Graph theoretic metrics for spectral imagery with application to change detection

Many spectral algorithms that are routinely applied to spectral imagery are based on the following models: statistical, linear mixture, and linear subspace. As a result, assumptions are made about the underlying distribution of the data such as multivariate normality or other geometric restrictions. Here we present a graph based model for spectral data that avoids these restrictive assumptions and apply graph based metrics to quantify certain aspects of the resulting graph. The construction of the spectral graph begins by connecting each pixel to its k-nearest neighbors with an undirected weighted edge. The weight of each edge corresponds to the spectral Euclidean distance between the adjacent pixels. The number of nearest neighbors, k, is chosen such that the graph is connected i.e., there is a path from each pixel xi to every other. This requirement ensures the existence of inter-cluster connections which will prove vital for our application to change detection. Once the graph is constructed, we calculate a metric called the Normalized Edge Volume (NEV) that describes the internal structural volume based on the vertex connectivity and weighted edges of the graph. Finally, we demonstrate a graph based change detection method that applies this metric.