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

Xiaohao Cai, Raymond Chan, Tieyong Zeng
2013 SIAM Journal of Imaging Sciences  
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.  ...  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 have proposed a two-stage method for segmentation that makes use of a convex model (2.6) based on the Mumford-Shah model.  ... 
doi:10.1137/120867068 fatcat:cqoomzag6jbstfhofjlejpdagu

On a Variational and Convex Model of the Blake–Zisserman Type for Segmentation of Low-Contrast and Piecewise Smooth Images

Liam Burrows, Anis Theljani, Ke Chen
2021 Journal of Imaging  
The model is motivated by the two-stage image segmentation work of Cai–Chan–Zeng (2013) for the MumfordShah model.  ...  This paper proposes a new variational model for segmentation of low-contrast and piecewise smooth images.  ...  type methods for low-contrast images. • CRCV: Convex relaxed Chan-Vese model [5]; • CCZ: The two-stage convex variant of the Mumford-Shah model by Cai et al. [12] given in (4); • CNC: The convex non-convex  ... 
doi:10.3390/jimaging7110228 pmid:34821859 pmcid:PMC8621176 fatcat:etsqm5wzwnhabl5pg2kdcep24e

A Two-Stage Image Segmentation Method for Blurry Images with Poisson or Multiplicative Gamma Noise

Raymond Chan, Hongfei Yang, Tieyong Zeng
2014 SIAM Journal of Imaging Sciences  
The first stage of our method is to find a smooth solution u to a convex variant of the Mumford-Shah model where the 2 datafidelity term is replaced by an I-divergence term.  ...  The method is inspired by a previous work on two-stage segmentation and the usage of an I-divergence term to handle the noise.  ...  In [11] , the authors proposed a novel two-stage segmentation method that can be considered as a convex variant of the Mumford-Shah model (1.1) .  ... 
doi:10.1137/130920241 fatcat:ragpprewfzaxdotwvqqmwxkuda

An efficient iterative thresholding method for image segmentation

Dong Wang, Haohan Li, Xiaoyu Wei, Xiao-Ping Wang
2017 Journal of Computational Physics  
We proposed an efficient iterative thresholding method for multi-phase image segmentation.  ...  The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step.  ...  In the first stage, the authors apply the split Bregman method [12] to find the minimizer of a convex variant of the Mumford-Shah functional.  ... 
doi:10.1016/j.jcp.2017.08.020 fatcat:brnmwl2kkfan3p5fbcevnperi4

A Three-stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT) [article]

Xiaohao Cai, Raymond Chan, Mila Nikolova, Tieyong Zeng
2015 arXiv   pre-print
At the first stage, a convex variant of the Mumford-Shah model is applied to each channel to obtain a smooth image. We show that the model has unique solution under the different degradations.  ...  In this paper, we propose a SLaT (Smoothing, Lifting and Thresholding) method with three stages for multiphase segmentation of color images corrupted by different degradations: noise, information loss,  ...  We note that the model (3) is a convex non-tight relaxation of the Mumford-Shah model in (1).  ... 
arXiv:1506.00060v1 fatcat:26bpep72qbc45dcsg3gb2dj6ge

A Three-Stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT)

Xiaohao Cai, Raymond Chan, Mila Nikolova, Tieyong Zeng
2017 Journal of Scientific Computing  
At the first stage, a convex variant of the Mumford-Shah model is applied to each channel to obtain a smooth image. We show that the model has unique solution under different degradations.  ...  In this paper, we propose a SLaT (Smoothing, Lifting and Thresholding) method with three stages for multiphase segmentation of color images corrupted by different degradations: noise, information loss  ...  Acknowledgment The authors thank G. Steidl and M. Bertalmío for constructive discussions. The work of X.  ... 
doi:10.1007/s10915-017-0402-2 fatcat:davqew6eqzeo5gqitv3wovobh4

Multiclass Segmentation by Iterated ROF Thresholding [chapter]

Xiaohao Cai, Gabriele Steidl
2013 Lecture Notes in Computer Science  
Variational models as the Mumford-Shah model and the active contour model have many applications in image segmentation.  ...  In this paper, we propose a new multiclass segmentation model by combining the Rudin-Osher-Fatemi model with an iterative thresholding procedure.  ...  In [12] a two-stage image segmentation method which finds the solution of a convex variant of the Mumford-Shah model in the first stage followed by one thresholding step in the second stage was proposed  ... 
doi:10.1007/978-3-642-40395-8_18 fatcat:bviuugls2zbg3if22zxowejve4

k-Means image segmentation using Mumford–Shah model

Nilima Shah, Dhanesh Patel, Pasi Fränti
2021 Journal of Electronic Imaging (JEI)  
Shah, Patel, and Fränti: k-Means image segmentation using MumfordShah model detexturing process and the analysis of the spatial constraint.  ...  than that of the existing optimization methods for MumfordShah model.  ... 
doi:10.1117/1.jei.30.6.063029 fatcat:fbaywgz77bdlbbmthwb2k4klyi

