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

arXiv:2202.04785v2 Announce Type: replace-cross Abstract: We present a method for multiclass thresholding of histograms whose modes may overlap so strongly that they merge into a unimodal distribution. The histogram is approximated by a nonparametric kernel density (KD) estimate, a mixture of Gaussians with one component per bin and a common bandwidth, whose parameters are determined by Expectation-Maximization (EM) iterations. Because the estimate is a Gaussian mixture, the semigroup property of Gaussian convolution yields its scale-space representation in closed form, at bandwidths both larger and smaller than the fitted one. The algorithm increases or decreases the bandwidth until the number of local minima of the estimate equals the number of requested classes minus one, and returns the positions of those minima as the threshold values. We validate the method on synthetic histograms with known thresholds, and we apply it to the histogram of X-ray computed tomography images of a natural porous sample in which the three phases strongly overlap. The porosity computed from the resulting segmentation agrees with the direct experimental measurement to within 4%, whereas K-means clustering misestimates it by 52%.

Source: arXiv cs.CV | 2026-10-14