Journal of Mathematical Imaging and Vision

, Volume 24, Issue 1, pp 19–35 | Cite as

The Theory and Use of the Quaternion Wavelet Transform

  • Eduardo Bayro-Corrochano


This paper presents the theory and practicalities of the quaternion wavelet transform (QWT). The major contribution of this work is that it generalizes the real and complex wavelet transforms and derives a quaternionic wavelet pyramid for multi-resolution analysis using the quaternionic phase concept. As a illustration we present an application of the discrete QWT for optical flow estimation. For the estimation of motion through different resolution levels we use a similarity distance evaluated by means of the quaternionic phase concept and a confidence mask. We show that this linear approach is amenable to be extended to a kind of quadratic interpolation.


image processing real and complex wavelets multi-resolution analysis wavelet pyramid quaternion wavelets quaternion wavelet pyramid disparity estimation optical flow 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Eduardo Bayro-Corrochano
    • 1
  1. 1.Computer Science Department, GEOVIS LaboratoryCentro de Investigación y de Estudios Avanzados, CINVESTAVGuadalajaraMexico

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