Construction of Hilbert transform pairs of wavelet bases and Gabor-like transforms
IEEE Transactions on Signal Processing
Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform
IEEE Transactions on Image Processing
Local quaternion Fourier transform and color image texture analysis
Signal Processing
Steerable wavelet frames based on the Riesz transform
IEEE Transactions on Image Processing
Quaternion multiplier inspired by the lifting implementation of plane rotations
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Quaternionic wavelets for texture classification
Pattern Recognition Letters
Information-Based scale saliency methods with wavelet sub-band energy density descriptors
ACIIDS'13 Proceedings of the 5th Asian conference on Intelligent Information and Database Systems - Volume Part II
New feature extraction approach for bank note classification using Quaternion Wavelets
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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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 2D 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.