Multiclass histogram-based thresholding using kernel density estimation and scale-space representations

TL;DR

This paper introduces a nonparametric, kernel density estimation-based method for multiclass histogram thresholding that adaptively adjusts bandwidth to identify optimal thresholds, validated on synthetic and real X-ray CT data.

Contribution

The paper proposes a novel adaptive kernel density estimation approach for multiclass histogram thresholding using EM, improving threshold detection accuracy.

Findings

Successfully verified on synthetic histograms with known thresholds.

Effectively applied to real X-ray CT images to estimate porosity.

Thresholding results align well with experimental measurements.

Abstract

We present a new method for multiclass thresholding of a histogram which is based on the nonparametric Kernel Density (KD) estimation, where the unknown parameters of the KD estimate are defined using the Expectation-Maximization (EM) iterations. The method compares the number of extracted minima of the KD estimate with the number of the requested clusters minus one. If these numbers match, the algorithm returns positions of the minima as the threshold values, otherwise, the method gradually decreases/increases the kernel bandwidth until the numbers match. We verify the method using synthetic histograms with known threshold values and using the histogram of real X-ray computed tomography images. After thresholding of the real histogram, we estimated the porosity of the sample and compare it with the direct experimental measurements. The comparison shows the meaningfulness of the thresholding.