem due to substantial variability in their shapes across populations. We present a Geodesic Curvature flow method for an automatic and accurate delineation of sulcal curves. We assume as input an atlas brain surface mesh on which a set of sulcal curves have been delineated. The sulcal curves are transferred to approximate corresponding locations on the subject brain using a transformation defined by an automatic surface based registration method. The locations of these curves are then refined to follow the true sulcal fundi more closely using Geodesic Curvature flow on the cortical surface. We present a level set based formulation of this flow on non-flat surfaces which represents the sulcal curves as zero level sets. We also incorporate a Curvature based weighting that drives the sulcal curves to the bottoms of the sulcal valleys in the cortical folds. The resulting PDE is discretized on a triangulated mesh using finite elements. Finally, we present a validation by comparing sets of automatically delineated sul-cal curves with sets of manually delineated sulcal curves and show that the proposed method is able to find them accurately.

  • ISBI - Geodesic Curvature flow on surfaces for automatic sulcal delineation
    Proceedings. IEEE International Symposium on Biomedical Imaging, 2012
    Co-Authors: Anand A Joshi, David W Shattuck, Hanna Damasio, Richard M Leahy
    Abstract:

    Sulcal folds (sulci) on the cortical surface are important landmarks of interest for investigating brain development and disease. Accurate and automatic delineation of the sulci is a challenging problem due to substantial variability in their shapes across populations. We present a Geodesic Curvature flow method for an automatic and accurate delineation of sulcal curves. We assume as input an atlas brain surface mesh on which a set of sulcal curves have been delineated. The sulcal curves are transferred to approximate corresponding locations on the subject brain using a transformation defined by an automatic surface based registration method. The locations of these curves are then refined to follow the true sulcal fundi more closely using Geodesic Curvature flow on the cortical surface. We present a level set based formulation of this flow on non-flat surfaces which represents the sulcal curves as zero level sets. We also incorporate a Curvature based weighting that drives the sulcal curves to the bottoms of the sulcal valleys in the cortical folds. The resulting PDE is discretized on a triangulated mesh using finite elements. Finally, we present a validation by comparing sets of automatically delineated sulcal curves with sets of manually delineated sulcal curves and show that the proposed method is able to find them accurately.

Anand A Joshi - One of the best experts on this subject based on the ideXlab platform.

  • Geodesic Curvature flow on surfaces for automatic sulcal delineation
    International Symposium on Biomedical Imaging, 2012
    Co-Authors: Anand A Joshi, David W Shattuck, Hanna Damasio, Richard M Leahy
    Abstract:

    Sulcal folds (sulci) on the cortical surface are important landmarks of interest for investigating brain development and disease. Accurate and automatic delineation of the sulci is a challenging problem due to substantial variability in their shapes across populations. We present a Geodesic Curvature flow method for an automatic and accurate delineation of sulcal curves. We assume as input an atlas brain surface mesh on which a set of sulcal curves have been delineated. The sulcal curves are transferred to approximate corresponding locations on the subject brain using a transformation defined by an automatic surface based registration method. The locations of these curves are then refined to follow the true sulcal fundi more closely using Geodesic Curvature flow on the cortical surface. We present a level set based formulation of this flow on non-flat surfaces which represents the sulcal curves as zero level sets. We also incorporate a Curvature based weighting that drives the sulcal curves to the bottoms of the sulcal valleys in the cortical folds. The resulting PDE is discretized on a triangulated mesh using finite elements. Finally, we present a validation by comparing sets of automatically delineated sul-cal curves with sets of manually delineated sulcal curves and show that the proposed method is able to find them accurately.

