Global minimum for active contour models: a minimal path approach

Cohen, Laurent D.; Kimmel, Ron

doi:10.1109/cvpr.1996.517144

Cited by 329 publications

(571 citation statements)

References 53 publications

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“…A minimal path, first introduced in the isotropic (P does not depend on the orientation of the path) case [6], is a pathway minimizing the energy functional,…”

Section: Background On Minimal Path Methodsmentioning

confidence: 99%

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Tubular Anisotropy Segmentation

Benmansour

Cohen

2009

Lecture Notes in Computer Science

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Abstract. In this paper we present a new interactive method for tubular structure extraction. The main application and motivation for this work is vessel tracking in 2D and 3D images. The basic tools are minimal paths solved using the fast marching algorithm. This allows interactive tools for the physician by clicking on a small number of points in order to obtain a minimal path between two points or a set of paths in the case of a tree structure. Our method is based on a variant of the minimal path method that models the vessel as a centerline and surface. This is done by adding one dimension for the local radius around the centerline. The crucial step of our method is the definition of the local metrics to minimize. We have chosen to exploit the tubular structure of the vessels one wants to extract to built an anisotropic metric giving higher speed on the center of the vessels and also when the minimal path tangent is coherent with the vessel's direction. This measure is required to be robust against the disturbance introduced by noise or adjacent structures with intensity similar to the target vessel. We obtain promising results on noisy synthetic and real 2D and 3D images.

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“…A minimal path, first introduced in the isotropic (P does not depend on the orientation of the path) case [6], is a pathway minimizing the energy functional,…”

Section: Background On Minimal Path Methodsmentioning

confidence: 99%

“…Deschamps and Cohen [5] proposed to use the minimal path method to find the centerline. The minimal path technique introduced by Cohen and Kimmel [6] captures the global minimum curve between two points given by the user. This leads to the global minimum of an active contour energy.…”

Section: Introductionmentioning

confidence: 99%

Tubular Anisotropy Segmentation

Benmansour

Cohen

2009

Lecture Notes in Computer Science

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“…Given a 3D image I : Ω → R + and two points p 1 and p 2 , the underlying idea introduced by Cohen and Kimmel [2] is to build a potential P : Ω → R * + which takes lower values near desired features of the image I. The choice of the potential P depends on the application.…”

Section: Background On Minimal Pathsmentioning

confidence: 99%

“…Cohen and Kimmel [2] introduced an approach to globally minimize the geodesic active contour energy, provided that two endpoints of the curve are initially supplied by the user. This energy is of the form γP where the incremental costP is chosen to take lower values on the contour of the image, and γ is a path joining the two points.…”

Section: Introductionmentioning

confidence: 99%

From a Single Point to a Surface Patch by Growing Minimal Paths

Benmansour

Cohen

2009

Lecture Notes in Computer Science

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Abstract. We introduce a novel implicit approach for surface patch segmentation in 3D images starting from a single point. Since the boundary surface of an object is locally homeomorphic to a disc, we know that the boundary of a small neighboring domain intersects the surface of interest on a single closed curve. Similarly to active surfaces, we use a cost potential which penalizes image regions of low interest. First, Using a front propagation approach from the source point chosen by the user, one can see that the closed curve corresponds to valley line of the arrival time from the source point. Next, we use an implicit 3D segmentation method. It assumes that the object boundary contains two known constraining curves. In our case, the first curve is reduced to a point and the other one is automatically detected by our approach. A partial differential equation is introduced and its solution is used for segmentation. The zero level set of this solution contains valley line and the source point as well as the set of minimal paths joining them. We present a fast implementation which has been successfully applied to 3D biomedical and synthetic images.

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“…One class involves the specification of an approximate boundary, which evolves towards the correct segmentation by minimizing a cost function derived from shape priors and image information [5,6]. Another class of algorithms requires the user to specify sequential points on or near the boundary, and then the boundary is filled in between these points using a minimal path approach [7,8]. A third class of algorithms asks the user to provide seeds, or pixels within specific regions, and then uses these seeds as a basis for the segmentation [9,10].…”

Section: Introductionmentioning

confidence: 99%

Fast Random Walker with Priors Using Precomputation for Interactive Medical Image Segmentation

Andrews

Hamarneh

Saad

2010

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010

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Abstract. Updating segmentation results in real-time based on repeated user input is a reliable way to guarantee accuracy, paramount in medical imaging applications, while making efficient use of an expert's time. The random walker algorithm with priors is a robust method able to find a globally optimal probabilistic segmentation with an intuitive method for user input. However, like many other segmentation algorithms, it can be too slow for real-time user interaction. We propose a speedup to this popular algorithm based on offline precomputation, taking advantage of the time images are stored on servers prior to an analysis session. Our results demonstrate the benefits of our approach. For example, the segmentations found by the original random walker and by our new precomputation method for a given 3D image have a Dice's similarity coefficient of 0.975, yet our method runs in 1/25 th of the time.

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Global minimum for active contour models: a minimal path approach

Cited by 329 publications

References 53 publications

Tubular Anisotropy Segmentation

Tubular Anisotropy Segmentation

From a Single Point to a Surface Patch by Growing Minimal Paths

Fast Random Walker with Priors Using Precomputation for Interactive Medical Image Segmentation

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