Statistical Detection Theory Approach to Hyperspectral Image Classification

摘要

This paper presents a statistical detection theory approach to hyperspectral image (HSI) classification which is quite different from many conventional approaches reported in the HSI classification literature. It translates a multi-target detection problem into a multi-class classification problem so that the well-established statistical detection theory can be readily applicable to solving classification problems. In particular, two types of classification, a priori classification and a posteriori classification, are developed in corresponding to Bayes detection and maximum a posteriori (MAP) detection, respectively, in detection theory. As a result, detection probability and false alarm probability can also be translated to classification rate and false classification rate derived from a confusion classification matrix used for classification. To evaluate the effectiveness of a posteriori classification, a new a posteriori classification measure, to be called precision rate (PR), is also introduced by MAP classification in contrast to overall accuracy (OA) that can be considered as a priori classification measure and has been used for Bayes classification. The experimental results provide evidence that a priori classifier as Bayes classifier which performs well in terms of OA does not necessarily perform well as a posteriori classifier in terms of PR. That is, PR is the only criterion that can be used as a posteriori classification measure to evaluate how well a classifier performs.