Backward Discrete Fourier Transform for an input 3d image. More...

IPSDKIPLINTENSITYTRANSFORM_API image::ImagePtr	ipsdk::imaproc::itrans::backwardDiscreteFourierTransform3dImg (const image::ImageConstPtr &pInDFTImg3d1, const image::ImageConstPtr &pInDFTImg3d2)
	wrapper function for Backward Discrete Fourier Transform for an input 3d image More...

IPSDKIPLINTENSITYTRANSFORM_API image::ImagePtr	ipsdk::imaproc::itrans::backwardDiscreteFourierTransform3dImg (const image::ImageConstPtr &pInDFTImg3d1, const image::ImageConstPtr &pInDFTImg3d2, const ipsdk::imaproc::attr::DFTConfigConstPtr &pInOptDFTConfig)
	wrapper function for Backward Discrete Fourier Transform for an input 3d image More...

IPSDKIPLINTENSITYTRANSFORM_API void	ipsdk::imaproc::itrans::backwardDiscreteFourierTransform3dImg (const image::ImageConstPtr &pInDFTImg3d1, const image::ImageConstPtr &pInDFTImg3d2, const ipsdk::imaproc::attr::DFTConfigConstPtr &pInOptDFTConfig, const image::ImagePtr &pOutRealImg)
	wrapper function for Backward Discrete Fourier Transform for an input 3d image More...

Detailed Description

Backward Discrete Fourier Transform for an input 3d image.

This algorithm allows to compute the real part of Backward Discrete Fourier Transformation of an input complex 3d image reprensented by its two components $ InDFTImg3d1 $ and $ InDFTImg3d2 $ .

In three dimensions, the real part of Backward Discrete Fourier Transformation (BDFT) of input images $ InDFTImg3d1 $ and $ InDFTImg3d2 $ with size $\left \{ S_x, S_y, S_z \right \}$ is defined as the following real image:

$bdft(x, y, z) = Re \left\{ \sum_{j=0}^{S_z}{\sum_{k=0}^{S_y}{\sum_{l=0}^{S_x}{InDFTImg3d(l, k, j)\exp^{+2\pi i \left (\frac{xl}{S_x}+\frac{yk}{S_y}+\frac{zj}{S_z} \right )}}}} \right\}$

This transformation allows to retrieve forward domain and can be usefull for example in case of filtering of Fourier Frequencies. The following image is an illustration of Backward Discrete Fourier Transformation results:

As in case of Forward Discrete Fourier Transform (see Forward Discrete Fourier Transform 3d), $InDFTConfig$ parameter allows to setup:

input images coordinates domain : if the input images are expressed using polar coordinates we proceed to a polar to cartesian conversion (see Polar to cartesian transformation)
input quadrants policy : if the input images quadrants are centered on lowest frequencies we proceed to a swap operation.
scale policy: during processing, Backward Discrete Fourier Transformation can be scaled by a constant value :
$bdft(x, y, z) = \lambda Re \left (\sum_{j=0}^{S_z}{\sum_{k=0}^{S_y}{\sum_{l=0}^{S_x}{InDFTImg3d(l, k, j)\exp^{+2\pi i \left (\frac{xl}{S_x}+\frac{yk}{S_y}+\frac{zj}{S_z} \right )}}}}\right )$
- eDFTScalePolicy::eDFTSP_Default for default behavior with $\lambda=\frac{1}{S_x}$ along x axis, $\lambda=\frac{1}{S_y}$ along y axis and $\lambda=\frac{1}{S_z}$ along z axis.
- eDFTScalePolicy::eDFTSP_Unitary for unitary BDFT with $\lambda=\frac{1}{\sqrt{S_x}}$ along x axis $\lambda=\frac{1}{\sqrt{S_y}}$ along y axis and $\lambda=\frac{1}{\sqrt{S_z}}$ along z axis.
  See also
  https://en.wikipedia.org/wiki/Discrete_Fourier_transform#The_unitary_DFT
- eDFTScalePolicy::eDFTSP_Custom for a user custom scale factor defined for each axis.

