QWT: Retrospective and New Applications

Abstract

Quaternion wavelet transform (QWT) achieves much attention in recent years as a new multiscale analysis tool for geometric image structures. It is an extension of the real wavelet transform and complex wavelet transform (CWT) by using the quaternion algebra and the 2-D Hilbert transform of filter theory. It brings exciting properties to many image applications, such as color image processing, face recognition, movement representation and so on. To give an overview of the development of QWT and investigate its potential applications, this paper provides a retrospective of QWT and focuses on the new applications of QWT in the domain of image registration and image fusion. As for multiscale image analysis tasks, we indicate that it is important for QWT to induce the mechanism of adaptive scale representation of geometric features, which is testified in two application instances of uncalibrated stereo matching and optical flow estimation. In addition, the potential of QWT in the new applications of image registration and image fusion is explored in this paper. Quaternionic phase congruency model in QWT domain is discussed and operates as the key step in image registration. With regard to the application of image fusion, the better representation of edges and textures is preferred. Therefore we incorporate Directonal Filter Bank (DFB) into the quaternion wavelet decomposition scheme to greatly enhance the direction selectivity and anisotropy of QWT. The experimental results demonstrate the interesting fusion property of the modified QWT scheme. Overall, the analytical and experimental investigations in this paper aim to give a suggestive reference for the use of QWT.