title: Coherent multiscale image processing using dual-tree quaternion wavelets.
abstract: The dual-tree 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.
authors.affiliation: Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA. wailam@rice.edu
authors.forename: Wai Lam
authors.initials: WL
authors.lastname: Chan
authors.forename: Hyeokho
authors.initials: H
authors.lastname: Choi
authors.forename: Richard G
authors.initials: RG
authors.lastname: Baraniuk
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D041623:Tomography, Optical Coherence / Q000379:methods*