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

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg	ipsdk::imaproc::itrans::forwardDiscreteFourierTransform3dImg (const image::ImageConstPtr &pInImg3d)
	wrapper function for forward Discrete Fourier Transform for an input 3d image More...

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg	ipsdk::imaproc::itrans::forwardDiscreteFourierTransform3dImg (const image::ImageConstPtr &pInImg3d, const ipsdk::imaproc::attr::DFTConfigConstPtr &pInOptDFTConfig)
	wrapper function for forward Discrete Fourier Transform for an input 3d image More...

IPSDKIPLINTENSITYTRANSFORM_API void	ipsdk::imaproc::itrans::forwardDiscreteFourierTransform3dImg (const image::ImageConstPtr &pInImg3d, const ipsdk::imaproc::attr::DFTConfigConstPtr &pInOptDFTConfig, const image::ImagePtr &pOutDFTImg1, const image::ImagePtr &pOutDFTImg2)
	wrapper function for forward Discrete Fourier Transform for an input 3d image More...

Detailed Description

Forward Discrete Fourier Transform for an input 3d image.

This algorithm allows to compute the Forward Discrete Fourier Transformation of an input 3d image $ InImg3d $ .

In three dimensions, the Forward Discrete Fourier Transformation (FDFT) of input image $ InImg3d $ with size $\left \{ S_x, S_y, S_z \right \}$ is defined as following complex image:

$fdft(x, y, z) = \sum_{j=0}^{S_z}{\sum_{k=0}^{S_y}{\sum_{l=0}^{S_x}{InImg3d(l, k, j)\exp^{-2\pi i \left (\frac{xl}{S_x}+\frac{yk}{S_y}+\frac{zj}{S_z} \right )}}}}$

On output this complex image is represented by a couple of images $ OutDFTImg1 = Re(fdft) $ and $ OutDFTImg2 = Im(fdft) $ (user should note that this is not the default output representation, see below).

A common 'user friendly' representation of FDFT results consists in:

applying a cartesian to polar conversion of FDFT complex representation (see Cartesian to polar transformation)
swaping image quadrants to center lowest frequencies

Output images $ OutDFTImg1 $ and $ OutDFTImg2 $ are then modified in function.

Input parameter $ InDFTConfig $ allows to setup:

targeted output coordinates :
- eDFTCoordinates::eDFTC_Polar for polar representation [default],
- eDFTCoordinates::eDFTC_Cartesian for cartesian representation (see Forward Discrete Fourier Transform 2d for an illustration of cartesian representation in 2d case).
output quadrants policy :
- eDFTQuadrantsPolicy::eDFTQP_Centered for centerer lowest frequencies [default],
- eDFTQuadrantsPolicy::eDFTQP_Native for centerer highest frequencies (see Forward Discrete Fourier Transform 2d for an illustration of quadrants swaping in 2d case),
a scale policy: during processing, Forward Discrete Fourier Transformation can be scaled by a constant value :
$fdft(x, y, z) = \lambda\sum_{j=0}^{S_z}{\sum_{k=0}^{S_y}{\sum_{l=0}^{S_x}{InImg3d(l, k, j)\exp^{-2\pi i \left (\frac{xl}{S_x}+\frac{yk}{S_y}+\frac{zj}{S_z} \right )}}}}$
- eDFTScalePolicy::eDFTSP_Default for default behavior with $\lambda=1$ ,
- eDFTScalePolicy::eDFTSP_Unitary for unitary FDFT 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.

The following image is an illustration of Forward Discrete Fourier Transformation results in case of polar coordinates, centered quadrants policy and default scale (which is the default configuration):

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

Attributes description

Attribute description for algorithm :

Name	ToolTip	Default Initializer
ipsdk::imaproc::attr::InImg3d	[Input] 3d image for operation	X
ipsdk::imaproc::attr::InOptDFTConfig	[Input Optional] configuration for Discrete Fourier Transform algorithm	X
ipsdk::imaproc::attr::OutDFTImg1	[Output] first element for Discrete Fourier Transform (can be real cartesian part or rho polar part [default] of signal depending on algorithm configuration)	duplicateInOut (_pOutDFTImg1, _pInImg3d, ipsdk::image::eImageBufferType::eIBT_Real32)
ipsdk::imaproc::attr::OutDFTImg2	[Output] second element for Discrete Fourier Transform (can be imaginary cartesian part or theta polar part [default] of signal depending on algorithm configuration)	duplicateInOut (_pOutDFTImg2, _pInImg3d, ipsdk::image::eImageBufferType::eIBT_Real32)

Global Rule description

Global rule description for algorithm :
ipsdk::imaproc::matchSize (_pInImg3d,_pOutDFTImg1,_pOutDFTImg2) &&
ipsdk::imaproc::noInSitu (_pInImg3d,_pOutDFTImg1)

Example of Python code :

Example imports

import PyIPSDK

import PyIPSDK.IPSDKIPLIntensityTransform as itrans

Code Example

    # opening of input image
    inImg = PyIPSDK.loadTiffImageFile(inputImgPath)
    
    # Forward Discrete Fourier Transform of input image
    outImg1, outImg2 = itrans.forwardDiscreteFourierTransform3dImg(inImg)

Example of C++ code :

Example informations

Associated library

IPSDKIPLIntensityTransform

Header file

#include <IPSDKIPL/IPSDKIPLIntensityTransform/Processor/ForwardDiscreteFourierTransform3dImg/ForwardDiscreteFourierTransform3dImg.h>

Code Example

    // opening of input image
    ImagePtr pInImg = loadTiffImageFile(inputImgPath);
    // Forward Discrete Fourier Transform of input image
    ForwardDFTImg forwardDFTImg = forwardDiscreteFourierTransform3dImg(pInImg);

See also: ForwardDiscreteFourierTransform3dImgLvl1

Function Documentation

◆ forwardDiscreteFourierTransform3dImg() [1/3]

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg ipsdk::imaproc::itrans::forwardDiscreteFourierTransform3dImg ( const image::ImageConstPtr & pInImg3d )

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

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ forwardDiscreteFourierTransform3dImg() [2/3]

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg ipsdk::imaproc::itrans::forwardDiscreteFourierTransform3dImg	(	const image::ImageConstPtr &	pInImg3d,
		const ipsdk::imaproc::attr::DFTConfigConstPtr &	pInOptDFTConfig
	)

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

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ forwardDiscreteFourierTransform3dImg() [3/3]

IPSDKIPLINTENSITYTRANSFORM_API void ipsdk::imaproc::itrans::forwardDiscreteFourierTransform3dImg	(	const image::ImageConstPtr &	pInImg3d,
		const ipsdk::imaproc::attr::DFTConfigConstPtr &	pInOptDFTConfig,
		const image::ImagePtr &	pOutDFTImg1,
		const image::ImagePtr &	pOutDFTImg2
	)

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

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure