An adaptive finite element procedure for the image segmentation problem

Yaacobson, Fiana S.; Givoli, Dan

doi:10.1002/(sici)1099-0887(199807)14:7<621::aid-cnm174>3.0.co;2-u

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…While the use of finite-elements and adaptive strategies is not new in the image segmentation context, see e.g. [4][5][6][7][8], those methods are rather complex as they are framed in a variational formulation and their objective is different from the one proposed here: the given image is split in several parts or components that can be easily identified via the location of edges. Hence those methodologies aim at locally reconstructing the profiles of these regions, but they do not address the problem of the classification of such regions.…”

Section: Introductionmentioning

confidence: 99%

Z2-$\gamma$: an Application of Zienkiewicz-Zhu Error Estimator to Brain Tumor Detection in MR Images

Falini¹

2022

Preprint

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Brain tumors are abnormal cells growth in the brain tissues that can be cancerous, or not. In any case, they could be a very aggressive disease that should be detected as early as possible. Usually, magnetic resonance imaging (MRI) is the main tool commonly adopted by neurologists and radiologists to identify and classify any possible anomalies present in the brain anatomy. In the present work, an automatic unsupervised method called Z2-$\gamma$, based on the use of adaptive finite-elements and suitable pre-processing and post-processing techniques, is introduced. In particular, the proposed methodology is able to automatically classify whether a given MR image represents a healthy or a diseased brain and in this latter case, is able to locate the tumor area.

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Section: Introductionmentioning

confidence: 99%

Z2-$\gamma$: an Application of Zienkiewicz-Zhu Error Estimator to Brain Tumor Detection in MR Images

Falini¹

2022

Preprint

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“…In the latter case, particular attention has been devoted to the local control of the geometric features of the mesh (i.e., shape, size and orientation of the elements), by means of anisotropic elements stretched along the direction orthogonal to the gradient of the quantity of interest [44][45][46][47][48][49][50][51][52][53][54][55]. It is worth noticing that the coupling of finite element approximations and mesh adaptation in the context of image segmentation was previously explored in [56][57][58] and [59][60][61] in isotropic and anisotropic settings, respectively. Nonetheless, all the above models were devised for images featuring sharp interfaces and regions with homogeneous intensities.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information

Giacomini,

Perotto

2021

Preprint

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A finite element-based image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented. The methodology relies on a split Bregman algorithm for the minimisation of a region-based energy functional and on an anisotropic recovery-based error estimate to drive mesh adaptation. More precisely, a Bayesian energy functional is considered to account for image spatial information, ensuring that the methodology is able to identify inhomogeneous spatial patterns in complex images. In addition, the anisotropic mesh adaptation guarantees a sharp detection of the interface between background and foreground of the image, with a reduced number of degrees of freedom. The resulting split-adapt Bregman algorithm is tested on a set of real images showing the accuracy and robustness of the method, even in the presence of Gaussian, salt and pepper and speckle noise.

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On the segmentation of vascular geometries from medical images

Radaelli

Peiró

2009

Numer Methods Biomed Eng

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SUMMARYA comprehensive analysis of vascular morphology and the application of generic models of vascular biomechanics to specific patients require the ability of extracting a geometrical representation of the vascular anatomy from medical images. Owing to the wide range of clinical manifestations of vascular disease and associated imaging modalities and protocols, several segmentation methods have been proposed over the last 20 years and are available in the literature. In this paper, we review the methods of segmentation of angiographic medical images and identify major advantages and disadvantages of stateof-the-art techniques. We further discuss the performance of some of the most popular intensity-based and gradient-based methods using a set of images of peripheral by-pass grafts acquired with magnetic resonance angiography (MRA). We then propose a threshold front method for the segmentation of MRA images and assess its performance using two anatomic scale replica models, reproducing a normal and a stenotic peripheral artery. The threshold front algorithm is a simple, fast and parameter-free (still adaptive) method achieving segmentation errors below pixel resolution.

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An adaptive finite element procedure for the image segmentation problem

Cited by 8 publications

References 16 publications

Z2-$\gamma$: an Application of Zienkiewicz-Zhu Error Estimator to Brain Tumor Detection in MR Images

Z2-$\gamma$: an Application of Zienkiewicz-Zhu Error Estimator to Brain Tumor Detection in MR Images

Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information

On the segmentation of vascular geometries from medical images

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