Histogram Optimal Multi-thresholding

The paper concerns the problem for the minimal number of Gaussian distributions approximating a given 1D histogram in the range of an admissible error. The problem is usually reached in one-dimensional (1D) tasks of classification and/or recognition, e.g., in image segmentation by intensity. Plenty of effective methods for segmentation are known that use image histogram thresholding, especially when the number M of the classes is given preliminarily. The task examined herein is when M is apriori unknown and the classes are statistically approximated by Gaussians. A direct treatment of the error of approximation is proposed herein to evaluate M optimally as well as to improve some classical methods for histogram thresholding and multi-thresholding. The theoretical background and the experimental evaluation of the proposed approach are described in the paper.