New hyperspectral discrimination measure for spectral similarity

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 xi and xj denote two hyperspectral image pixel vectors with their corresponding spectra specified by si and sj. SAM is the spectral angle of xi and xj and is defined by [SAM(si,sj)]. Similarly, SID measures the information divergence between xi and xj and is defined by [SID(si,sj)]. The new measure, referred to as (SID,SAM)-mixed measure has two variations defined by SID(si,sj)xtan(SAM(si,sj)] and SID(si,sj)xsin[SAM(si,sj)] where tan [SAM(si,sj)] and sin[SAM(si,sj)] 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.