Local quaternion Fourier transform and color image texture analysis

Color images can be treated as two-dimensional quaternion functions. For analysis of quaternion images, a joint space-wavenumber localized quaternion S transform (QS) is presented in this study for a simultaneous determination of the local color image spectra. The QS transform uses a two-dimensional Gaussian localizing window that scales with wavenumbers. Rotation invariance, invertibility and computational aspects of the QS transform are discussed. The power map of the QS transform is presented here as a powerful tool in color image texture and pattern analysis. Examples are presented.