A class to hold spectral bands of an image. More...

#include <FFT.h>

Public Member Functions
	FFT ()
	Constructor.

	~FFT ()
	Destructor.

Static Public Member Functions
static ArrayGrid< std::complex< double > > *	CreateComplexGridFromRealGrid (ArrayGrid< double > *pGridIn)
	creates a grid of complex values from a real-valued grid in which the imaginary components are 0 More...

static ArrayGrid< double > *	CreateRealGridFromComplexGrid (ArrayGrid< std::complex< double > > *pGridIn)
	creates a grid of real values from a complex-valued grid; we just take the real component of each complex number More...

static ArrayGrid< double > *	ComputePowerSpectrum (ArrayGrid< double > *pInputGrid)
	Computes power spectrum, and returns it as a grid. More...

static ArrayGrid< double > *	ComputeLogPowerSpectrum (ArrayGrid< double > *pInputGrid)
	Computes logarithm of the power spectrum, and returns it as a grid. Logarithm is used for compression of dynamic range of values, for visualization. More...

static std::vector< double >	ComputeRadiallyAveragedSpectrum (ArrayGrid< double > *pInputImage, int thetaSteps=500)
	Computes radially averaged power spectrum, and returns it rescaled logaritmically as a 1D vector of doubles. More...

static ArrayGrid< double > *	Convolve (ArrayGrid< double > pInputGrid, ArrayGrid< double > pFilterKernel)
	Computes the convolution of a single grid with the filterKernel in the argument. More...

static Image *	Convolve (Image pInputImage, ArrayGrid< double > pFilterKernel)
	Overloaded method to computes the convolution of an image with the filterKernel. More...

static Image *	GaussConvolve (Image *pInputImage, double sigma)
	Computes the convolution of an image with a Gaussian PSF with given sigma. More...

static ArrayGrid< double > *	GaussConvolve (ArrayGrid< double > *pInputGrid, double sigma)
	Computes the convolution of a single grid with a Gaussian PSF with given sigma. More...

static FFTBand *	ApplyTransferFunction (FFTBand pFFTImageData, ArrayGrid< double > transferFunction)
	Applies a transfer function to a FFTBand (= Fourier-transformed input data) More...

static FFTBand *	ApplyTransferFunction (FFTBand pFFTImageData, FFTBand transferFunction)
	Applies a transfer function to a FFTBand (= Fourier-transformed input data) Overloaded ApplyTransferFunction to allow that the transfer function is also in complex format already. More...

static FFTBand *	ApplyTransferFunctionFFT (ArrayGrid< double > pInputGrid, ArrayGrid< double > transferFunction)
	yet another method to apply a transfer function This time, it takes real input and gives output in the Fourier domain Motivation: when reconstructing a pyramid, we can sum all the bands in the Fourier domain, so we only need the inverse Fourier transform once. More...

static FFTBand *	ApplyTransferFunctionFFT (ArrayGrid< double > pInputGrid, FFTBand transferFunction)
	yet another method to apply a transfer function Overloaded previous method to allow that the transfer function is also in complex format already More...

static FFTBand *	ApplyTransferFunctionFFT (ArrayGrid< std::complex< double > > pInputGrid, FFTBand transferFunction)
	yet another method to apply a transfer function Overloaded previous method to allow that the transfer function is also in complex format already More...

static ArrayGrid< double > *	ApplyTransferFunctionSpatial (ArrayGrid< double > pInputGrid, ArrayGrid< double > transferFunction, FFTDataType myDataType=RE)
	yet another method to apply a transfer function More...

static std::pair< ArrayGrid< double > , ArrayGrid< double > >	ApplyTransferFunctionSpatialComplex (ArrayGrid< double > pInputGrid, ArrayGrid< double > transferFunction)
	yet another method to apply a transfer function More...

static ArrayGrid< double > *	SuppressOuterFrequencies (ArrayGrid< double > *pInputGrid)
	supresses the outer frequencies in an image; essentially makes an image band-limited More...

Static Protected Member Functions
static void	RescaleGrid (ArrayGrid< double > *pGrid, double newMin, double newMax)
	rescales the intensities in pGrid More...

static void	WriteFFTDataToPPM (FFTBand pFFTData, FFTDataType myDataType, char pFileName, double factor)
	Writes for diagnostic purposes the real or imaginary part of FFTData to disk. More...

Detailed Description

A class to hold spectral bands of an image.

Member Function Documentation

FFTBand * stira::fouriertools::FFT::ApplyTransferFunction	(	FFTBand *	pFFTImageData,
		ArrayGrid< double > *	transferFunction
	)

static

Applies a transfer function to a FFTBand (= Fourier-transformed input data)

Takes the Fourier Transformed image as input and creates a complex-valued grid in the spatial domain (so output is NOT in the Fourier domain anymore!!)

