This talk will deal with multivariate statistical methods applied to semi-automatic generation of training and validation data for classification of image data. First, training and validation sets are grown from one or a few seed points by a method that ensures spatial and spectral closeness of observations. Spectral closeness is obtained by excluding observations that have high Mahalanobis distances to the training class mean. Spatial closeness is obtained by requesting connectivity. Second, class consistency is controlled by forcing each class into 5-10 subclasses and checking the separability of these sub-classes by means of canonical discriminant analysis. Third, class separability is checked by means of the Jeffreys-Matusita distance and the posterior probability of a class mean being classified as another class. Fourth, the actual classification is carried out based on four supervised classifiers all assuming multi-normal distributions: simple quadratic, a contextual quadratic and two hierarchical quadratic classifiers.
A case study addresses the problem of classifying minerals common in siliciclastic and carbonate rocks. Twelve chemical elements are mapped from thin sections by energy dispersive spectroscopy (EDS) in a scanning electron microscope (SEM). Overall weighted misclassification rates for all quadratic classifiers are very low, for both the training (0.25%-0.33%) and validation sets (0.65%-1.13%). The number of rejectedobservations in routine runs is checked to control the performance of the SEM image acquisition and the classification. Although the contextual classifier performs (marginally) best on the validation set, the simple quadratic classifier is chosen in routine classifications because of the lower processing time required. This method is presently used as a routine petrographical analysis method at Norsk Hydro Research Centre, Bergen, Norway.
Unmixing can be considered as a supplement or an alternative to the classification task. A method that ensures positive abundancies that add to 100% (possibly including a contribution not accounted for by the defined end-members) is described and applied to the SEM EDS data described above.