In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted
difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in
an image. In particular, we replace the total variation regularization in the Chan--Vese segmentation
model and a fuzzy region competition model by the proposed AITV. To deal with the nonconvex
nature of AITV, we apply the difference-of-convex algorithm (DCA), in which the subproblems can
be minimized by the primal-dual hybrid gradient method with linesearch. The convergence of the
DCA scheme is analyzed. In addition, a generalization to color image segmentation is discussed. In
the numerical experiments, we compare the proposed models with the classic convex approaches and
the two-stage segmentation methods (smoothing and then thresholding) on various images, showing
that our models are effective in image segmentation and robust with respect to impulsive noises.
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This content will become publicly available on June 28, 2024
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 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.
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- NSF-PAR ID:
- 10440861
- Date Published:
- Journal Name:
- Frontiers in Computer Science
- Volume:
- 5
- ISSN:
- 2624-9898
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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