Flesche, Harald5; Nielsen, Allan Aasbjerg4; Larsen, Rasmus4
1 Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Norsk Hydro4 Department of Applied Mathematics and Computer Science, Technical University of Denmark5 Norsk Hydro
This paper addresses the problem of classifying minerals common in siliciclastic and carbonate rocks. Twelve chemical elements are mapped from thin sections by energy dispersive spectroscopy in a scanning electron microscope (SEM). Extensions to traditional multivariate statistical methods are applied to perform the classification. 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 subclasses 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 multinormal distributions: simple quadratic, a contextual quadratic, and two hierarchical quadratic classifiers. 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%). Finally, the number of rejected observations 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. The method is presently used as a routine petrographical analysis method at Norsk Hydro Research Centre. The data can be approximated by a Poisson distribution. Accordingly, the square root of the data has constant variance and a linear classifier can be used. Near orthogonal input data, enable the use of a minimum distance classifier. Results from both linear and quadratic minimum distance classifications are described briefly.
Mathematical Geology, 2000, Vol 32, Issue 3, p. 337-366