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

Journal of Mathematical Imaging and Vision volume 41, pages 194–209 (2011)Cite this article

Abstract

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.

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Authors and Affiliations

  1. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, P.R. China

    Chunxiao Liu & Kefeng Liu

  2. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, P.R. China

    Fangfang Dong

  3. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Shengfeng Zhu & Dexing Kong

Authors
  1. Chunxiao Liu
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  2. Fangfang Dong
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  3. Shengfeng Zhu
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  4. Dexing Kong
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  5. Kefeng Liu
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Correspondence to Chunxiao Liu.

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Liu, C., Dong, F., Zhu, S. et al. New Variational Formulations for Level Set Evolution Without Reinitialization with Applications to Image Segmentation. J Math Imaging Vis 41, 194–209 (2011). https://doi.org/10.1007/s10851-011-0269-z

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  • DOI: https://doi.org/10.1007/s10851-011-0269-z

Keywords

  • Level set method
  • Reinitialization
  • Augmented Lagrangian method
  • Projection Lagrangian method
  • Chan-Vese model
  • Additive operator splitting