Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets

The dual-tree quaternion wavelet transform (QWT) is a new multiscale analysis tool for geometric image features. The QWTis 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.

Authors: Wai Lam Chan, Hyeokho Choi, Richard G. Baraniuk

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