A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Zsuzsanna Püspöki and Nicolas Chenouard

Outline

A complete parametric framework and set of MATLAB tools for computing steerable wavelet frames in 2-D. Available designs include Simoncelli's pyramid, Marr and monogenic wavelets, Prolate spheroidal wavelets, gradient and Hessian wavelets, etc.

Reference

[1] Z. Püspöki, M. Unser, "Template-Free Wavelet-Based Detection of Local Symmetries," IEEE Transactions on Image Processing, vol. 24, no. 10, pp. 3009-3018, October 2015.

[2] M. Unser, N. Chenouard, "A Unifying Parametric Framework for 2D Steerable Wavelet Transforms," SIAM Journal on Imaging Sciences, vol. 6, no. 1, pp. 102-135, 2013.

Download Matlab Code Zip archive, 92Kb, version of 09.12.2015.

Conditions of Use

You are free to use this software for research purposes, but you should not redistribute it without our consent. In addition, we expect you to include citations on [1] and [2] and acknowledgments on this webpage whenever you present or publish results that are based on it.

Matlab functions	function m-files define the main interface of the implementation
Init.m	initialize parameters of wavelet construction
SteerableDesign.m	return U matrix for a desired wavelet construction
U/EquiAng.m	return U matrix for a generalized equiangular design
CompleteAnalysis.m	steerable wavelet analysis
CompleteSynthesis.m	steerable wavelet synthesis
Projection.m	compute coefficients for a given construction (U matrix) from the output of CompleteAnalysis

Matlab Scripts	Demonstration
demoAnalysisSynthesis.m	demonstrates the perfect reconstruction property and visualizes wavelet coefficients for the chosen construction, as described in the reference.
demoWavelet.m	plots wavelets from chosen construction

Additional functions, typically not meant to be used directly, are found in subfolders.

For more information please refer to the help of individual functions. For examples of use see the demos.