Statistical Affine Invariant Hyperspectral Texture Descriptors Based Upon Harmonic Analysis.
This chapter focuses on the problem of recovering a hyperspectral texture descriptor based upon harmonic analysis. The chapter departs from the use of Fourier transforms to model hyperspectral textures in terms of probability distributions. This provides a link to affine geometric transformations between texture planes and the Fourier domain. Moreover, the use of Fourier analysis permits, in a straightforward manner, the use of harmonic analysis to study these descriptors in the context of Hilbert spaces. This in turn provides a connection to functional analysis to capture the spectral cross-correlation between bands in the image for the generation of a descriptor with a high energy compaction ratio. The method permits the computation of descriptors based upon orthogonal bases with high information compaction properties which can capture the space and wavelength correlation for the spectra in hyperspectral images. We illustrate the robustness of the descriptors to affine transformations by providing a sensitivity analysis on the textures under study and show their utility for purposes of recognition.