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This master thesis investigates a new method for the feature extraction of gray scale images, the so called „Non-Euclidean Principal Component Analysis“ 1. Thereby the standard inner product of the Euclidean space is substituted by a semi inner product in the well known learning rule of Oja and Sanger. The new method is compared with the standard principal component analysis (PCA) by extracting features (feature vectors) of different databases with class labels and judged regarding the accuracies of „Border Sensitive Generalized Learning Vector Quantization“ (BSGLVQ), „Feed Forward Neural Networks“ (FFNN) and the „Support Vector Machines“ (SVM).