  • ISBI - Geodesic Curvature flow on surfaces for automatic sulcal delineation
    Proceedings. IEEE International Symposium on Biomedical Imaging, 2012
    Co-Authors: Anand A Joshi, David W Shattuck, Hanna Damasio, Richard M Leahy
    Abstract:

    Sulcal folds (sulci) on the cortical surface are important landmarks of interest for investigating brain development and disease. Accurate and automatic delineation of the sulci is a challenging problem due to substantial variability in their shapes across populations. We present a Geodesic Curvature flow method for an automatic and accurate delineation of sulcal curves. We assume as input an atlas brain surface mesh on which a set of sulcal curves have been delineated. The sulcal curves are transferred to approximate corresponding locations on the subject brain using a transformation defined by an automatic surface based registration method. The locations of these curves are then refined to follow the true sulcal fundi more closely using Geodesic Curvature flow on the cortical surface. We present a level set based formulation of this flow on non-flat surfaces which represents the sulcal curves as zero level sets. We also incorporate a Curvature based weighting that drives the sulcal curves to the bottoms of the sulcal valleys in the cortical folds. The resulting PDE is discretized on a triangulated mesh using finite elements. Finally, we present a validation by comparing sets of automatically delineated sulcal curves with sets of manually delineated sulcal curves and show that the proposed method is able to find them accurately.

Arthur W. Toga - One of the best experts on this subject based on the ideXlab platform.

  • Automated corpus callosum extraction via Laplace-Beltrami nodal parcellation and intrinsic Geodesic Curvature flows on surfaces
    Proceedings of the IEEE International Conference on Computer Vision, 2011
    Co-Authors: Rongjie Lai, Nancy Sicotte, Yonggang Shi, Arthur W. Toga
    Abstract:

    Corpus callosum (CC) is an important structure in human brain anatomy. In this work, we propose a fully automated and robust approach to extract corpus callosum from T1-weighted structural MR images. The novelty of our method is composed of two key steps. In the first step, we find an initial guess for the curve representation of CC by using the zero level set of the first nontrivial Laplace-Beltrami (LB) eigenfunction on the white matter surface. In the second step, the initial curve is deformed toward the final solution with a Geodesic Curvature flow on the white matter surface. For numerical solution of the Geodesic Curvature flow on surfaces, we represent the contour implicitly on a triangular mesh and develop efficient numerical schemes based on finite element method. Because our method depends only on the intrinsic geometry of the white matter surface, it is robust to orientation differences of the brain across population. In our experiments, we validate the proposed algorithm on 32 brains from a clinical study of multiple sclerosis disease and demonstrate that the accuracy of our results.

  • ICCV - Automated corpus callosum extraction via Laplace-Beltrami nodal parcellation and intrinsic Geodesic Curvature flows on surfaces
    2011 International Conference on Computer Vision, 2011
    Co-Authors: Rongjie Lai, Nancy Sicotte, Yonggang Shi, Arthur W. Toga
    Abstract:

    Corpus callosum (CC) is an important structure in human brain anatomy. In this work, we propose a fully automated and robust approach to extract corpus callosum from T1-weighted structural MR images. The novelty of our method is composed of two key steps. In the first step, we find an initial guess for the curve representation of CC by using the zero level set of the first nontrivial Laplace-Beltrami (LB) eigenfunction on the white matter surface. In the second step, the initial curve is deformed toward the final solution with a Geodesic Curvature flow on the white matter surface. For numerical solution of the Geodesic Curvature flow on surfaces, we represent the contour implicitly on a triangular mesh and develop efficient numerical schemes based on finite element method. Because our method depends only on the intrinsic geometry of the white matter surface, it is robust to orientation differences of the brain across population. In our experiments, we validate the proposed algorithm on 32 brains from a clinical study of multiple sclerosis disease and demonstrate that the accuracy of our results.

Xuecheng Tai - One of the best experts on this subject based on the ideXlab platform.

