A Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation
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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 ℓ_1 -αℓ_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.
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