A comparison of error metrics and constraints for multiple endmember spectral mixture analysis and spectral angle mapper

Abstract

Spectral matching algorithms can be used for the identification of unknown spectra based on a measure of similarity with one or more known spectra. Two popular spectral matching algorithms use different error metrics and constraints to determine the existence of a spectral match. Multiple endmember spectral mixture analysis (MESMA) is a linear mixing model that uses a root mean square error (RMSE) error metric. Spectral angle mapper (SAM) compares two spectra using a spectral angle error metric. This paper compares two endmember MESMA and SAM using a spectral library containing six land cover classes. RMSE and spectral angle for models within each land cover class were directly compared. The dependence of RMSE on the albedo of the modeled spectrum was also explored. RMSE and spectral angle were found to be closely related, although not equivalent, due to variations in the albedo of the modeled spectra. Error constraints applied to both models resulted in large differences in the number of spectral matches. Using MESMA, the number of spectra modeled within the error constraint increased as the albedo of the modeled spectra decreased. The value of the error constraint used was shown to make a much larger difference in the number of spectra modeled than the choice of spectral matching algorithm.