fft_genericfft_genericFftGenericFftGeneric (Operator)

Name

fft_genericfft_genericFftGenericFftGeneric — Compute the fast Fourier transform of an image.

Signature

fft_generic(Image : ImageFFT : Direction, Exponent, Norm, Mode, ResultType : )

Herror fft_generic(const Hobject Image, Hobject* ImageFFT, const char* Direction, const Hlong Exponent, const char* Norm, const char* Mode, const char* ResultType)

Herror T_fft_generic(const Hobject Image, Hobject* ImageFFT, const Htuple Direction, const Htuple Exponent, const Htuple Norm, const Htuple Mode, const Htuple ResultType)

void FftGeneric(const HObject& Image, HObject* ImageFFT, const HTuple& Direction, const HTuple& Exponent, const HTuple& Norm, const HTuple& Mode, const HTuple& ResultType)

HImage HImage::FftGeneric(const HString& Direction, Hlong Exponent, const HString& Norm, const HString& Mode, const HString& ResultType) const

HImage HImage::FftGeneric(const char* Direction, Hlong Exponent, const char* Norm, const char* Mode, const char* ResultType) const

HImage HImage::FftGeneric(const wchar_t* Direction, Hlong Exponent, const wchar_t* Norm, const wchar_t* Mode, const wchar_t* ResultType) const   (Windows only)

static void HOperatorSet.FftGeneric(HObject image, out HObject imageFFT, HTuple direction, HTuple exponent, HTuple norm, HTuple mode, HTuple resultType)

HImage HImage.FftGeneric(string direction, int exponent, string norm, string mode, string resultType)

Description

fft_genericfft_genericFftGenericFftGenericFftGeneric computes the fast Fourier transform of the input image ImageImageImageImageimage. Because several definitions of the forward and reverse transforms exist in the literature, this operator allows the user to select the most convenient definition.

The general definition of a Fourier transform is as follows: Opinions vary on whether the sign s in the exponent should be set to 1 or -1 for the forward transform, i.e., the transform for going to the frequency domain. There is also disagreement on the magnitude of the normalizing factor c. This is sometimes set to 1 for the forward transform, sometimes to M*N, and sometimes (in case of the unitary FFT) to . Especially in image processing applications the DC term is shifted to the center of the image.

fft_genericfft_genericFftGenericFftGenericFftGeneric allows to select these choices individually. The parameter DirectionDirectionDirectionDirectiondirection allows to select the logical direction of the FFT. (This parameter is not unnecessary; it is needed to discern how to shift the image if the DC term should rest in the center of the image.) Possible values are 'to_freq'"to_freq""to_freq""to_freq""to_freq" and 'from_freq'"from_freq""from_freq""from_freq""from_freq". The parameter ExponentExponentExponentExponentexponent is used to determine the sign of the exponent. It can be set to 1 or -1. The normalizing factor can be set with NormNormNormNormnorm, and can take on the values 'none'"none""none""none""none", 'sqrt'"sqrt""sqrt""sqrt""sqrt" and 'n'"n""n""n""n". The parameter ModeModeModeModemode determines the location of the DC term of the FFT. It can be set to 'dc_center'"dc_center""dc_center""dc_center""dc_center" or 'dc_edge'"dc_edge""dc_edge""dc_edge""dc_edge".

In any case, the user must ensure the consistent use of the parameters. This means that the normalizing factors used for the forward and backward transform must yield M*N when multiplied, the exponents must be of opposite sign, and ModeModeModeModemode must be equal for both transforms.

A consistent combination is, for example '(to_freq,-1,n,dc_edge)'"(to_freq,-1,n,dc_edge)""(to_freq,-1,n,dc_edge)""(to_freq,-1,n,dc_edge)""(to_freq,-1,n,dc_edge)" for the forward transform and '(from_freq,1,none,dc_edge)'"(from_freq,1,none,dc_edge)""(from_freq,1,none,dc_edge)""(from_freq,1,none,dc_edge)""(from_freq,1,none,dc_edge)" for the reverse transform. In this case, the FFT can be interpreted as interpolation with trigonometric basis functions. Another possible combination is '(to_freq,-1,sqrt,dc_center)'"(to_freq,-1,sqrt,dc_center)""(to_freq,-1,sqrt,dc_center)""(to_freq,-1,sqrt,dc_center)""(to_freq,-1,sqrt,dc_center)" and '(from_freq,1,sqrt,dc_center)'"(from_freq,1,sqrt,dc_center)""(from_freq,1,sqrt,dc_center)""(from_freq,1,sqrt,dc_center)""(from_freq,1,sqrt,dc_center)".

