Chan, Wai LamChoi, HyeokhoBaraniuk, Richard G.2007-10-312007-10-312006-10-012006-10-24W. L. Chan, H. Choi and R. G. Baraniuk, "Coherent Multiscale Image Processing using Quaternion Wavelets," <i>IEEE Transactions on Image Processing,</i> 2006.https://hdl.handle.net/1911/19786Journal PaperThe quaternion wavelet transform (QWT) is 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 phases: two phases encode local image shifts while the third contains image texture information. The QWT is based on an alternative theory for the 2-D Hilbert transform and can be computed using a dual-tree filter bank with linear computational complexity. To demonstrate the properties of the QWT's coherent magnitude/phase representation, we develop an efficient and accurate procedure for estimating the local geometrical structure of an image. We also develop a new multiscale algorithm for estimating the disparity between a pair of images that is promising for image registration and flow estimation applications. The algorithm features multiscale phase unwrapping, linear complexity, and sub-pixel estimation accuracy.engquaternioncomplexwavelet transformphasedisparity estimationWavelet based Signal/Image ProcessingJournal articlequaternioncomplexwavelet transformphasedisparity estimation