Cortex segmentation - a fast variational geometric approach

Goldenberg, Roman; Kimmel, Ron; Rivlin, Ehud; Rudzsky, Michael

doi:10.1109/vlsm.2001.938891

Cited by 40 publications

(54 citation statements)

References 33 publications

(14 reference statements)

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“…The method by Zeng et al (1999) has an additional drawback that the topology of the final surfaces is typically incorrect, because the geometric deformable model method it applies lacks control of surface topology. The same drawback exits in another very similar approach proposed by Goldenberg et al (2002). The method by MacDonald et al (2000) guarantees the correct surface topology by using a parametric deformable surface model and initializing it with two ellipsoidal surfaces.…”

Section: Discussionmentioning

confidence: 98%

“…These surface properties-topologically equivalent to a sphere, smooth, and having no selfintersections-are difficult to maintain simultaneously in practice. Reconstructing a smooth surface is usually accomplished by using a deformable surface model having internal btensionQ or bbendingQ forces (Dale et al, 1999;Goldenberg et al, 2002;MacDonald et al, 2000;Xu et al, 1999;Zeng et al, 1999). We follow this approach here as well.…”

Section: Introductionmentioning

confidence: 99%

“…The deforming surface in parametric deformable models, however, can easily develop self-intersections; the detection and prevention of which is usually very time-consuming (Dale et al, 1999;MacDonald et al, 2000). Methods that use geometric or level-set deformable models (Zeng et al, 1999;Goldenberg et al, 2002) automatically avoid the self-intersection problem, but the topology of the final result can be arbitrary. The present work differs from previous approaches in that we employ a new topology-preserving geometric deformable model (TGDM; Han et al, 2003), which maintains topology like parametric deformable models but retains the advantage of geometric deformable models of automatically generating simple surfaces (i.e., no selfintersections) without special computational constraints.…”

Section: Introductionmentioning

confidence: 99%

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CRUISE: Cortical reconstruction using implicit surface evolution

et al. 2004

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Segmentation and representation of the human cerebral cortex from magnetic resonance (MR) images play an important role in neuroscience and medicine. A successful segmentation method must be robust to various imaging artifacts and produce anatomically meaningful and consistent cortical representations. A method for the automatic reconstruction of the inner, central, and outer surfaces of the cerebral cortex from T1-weighted MR brain images is presented. The method combines a fuzzy tissue classification method, an efficient topology correction algorithm, and a topology-preserving geometric deformable surface model (TGDM). The algorithm is fast and numerically stable, and yields accurate brain surface reconstructions that are guaranteed to be topologically correct and free from selfintersections. Validation results on real MR data are presented to demonstrate the performance of the method. D 2004 Elsevier Inc. All rights reserved.

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Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CRUISE: Cortical reconstruction using implicit surface evolution

et al. 2004

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“…Calculus of variation [8,17] had proved that the curve C that minimize ( ) E C should satisfy the Euler equation [14]:…”

Section: An Active Contour Is a Curve ( ) ( ( ) ( ))mentioning

confidence: 99%

Digital Riemannian Geometry and Its Application

Chen¹

2013

Proceedings of the 2nd International Conference on Advances in Computer Science and Engineering

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Abstract-The key characteristic of Riemannian geometry isRiemannian metric. The most important work for the discretion of Riemannian geometry is to seek a discret representation of Riemannian metric, which forms the foundation of digital Riemannian geometry. This paper initiated the conception of Digital Riemannian geometry which imposes a Riemannian metric on a rectangle grid to make them curved and induced a weighted distance on them. The main task of Digital Riemannian geometry is to obtain quantitative information about objects in pictures with the help of a discrete Riemannian metric defined on them.

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“…Given the curve C, we denote the inside and outside of the curve as Ω c and Ω\Ω c , respectively. The energy functional E(C) for a contour C can be defined as two types of integral measures that are related via the Green theorem [7], [8]. The first functional integrates the function L(C s , C) defined on the curve and is considered as a boundary-based measure in the general form of:…”

Section: Geometric Integral Measures For Active Contoursmentioning

confidence: 99%

Medical Image Segmentation Using Level Set Method with a New Hybrid Speed Function Based on Boundary and Region Segmentation

Park

Cho

2012

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper presents a new hybrid speed function needed to perform image segmentation within the level-set framework. The proposed speed function uses both the boundary and region information of objects to achieve robust and accurate segmentation results. This speed function provides a general form that incorporates the robust alignment term as a part of the driving force for the proper edge direction of an active contour, an active region term derived from the region partition scheme, and the smoothing term for regularization. First, we use an external force for active contours as the Gradient Vector Flow field. This is computed as the diffusion of gradient vectors of a gray level edge map derived from an image. Second, we partition the image domain by progressively fitting statistical models to the intensity of each region. Here we adopt two Gaussian distributions to model the intensity distribution of the inside and outside of the evolving curve partitioning the image domain. Third, we use the active contour model that has the computation of geodesics or minimal distance curves, which allows stable boundary detection when the model's gradients suffer from large variations including gaps or noise. Finally, we test the accuracy and robustness of the proposed method for various medical images. Experimental results show that our method can properly segment low contrast, complex images. key words: image segmentation, geometric deformable model, level set method, gradient vector flow

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Cortex segmentation - a fast variational geometric approach

Abstract: Abstract

Cited by 40 publications

References 33 publications

CRUISE: Cortical reconstruction using implicit surface evolution

CRUISE: Cortical reconstruction using implicit surface evolution

Digital Riemannian Geometry and Its Application

Medical Image Segmentation Using Level Set Method with a New Hybrid Speed Function Based on Boundary and Region Segmentation

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