The use of bispectrum in testing Gaussianity and linearity for texture image projections

Abstract

Classical methods for texture analysis assume that textures are Gaussian and linear processes which provide an independent relation between pixels. The reason behind these limited assumptions, is the use of first and second order statistics which introduce a simplicity of computation and interpretation. However, important structures in the texture emerge when we deviate from Gaussianity and linearity introduced by higher order correlation between pixels or between frequencies in the frequency domain. Higher order spectra and especially the third order namely the bispectrum can detect the non linear interaction and the dependency between frequencies. In this paper, we present a statistical analysis using 1D Hinich test on radon projections of textures to reject Gaussianity and linearity assumptions via the bispectrum and its normalized version named the bicoherence. Statistical results show a non Gaussian and a non linear behaviour of textures.