Volume 14, Issue 6
A Simple Fast Algorithm for Minimization of the Elastica Energy Combining Binary and Level Set Representations

Xue-Cheng Tai & Jinming Duan

DOI:

Int. J. Numer. Anal. Mod., 14 (2017), pp. 809-821.

Published online: 2017-10

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  • Abstract

For curves or general interfaces, Euler’s elastica energy has a wide range of applications in computer vision and image processing. It is however difficult to minimize the functionals related to the elastica energy due to its non-convexity, nonlinearity and higher order with derivatives. In this paper, we propose a very simple way to combine level set and binary representations for interfaces and then use a fast algorithm to minimize the functionals involving the elastica energy. The proposed algorithm essentially just needs to solve a total variation type minimization problem and a re-distance problem. Nowadays, there are many fast algorithms to solve these two problems and thus the overall efficiency of the proposed algorithm is very high. We then apply the new Euler’s elastica minimization algorithm to image segmentation, image inpainting and illusory shape reconstruction problems. Extensive experimental results are finally conducted to validate the effectiveness of the proposed algorithm.

  • Keywords

Euler's elastica energy image segmentation image inpainting illusory shape corner fusion level set method binary level set method fast sweeping

  • AMS Subject Headings

35R35 49J40 60G40.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-809, author = {Xue-Cheng Tai and Jinming Duan}, title = {A Simple Fast Algorithm for Minimization of the Elastica Energy Combining Binary and Level Set Representations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {6}, pages = {809--821}, abstract = {

For curves or general interfaces, Euler’s elastica energy has a wide range of applications in computer vision and image processing. It is however difficult to minimize the functionals related to the elastica energy due to its non-convexity, nonlinearity and higher order with derivatives. In this paper, we propose a very simple way to combine level set and binary representations for interfaces and then use a fast algorithm to minimize the functionals involving the elastica energy. The proposed algorithm essentially just needs to solve a total variation type minimization problem and a re-distance problem. Nowadays, there are many fast algorithms to solve these two problems and thus the overall efficiency of the proposed algorithm is very high. We then apply the new Euler’s elastica minimization algorithm to image segmentation, image inpainting and illusory shape reconstruction problems. Extensive experimental results are finally conducted to validate the effectiveness of the proposed algorithm.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10481.html} }
TY - JOUR T1 - A Simple Fast Algorithm for Minimization of the Elastica Energy Combining Binary and Level Set Representations AU - Xue-Cheng Tai & Jinming Duan JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 809 EP - 821 PY - 2017 DA - 2017/10 SN - 14 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10481.html KW - Euler's elastica energy KW - image segmentation KW - image inpainting KW - illusory shape KW - corner fusion KW - level set method KW - binary level set method KW - fast sweeping AB -

For curves or general interfaces, Euler’s elastica energy has a wide range of applications in computer vision and image processing. It is however difficult to minimize the functionals related to the elastica energy due to its non-convexity, nonlinearity and higher order with derivatives. In this paper, we propose a very simple way to combine level set and binary representations for interfaces and then use a fast algorithm to minimize the functionals involving the elastica energy. The proposed algorithm essentially just needs to solve a total variation type minimization problem and a re-distance problem. Nowadays, there are many fast algorithms to solve these two problems and thus the overall efficiency of the proposed algorithm is very high. We then apply the new Euler’s elastica minimization algorithm to image segmentation, image inpainting and illusory shape reconstruction problems. Extensive experimental results are finally conducted to validate the effectiveness of the proposed algorithm.

Xue-Cheng Tai & Jinming Duan. (1970). A Simple Fast Algorithm for Minimization of the Elastica Energy Combining Binary and Level Set Representations. International Journal of Numerical Analysis and Modeling. 14 (6). 809-821. doi:
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