  • a level set formulation of Geodesic Curvature flow on simplicial surfaces
    IEEE Transactions on Visualization and Computer Graphics, 2010
    Co-Authors: Xuecheng Tai
    Abstract:

    Curvature flow (planar geometric heat flow) has been extensively applied to image processing, computer vision, and material science. To extend the numerical schemes and algorithms of this flow on surfaces is very significant for corresponding motions of curves and images defined on surfaces. In this work, we are interested in the Geodesic Curvature flow over triangulated surfaces using a level set formulation. First, we present the Geodesic Curvature flow equation on general smooth manifolds based on an energy minimization of curves. The equation is then discretized by a semi-implicit finite volume method (FVM). For convenience of description, we call the discretized Geodesic Curvature flow as dGCF. The existence and uniqueness of dGCF are discussed. The regularization behavior of dGCF is also studied. Finally, we apply our dGCF to three problems: the closed-curve evolution on manifolds, the discrete scale-space construction, and the edge detection of images painted on triangulated surfaces. Our method works for compact triangular meshes of arbitrary geometry and topology, as long as there are no degenerate triangles. The implementation of the method is also simple.

  • mesh snapping robust interactive mesh cutting using fast Geodesic Curvature flow
    Computer Graphics Forum, 2010
    Co-Authors: Juyong Zhang, Jianfei Cai, Jianmin Zheng, Xuecheng Tai
    Abstract:

    This paper considers the problem of interactively finding the cutting contour to extract components from a given mesh. Some existing methods support cuts of arbitrary shape but require careful and tedious input from the user. Others need little user input however they are sensitive to user input and need a postprocessing step to smooth the generated jaggy cutting contours. The popular geometric snake can be used to optimize the cutting contour, but it cannot deal with the topology change. In this paper, we propose a Geodesic Curvature flow based framework to overcome all these problems. Since in many cases the meaningful cutting contour on a 3D mesh is locally shortest in the sense of some weighted curve length, the Geodesic Curvature flow is an ideal tool for our problem. It evolves the cutting contour to the nearby local minimum. We should mention that the previous numerical scheme, discretized Geodesic Curvature flow (dGCF) is too slow and has not been applied to mesh segmentation. With a careful observation to dGCF, we devise here a fast computation scheme called fast Geodesic Curvature flow (FGCF), which only needs to solve a smaller and easier problem. The initial cutting contour is generated by a variant of random walks algorithm, which is very fast and gives reasonable cutting result with little user input. Experiment results on the benchmark mesh segmentation data set show that our proposed framework is robust to user input and capable of producing good results reflecting geometric features and human shape perception.

Esra Betul Koc Ozturk - One of the best experts on this subject based on the ideXlab platform.

  • Smarandache Curves According to Curves on a Spacelike Surface in Minkowski 3-Space R31
    viXra, 2014
    Co-Authors: Ufuk Öztürk, Esra Betul Koc Ozturk
    Abstract:

    In this paper, we introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on spacelike surface in Minkowski 3-space R 3 1. Also, we obtain the Sabban frame and the Geodesic Curvature of the Smarandache curves and give some characterizations on the curves when the curve is an asymptotic curve or a principal curve. And, we give an example to illustrate these curves.

  • Smarandache Curves according to Curves on a Spacelike Surface in Minkowski 3-Space
    Journal of Discrete Mathematics, 2014
    Co-Authors: Ufuk Öztürk, Esra Betul Koc Ozturk
    Abstract:

    We introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on spacelike surface in Minkowski 3-space . Also, we obtain the Sabban frame and the Geodesic Curvature of the Smarandache curves and give some characterizations on the curves when the curve α is an asymptotic curve or a principal curve. And we give an example to illustrate these curves.

  • On Pseudospherical Smarandache Curves in Minkowski 3-Space
    Journal of Applied Mathematics, 2014
    Co-Authors: Esra Betul Koc Ozturk, Ufuk Öztürk, Kazım İlarslan, Emilija Nešović
    Abstract:

    In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the Geodesic Curvature and the expressions for the Sabban frame’s vectors of spacelike and timelike pseudospherical Smarandache curves. We also prove that if the pseudospherical null straight lines are the Smarandache curves of a spacelike pseudospherical curveα, thenαhas constant Geodesic Curvature. Finally, we give some examples of pseudospherical Smarandache curves.