Multivariate statistical methods for the analysis of microscope image series: applications in materials science

Multivariate data sets are now produced in several types of microscopy. Multivariate statistical methods are necessary in order to extract the useful information contained in such (image or spectrum) series. In this review, linear and nonlinear multivariate methods are described and illustrated with examples related both to the segmentation of microanalytical maps and to the study of variability in the images of unit cells in high-resolution transmission electron microscopy. Concerning linear multivariate statistical analysis, emphasis is put on the need to go beyond the classical orthogonal decomposition already routinely performed through principal components analysis or correspondence analysis. It is shown that oblique analysis is often necessary when quantitative results are expected. Concerning nonlinear multivariate analysis, several methods are first described for performing the mapping of data from a high-dimensional space to a space of lower dimensionality. Then, automatic classification methods are described. These methods, which range from classical methods (hard and fuzzy C-means) to neural networks through clustering methods which do not make assumptions concerning the shape of classes, can be used for multivariate image segmentation and image classification and averaging.