See also: https://en.wikipedia.org/wiki/Discrete_Fourier_transform

Attributes description

Attribute description for algorithm :

Name	ToolTip	Default Initializer
ipsdk::imaproc::attr::InDFTImg3d1	[Input] first element for 3d Discreet Fourier Transform (can be real cartesian part or rho polar part [default] of signal depending on algorithm configuration)	X
ipsdk::imaproc::attr::InDFTImg3d2	[Input] second element for 3d Discreet Fourier Transform (can be imaginary cartesian part or theta polar part [default] of signal depending on algorithm configuration)	X
ipsdk::imaproc::attr::InOptDFTConfig	[Input Optional] configuration for Discrete Fourier Transform algorithm	X
ipsdk::imaproc::attr::OutRealImg	[Output] image for processing operation (data contained in image buffer are reals)	duplicateInOut (_pOutRealImg, _pInDFTImg3d1, ipsdk::image::eImageBufferType::eIBT_Real32)
ipsdk::imaproc::attr::OutWk1RealImg	[Output] Temporary working image for algorithm	duplicateInOut (_pOutWk1RealImg, _pInDFTImg3d1, ipsdk::image::eImageBufferType::eIBT_Real32)

Global Rule description

Global rule description for algorithm :
ipsdk::imaproc::matchSize (_pInDFTImg3d1,_pInDFTImg3d2,_pOutRealImg,_pOutWk1RealImg) &&
ipsdk::imaproc::noInSitu (_pInDFTImg3d1,_pOutWk1RealImg) &&
ipsdk::imaproc::noInSitu (_pInDFTImg3d2,_pOutRealImg)

Example of Python code :

Example imports

import PyIPSDK

import PyIPSDK.IPSDKIPLIntensityTransform as itrans

Code Example

    # opening of input images
    inImg1 = PyIPSDK.loadTiffImageFile(inputImgPath1)
    inImg2 = PyIPSDK.loadTiffImageFile(inputImgPath2)
    
    # Backward Discrete Fourier Transform of input images
    outImg = itrans.backwardDiscreteFourierTransform3dImg(inImg1, inImg2)

Example of C++ code :

Example informations

Associated library

IPSDKIPLIntensityTransform

Header file

#include <IPSDKIPL/IPSDKIPLIntensityTransform/Processor/BackwardDiscreteFourierTransform3dImg/BackwardDiscreteFourierTransform3dImg.h>

Code Example

    // opening of input images
    ImagePtr pInImg1 = loadTiffImageFile(inputImgPath1);
    ImagePtr pInImg2 = loadTiffImageFile(inputImgPath2);
    // Backward Discrete Fourier Transform of input images
    ImagePtr pOutImg = backwardDiscreteFourierTransform3dImg(pInImg1, pInImg2);

See also: BackwardDiscreteFourierTransform3dImgLvl1

Function Documentation

◆ backwardDiscreteFourierTransform3dImg() [1/3]

IPSDKIPLINTENSITYTRANSFORM_API image::ImagePtr ipsdk::imaproc::itrans::backwardDiscreteFourierTransform3dImg	(	const image::ImageConstPtr &	pInDFTImg3d1,
		const image::ImageConstPtr &	pInDFTImg3d2
	)

wrapper function for Backward Discrete Fourier Transform for an input 3d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ backwardDiscreteFourierTransform3dImg() [2/3]

IPSDKIPLINTENSITYTRANSFORM_API image::ImagePtr ipsdk::imaproc::itrans::backwardDiscreteFourierTransform3dImg	(	const image::ImageConstPtr &	pInDFTImg3d1,
		const image::ImageConstPtr &	pInDFTImg3d2,
		const ipsdk::imaproc::attr::DFTConfigConstPtr &	pInOptDFTConfig
	)

wrapper function for Backward Discrete Fourier Transform for an input 3d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ backwardDiscreteFourierTransform3dImg() [3/3]

IPSDKIPLINTENSITYTRANSFORM_API void ipsdk::imaproc::itrans::backwardDiscreteFourierTransform3dImg	(	const image::ImageConstPtr &	pInDFTImg3d1,
		const image::ImageConstPtr &	pInDFTImg3d2,
		const ipsdk::imaproc::attr::DFTConfigConstPtr &	pInOptDFTConfig,
		const image::ImagePtr &	pOutRealImg
	)

wrapper function for Backward Discrete Fourier Transform for an input 3d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure