Segmentation of images with separating layers by fuzzy c-means and convex optimization

Shafei, Behrang; Steidl, Gabriele

doi:10.1016/j.jvcir.2012.02.006

Cited by 21 publications

(19 citation statements)

References 31 publications

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“…In order to overcome the problem, convex relaxation approaches [7,14,45] and the graph cut method [27] were proposed. There are also many other models related to the Chan-Vese model [16,49], for example, the twophase segmentation algorithms in [19,52,53] and multiphase segmentation algorithms in [3,8,21,32,33,34,35,47,48,54]. Specifically, in [33], the piecewise constant Mumford-Shah model was convexified by using fuzzy membership functions.…”

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confidence: 99%

“…Another nice aspect is that there is no need to specify K in the first stage, i.e., before finding g. We can obtain any K-phase segmentation (K ≥ 2) by choosing (K − 1) thresholds after g is computed in the first stage. In contrast, multiphase methods such as those in [3,8,21,32,33,34,35,45,48,54] require K to be given first; and, if K changes, the minimization problem has to be solved again.…”

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confidence: 99%

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A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford--Shah Model and Thresholding

Cai¹,

Chan²,

Zeng³

2013

SIAM J. Imaging Sci.

191

243

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Abstract. The Mumford-Shah model is one of the most important image segmentation models and has been studied extensively in the last twenty years. In this paper, we propose a two-stage segmentation method based on the Mumford-Shah model. The first stage of our method is to find a smooth solution g to a convex variant of the Mumford-Shah model. Once g is obtained, then in the second stage the segmentation is done by thresholding g into different phases. The thresholds can be given by the users or can be obtained automatically using any clustering methods. Because of the convexity of the model, g can be solved efficiently by techniques like the split-Bregman algorithm or the Chambolle-Pock method. We prove that our method is convergent and that the solution g is always unique. In our method, there is no need to specify the number of segments K (K ≥ 2) before finding g. We can obtain any K-phase segmentations by choosing (K − 1) thresholds after g is found in the first stage, and in the second stage there is no need to recompute g if the thresholds are changed to reveal different segmentation features in the image. Experimental results show that our two-stage method performs better than many standard two-phase or multiphase segmentation methods for very general images, including antimass, tubular, MRI, noisy, and blurry images.

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confidence: 99%

A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford--Shah Model and Thresholding

Cai¹,

Chan²,

Zeng³

2013

SIAM J. Imaging Sci.

191

243

View full text Add to dashboard Cite

show abstract

“…Many of the initial segmentation models focused on two-class segmentation such as the active contour approach [12,31] and the Chan-Vese model [15]. Later multi-class segmentation models followed such as [4,8,14,17,30,41,51,33,44,53,58,61]. In this paper, we focus on supervised multi-class segmentation considering single images as well as collections of images.…”

Section: Introductionmentioning

confidence: 99%

Supervised and transductive multi-class segmentation using p-Laplacians and RKHS methods

Kang

Shafei

Steidl

2014

Journal of Visual Communication and Image Representation

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Abstract. This paper considers supervised multi-class image segmentation: from a labeled set of pixels in one image, we learn the segmentation and apply it to the rest of the image or to other similar images. We study approaches with p-Laplacians, (vector-valued) Reproducing Kernel Hilbert Spaces (RKHSs) and combinations of both. In all approaches we construct segment membership vectors. In the p-Laplacian model the segment membership vectors have to fulfill a certain probability simplex constraint. Interestingly, we could prove that this is not really a constraint in the case p = 2 but is automatically fulfilled. While the 2-Laplacian model gives a good general segmentation, the case of the 1-Laplacian tends to neglect smaller segments. The RKHS approach has the benefit of fast computation. This direction is motivated by image colorization, where a given dab of color is extended to a nearby region of similar features or to another image. The connection between colorization and multi-class segmentation is explored in this paper with an application to medical image segmentation. We further consider an improvement using a combined method. Each model is carefully considered with numerical experiments for validation, followed by medical image segmentation at the end.

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“…Thus we first segment the carbon, silicon carbide, and silicon components applying a recently developed method [6] that exploits the fact that Si and C react to form the SiC layer. The new segmentation method is based on convex optimization incorporating spatial regularity.…”

Section: Introductionmentioning

confidence: 99%

Microstructural analysis of a C/SiC ceramic based on the segmentation of X-ray phase contrast tomographic data

Wirjadi

Rack

Liebscher

et al. 2014

International Journal of Materials Research

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This paper is dedicated to the analysis of 3D data of carbon fiber reinforced silicon carbide ceramics. In the production process of C/SiC, a porous carbon preform reinforced with bundles of carbon fibers is infiltrated with liquid silicon at approximately 1 500 °C. The reaction between liquid silicon and carbon creates a layer of silicon carbide while the silicon vanishes almost completely. This material is able to withstand extremely high temperatures and it is extremely tough with respect to fracture. To increase the efficiency of the costly and time consuming production process, methods for monitoring the quality of the material are helpful. For instance, the thickness of the silicon carbide layer is a valuable measure. Moreover, due to different coefficients of thermal expansion of the components, typically cracks appear during the production process. For effective analysis 3D high resolution image data are necessary that can be acquired by synchrotron computed tomography. In a first image processing step, we segment the 3D image data with a convex optimization approach incorporating spatial regularity. Further, we work on the detection of cracks using an eigenvalue analysis of the 3D Hessian matrix determined in each pixel

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Segmentation of images with separating layers by fuzzy c-means and convex optimization

Cited by 21 publications

References 31 publications

A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford--Shah Model and Thresholding

A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford--Shah Model and Thresholding

Supervised and transductive multi-class segmentation using p-Laplacians and RKHS methods

Microstructural analysis of a C/SiC ceramic based on the segmentation of X-ray phase contrast tomographic data

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