Segmentation of SEM images of multiphase materials: When Gaussian mixture models are accurate?

Scanning electron microscopy has been a powerful technique to investigate the structural and chemical properties of multiphase materials on micro and nanoscale due to its high-resolution capabilities. One of the main outcomes of the SEM-based analysis is the calculation of the fractions of material components constituting the multiphase material by means of the segmentation of their back scattered electron SEM images. In order to segment multiphase images, Gaussian mixture models (GMMs) are commonly used based on the deconvolution of the image pixel histogram. Despite its extensive use, the accuracy of GMM predictions has not been validated yet. In this paper, we proceed to a systematic study of the evaluation of the accuracy and the limitations of the GMM method when applied to the segmentation of a four-phase material. To this end, first, we build a modelling framework and propose an index to quantify the accuracy of GMM predictions for all phases. Then we apply this framework to calculate the impact of collective parameters of image histogram on the accuracy of GMM predictions. Finally, some rules of thumb are concluded to guide SEM users about the suitability of using GMM for the segmentation of their SEM images based only on the inspection of the image histogram. A suitable histogram for GMM is a histogram with number of peaks equal to the number of Gaussian components, and if that is not the case, kurtosis and skewness should be smaller than 2.35 and 0.1, respectively.