Isotropic and Steerable Wavelets in N Dimensions. A multiresolution analysis framework.

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This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for state of the art filters for denoising, feature detection or phase analysis in N-dimensions. It focus on reusability, and highly decoupled modules for easy extension and implementation of new filters, and it contains a filter for multiresolution phase analysis,

The backbone of the multi-scale analysis is provided by an isotropic band-limited wavelet pyramid, and the detection of directional features is provided by coupling the pyramid with a generalized Riesz transform.
The generalized Riesz transform of order N behaves like a smoothed version of the Nth order derivatives of the signal. Also, it is steerable: its components impulse responses can be rotated to any spatial orientation, reducing computation time when detecting directional features.

This paper is accompanied with the source code, input data, parameters and
output data that the author used for validating the algorithm described in
this paper. This adheres to the fundamental principle that scientific
publications must facilitate reproducibility of the reported results.
There is no code review at this time.

minus Very interesting work by Le Zheng on 2017-06-02 11:07:04 for revision #1
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Comment by Pablo Hernandez cerdan yellow
Hello Juju
I think those errors in the macros can be solved if you update ITK. Not sure what is the minimum version but some people reported similar errors that were solved for 4.10 maybe? ( This module is tested using the latest ITK (from master) and it has no errors in any platform there. Hope it helps.
Comment by Juju Tardon yellow
Thank you for this implementation.

I Have same bugs when I try to test your project

itkFFTPadPositiveIndexImageFilterTest.cxx:55:24: error: macro "EXERCISE_BASIC_OBJECT_METHODS" passed 3 arguments but takes just 2

itkFFTPadPositiveIndexImageFilter.h:109: error: ISO C++ forbids declaration of 'ITK_DISALLOW_COPY_AND_ASSIGN' with no type

itkFFTPadPositiveIndexImageFilterTest.cxx: In function 'itkFFTPadPositiveIndexImageFilterTest(int char**)':
itkFFTPadPositiveIndexImageFilterTest.cxx:54: error: 'EXERCISE_BASIC_OBJECT_METHODS'was not declared in this scope

thank you
Comment by Pablo Hernandez cerdan yellow
Nice! Good to know that you are working on this. I have implemented the itkRieszRotationMatrix --S_U-- and also the StructureTensor --J(x_0)--. I will read more carefully your manuscript and the Matlab code but maybe isn't that much work to implement it in ITK?. I am busy right now writing up but I am sure in the future I'll tackle more of this. Thanks for pointing it.
Comment by Yashin Dicente yellow
Thank you for implementing these features into ITK. It would be very helpful.
Recently we published an extension to the Riesz-wavelet transform:
In this work we presented 3 methods to locally align high-order Riesz-wavelet filters. This translates into rotation-invariant features with no loss of directional information.
It would be great if you could also add these methods into ITK. You can find the Matlab code used in the paper here:
Feel free to contact me if you have any question or comment.

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Categories: Image, Information Theory, Iterators
Keywords: Wavelet, Filter Bank, Pyramid, MRA, Isotropic, Riesz, Phase, Denoise, Feature Detection, External
Toolkits: ITK, CMake
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