We use physical considerations to show that an affine transformation can be used to model the effect of environmental changes on hyperspectral image distributions. This allows the generation of a vector of moment invariants that describes an image distribution but does not depend on the environmental conditions. These vectors maintain the invariant property after each image band is spatially filtered which allows the representation to capture spatial properties. We use the distribution invariants and the Fisher discriminant to reduce the size of the representation by selecting optimized spectral bands. We apply the methods developed in this work to the illumination-invariant classification and recognition of regions in airborne images. We also show that the distribution transformation model can be used for change detection in regions viewed under unknown conditions.