Results 1  10
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19
Snakes, Shapes, and Gradient Vector Flow
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1998
"... Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new extern ..."
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Cited by 491 (16 self)
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Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a graylevel or binary edge map derived from the image. It differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation. Using several twodimensional (2D) examples and one threedimensional (3D) example, we show that GVF has a large capture range and is able to move snakes into boundary concavities.
Gradient vector flow: A new external force for snakes
 In Proceedings of the Conference on Computer Vision and Pattern Recognition
, 1997
"... Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to concave boundaries, howevel; have limited their utility. This paper develops a new external ..."
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Cited by 137 (5 self)
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Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to concave boundaries, howevel; have limited their utility. This paper develops a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a dijhsion of the gradient vectors of a graylevel or binary edge map derived from the image. The resultant field has a large capture range and forces active contours into concave regions. Examples on simulated images and one real image are presented. 1
Tracking Leukocytes In Vivo With Shape And Size Constrained Active Contours
, 2002
"... Inflammatory disease is initiated by leukocytes (white blood cells) rolling along the inner surface Hning of small blood vessels called postcapillary venules. Studying the number and velocity of rolling leukocytes is essential to understanding and successfully treating inflammatory diseases. Potent ..."
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Cited by 44 (12 self)
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Inflammatory disease is initiated by leukocytes (white blood cells) rolling along the inner surface Hning of small blood vessels called postcapillary venules. Studying the number and velocity of rolling leukocytes is essential to understanding and successfully treating inflammatory diseases. Potential inhibitors of leukocyte recruitment can be screened by leukocyte rolling assays and successful inhibitors validated by intravital microscopy. In this paper we present an active contour or snakebased technique to automatically track the movement of the leukocytes. The novelty of the proposed method Hes in the energy functional that constrains the shape and size of the active contour. This paper introduces a significant enhancement over existing gradientbased snakes in the form of a modified gradient vector flow. Using the gradient vector flow, we can track leukocytes rolling at high speeds that are not amenable to tracking with the existing edgebased techniques. We also propose a new energy based implicit sampling method of the points on the active contour that replaces the computationally expensive explicit method. To enhance the performance of this shape and size constrained snake model we have coupled it with Kalman f'fiter, so that during coasting (when the leukocytes are completely occluded or obscured), the tracker may infer the location of the center of the leukocyte. Finally we have compared the performance of the proposed snake tracker with that of the correlation and centroidbased trackers. The proposed snake tracker results in superior performance measures such as reduced error in locating the leukocyte under tracking and improvements in the percentage of frames successfully tracked. For screening and drug validation, the tracker shows promise as an automat...
A MemoryEfficient Finite Element Method for Systems of ReactionDiffusion Equations with NonSmooth Forcing
, 2003
"... The release of calcium ions in a human heart cell is modeled by a system of reactiondi #usion equations, which describe the interaction of the chemical species and the e#ects of various cell processes on them. The release is modeled by a forcing term in the calcium equation that involves a superposi ..."
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Cited by 13 (10 self)
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The release of calcium ions in a human heart cell is modeled by a system of reactiondi #usion equations, which describe the interaction of the chemical species and the e#ects of various cell processes on them. The release is modeled by a forcing term in the calcium equation that involves a superposition of many Dirac delta functions in space; such a nonsmooth righthand side leads to divergence for many numerical methods. The calcium ions enter the cell at a large number of regularly spaced points throughout the cell; to resolve those points adequately for a cell with realistic threedimensional dimensions, an extremely fine spatial mesh is needed. A finite element method is developed that addresses the two crucial issues for this and similar applications: Convergence of the method is demonstrated in extension of the classical theory that does not apply to nonsmooth forcing functions like the Dirac delta function; and the memory usage of the method is optimal and thus allows for extremely fine threedimensional meshes with many millions of degrees of freedom, already on a serial computer. Additionally, a coarsegrained parallel implementation of the algorithm allows for the solution on meshes with yet finer resolution than possible in serial.
