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

B. A. Jacobs, T. Celik

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Article number126806
JournalApplied Mathematics and Computation
Publication statusPublished - 1 Apr 2022


  • Finite Difference
  • Fitzhugh-Nagumo
  • Image Processing
  • Partial Differential Equations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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