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://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10481.html
KW - Euler's elastica energy, image segmentation, image inpainting, illusory shape, corner fusion, level set method, binary level set method, fast sweeping.
AB - <p style="text-align: justify;">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.</p>