A Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

Abstract

In this paper, we propose a multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation (AITV). The segmentation framework generally consists of two stages: smoothing and thresholding, thus referred to as SaT. In the first stage, a smoothed image is obtained by an AITV-regularized Mumford-Shah (MS) model, which can be solved efficiently by the alternating direction method of multipliers (ADMM) with a closed-form solution of a proximal operator of the 1 − α 2 regularizer. Convergence of the ADMM algorithm is analyzed. In the second stage, we threshold the smoothed image by k-means clustering to obtain the final segmentation result. Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images, efficient in producing high-quality segmentation results within a few seconds, and robust to input images that are corrupted with noise, blur, or both. We compare the AITV method with its original convex and nonconvex TV p (0 < p < 1) counterparts, showcasing the qualitative and quantitative advantages of our proposed method.

Adaptive‐weighted high order TV algorithm for sparse‐view CT reconstruction

“…Subsequently, the AwTV algorithm has been widely used and developed in image reconstruction, denoising, and restoration. 11,12 These TV variants algorithms [13][14][15] and the improvement of the optimization method significantly promote the development of sparse-view reconstruction.…”

Efficient Image Segmentation Framework with Difference of Anisotropic and Isotropic Total Variation for Blur and Poisson Noise Removal

“…[ 25,28,39,42,44], 1 / 2 [53,63,66], and an error function [30]. Lou et al [45] designed a TV version of 1 − α 2 called the weighted anisotropic-isotropic total variation (AITV), which outperforms TV in various imaging applications, such as image denoising [45], image reconstruction [45,39], and image segmentation [8,9].…”

“…In this paper, we propose an AITV variant of (4) to improve the smoothing step of the SaT/SLaT framework for images degraded by Poisson noise and/or blur. Incorporating AITV regularization is motivated by our previous works [8,9,50], where we demonstrated that AITV regularization is effective in preserving edges and details especially under Gaussian and impulsive noise. To maintain similar computational efficiency as the original SaT/SLaT framework, we propose an ADMM algorithm that utilizes the 1 − α 2 proximal operator [43].…”

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

“…Examples of nonconvex regularization include ℓ p , 0 < p < 1 (Chartrand, 2007;Cao et al, 2013), et al, 2015a,b;Ding and Han, 2019;Li P. et al, 2020;Ge and Li, 2021), ℓ 1 /ℓ 2 (Rahimi et al, 2019;Wang et al, 2020;Xu et al, 2021), and an error function (Guo et al, 2021). Lou et al (2015c) designed a TV version of ℓ 1 − αℓ 2 called the weighted difference of anisotropic-isotropic total variation (AITV), which outperforms TV in various imaging applications, such as image denoising (Lou et al, 2015c), image reconstruction (Lou et al, 2015c;Li P. et al, 2020), and image segmentation (Bui et al, 2021(Bui et al, , 2022Wu et al, 2022b).…”

“…In this paper, we propose an AITV variant of (4) to improve the smoothing step of the SaT/SLaT framework for images degraded by Poisson noise and/or blur. Incorporating AITV regularization is motivated by our previous works (Park et al, 2016;Bui et al, 2021Bui et al, , 2022, where we demonstrated that AITV regularization is effective in preserving edges and details, especially under Gaussian and impulsive noise. To maintain similar computational efficiency as the original SaT/SLaT framework, we propose an ADMM algorithm that utilizes the ℓ 1 − αℓ 2 proximal operator (Lou and Yan, 2018).…”