The spectral similarity scale and its application to the classification of hyperspectral remote sensing data

Abstract

Hyperspectral images have considerable information content and are becoming common. Analysis tools must keep up with the changing demands and opportunities posed by the new datasets. Many spectral image analysis algorithms depend on a scalar measure of spectral similarity or 'spectral distance' to provide an estimate of how closely two spectra resemble each other. Unfortunately, traditional spectral similarity measures are ambiguous in their distinction of similarity. Traditional metrics can define a pair of spectra to be nearly identical mathematically yet visual inspection shows them to be spectroscopically dissimilar. These algorithms do not separately quantify both magnitude and direction differences. Three common algorithms used to measure the distance between remotely sensed reflectance spectra are Euclidean distance, correlation coefficient, and spectral angle. Euclidean distance primarily measures overall brightness differences but does not respond to the correlation (or lack thereof) between two spectra. The correlation coefficient is very responsive to differences in direction (i.e. spectral shape) but does not respond to brightness differences due to band-independent gain or offset factors. Spectral angle is closely related mathematically to the correlation coefficient and is primarily responsive to differences in spectral shape. However, spectral angle does respond to brightness differences due to a uniform offset, which confounds the interpretation of the spectral angle value. This paper proposes the spectral similarity scale (SSS) as an algorithm that objectively quantifies differences between reflectance spectra in both magnitude and direction dimensions (i.e. brightness and spectral shape). Therefore, the SSS is a fundamental improvement in the description of distance or similarity between two reflectance spectra. In addition, it demonstrates the use of the SSS by discussing an unsupervised classification algorithm based on the SSS named ClaSSS.