Image segmentation based on the hybrid total variation model and the K-means clustering strategy

Baoli Shi, Zhi-Feng Pang, Jing Xu
2016 Inverse Problems and Imaging  
In order to efficiently segment the contaminated image, this paper proposes a two step method based on the hybrid total variation model with a box constraint and the K-means clustering method.  ...  The performance of image segmentation highly relies on the original inputting image.  ...  Huibin Chang for his suggestions on the numerical experiments and anonymous referees for their helpful comments and suggestions for improving this paper.  ... 
doi:10.3934/ipi.2016022 fatcat:2sbmgisvgjcyrndpinhmnot7im

Image segmentation based on the hybrid total variation model and the K-means clustering strategy [article]

Baoli Shi, Zhi-Feng Pang, Jing Xu
2016 arXiv   pre-print
In order to efficiently segment the contaminated image, this paper proposes a two step method based on the hybrid total variation model with a box constraint and the K-means clustering method.  ...  The performance of image segmentation highly relies on the original inputting image.  ...  Huibin Chang for his suggestions on the numerical experiments and anonymous referees for their helpful comments and suggestions for improving this paper.  ... 
arXiv:1605.09116v1 fatcat:nfwdrt5ljnbgpf2a3qzv3gx7vy

Fuzzy clustering using local and global region information for cell image segmentation

Amin Gharipour, Alan Wee-Chung Liew
2014 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)  
The segmentation procedure is divided into two stages: the first stage involves processing the local and global spatial information of the given cell image and a final segmentation stage which is based  ...  Our idea can be considered as a sequential integration of region based methods and fuzzy clustering for cell image segmentation.  ...  Stage 1: a) Image pre-segmentation based on the globally convex local Chan-Vese model (GCLCV) The GCS and split Bergman methods are used to presegment the cell image based on the local and global region  ... 
doi:10.1109/fuzz-ieee.2014.6891714 dblp:conf/fuzzIEEE/GharipourL14 fatcat:etw2bbrrpfhcvmduwljogqo6ga

Variational Image Segmentation Model Coupled with Image Restoration Achievements [article]

Xiaohao Cai
2014 arXiv   pre-print
In particular, one of the most important segmentation models, the piecewise constant Mumford-Shah model, can be extended easily in this way to segment gray and vector-valued images corrupted for example  ...  Experiments on many synthetic and real-world images demonstrate that our method gives better segmentation results in comparison to others state-of-the-art segmentation models especially for blurry images  ...  Acknowledgement: The main part of this work has been done in the University of Kaiserslautern, Germany. Thanks to Prof.  ... 
arXiv:1405.2128v1 fatcat:qab4o6gyxbgh5pqh75yq4oswfa

Variational mesh decomposition

Juyong Zhang, Jianmin Zheng, Chunlin Wu, Jianfei Cai
2012 ACM Transactions on Graphics  
The algorithm extends the Mumford-Shah model to 3D meshes that contains a data term measuring the variation within a segment using eigenvectors of a dual Laplacian matrix whose weights are related to the  ...  The efficiency is achieved by solving the Mumford-Shah model through a saddle-point problem that is solved by a fast primal-dual method.  ...  ACKNOWLEDGMENTS We are grateful to the reviewers for their helpful comments and suggestions.  ... 
doi:10.1145/2167076.2167079 fatcat:ayxiihbnpjea5k2ix6zcfyuu7i

Deep Variational Instance Segmentation [article]

Jialin Yuan, Chao Chen, Li Fuxin
2020 arXiv   pre-print
State-of-the-art algorithms often employ two separate stages, the first one generating object proposals and the second one recognizing and refining the boundaries.  ...  It extends the classical Mumford-Shah variational segmentation problem to be able to handle permutation-invariant labels in the ground truth of instance segmentation.  ...  Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Defense Advanced Research Projects Agency  ... 
arXiv:2007.11576v2 fatcat:kbchfbtsqjetpejtkqrj7lfi3e

Model-Based Learning of Local Image Features for Unsupervised Texture Segmentation

Martin Kiechle, Martin Storath, Andreas Weinmann, Martin Kleinsteuber
2018 IEEE Transactions on Image Processing  
The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model.  ...  Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation.  ...  ACKNOWLEDGMENT This work has been supported by the German Research Foundation (DFG) through grants number KL 2189/9-1, STO1126/2-1, and WE5886/4-1.  ... 
doi:10.1109/tip.2018.2792904 pmid:29994498 fatcat:d37fonhbejhizbv6ayuif5hcze
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