American Journal of Applied Sciences

Multi-Level Image Thresholding via Nonlinear Fitting of the Histogram

Salah Ameer

DOI : 10.3844/ajassp.2019.336.345

American Journal of Applied Sciences

Volume 16, 2019

Pages 336-345


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.


© 2019 Salah Ameer. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.