On the classification of classes with nearly equal spectral response in remote sensing hyperspectral image data

It is well known that high-dimensional image data allows for the separation of classes that are spectrally very similar, i.e., possess nearly equal first-order statistics, provided that their second-order statistics differ significantly. The aim of this study is to contribute to a better understanding, from a more geometrically oriented point of view, of the role played by the second-order statistics in remote sensing digital image classification of natural scenes when the classes of interest are spectrally very similar and high dimensional multispectral image data is available. A number of the investigations that have been developed in this area deal with the fact that as the data dimensionality increases, so does the difficulty in obtaining a reasonably accurate estimate of the within-class covariance matrices from the number of available labeled samples, which is usually limited. Several approaches have been proposed to deal with this problem. This study aims toward a complementary goal. Assuming that reasonably accurate estimates for the within-class covariance matrices have been obtained, we seek to better understand what kind of geometrically-oriented interpretation can be given to them as the data dimensionality increases and also to understand how this knowledge can help the design of a classifier. In order to achieve this goal, the covariance matrix is decomposed into a number of parameters that are then analyzed separately with respect to their ability to separate the classes. Methods for image classification based on these parameters are investigated. Results of tests using data provided by the sensor system AVIRIS are presented and discussed.