New hyperspectral discrimination measure for spectral similarity

Abstract

Spectral angle mapper (SAM) has been widely used as a spectral similarity measure for multispectral and hyperspectral image analysis. It has been shown to be equivalent to Euclidean distance when the spectral angle is relatively small. Most recently, a stochastic measure, called spectral information divergence (SID) has been introduced to model the spectrum of a hyperspectral image pixel as a probability distribution so that spectral variations can be captured more effectively in a stochastic manner. This paper develops a new hyperspectral spectral discriminant measure, which is a mixture of SID and SAM. More specifically, let x_i and x_j denote two hyperspectral image pixel vectors with their corresponding spectra specified by s_i and s_j. SAM is the spectral angle of x_i and x_j and is defined by [SAM(s_i,s_j)]. Similarly, SID measures the information divergence between x_i and x_j and is defined by [SID(s_i,s_j)]. The new measure, referred to as (SID,SAM)-mixed measure has two variations defined by SID(s_i,s_j)xtan(SAM(s_i,s_j)] and SID(s_i,s_j)xsin[SAM(s_i,s_j)] where tan [SAM(s_i,s_j)] and sin[SAM(s_i,s_j)] are the tangent and the sine of the angle between vectors x and y. The advantage of the developed (SID,SAM)-mixed measure combines both strengths of SID and SAM in spectral discriminability. In order to demonstrate its utility, a comparative study is conducted among the new measure, SID and SAM where the discriminatory power of the (SID,SAM)-mixed measure is significantly improved over SID and SAM.