Affine invariant hyperspectral image descriptors based upon harmonic analysis

This chapter focuses on the problem of recovering a hyperspectral image descriptor based upon harmonic analysis. It departs from the use of integral transforms to model hyperspectral images in terms of probability distributions. This provides a link between harmonic analysi and affine geometric transformations between object surface planes in the scene. Moreover, the use of harmonic analysis permits the study of these descriptors in the context of Hilbert spaces. This, in turn, provides a connection to functional analysis to capture the spectral crosscorrelation between bands in the image for the generation of a descriptor with a high energy compaction ratio. Thus, descriptors can be computed based upon orthogonal bases capable of capturing the space and wavelength correlation for the spectra in the hyperspectral imagery under study. We illustrate the utility of our descriptor for purposes of object recognition on a hyperspectral image dataset of real-world objects and compare our results to those yielded using an alternative.