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Unsupervised document image binarization using a system of nonlinear partial differential equations

Author

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  • Jacobs, B.A.
  • Celik, T.

Abstract

Partial differential equations have recently been established as a viable framework for image processing, particularly for image binarization. One drawback of this framework is the requirement for manual parameter tuning. In this work we propose a novel development wherein the spatio-temporal dynamics of the thresholding parameter are governed by an additional partial differential equation which is engineered to exhibit desirable traits. While the model can still be tuned manually to achieve optimal results, we show experimentally that the present framework is near optimal for the default choice of parameter, τ. This novel system enforces a smooth evolution of the threshold map while still offering locally adaptive thresholding properties, a requirement for non-uniformly illuminated images. The proposed model is applied to images through a rudimentary finite difference based numerical method due to the parallelizability and provable stability of the method. The proposed work offers an unsupervised binarization scheme and is benchmarked against state-of-the-art methods in the field.

Suggested Citation

  • Jacobs, B.A. & Celik, T., 2022. "Unsupervised document image binarization using a system of nonlinear partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 418(C).
  • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008882
    DOI: 10.1016/j.amc.2021.126806
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    References listed on IDEAS

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    1. Guo, Jiebin & He, Chuanjiang & Zhang, Xiaoting, 2019. "Nonlinear edge-preserving diffusion with adaptive source for document images binarization," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 8-22.
    2. Jacobs, B.A. & Momoniat, E., 2015. "A locally adaptive, diffusion based text binarization technique," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 464-472.
    3. B. A. Jacobs & C. Harley, 2018. "Application of Nonlinear Time-Fractional Partial Differential Equations to Image Processing via Hybrid Laplace Transform Method," Journal of Mathematics, Hindawi, vol. 2018, pages 1-9, September.
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    Citations

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    Cited by:

    1. Wang, Yan & Zhou, Lingxin & Zhang, Xuyuan, 2023. "Spatio-temporal regularized shock-diffusion filtering with local entropy for restoration of degraded document images," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    2. Meijun Zhou & Jiayu Qin & Zenan Huo & Fabio Giampaolo & Gang Mei, 2022. "epSFEM: A Julia-Based Software Package of Parallel Incremental Smoothed Finite Element Method (S-FEM) for Elastic-Plastic Problems," Mathematics, MDPI, vol. 10(12), pages 1-25, June.
    3. Du, Zhongjie & He, Chuanjiang, 2023. "Anisotropic diffusion with fuzzy-based source for binarization of degraded document images," Applied Mathematics and Computation, Elsevier, vol. 441(C).

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