Hyperspectral image segmentation using spatial-spectral graphs

Spectral graph theory has proven to be a useful tool in the analysis of high-dimensional data sets. Recall that, mathematically, a graph is a collection of objects (nodes) and connections between them (edges); a weighted graph additionally assigns numerical values (weights) to the edges. Graphs are represented by their adjacency whose elements are the weights between the nodes. Spectral graph theory uses the eigendecomposition of the adjacency matrix (or, more generally, the Laplacian of the graph) to derive information about the underlying graph. In this paper, we develop a spectral method based on the 'normalized cuts' algorithm to segment hyperspectral image data (HSI). In particular, we model an image as a weighted graph whose nodes are the image pixels, and edges defined as connecting spatial neighbors; the edge weights are given by a weighted combination of the spatial and spectral distances between nodes. We then use the Laplacian of the graph to recursively segment the image. The advantages of our approach are that, first, the graph structure naturally incorporates both the spatial and spectral information present in HSI; also, by using only spatial neighbors, the adjacency matrix is highly sparse; as a result, it is possible to apply our technique to much larger images than previous techniques. In the paper, we present the details of our algorithm, and include experimental results from a variety of hyperspectral images.