We develop a quaternion wavelet transform (QWT) as a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant, tight frame representation whose coefficients sport a magnitude and three phase values, two of which are directly proportional to local image shifts. The QWT can be efficiently computed using a dual-tree filter bank and is based on a 2-D Hilbert transform. We demonstrate how the QWT's magnitude and phase can be used to accurately analyze local geometric structure in images. We also develop a multiscale flow/motion estimation algorithm that computes a disparity flow map between two images with respect to local object motion.

Date Published: 17 September 2005
PDF: 10 pages
Proc. SPIE 5914, Wavelets XI, 59140Z (17 September 2005); doi: 10.1117/12.615393

Published in SPIE Proceedings Vol. 5914:
Wavelets XI
Manos Papadakis; Andrew F. Laine; Michael A. Unser, Editor(s)