Multiclass histogram-based thresholding using kernel density estimation and scale-space representations
This work addresses a domain-specific problem in image processing for porosity estimation, but it is incremental as it builds on existing kernel density and EM techniques.
The authors tackled the problem of multiclass thresholding for histograms by developing a method using kernel density estimation and scale-space representations, which was validated on synthetic data and real X-ray computed tomography images, showing meaningful porosity estimates that matched experimental measurements.
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.