Complex-valued output is convenient though for generalization purposes: both real-valued as complex valued output can be generated, and can be postprocessed according to the specific case

Handy when building a pyramid: needs to extract bands from same image, so: FFT once, apply different transfer functions and IFFT for each extracted band

Parameters

pFFTImageData	input data already fourier-transformed
transferFunction	transfer functions to be applied on this FFTBand

Referenced by stira::steerable::PyramidMaster< T >::ExtractB(), stira::steerable::PyramidMaster< T >::ExtractB0(), stira::steerable::PyramidMaster< T >::ExtractL(), and stira::steerable::PyramidMaster< T >::ExtractL0().

FFTBand * stira::fouriertools::FFT::ApplyTransferFunction	(	FFTBand *	pFFTImageData,
		FFTBand *	transferFunction
	)

static

Applies a transfer function to a FFTBand (= Fourier-transformed input data) Overloaded ApplyTransferFunction to allow that the transfer function is also in complex format already.

Parameters

pFFTImageData	input data already fourier-transformed
transferFunction	transfer functions to be applied on this FFTBand

References stira::fouriertools::FFTBand::ApplyInverseTransform(), stira::fouriertools::FFTBand::GetHeight(), stira::fouriertools::FFTBand::GetValue(), stira::fouriertools::FFTBand::GetWidth(), stira::fouriertools::FFTBand::SetValue(), and stira::fouriertools::FFTBand::SwitchQuadrants().

FFTBand * stira::fouriertools::FFT::ApplyTransferFunctionFFT	(	ArrayGrid< double > *	pInputGrid,
		ArrayGrid< double > *	transferFunction
	)

static

yet another method to apply a transfer function This time, it takes real input and gives output in the Fourier domain Motivation: when reconstructing a pyramid, we can sum all the bands in the Fourier domain, so we only need the inverse Fourier transform once.

Parameters

pInputGrid	the input grid to be filtered
transferFunction	the transfer function to be applied on this FFTBand

Referenced by ApplyTransferFunctionFFT(), stira::steerable::PyramidMaster< T >::ReconstructB(), stira::steerable::PyramidMaster< T >::ReconstructB0(), and stira::steerable::PyramidMaster< T >::ReconstructL().

FFTBand * stira::fouriertools::FFT::ApplyTransferFunctionFFT	(	ArrayGrid< double > *	pInputGrid,
		FFTBand *	transferFunction
	)

static

yet another method to apply a transfer function Overloaded previous method to allow that the transfer function is also in complex format already

Parameters

pInputGrid	the input grid to be filtered
transferFunction	the transfer function to be applied on this FFTBand

References stira::fouriertools::FFTBand::ApplyForwardTransform(), ApplyTransferFunctionFFT(), stira::fouriertools::FFTBand::GetHeight(), stira::imagedata::ArrayGrid< T >::GetHeight(), stira::fouriertools::FFTBand::GetValue(), stira::fouriertools::FFTBand::GetWidth(), stira::imagedata::ArrayGrid< T >::GetWidth(), and stira::fouriertools::FFTBand::SetValue().

static FFTBand* stira::fouriertools::FFT::ApplyTransferFunctionFFT	(	ArrayGrid< std::complex< double > > *	pInputGrid,
		FFTBand *	transferFunction
	)

static

yet another method to apply a transfer function Overloaded previous method to allow that the transfer function is also in complex format already

Parameters

pInputGrid	the input grid to be filtered
transferFunction	the transfer function to be applied on this FFTBand

ArrayGrid< double > * stira::fouriertools::FFT::ApplyTransferFunctionSpatial	(	ArrayGrid< double > *	pInputGrid,
		ArrayGrid< double > *	transferFunction,
		FFTDataType	myDataType = `RE`
	)

static

yet another method to apply a transfer function

Parameters

pInputGrid	the input grid to be filtered
transferFunction	the transfer function to be applied on this real-valued grid
myDataType	specifies if we want the real or imaginary component as output

References stira::fouriertools::FFTBand::ApplyInverseTransform(), stira::fouriertools::FFTBand::ConvertToImaginaryGrid(), stira::fouriertools::FFTBand::ConvertToRealGrid(), and stira::imagedata::ArrayGrid< T >::SwitchQuadrants().