Merging Parametric Active Contours within Homogeneous Image Regions for MRIBased Lung Segmentation
 IEEE Transactions on Medical Imaging
, 2003
"... Inhaled hyperpolarized helium3 (or use He) gas is a new magnetic resonance (MR) contrast agent that is being used to study lung functionality. To evaluate the total lung ventilation from the hyperpolarized He MR images, it is necessary to segment the lung cavities. This is difficult to accom ..."
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Cited by 13 (7 self)
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Inhaled hyperpolarized helium3 (or use He) gas is a new magnetic resonance (MR) contrast agent that is being used to study lung functionality. To evaluate the total lung ventilation from the hyperpolarized He MR images, it is necessary to segment the lung cavities. This is difficult to accomplish using only the hyperpolarized He MR images, so traditional proton ( H) MR images are frequently obtained concurrent with the hyperpolarized He MR examination. Segmentation of the lung cavities from traditional proton ( H) MRI is a necessary first step in the analysis of hyperpolarized He MR images. In this paper, we develop an active contour model that provides a smooth boundary and accurately captures the high curvature features of the lung cavities from the H MR images. This segmentation method is the first parametric active contour model that facilitates straightforward merging of multiple contours. The proposed method of merging computes an external force field that is based on the solution of partial differential equations (PDE's) with boundary condition defined by the initial positions of the evolving contours. A theoretical connection with fluid flow in porous media and the proposed force field is established. Then by using the properties of fluid flow we prove that the proposed method indeed achieves merging and the contours stop at the object boundary as well. Experimental results involving merging in synthetic images are provided. The segmentation technique has been employed in lung H MR imaging for segmenting the total lung air space. This technology plays a key role in computing the functional air space from MR images that use hyperpolarized He gas as a contrast agent.
Absorbing Boundary Conditions for the Schrödinger Equation
 SIAM J. Sci. Comput
, 1999
"... A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artif ..."
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Cited by 8 (0 self)
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A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artificial boundary condition which can minimize the size of such subdomains is the absorbing boundary condition. The imposition of absorbing boundary conditions is a technique used to reduce the necessary spatial domain when numerically solving partial differential equations that admit traveling waves. Such absorbing boundary conditions have been extensively studied in the context of hyperbolic wave equations. In this paper, general absorbing boundary conditions will be developed for the Schrödinger equation with one spatial dimension, using group velocity considerations. Previously published absorbing boundary conditions will be shown to reduce to special cases of this absorbing boundary condition. The wellposedness of the initial boundary value problem of the absorbing boundary condition, coupled to the interior Schrödinger equation, will also be discussed. Extension of the general absorbing boundary condition to higher spatial dimensions will be demonstrated. Numerical simulations using initial single Gaussian, double Gaussian, and a narrow Gaussian pulse distributions will be given, with comparision to exact solutions, to demonstrate the reflectivity properties of various orders of the absorbing boundary condition.
CoarseGrained Parallel MatrixFree Solution of a ThreeDimensional Elliptic Prototype Problem
"... Abstract. The finite difference discretization of the Poisson equation in three dimensions results in a large, sparse, and highly structured system of linear equations. This prototype problem is used to analyze the performance of the parallel linear solver on coarsegrained clusters of workstations. ..."
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Cited by 5 (5 self)
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Abstract. The finite difference discretization of the Poisson equation in three dimensions results in a large, sparse, and highly structured system of linear equations. This prototype problem is used to analyze the performance of the parallel linear solver on coarsegrained clusters of workstations. The conjugate gradient method with a matrixfree implementation of the matrixvector product with the system matrix is shown to be optimal with respect to memory usage and runtime performance. Parallel performance studies confirm that speedup can be obtained. When only an ethernet interconnect is available, best performance is limited to up to 4 processors, since the conjugate gradient method involves several communications per iteration. Using a high performance Myrinet interconnect, excellent speedup is possible for at least up to 32 processors. These results justify the use of this linear solver as the computational kernel for the timestepping in a system of reactiondiffusion equations. 1
Quadratic Spline Collocation Methods for Systems of Elliptic PDEs
, 2001
"... We consider Quadratic Spline Collocation (QSC) methods for solving systems of two coupled linear secondorder PDEs in two dimensions. The system of PDEs is treated as one entity; no decoupling is applied. Optimal order approximation to the solution is obtained, in the sense that the convergence orde ..."
