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Efficient numerical schemes for Chan-Vese active contour models in image segmentation

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Abstract

In this paper, we introduce multi-symplectic Lagrangian variational integrators for solving Chan-Vese active contour models in image segmentation. Energy functionals are discretized firstly, and numerical schemes are derived from discrete Euler-Lagrange equations based on discrete variational principle. Lagrangian variational integrators preserve native differential structure-multi-symplecticity, that makes the numerical methods have a satisfied behavior. Experiments are performed on the benchmark images from literature. We further evaluated the methods in a segmentation database containing 1023 images. It shows that the proposed numerical schemes attain relatively faster convergence rates and better segmentation accuracy. Comparisons with the standard explicit Euler method of the original Chan-Vese model and other fast numerical optimization methods show that the proposed methods have better stability, higher accuracy, and are more robust when dealing with a large number of pictures. This study provides an example for further research to improve the performance of other existing image segmentation methods based on active contour models.

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Acknowledgements

The authors would like to thank all the reviewers for their constructive comments. This research was supported by National Natural Science Foundation of China(Grant No.61170121, No.11401259), Blue Project of Universities in Jiangsu Province Training Young Academic Leaders Object, Fundamental Research Funds for the Central Universities(JUSRR11407).

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Authors and Affiliations

  1. Changzhou University, N0.1 Gehu Road, Changzhou, 213164, China

    Jiuzhen Liang

  2. Jiangnan University, No. 1800 Lihu Avenue, Wuxi, 214122, China

    Min Li & Cuicui Liao

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  1. Jiuzhen Liang
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  2. Min Li
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  3. Cuicui Liao
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Correspondence to Jiuzhen Liang.

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Liang, J., Li, M. & Liao, C. Efficient numerical schemes for Chan-Vese active contour models in image segmentation. Multimed Tools Appl 77, 16661–16684 (2018). https://doi.org/10.1007/s11042-017-5232-6

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  • DOI: https://doi.org/10.1007/s11042-017-5232-6

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