Referenced by SuppressOuterFrequencies().

std::pair< ArrayGrid< double > , ArrayGrid< double > > stira::fouriertools::FFT::ApplyTransferFunctionSpatialComplex	(	ArrayGrid< double > *	pInputGrid,
		ArrayGrid< double > *	transferFunction
	)

static

yet another method to apply a transfer function

Parameters

pInputGrid	the input grid to be filtered
transferFunction	the transfer function to be applied on this real-valued grid

Returns: a pair with as first element the real components of the complex values and as second element the imaginary components

References stira::fouriertools::FFTBand::ApplyInverseTransform(), stira::fouriertools::FFTBand::ConvertToImaginaryGrid(), stira::fouriertools::FFTBand::ConvertToRealGrid(), and stira::imagedata::ArrayGrid< T >::SwitchQuadrants().

Referenced by stira::filter::LogGabor::Run().

ArrayGrid< double > * stira::fouriertools::FFT::ComputeLogPowerSpectrum ( ArrayGrid< double > * pInputGrid )

static

Computes logarithm of the power spectrum, and returns it as a grid. Logarithm is used for compression of dynamic range of values, for visualization.

Parameters

pInputGrid input grid to compute the power spectrum for

References stira::imagedata::ArrayGrid< T >::GetHeight(), stira::imagedata::GridStatistics< T >::GetMinMax(), stira::imagedata::ArrayGrid< T >::GetValue(), stira::imagedata::ArrayGrid< T >::GetWidth(), and stira::imagedata::ArrayGrid< T >::SetValue().

ArrayGrid< double > * stira::fouriertools::FFT::ComputePowerSpectrum ( ArrayGrid< double > * pInputGrid )

static

Computes power spectrum, and returns it as a grid.

Parameters

pInputGrid input grid to compute the power spectrum for

References stira::fouriertools::FFTBand::ApplyForwardTransform(), stira::fouriertools::FFTBand::GetHeight(), stira::fouriertools::FFTBand::GetValue(), stira::fouriertools::FFTBand::GetWidth(), stira::imagedata::ArrayGrid< T >::SetValue(), and stira::imagedata::ArrayGrid< T >::SwitchQuadrants().

vector< double > stira::fouriertools::FFT::ComputeRadiallyAveragedSpectrum	(	ArrayGrid< double > *	pInputImage,
		int	thetaSteps = `500`
	)

static

Computes radially averaged power spectrum, and returns it rescaled logaritmically as a 1D vector of doubles.

Ref: R. Ulichney, "Dithering with Blue Noise", Proc. of the IEEE, vol. 76, no. 1, pp. 56-79, 1988. http://www.hpl.hp.com/personal/Robert_Ulichney/publications.html

Parameters

pInputImage	input grid to compute the power spectrum for
thetaSteps	number of steps to take along a circle with given radius to average the spectrum

References stira::imagedata::ArrayGrid< T >::GetHeight(), stira::imagedata::ArrayGrid< T >::GetValue(), and stira::imagedata::ArrayGrid< T >::GetWidth().

ArrayGrid< double > * stira::fouriertools::FFT::Convolve	(	ArrayGrid< double > *	pInputGrid,
		ArrayGrid< double > *	pFilterKernel
	)

static

Computes the convolution of a single grid with the filterKernel in the argument.

Parameters

pInputGrid	grid to be convolved
pFilterKernel	the PSF to convolve the band with

Returns: result of convolution as a new grid.

References stira::fouriertools::FFTBand::ApplyForwardTransform(), stira::fouriertools::FFTBand::ApplyInverseTransform(), stira::fouriertools::FFTBand::ConvertToRealGrid(), stira::imagedata::ArrayGrid< T >::GetHeight(), stira::fouriertools::FFTBand::GetValue(), stira::imagedata::ArrayGrid< T >::GetWidth(), and stira::fouriertools::FFTBand::SetValue().

Referenced by Convolve(), stira::filter::GaussConvolve::DerivativeConvolveFFT(), GaussConvolve(), stira::filter::DifferenceOfGaussians::Run(), stira::deconvolve::TikhonovMillerDeconvolve::Run(), stira::deconvolve::GNCDeconvolve::Run(), stira::deconvolve::RichardsonLucyDeconvolve::Run(), stira::deconvolve::VanCittertLandweberDeconvolve::Run(), and stira::deconvolve::SimulateDegradation::~SimulateDegradation().

Image * stira::fouriertools::FFT::Convolve	(	Image *	pInputImage,
		ArrayGrid< double > *	pFilterKernel
	)

static

Overloaded method to computes the convolution of an image with the filterKernel.

Parameters

pInputImage	image to be convolved (band by band)
pFilterKernel	the PSF to convolve the bands with

Returns: result of convolution as a new image.

References stira::imagedata::Image::AddBand(), Convolve(), stira::imagedata::Image::GetBands(), stira::imagedata::Image::GetHeight(), stira::imagedata::Image::GetNumberOfBands(), and stira::imagedata::Image::GetWidth().

