Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise
In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the leas...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2023-06-01
|
| Series: | Frontiers in Computer Science |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fcomp.2023.1131317/full |
| _version_ | 1797793742608924672 |
|---|---|
| author | Kevin Bui Yifei Lou Fredrick Park Jack Xin |
| author_facet | Kevin Bui Yifei Lou Fredrick Park Jack Xin |
| author_sort | Kevin Bui |
| collection | DOAJ |
| description | In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT. |
| first_indexed | 2024-03-13T02:52:40Z |
| format | Article |
| id | doaj.art-9598296776364d1894614672984afcdf |
| institution | Directory Open Access Journal |
| issn | 2624-9898 |
| language | English |
| last_indexed | 2024-03-13T02:52:40Z |
| publishDate | 2023-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Computer Science |
| spelling | doaj.art-9598296776364d1894614672984afcdf2023-06-28T09:26:49ZengFrontiers Media S.A.Frontiers in Computer Science2624-98982023-06-01510.3389/fcomp.2023.11313171131317Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noiseKevin Bui0Yifei Lou1Fredrick Park2Jack Xin3Department of Mathematics, University of California, Irvine, Irvine, CA, United StatesDepartment of Mathematical Sciences, University of Texas at Dallas, Richardson, TX, United StatesDepartment of Mathematics & Computer Science, Whittier College, Whittier, CA, United StatesDepartment of Mathematics, University of California, Irvine, Irvine, CA, United StatesIn this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.https://www.frontiersin.org/articles/10.3389/fcomp.2023.1131317/fullimage segmentationtotal variationnonconvex optimizationADMMPoisson noise |
| spellingShingle | Kevin Bui Yifei Lou Fredrick Park Jack Xin Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise Frontiers in Computer Science image segmentation total variation nonconvex optimization ADMM Poisson noise |
| title | Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise |
| title_full | Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise |
| title_fullStr | Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise |
| title_full_unstemmed | Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise |
| title_short | Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise |
| title_sort | difference of anisotropic and isotropic tv for segmentation under blur and poisson noise |
| topic | image segmentation total variation nonconvex optimization ADMM Poisson noise |
| url | https://www.frontiersin.org/articles/10.3389/fcomp.2023.1131317/full |
| work_keys_str_mv | AT kevinbui differenceofanisotropicandisotropictvforsegmentationunderblurandpoissonnoise AT yifeilou differenceofanisotropicandisotropictvforsegmentationunderblurandpoissonnoise AT fredrickpark differenceofanisotropicandisotropictvforsegmentationunderblurandpoissonnoise AT jackxin differenceofanisotropicandisotropictvforsegmentationunderblurandpoissonnoise |