Piecewise-Smooth Image Segmentation Models with \(L^1\) Data-Fidelity Terms

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• 作者：Miyoun Jung
• 关键词：Image segmentation ; Intensity inhomogeneity ; \(L^1\) ; fidelity measure ; Convex relaxation ; Augmented Lagrangian method ; Multiphase representation
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：70
• 期：3
• 页码：1229-1261
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

In this article, we propose a class of piecewise-smooth image segmentation models in a variational framework. The models involve \(L^1\) data fidelity measures and assume that an image can be approximated by the sum of a piecewise-constant function and a smooth function. The smooth function models intensity inhomogeneity, and the \(L^1\) data-fitting terms enable to segment images with low contrast or outliers such as impulsive noise. The regions to be segmented are represented as smooth functions, almost binary functions, instead of the Heaviside expression of level set functions. The existence of minimizers of our main model is shown. Furthermore, we design fast and efficient optimization algorithms based on the augmented Lagrangian method and present a partial convergence result. Numerical results validate the effectiveness of the proposed models compared with other state-of-the-art methods.