New Variational Formulations for Level Set Evolution Without?Reinitialization?with Applications to Image Segmentation

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• 作者：Chunxiao Liu (1) xxliu198431@126.com
  Fangfang Dong (2)
  Shengfeng Zhu (3)
  Dexing Kong (3)
  Kefeng Liu (1)
• 关键词：Level set method – Reinitialization – Augmented Lagrangian method – Projection Lagrangian method – Chan ; Vese model – Additive operator splitting
• 刊名：Journal of Mathematical Imaging and Vision
• 出版年：2011
• 出版时间：November 2011
• 年：2011
• 卷：41
• 期：3
• 页码：194-209
• 全文大小：2.9 MB
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• 作者单位：1. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027 P.R. China2. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018 P.R. China3. Department of Mathematics, Zhejiang University, Hangzhou, 310027 P.R. China
• 刊物类别：Computer Science
• 刊物主题：Computer Imaging, Vision, Pattern Recognition and Graphics
  Image Processing and Computer Vision
  Artificial Intelligence and Robotics
  Automation and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-7683

文摘

Interface evolution problems are often solved elegantly by the level set method, which generally requires the time-consuming reinitialization process. In order to avoid reinitialization, we reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian method and a projection Lagrangian method to solve the constrained model and propose two gradient-type algorithms. For the augmented Lagrangian method, we employ the Uzawa scheme to update the Lagrange multiplier. For the projection Lagrangian method, we use the variable splitting technique and get an explicit expression for the Lagrange multiplier. We apply the two approaches to the Chan-Vese model and obtain two efficient alternating iterative algorithms based on the semi-implicit additive operator splitting scheme. Numerical results on various synthetic and real images are provided to compare our methods with two others, which demonstrate effectiveness and efficiency of our algorithms.