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A fast computational approach for illusory contour reconstruction

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Abstract

Illusory contour reconstruction can be modeled as a minimization problem with a tractable variational level set formulation, utilizing Euler’s elastica to reconstruct the illusory boundaries. However, this kind of formulation is very difficult to solve numerically as it is hard to implement such optimization algorithms efficiently in practice. In this paper, we propose an equivalently reduced variational level set formulation by taking the level set functions as signed distance functions. Technically, an alternating direction method of multipliers (ADMM) is developed by introducing some auxiliary variables, Lagrange multipliers and applying an alternating optimization strategy. With the proposed ADMM method, the minimization problem can be transformed into a series of sub-problems, which can be solved easily via using the Gauss-Seidel iterations and Fast Fourier Transform (FFT). The corresponding level set functions are regarded as signed distance functions during computation process using a simple algebraic projection method, which avoids the traditional re-initialization process for conventional level set functions. Extensive experiments have been conducted on both synthetic and real images, which validated the proposed approach, and demonstrated the advantages of the proposed ADMM-Projection (ADMM-P) method over the existing algorithms based on traditional gradient descent method (GDM) in terms of computational efficiency.

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Acknowledgments

The work has been partially supported by research funds from the National Natural Science Foundation of China with grant Nos.61602321, 61305045, 61363066 and 61303079.

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Authors and Affiliations

  1. Department of Computing, Curtin University, Perth, Australia

    Lu Tan, Wanquan Liu & Ling Li

  2. College of Computer Science and Technology, Qingdao University, Qingdao, China

    Zhenkuan Pan

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  1. Lu Tan
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  2. Wanquan Liu
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  3. Ling Li
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  4. Zhenkuan Pan
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Correspondence to Lu Tan.

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Tan, L., Liu, W., Li, L. et al. A fast computational approach for illusory contour reconstruction. Multimed Tools Appl 78, 10449–10472 (2019). https://doi.org/10.1007/s11042-018-6546-8

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  • DOI: https://doi.org/10.1007/s11042-018-6546-8

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