Research Article Open Access

Multi-Level Image Thresholding via Nonlinear Fitting of the Histogram

Salah Ameer1
  • 1 Faculty of Applied Science and Technology, Humber College, Brampton, ON, Canada


This paper proposes a novel scheme for multi-level image thresholding. The 1D cumulative histogram is curve-fitted to a polynomial of nonlinear basis function, the hyperbolic tangent (tanh). The thresholds are the positions of the minima of the first (odd) derivative of the fitting polynomial, since the histogram is the derivative of the cumulative histogram. The tanh function is considered as an approximation to the integral of the Gaussian function. However, better results were obtained by fitting the derivative of the polynomial to the histogram. The scheme is a direct solution (solving a linear system) and does not require iterations or exhaustive search. Some results are presented to demonstrate the effectiveness of the proposed scheme.

American Journal of Applied Sciences
Volume 16 No. 12, 2019, 336-345


Submitted On: 24 September 2019 Published On: 28 December 2019

How to Cite: Ameer, S. (2019). Multi-Level Image Thresholding via Nonlinear Fitting of the Histogram. American Journal of Applied Sciences, 16(12), 336-345.

  • 4 Citations



  • Image Thresholding
  • Histogram Fitting