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An Accurate and Practical Explicit Hybrid Method for the Chan–Vese Image Segmentation Model

Author

Listed:
  • Darae Jeong

    (Department of Mathematics, Kangwon National University, Gangwon-do 24341, Korea)

  • Sangkwon Kim

    (Department of Mathematics, Korea University, Seoul 02841, Korea)

  • Chaeyoung Lee

    (Department of Mathematics, Korea University, Seoul 02841, Korea)

  • Junseok Kim

    (Department of Mathematics, Korea University, Seoul 02841, Korea)

Abstract

In this paper, we propose a computationally fast and accurate explicit hybrid method for image segmentation. By using a gradient flow, the governing equation is derived from a phase-field model to minimize the Chan–Vese functional for image segmentation. The resulting governing equation is the Allen–Cahn equation with a nonlinear fidelity term. We numerically solve the equation by employing an operator splitting method. We use two closed-form solutions and one explicit Euler’s method, which has a mild time step constraint. However, the proposed scheme has the merits of simplicity and versatility for arbitrary computational domains. We present computational experiments demonstrating the efficiency of the proposed method on real and synthetic images.

Suggested Citation

  • Darae Jeong & Sangkwon Kim & Chaeyoung Lee & Junseok Kim, 2020. "An Accurate and Practical Explicit Hybrid Method for the Chan–Vese Image Segmentation Model," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1173-:d:385808
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    References listed on IDEAS

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    1. Pravitra Oyjinda & Nopparat Pochai, 2017. "Numerical Simulation to Air Pollution Emission Control near an Industrial Zone," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-7, October.
    2. Bo Chen & Xiao-Hui Zhou & Li-Wei Zhang & Jie Wang & Wei-Qiang Zhang & Chen Zhang, 2016. "A New Nonlinear Diffusion Equation Model for Noisy Image Segmentation," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-7, March.
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