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

• URL: http://arxiv.org/abs/2202.10115v5
• Date: Wed, 15 Nov 2023 22:57:49 GMT
• Title: An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation
• Authors: Kevin Bui, Yifei Lou, Fredrick Park, Jack Xin
• Abstract summary: We present a multi-stage image segmentation framework that incorporates a weighted difference of anisotropic isotropic variation (AITV) In the second stage, we threshold the smoothed image by $K$-meansizer to obtain the final result.
• Score: 1.9581049654950413
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we design an efficient, 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 $\ell_1 -\alpha \ell_2$ 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 TV and nonconvex TV$^p (0<p<1)$ counterparts, showcasing the qualitative and quantitative advantages of our proposed method.

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