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713
Geodesic Active Contours
, 1997
"... A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both in ..."
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Cited by 1143 (44 self)
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A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical "snakes" based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. The scheme was implemented using an efficient algorithm for curve evolution. Experimental results of applying the scheme to real images including objects with holes and medical data imagery demonstrate its power. The results may be extended to 3D object segmentation as well.
Active Contours without Edges
, 2001
"... In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy ..."
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Cited by 868 (36 self)
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In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "meancurvature flow"like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We will give a numerical algorithm using finite differences. Finally, we will present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.
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 529 (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.
Deformable models in medical image analysis: A survey
 Medical Image Analysis
, 1996
"... This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They hav ..."
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Cited by 478 (7 self)
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This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottomup) constraints derived from the image data together with (topdown) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2002
"... This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and regionbased segmentation modules under a curvebased optimization objective function. The task of supervised texture segmentation is considered to demonst ..."
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Cited by 243 (8 self)
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This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and regionbased segmentation modules under a curvebased optimization objective function. The task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework. The textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters, and analyzing their responses as multicomponent conditional probability density functions. The texture segmentation is obtained by unifying region and boundarybased information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradientdescent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution is guided by boundary and regionbased segmentation forces, and is constrained by a regularity force. The level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled. The performance of our method is demonstrated on a variety of synthetic and real textured frames.
Shock Graphs and Shape Matching
, 1998
"... We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a ..."
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Cited by 224 (35 self)
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We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Keywords: shape representation; shape matching; shock graph; shock graph grammar; subgraph isomorphism. 1 I...
Computing Geodesic Paths on Manifolds
 Proc. Natl. Acad. Sci. USA
, 1998
"... The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. A ..."
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Cited by 223 (26 self)
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The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds. 1 Introduction Sethian`s Fast Marching Method [8], is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M ) steps, where M is the total number of grid points in the domain. The technique hinges on producing numerically consistent approximations to the operators in the Eikonal equation that select the correct viscosity solution; this is done through the use of upwind nite dierence operators. The structure of this upwinding is then used to systematically construct the solution to the Eik...
Gradient flows and geometric active contour models
 in Proc. of the 5th International Conference on Computer Vision
, 1995
"... In this paper, we analyze the geometric active contour models discussed in [6, 181 from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel snake paradigm in which the feature of interes ..."
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Cited by 213 (17 self)
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In this paper, we analyze the geometric active contour models discussed in [6, 181 from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and eficiently to the desired feature. Moreover, we consider some 30 active surface models based on these ideas. 1
Topologically Adaptable Snakes
 Medical Image Analysis
, 1995
"... This paper presents a topologically adaptable snakes model for image segmentation and object representation. The model is embedded in the framework of domain subdivision using simplicial decomposition. This framework extends the geometric and topological adaptability of snakes while retaining all of ..."
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Cited by 202 (5 self)
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This paper presents a topologically adaptable snakes model for image segmentation and object representation. The model is embedded in the framework of domain subdivision using simplicial decomposition. This framework extends the geometric and topological adaptability of snakes while retaining all of the features of traditionalsnakes, such as user interaction, and overcoming many of the limitations of traditionalsnakes. By superposing a simplicial grid over the image domain and using this grid to iteratively reparameterize the deforming snakes model, the model is able to flow into complex shapes, even shapes with significant protrusions or branches, and to dynamically change topology as necessitated by the data. Snakes can be created and can split into multiple parts or seamlessly merge into other snakes. The model can also be easily converted to and from the traditional parametric snakes model representation. We apply a 2D model to various synthetic and real images in order to segment ...
Global Minimum for Active Contour Models: A Minimal Path Approach
, 1997
"... A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the ..."
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Cited by 202 (64 self)
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A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the internal regularization term in the external potential term. Our method is based on finding a path of minimal length in a Riemannian metric. We then make use of a new efficient numerical method to find this shortest path. It is shown that the proposed energy, though based only on a potential integrated along the curve, imposes a regularization effect like snakes. We explore the relation between the maximum curvature along the resulting contour and the potential generated from the image. The method is capable to close contours, given only one point on the objects’ boundary by using a topologybased saddle search routine. We show examples of our method applied to real aerial and medical images.