Multi-Level Image Thresholding via Nonlinear Fitting of the Histogram

Abstract

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.