ArrayGrid< complex< double > > * stira::fouriertools::FFT::CreateComplexGridFromRealGrid ( ArrayGrid< double > * pGridIn )

static

creates a grid of complex values from a real-valued grid in which the imaginary components are 0

Parameters

pGridIn real-valued input grid

References stira::imagedata::ArrayGrid< T >::GetHeight(), stira::imagedata::ArrayGrid< T >::GetValue(), stira::imagedata::ArrayGrid< T >::GetWidth(), and stira::imagedata::ArrayGrid< T >::SetValue().

ArrayGrid< double > * stira::fouriertools::FFT::CreateRealGridFromComplexGrid ( ArrayGrid< std::complex< double > > * pGridIn )

static

creates a grid of real values from a complex-valued grid; we just take the real component of each complex number

Parameters

pGridIn complex-valued input grid

References stira::imagedata::ArrayGrid< T >::GetWidth(), and stira::imagedata::ArrayGrid< T >::SetValue().

Image * stira::fouriertools::FFT::GaussConvolve	(	Image *	pInputImage,
		double	sigma
	)

static

Computes the convolution of an image with a Gaussian PSF with given sigma.

Parameters

pInputImage	image to be convolved
sigma	the sigma for the Gaussian PSF

Returns: result of convolution as an image.

References stira::imagedata::Image::AddBand(), Convolve(), stira::imagetools::ImageTools::CropBorder(), stira::imagetools::GridGenerator::GenerateGaussian(), stira::imagedata::Image::GetBands(), stira::imagedata::Image::GetHeight(), stira::imagedata::Image::GetNumberOfBands(), stira::imagedata::Image::GetWidth(), and stira::imagetools::ImageTools::MirrorBorder().

Referenced by stira::imageanalysis::CannyEdgeDetector::Run(), and stira::filter::GaussConvolve::UpsampleGaussianInterpolated().

ArrayGrid< double > * stira::fouriertools::FFT::GaussConvolve	(	ArrayGrid< double > *	pInputGrid,
		double	sigma
	)

static

Computes the convolution of a single grid with a Gaussian PSF with given sigma.

Parameters

pInputGrid	grid to be convolved
sigma	the sigma for the Gaussian PSF

Returns: result of convolution as a grid.

References Convolve(), stira::imagedata::GridExtender< T >::CropBorder(), stira::imagetools::GridGenerator::GenerateGaussian(), stira::imagedata::ArrayGrid< T >::GetHeight(), stira::imagedata::ArrayGrid< T >::GetWidth(), and stira::imagedata::GridExtender< T >::MirrorBorder().

void stira::fouriertools::FFT::RescaleGrid	(	ArrayGrid< double > *	pGrid,
		double	newMin,
		double	newMax
	)

staticprotected

rescales the intensities in pGrid

Parameters

pGrid	Grid to rescale intensites of
newMin	minimum after rescaling
newMax	maximum after rescaling

References stira::imagedata::ArrayGrid< T >::GetHeight(), stira::imagedata::ArrayGrid< T >::GetValue(), stira::imagedata::ArrayGrid< T >::GetWidth(), and stira::imagedata::ArrayGrid< T >::SetValue().

ArrayGrid< double > * stira::fouriertools::FFT::SuppressOuterFrequencies ( ArrayGrid< double > * pInputGrid )

static

supresses the outer frequencies in an image; essentially makes an image band-limited

Parameters

pInputGrid grid to be convolved

References ApplyTransferFunctionSpatial(), stira::fouriertools::TransferFunctionGenerator::GenerateLowPassTransferFunction(), stira::imagedata::ArrayGrid< T >::GetHeight(), and stira::imagedata::ArrayGrid< T >::GetWidth().

void stira::fouriertools::FFT::WriteFFTDataToPPM	(	FFTBand *	pFFTData,
		FFTDataType	myDataType,
		char *	pFileName,
		double	factor
	)

staticprotected

Writes for diagnostic purposes the real or imaginary part of FFTData to disk.

Parameters

pFFTData	data to write to disk
myDataType	enum if the real or imaginary part is to be written to disk
pFileName	name of the file to write to
factor	rescaling factor with which all intensities are multiplied before they are written to disk

References stira::fouriertools::FFTBand::GetHeight(), stira::fouriertools::FFTBand::GetValue(), and stira::fouriertools::FFTBand::GetWidth().

The documentation for this class was generated from the following files:

fouriertools/fouriertools/FFT.h
fouriertools/fouriertools/FFT.cpp

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Detailed Description

Member Function Documentation