New second order Mumford–Shah model based on Γ-convergence approximation for image processing

Duan, Jinming; Lu, Wenqi; Pan, Zhenkuan; Li, Bai

doi:10.1016/j.infrared.2016.04.016

Cited by 16 publications

(7 citation statements)

References 33 publications

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“…Finally we have confirmed the advantages of using the geodesic distance with some experimental results. Future works will look for further extension of selective segmentation to other frameworks such as using high order regularizers [46,13] where only incomplete theories exist.…”

Section: Discussionmentioning

confidence: 99%

A Convex Geodesic Selective Model for Image Segmentation

2018

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Selective segmentation is an important application of image processing. In contrast to global segmentation in which all objects are segmented, selective segmentation is used to isolate specific objects in an image and is of particular interest in medical imaging -permitting segmentation and review of a single organ. An important consideration is to minimise the amount of user input to obtain the segmentation; this differs from interactive segmentation in which more user input is allowed than selective segmentation. To achieve selection, we propose a selective segmentation model which uses the edge-weighted geodesic distance from a marker set as a penalty term. It is demonstrated that this edge-weighted geodesic penalty term improves on previous selective penalty terms. A convex formulation of the model is also presented, allowing arbitrary initialisation. It is shown that the proposed model is less parameter dependent and requires less user input than previous models. Further modifications are made to the edgeweighted geodesic distance term to ensure segmentation robustness to noise and blur. We can show that the overall Euler-Lagrange equation admits a unique viscosity solution. Numerical results show that the result is robust to user input and permits selective segmentations that are not possible with other models.

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Section: Discussionmentioning

confidence: 99%

A Convex Geodesic Selective Model for Image Segmentation

2018

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“…Denoising with Mumford-Shah Total Variation: Our previous research [25], [26], [33] has shown that the classical variational Mumford-Shah model [22], [24] that uses a total variation regulariser (named as MSTV model in this paper) [23] is fast and accurate and is therefore chosen to denoise microglia images. The MSTV model can smooth microglia images and preserve the edges of objects, making it easier to detect microglia in the image.…”

Section: A Segmentationmentioning

confidence: 99%

Novel Methods for Microglia Segmentation, Feature Extraction, and Classification

Ding

Pardon

Agostini

et al. 2017

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Abstract-Segmentation and analysis of histological images provides a valuable tool to gain insight into the biology and function of microglial cells in health and disease. Common image segmentation methods are not suitable for inhomogeneous histology image analysis and accurate classification of microglial activation states has remained a challenge. In this paper, we introduce an automated image analysis framework capable of efficiently segmenting microglial cells from histology images and analysing their morphology. The framework makes use of variational methods and the fast-split Bregman algorithm for image denoising and segmentation, and of multifractal analysis for feature extraction to classify microglia by their activation states. Experiments show that the proposed framework is accurate and scalable to large datasets and provides a useful tool for the study of microglial biology.Index Terms-microglia analysis, Mumford-Shah, fast split Bregman, fast Fourier transform, multifractal analysis, histology data analysis.

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“…However, the inpainting results of the model highly depend on the geometry of the inpainting region, and it also tends to blur the inpainted area [2,22]. Further, according to the numerical experimental results displayed in [1][2][3][4][5] the SOTV model tends to blur object edges for image denoising.…”

Section: Introductionmentioning

confidence: 97%

“…However, such models tend to blur the reconstructed image when discretised for numerical solution [1][2][3][4][5]. To overcome this drawback, we introduce a new tensor weighted second order (TWSO) model for image restoration.…”

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confidence: 99%

Introducing diffusion tensor to high order variational model for image reconstruction

Duan

Ward

Sibbett

et al. 2017

Digital Signal Processing

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The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk JID:YDSPR AID:2153 /FLA [m5G; v1.219; Prn:17/07/2017; 11:02] Second order total variation (SOTV) models have advantages for image restoration over their first order counterparts including their ability to remove the staircase artefact in the restored image. However, such models tend to blur the reconstructed image when discretised for numerical solution [1][2][3][4][5]. To overcome this drawback, we introduce a new tensor weighted second order (TWSO) model for image restoration. Specifically, we develop a novel regulariser for the SOTV model that uses the Frobenius norm of the product of the isotropic SOTV Hessian matrix and an anisotropic tensor. We then adapt the alternating direction method of multipliers (ADMM) to solve the proposed model by breaking down the original problem into several subproblems. All the subproblems have closed-forms and can be solved efficiently. The proposed method is compared with state-of-the-art approaches such as tensor-based anisotropic diffusion, total generalised variation, and Euler's elastica. We validate the proposed TWSO model using extensive experimental results on a large number of images from the Berkeley BSDS500. We also demonstrate that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.

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New second order Mumford–Shah model based on Γ-convergence approximation for image processing

Cited by 16 publications

References 33 publications

A Convex Geodesic Selective Model for Image Segmentation

A Convex Geodesic Selective Model for Image Segmentation

Novel Methods for Microglia Segmentation, Feature Extraction, and Classification

Introducing diffusion tensor to high order variational model for image reconstruction

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