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.

Altered hemodynamics by 4D flow cardiovascular magnetic resonance predict exercise intolerance in repaired coarctation of the aorta: an in vitro study

“…Each dataset was segmented to isolate the velocity flow fields within the region of interest. To obtain consistent results, a semi-automated threshold technique was developed based on a modified Otsu method [ 36 ] using the logarithm of the histogram to avoid bias toward the larger background region [ 37 ]. Further post-processing was performed using iTFlow, commercially available software (Cardio Flow Design, Tokyo, Japan), for qualitative assessment of streamline flow and quantitative assessment of peak systolic WSS, vorticity, and helicity.…”