Improved manifold coordinate representations of hyperspectral imagery

There are many well-known sources of nonlinearity present in hyperspectral imagery; these include hi-directional reflectance distribution function (BRDF) effects, multi-path scatter between heterogeneous pixel constituents, and the variable presence of water, an attenuating medium, in the scene. In recent puhlications, we have presented a data-driven approach to representing the nonlinear structure of hyperspectral imagery [4]. The approach relies on graph methods to derive geodesic distances on the high-dimensional hyperspectral data manifold. From these distances, a set of manifold coordinates that parameterizes the data manifold is derived. Because of the computational and memory overhead required in the geodesic coordinate calculations, the approach relies on partitioning the scene into subsets where the optimal manifold coordinates can he derived in an efficient manner, followed by an alignment stage during which the embedded manifold coordinates for each subset are aligned to a common manifold coordinate system. In [4], we demonstrated the feasihility of the coordinate and alignment methodology and the ability of the manifold approach to provide higher data compression and more effective classification when compared with linear methods. In this paper we develop an improved approach to the manifold coordinate alignment phase with an improved sampling methodology. Results are demonstrated using examples of hyperspectral imagery derived from PROBE2 hyperspectral scenes of the Virginia Coast Reserve barrier islands.