首页|An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation
An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation
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In this paper,we design an efficient,multi-stage image segmentation framework that incor-porates a weighted difference of anisotropic and isotropic total variation(AITV).The seg-mentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved effi-ciently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l1-al2 regularizer.The 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,effi-cient 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 TVp(0＜p＜1)counterparts,showcasing the qualitative and quantitative advantages of our proposed method.
Image segmentationNon-convex optimizationMumford-Shah(MS)modelAlternating direction method of multipliers(ADMMs)Proximal operator
Kevin Bui、Yifei Lou、Fredrick Park、Jack Xin
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Department of Mathematics,University of California,Irvine,Irvine,CA 92697-3875,USA
Department of Mathematics,University of North Carolina,Chapel Hill,Chapel Hill,NC 27599,USA
Department of Mathematics and Computer Science,Whittier College,Whittier,CA 90602,USA
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