Quaternionic wavelets for texture classification

This article proposes a study of the recent quaternionic wavelet transform (QWT) from a practical point of view through a digital image analysis application. Based on a theoretic 2D generalization of the analytic signal leading to a strong 2D signal modeling, this representation uses actual 2D analytic wavelets and yields subbands having a shift-invariant magnitude and a 3-angle phase, using the quaternion algebra.Our experiment furthers the understanding of this quite sophisticated tool, and shows its practical interest by a clear improvement of a famous wavelet application: texture classification. Thanks to coherent multiscale analysis brought by the QWT we obtain better classification results than with standard wavelets in a similar process.

► We propose to use an improvement of classical wavelets: quaternion wavelets (QWT).
► QWT should perform better local geometric analysis of 2D signals like images.
► We conduct a wavelet based texture classification to verify this with textures.
► The QWT outperforms classical wavelets (and complex wavelets).
► We give geometrical interpretation of this result.