The parameter ResultTypeResultTypeResultTypeResultTyperesultType can be used to specify the result image type of the reverse transform (DirectionDirectionDirectionDirectiondirection = 'from_freq'"from_freq""from_freq""from_freq""from_freq"). In the forward transform (DirectionDirectionDirectionDirectiondirection = 'to_freq'"to_freq""to_freq""to_freq""to_freq"), ResultTypeResultTypeResultTypeResultTyperesultType must be set to 'complex'"complex""complex""complex""complex".

Attention

The transformation is always performed for the entire image, i.e., the domain of the image is ignored.

Execution Information

Parameters

ImageImageImageImageimage (input_object)  (multichannel-)image(-array) objectHImageHImageHobject (byte / direction / cyclic / int1 / int2 / uint2 / int4 / real / complex)

Input image.

ImageFFTImageFFTImageFFTImageFFTimageFFT (output_object)  image(-array) objectHImageHImageHobject * (byte / direction / cyclic / int1 / int2 / uint2 / int4 / real / complex)

Fourier-transformed image.

DirectionDirectionDirectionDirectiondirection (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Calculate forward or reverse transform.

Default value: 'to_freq' "to_freq" "to_freq" "to_freq" "to_freq"

List of values: 'from_freq'"from_freq""from_freq""from_freq""from_freq", 'to_freq'"to_freq""to_freq""to_freq""to_freq"

ExponentExponentExponentExponentexponent (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Sign of the exponent.

Default value: -1

List of values: -1, 1

NormNormNormNormnorm (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Normalizing factor of the transform.

Default value: 'sqrt' "sqrt" "sqrt" "sqrt" "sqrt"

List of values: 'n'"n""n""n""n", 'none'"none""none""none""none", 'sqrt'"sqrt""sqrt""sqrt""sqrt"

ModeModeModeModemode (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Location of the DC term in the frequency domain.

Default value: 'dc_center' "dc_center" "dc_center" "dc_center" "dc_center"

List of values: 'dc_center'"dc_center""dc_center""dc_center""dc_center", 'dc_edge'"dc_edge""dc_edge""dc_edge""dc_edge"

ResultTypeResultTypeResultTypeResultTyperesultType (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Image type of the output image.

Default value: 'complex' "complex" "complex" "complex" "complex"

List of values: 'byte'"byte""byte""byte""byte", 'complex'"complex""complex""complex""complex", 'cyclic'"cyclic""cyclic""cyclic""cyclic", 'direction'"direction""direction""direction""direction", 'int1'"int1""int1""int1""int1", 'int2'"int2""int2""int2""int2", 'int4'"int4""int4""int4""int4", 'real'"real""real""real""real", 'uint2'"uint2""uint2""uint2""uint2"

Example (C)

/* simulation of fft_image */
void my_fft(Hobject In, Hobject *Out)
{
  fft_generic(In,Out,"to_freq",-1,"sqrt","dc_center","complex");
}

/* simulation of fft_image_inv */
void my_fft_image_inv(Hobject In, Hobject *Out)
{
  fft_generic(In,Out,"from_freq",1,"sqrt","dc_center","byte");
}

Result

fft_genericfft_genericFftGenericFftGenericFftGeneric returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>). If necessary, an exception is raised.

Possible Predecessors

optimize_fft_speedoptimize_fft_speedOptimizeFftSpeedOptimizeFftSpeedOptimizeFftSpeed, read_fft_optimization_dataread_fft_optimization_dataReadFftOptimizationDataReadFftOptimizationDataReadFftOptimizationData

Possible Successors

convol_fftconvol_fftConvolFftConvolFftConvolFft, correlation_fftcorrelation_fftCorrelationFftCorrelationFftCorrelationFft, phase_correlation_fftphase_correlation_fftPhaseCorrelationFftPhaseCorrelationFftPhaseCorrelationFft, convol_gaborconvol_gaborConvolGaborConvolGaborConvolGabor, convert_image_typeconvert_image_typeConvertImageTypeConvertImageTypeConvertImageType, power_bytepower_bytePowerBytePowerBytePowerByte, power_realpower_realPowerRealPowerRealPowerReal, power_lnpower_lnPowerLnPowerLnPowerLn, phase_degphase_degPhaseDegPhaseDegPhaseDeg, phase_radphase_radPhaseRadPhaseRadPhaseRad, energy_gaborenergy_gaborEnergyGaborEnergyGaborEnergyGabor

Alternatives

fft_imagefft_imageFftImageFftImageFftImage, fft_image_invfft_image_invFftImageInvFftImageInvFftImageInv, rft_genericrft_genericRftGenericRftGenericRftGeneric

Module

Foundation