ITK/Release 4/Refactor Numerical Libraries/Inventory/Fourier Transforms

The Problem

ITK obtains Fast Fourier Transform (FFT) functionalities from

• VXL - as software included as third party library
• FFTW - as a configuration time option

When using the VXL code that is shipped with ITK, the FFT operations are very slow.

FFTW is a lot faster, but it is licensed under GPL and can not be included as part of the ITK distribution.

To choose between these two options you use, at CMake configuration time, the following variables

• USE_FFTWF to use the float version of FFTW
• USE_FFTWD to use the double version of FFTW
• USE_SYSTEM_FFTW to use an FFTW library installed in your system

Where is the Code

ITK classes that provide FFT filters can be found in the Module:

   ITK/Modules/Filtering/FFT

They include

• itkFFTShiftImageFilter.h
• itkFFTWForwardFFTImageFilter.h
• itkFFTWInverseFFTImageFilter.h
• itkForwardFFTImageFilter.h
• itkInverseFFTImageFilter.h
• itkVnlForwardFFTImageFilter.h
• itkVnlInverseFFTImageFilter.h
• vnl_fft_3d.h

VXL

Code

The FFT code in VXL is in the directory

 ITK/Modules/ThirdParty/VNL/src/vxl/core/vnl/algo

and include the following files

• vnl_fft_1d.h
• vnl_fft_1d.txx
• vnl_fft_2d.h
• vnl_fft_2d.txx
• vnl_fft_base.h
• vnl_fft_base.txx
• vnl_fft.cxx
• vnl_fft.h
• vnl_fft_prime_factors.h
• vnl_fft_prime_factors.txx

It seems that VXL ultimately calls FFT functions from FORTRAN

  CALL GPFA(A,B,TRIGS,INC,JUMP,N,LOT,ISIGN,NIPQ,INFO)

in the file

  vnl_fft.h

Conditions

Image Size

The code accepts images whose number of pixels along every dimension is a multiple of powers of the following prime numbers:

• 2
• 3
• 5

That is, it should be an expression such as

   2^P * 3^Q * 5^R

Image Dimensions

• Implementations are available for 1D and 2D in VXL.
• ITK added a 3D instantiation outside of VXL

Benchmark Test

Quick Tests

Quick Test that verify correctness are available here:

  ITK/Release/Modules/Filtering/FFT/test

They can run the following

 Test #1: itkVnlFFTTest
 Test #2: itkFFTShiftImageFilterTestOdd0
 Test #3: itkFFTShiftImageFilterTestOdd1
 Test #4: itkFFTShiftImageFilterTestEven0
 Test #5: itkFFTShiftImageFilterTestEven1

Longer Tests

More demanding tests are available here

  ITK/Release/Examples/Filtering/test

and can be run with

  ctest  -R FFT   -VV

they are

 Test #67: FFTImageFilterTest
 Test #68: FFTDirectInverseTest
 Test #69: FFTImageFilterTest2
 Test #70: FFTImageFilterTest3

Options

Options that have been considered:

• INTEL Library