Statistical characterization of natural hyperspectral backgrounds using t -elliptically contoured distributions

Abstract

The objective of this paper is the statistical characterization of natural hyperspectral backgrounds using the multivariate <i>t</i>-elliptically contoured distribution. Traditionally, hyperspectral backgrounds have been modeled using multivariate Gaussian distributions; however it is well known that real data often exhibit "long-tail" behavior that cannot be accounted by normal distribution models. The proposed multivariate <i>t</i>-distribution model has elliptical equiprobability contours whose center and ellipticity is specified by the mean vector and covariance matrix of the data. The density of the contours, which is reflected into the distribution of the Mahalanobis distance, is controlled by an extra parameter, the number of degrees of freedom. As the number of degrees of freedom increases, the tails decrease and approach those of a normal distribution with the same mean and covariance. In this work we investigate the application of <i>t</i>-elliptically contoured distributions to the characterization of different hyperspectral background data obtained by visually interactive spatial segmentation ("physically" homogeneous classes), automated clustering algorithms using spectral similarity metrics (spectrally homogeneous classes), and by fitting normal mixture models (statistically homogeneous classes). These investigations are done using hyperspectral data from the AVIRIS sensor.