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Cited by 4 (2 self)
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We consider Quadratic Spline Collocation (QSC) methods for solving systems of two coupled linear secondorder PDEs in two dimensions. The system of PDEs is treated as one entity; no decoupling is applied. Optimal order approximation to the solution is obtained, in the sense that the convergence order of the QSC approximation is the same as the order of the quadratic spline interpolant. We study the matrix properties of the linear system arising from the discretization of systems of two PDEs by QSC. We give sufficient conditions under which the QSC linear system is uniquely solvable and the optimal order of convergence for the QSC approximation is guaranteed. We develop analytic formulae for the eigenvalues and eigenvectors of the QSC matrix from 2 x 2 Helmholtz operators with constant coefficients. Numerical results demonstrate that the QSC methods are optimal, that is, fourth order locally at certain points and third order globally, even for some problems that do not satisfy the conditions of the analysis. The QSC methods are compared to conventional secondorder discretization methods and are shown to produce smaller approximation errors in the same computation time, while they achieve the same accuracy in less time. The formulation of the optimal twostep QSC method for a 2 x 2 system of PDEs can be extended in a straightforward way to a n x n system of PDEs.
Active Contours for Cell Tracking
 in Proc. Fifth IEEE Southwest Symp. on Image Analysis and Interpretation
, 2002
"... This paper introduces an active contour or snakebased method for tracking cells within a video sequence. Specifically, we apply our cell tracking techniques to rolling leukocytes observed in vivo (in living animal) from video microscopy. The analysis of leukocyte motion reveals cues about the mechan ..."
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Cited by 4 (0 self)
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This paper introduces an active contour or snakebased method for tracking cells within a video sequence. Specifically, we apply our cell tracking techniques to rolling leukocytes observed in vivo (in living animal) from video microscopy. The analysis of leukocyte motion reveals cues about the mechanism of inflammatory disease. To attack the problem of tracking leukocytes in vivo, the proposed snake tracker utilizes shape and size information specific to the leukocytes. The principal contribution of this work lies in introducing the shape and size constraint as a geometric primitive in the parametric snake energy model. The energy functional is then minimized through the basic principles of the calculus of variations to obtain the Euler equations used in contour updating. We have developed a partial differential equation (PDE) based generalized gradient vector flow (GVF) that accommodates for contrast changes and weak cell edges. Whereas previous GVF models are sensitive to initial contour placement, the modified GVF construction with Dirichlet type boundary condition (BC) allows a snake tracker to be robust for a wide range of initial positions. Another contribution in this work is to incorporate an energy term in the snake model that eliminates the need for explicitly resampling the snake contour intermittently as performed in traditional snake evolution. Using animal experiments, we compare the accuracy of the proposed snake tracker with the correlation and centroid based tracker and show that the proposed tracker is superior in terms of increased number of frames tracked and reduced localization error.
Minimum Weight Convex Quadrangulation of a Constrained Point Set
, 1997
"... Summary: A convex quadrangulation with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and every bounded interior face is convex and has four points from S on its boundary. A ..."
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Cited by 1 (1 self)
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Summary: A convex quadrangulation with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and every bounded interior face is convex and has four points from S on its boundary. A minimum weight convex quadrangulation with respect to S is a convex quadrangulation of S such that the sum of the Euclidean lengths of the edges of the subdivision is minimised. In this extended abstract, we will present a polynomial time algorithm to determine whether a set of points S admits a convex quadrangulation if S is constrained to lie on a fixed number of nested convex polygons, where the time complexity is polynomial in the cardinality of S. This algorithm can also be used to find a minimum weight convex quadrangulation of the point set. We use a similar approach to construct a convex subdivision with respect to S using three or four points from S per face, and minimising the tota...