论文标题
具有加权各向异性的总变化的有效平滑和阈值图像分割框架
An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation
论文作者
论文摘要
在本文中，我们设计了一个高效的多阶段图像分割框架，该框架结合了各向异性和各向同性总变化的加权差异（AITV）。分割框架通常包括两个阶段：平滑和阈值，因此称为SAT。在第一阶段，通过AITV规范化的Mumford-Shah（MS）模型获得了平滑的图像，该模型可以通过乘数的交替方向方法（ADMM）有效地求解，并使用$ \ ell_1-al_1-α\ ell_2 $ unorisuer的近端操作员的封闭形式解决方案。分析了ADMM算法的收敛性。在第二阶段，我们通过$ k $ -MEANS聚类阈值以获得最终的分割结果。数值实验表明，所提出的分割框架对于灰度和颜色图像都具有多功能性，有效地在几秒钟内产生了高质量的分割结果，并且强大的输入图像损坏了噪声，模糊或两者兼而有之。我们将AITV方法与其原始凸电视和NonConvex TV $^P（0 <P <1）$对应物进行了比较，展示了我们所提出的方法的定性和定量优势。
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 $\ell_1 -α\ell_2$ 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.
