An affine Invariant hyperspectral texture descriptor based upon heavy-tailed distributions and fourier analysis

Abstract

In this paper, we address the problem of recovering a hyperspectral texture descriptor. We do this by viewing the wavelength-indexed bands corresponding to the texture in the image as those arising from a stochastic process whose statistics can be captured making use of the relationships between moment generating functions and Fourier kernels. In this manner, we can interpret the probability distribution of the hyper-spectral texture as a heavy-tailed one which can be rendered invariant to affine geometric transformations on the texture plane making use of the spectral power of its Fourier cosine transform. We do this by recovering the affine geometric distortion matrices corresponding to the probability density function for the texture under study. This treatment permits the development of a robust descriptor which has a high information compaction property and can capture the space and wavelength correlation for the spectra in the hyperspectral images. We illustrate the utility of our descriptor for purposes of recognition and provide results on real-world datasets. We also compare our results to those yielded by a number of alternatives.

Imaging Spectroscopy for Scene Analysis

“…Huynh and Robles-Kelly (2008) have presented a method to represent reflectance data making use of a continuous basis by fitting a B-spline to the spectra under study. Recently, Khuwuthyakorn et al (2009) proposed a texture descriptor for imaging spectroscopy based on Fourier analysis and heavy-tailed probability distributions. This is reminiscent of time-dependent textures, whose probability density functions exhibit first and second-order moments which are space and time-shift invariant (Doretto et al 2003).…”

“…This is reminiscent of time-dependent textures, whose probability density functions exhibit first and second-order moments which are space and time-shift invariant (Doretto et al 2003). Unfortunately, the descriptor presented in Khuwuthyakorn et al (2009) cannot be used to recover the spectral signatures but rather has been designed for purposes of recognition where precise material matching is not necessary.…”