Spectral image complexity estimated through local convex hull volume

Abstract

Most spectral image processing schemes develop models of the data in the hyperspace by using first and second order statistics or linear subspace geometries applied to the image globally. However, it is simple to show that the data are typically not multivariate Gaussian or are not well defined by linear geometries when considering the entire image, particularly as the spatial resolution improves and the scene becomes more cluttered. Here, we use the concept of a convex hull that encloses the data to rank local regions within an image by an estimate of their complexity. The complexity as defined here is directly related to the volume of the hull in n dimensions that encloses the data under the assumptions that less complex data will have fewer distinct materials and more complex data will have more materials. They will also be more widely separated in the hyperspace. The method uses the Gram Matrix approach to estimate the volume of the hull and is applied to an image that has been tiled. The complexity of each tile is then estimated showing the relative changes in complexity over a large area spectral image. Results will be shown for reflective hyperspectral imagery over different scene contents with resolutions of ≈2-3 m. Ultimately this methodology can be used to develop localized models of an image and may provide insight into the large area search problem.