Hyperspectral Data Processing: Algorithm Design and Analysis

11.1 Introduction

A wide variety of algorithms have been developed for endmember extraction in recent years. One of early developed EEAs is the so-called pixel purity index (PPI) proposed by Boardman (1994), which has become one of most popular EEAs due to its availability in the software, environment for visualizing images (ENVI). The design rationale of PPI is based on the concept of convex geometry, especially on the fact that a line segment connected by two points includes all the points mixed by the two end points as a result of convexity in which case two end points are considered as pure points, whereas the points right in between can be obtained by mixing these end points with appropriate portions. In order to make it work, PPI randomly generates a set of unit vectors to be considered as line segments, called skewers, and then use these skewers as basis vectors onto which all data sample vectors are projected. The number of times a data sample vector orthogonally projected at end points of these skewers is defined as its PPI count that will be used to determine if this data sample vector is an endmember (see Figure 7.1). Theoretically speaking, higher the PPI count of a data sample vector, more likely the data sample vector to be an endmember. As already demonstrated in the experiments of six scenarios conducted in Chapter 4, this is generally not the case. Nevertheless, it is usually true that the PPI count of an endmember is always nonzero, that is, greater than 0, but ...