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351
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 743 (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 199 (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
Multiview Stereo via Volumetric Graphcuts and Occlusion Robust PhotoConsistency
, 2007
"... This paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimisation using Graphcuts. Our approach is to seek the optimal partitioning of 3D space into two regions labelled as ‘object’ and ‘empty’ under a cost functional ..."
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Cited by 187 (9 self)
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This paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimisation using Graphcuts. Our approach is to seek the optimal partitioning of 3D space into two regions labelled as ‘object’ and ‘empty’ under a cost functional consisting of the following two terms: (1) A term that forces the boundary between the two regions to pass through photoconsistent locations and (2) a ballooning term that inflates the ‘object ’ region. To take account of the effect of occlusion on the first term we use an occlusion robust photoconsistency metric based on Normalised Cross Correlation, which does not assume any geometric knowledge about the reconstructed object. The globally optimal 3D partitioning can be obtained as the minimum cut solution of a weighted graph.
Automated 3D Extraction of Inner and Outer Surfaces of Cerebral Cortex from MRI
 NEUROIMAGE
, 2000
"... Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented h ..."
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Cited by 179 (17 self)
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Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented here, with two novel features. First, explicit prevention of selfintersecting surface geometries is provided, unlike conventional deformable models, which use regularization constraints to discourage but not necessarily prevent such behavior. Second, deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using modelbased constraints such as expected thickness of an anatomic surface. These two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human MR images, accurately locating the depths of the sulci, even where noise and partial volume artifacts in the image obscure the visibility of sulci. The extracted surfaces are enforced to be simple twodimensional manifolds (having the topology of a sphere), even though the data may have topological holes. This automatic 3D cortex segmentation technique has been applied to 150 normal subjects, simultaneously extracting both the gray/white and gray/cerebrospinal fluid interface from each individual. The collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter. Three alternative criteria for defining cortical thickness at each cortical location were developed and compared. These results are shown to corroborate published postmortem and in vivo measurements of cortical thickness.
A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape
 International Journal of Computer Vision
, 2007
"... Abstract. Since their introduction as a means of front propagation and their first application to edgebased segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of reg ..."
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Cited by 163 (4 self)
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Abstract. Since their introduction as a means of front propagation and their first application to edgebased segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of regionbased level set segmentation methods and clarify how they can all be derived from a common statistical framework. Regionbased segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edgebased schemes such as the classical Snakes, regionbased methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly wellsuited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals and point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.
Matching 3D Anatomical Surfaces with NonRigid Deformations using OctreeSplines
 International Journal of Computer Vision
, 1996
"... Abstract. This paper presents a new method for determining the minimal nonrigid deformation between two 3D surfaces, such as those which describe anatomical structures in 3D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method perform ..."
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Cited by 156 (2 self)
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Abstract. This paper presents a new method for determining the minimal nonrigid deformation between two 3D surfaces, such as those which describe anatomical structures in 3D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3D surfaces. 1.
Fast surface reconstruction using the level set method
 In VLSM ’01: Proceedings of the IEEE Workshop on Variational and Level Set Methods
, 2001
"... In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data ..."
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Cited by 149 (12 self)
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In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surfacelike model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
Generalized Gradient Vector Flow External Forces for Active Contours
 Signal Processing
, 1998
"... Active contours, or snakes, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. A new type of external force for active contours, called gradient vector flow (GVF) was introduced recently to address problems associated with initializat ..."
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Cited by 144 (6 self)
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Active contours, or snakes, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. A new type of external force for active contours, called gradient vector flow (GVF) was introduced recently to address problems associated with initialization and poor convergence to boundary concavities. GVF is computed as a di#usion of the gradient vectors of a graylevel or binary edge map derived from the image. In this paper, we generalize the GVF formulation to include two spatially varying weighting functions. This improves active contour convergence to long, thin boundary indentations, while maintaining other desirable properties of GVF, such as an extended capture range. The original GVF is a special case of this new generalized GVF (GGVF) model. An error analysis for active contour results on simulated test images is also presented. # 1998 Elsevier Science B.V. All rights reserved. Zusammenfassung Aktive Umrisse, oder Schlangen, we...
Segmentation and measurement of the cortex from 3D MR images using coupled surfaces propagation
 IEEE Trans. Med. Imag
, 1999
"... Abstract—The cortex is the outermost thin layer of gray matter in the brain; geometric measurement of the cortex helps in understanding brain anatomy and function. In the quantitative analysis of the cortex from MR images, extracting the structure and obtaining a representation for various measureme ..."
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Cited by 106 (2 self)
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Abstract—The cortex is the outermost thin layer of gray matter in the brain; geometric measurement of the cortex helps in understanding brain anatomy and function. In the quantitative analysis of the cortex from MR images, extracting the structure and obtaining a representation for various measurements are key steps. While manual segmentation is tedious and labor intensive, automatic reliable efficient segmentation and measurement of the cortex remain challenging problems, due to its convoluted nature. Here we present a new approach of coupledsurfaces propagation, using level set methods to address such problems. Our method is motivated by the nearly constant thickness of the cortical mantle and takes this tight coupling as an important constraint. By evolving two embedded surfaces simultaneously, each driven by its own imagederived information while maintaining the coupling, a final representation of the cortical bounding surfaces and an automatic segmentation of the cortex are achieved. Characteristics of the cortex, such as cortical surface area, surface curvature, and cortical thickness, are then evaluated. The level set implementation of surface propagation offers the advantage of easy initialization, computational efficiency, and the ability to capture deep sulcal folds. Results and validation from various experiments on both simulated and real threedimensional (3D) MR images are provided. Index Terms — Coupledsurfaces propagation, level set, 3D segmentation, volumetric layer.