Forward Discrete Fourier Transform for an input 2d image. More...

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg	ipsdk::imaproc::itrans::forwardDiscreteFourierTransform2dImg (const image::ImageConstPtr &pInImg)
	wrapper function for forward Discrete Fourier Transform for an input 2d image More...

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg	ipsdk::imaproc::itrans::forwardDiscreteFourierTransform2dImg (const image::ImageConstPtr &pInImg, const ipsdk::imaproc::attr::DFTConfigConstPtr &pInOptDFTConfig)
	wrapper function for forward Discrete Fourier Transform for an input 2d image More...

IPSDKIPLINTENSITYTRANSFORM_API void	ipsdk::imaproc::itrans::forwardDiscreteFourierTransform2dImg (const image::ImageConstPtr &pInImg, const ipsdk::imaproc::attr::DFTConfigConstPtr &pInOptDFTConfig, const image::ImagePtr &pOutDFTImg1, const image::ImagePtr &pOutDFTImg2)
	wrapper function for forward Discrete Fourier Transform for an input 2d image More...

Detailed Description

Forward Discrete Fourier Transform for an input 2d image.

This algorithm allows to compute the Forward Discrete Fourier Transformation of an input 2d image $ InImg $ .

In two dimensions, the Forward Discrete Fourier Transformation (FDFT) of input image $ InImg $ with $ S_y $ rows and $ S_x $ columns is defined as the following complex image:

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

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).

The following image is an illustration of Forward Discrete Fourier Transformation results in case of previous configuration :

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.
output quadrants policy :
- eDFTQuadrantsPolicy::eDFTQP_Centered for centerer lowest frequencies [default],
- eDFTQuadrantsPolicy::eDFTQP_Native for centerer highest frequencies
a scale policy: during processing, Forward Discrete Fourier Transformation can be scaled by a constant value :
$fdft(x, y) = \lambda\sum_{k=0}^{S_y}{\sum_{l=0}^{S_x}{InImg(l, k)\exp^{-2\pi i \left (\frac{xl}{S_x}+\frac{yk}{S_y} \right )}}}$
- 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 and $\lambda=\frac{1}{\sqrt{S_y}}$ along y 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::InImg	[Input] image for processing operation	X
ipsdk::imaproc::attr::InOptDFTConfig	[Input Optional] configuration for Discrete Fourier Transform algorithm	X
ipsdk::imaproc::attr::OutOptWk1RealGpuImg	[Output Optional] Temporary working image for GPU processes (data contained in image buffer are reals)	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, _pInImg, 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, _pInImg, ipsdk::image::eImageBufferType::eIBT_Real32)

Global Rule description

Global rule description for algorithm :
ipsdk::processor::none () &&
//ipsdk::imaproc::matchSize (_pInImg,_pOutDFTImg1,_pOutDFTImg2) &&
//ipsdk::processor::If (
ipsdk::processor::isSet (_pOutOptWk1RealGpuImg), //
CustomRuleTODO (_pInImg,_pOutOptWk1RealGpuImg), //
ipsdk::processor::none ()),
ipsdk::imaproc::noInSitu (_pInImg,_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.forwardDiscreteFourierTransform2dImg(inImg)

Example of C++ code :

Example informations

Associated library

IPSDKIPLIntensityTransform

Header file

#include <IPSDKIPL/IPSDKIPLIntensityTransform/Processor/ForwardDiscreteFourierTransform2dImg/ForwardDiscreteFourierTransform2dImg.h>

Code Example

    // opening of input image
    ImagePtr pInImg = loadTiffImageFile(inputImgPath);
    // Forward Discrete Fourier Transform of input image
    ForwardDFTImg forwardDFTImg = forwardDiscreteFourierTransform2dImg(pInImg);

See also: ForwardDiscreteFourierTransform2dImgLvl1

Function Documentation

◆ forwardDiscreteFourierTransform2dImg() [1/3]

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg ipsdk::imaproc::itrans::forwardDiscreteFourierTransform2dImg ( const image::ImageConstPtr & pInImg )

wrapper function for forward Discrete Fourier Transform for an input 2d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ forwardDiscreteFourierTransform2dImg() [2/3]

IPSDKIPLINTENSITYTRANSFORM_API ForwardDFTImg ipsdk::imaproc::itrans::forwardDiscreteFourierTransform2dImg	(	const image::ImageConstPtr &	pInImg,
		const ipsdk::imaproc::attr::DFTConfigConstPtr &	pInOptDFTConfig
	)

wrapper function for forward Discrete Fourier Transform for an input 2d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ forwardDiscreteFourierTransform2dImg() [3/3]

IPSDKIPLINTENSITYTRANSFORM_API void ipsdk::imaproc::itrans::forwardDiscreteFourierTransform2dImg	(	const image::ImageConstPtr &	pInImg,
		const ipsdk::imaproc::attr::DFTConfigConstPtr &	pInOptDFTConfig,
		const image::ImagePtr &	pOutDFTImg1,
		const image::ImagePtr &	pOutDFTImg2
	)

wrapper function for forward Discrete Fourier Transform for an input 2d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure