Coherent multiscale image processing using dual-tree quaternion wavelets

Wai Lam Chan, Hyeokho Choi, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

124 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1069-1082
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number7
StatePublished - Jul 2008


  • Coherent processing
  • Dual-tree
  • Multiscale disparity estimation
  • Phase
  • Quaternion
  • Wavelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition


Dive into the research topics of 'Coherent multiscale image processing using dual-tree quaternion wavelets'. Together they form a unique fingerprint.

Cite this