Multiscale Representation and Segmentation of Hyperspectral Imagery Using Geometric Partial Differential Equations and Algebraic Multigrid Methods (PREPRINT)

A fast algorithm for multiscale representation and segmentation of hyperspectral imagery is introduced in this paper. The multiscale/scale-space representation is obtained by solving a nonlinear diffusion Partial Differential Equation (PDE) for vector-valued images. We use Algebraic Multigrid (AMG) techniques to obtain a fast and scalable solution of the PDE and to segment the hyperspectral image following the intrinsic multigrid structure. We test our algorithm on four standard hyperspectral images that represent different environments commonly found in remote sensing applications: agricultural, urban, mining, and marine. The experimental results show that the segmented images lead to better classification than using the original data directly, in spite of the use of simple similarity metrics and piecewise constant approximations obtained from the segmentation maps. Sponsored in part by the National Geospatial Intelligence Agency, Office of Naval Research and Defense Advanced Research Projects Agency.