correlation_fft🔗
Short description🔗
correlation_fft — Multiply one image with the complex conjugate of another image in the
frequency domain.
Signature🔗
correlation_fft( image ImageFFT1, image ImageFFT2, out image ImageCorrelation )
Description🔗
As part of calculating the correlation between two images,
correlation_fft multiplies the Fourier transform of the first image
ImageFFT1 with the complex conjugate of the Fourier-transformed
second image ImageFFT2.
According to the correlation theorem, the non-normalized correlation of two images in pixel space can be obtained in three steps:
-
Transforming the images into frequency space using a Fourier transform (see, e.g.,
fft_generic). -
Multiplying one transformed image with the complex conjugate of the other transformed image (pixel-wise).
-
Transforming the result back into pixel space using an inverse Fourier transform (see, e.g.,
fft_generic).
The operator correlation_fft is used to perform the second step,
i.e., ImageFFT1 is pixel-wise multiplied with the complex
conjugate of ImageFFT2.
It should be noted that in order to achieve a correct scaling of the
correlation in the spatial domain, the operators
fft_generic or rft_generic with
Norm \(=\) 'none' must be used for the forward
transform (step 1) and fft_generic or rft_generic with
Norm \(=\) 'n' for the reverse transform (step 3).
If ImageFFT1 and ImageFFT2 contain the same number
of images, the corresponding images are multiplied pairwise.
Otherwise, ImageFFT2 must contain only one single image.
In this case, the multiplication is performed for each image of
ImageFFT1 with ImageFFT2.
Attention🔗
The filtering is always performed on the entire image, i.e., the domain of the image is ignored.
Execution information🔗
Execution information
-
Multithreading type: reentrant (runs in parallel with non-exclusive operators).
-
Multithreading scope: global (may be called from any thread).
Parameters🔗
ImageFFT1 (input_object) (multichannel-)image(-array) → object (complex)
Fourier-transformed input image 1.
ImageFFT2 (input_object) (multichannel-)image(-array) → object (complex)
Fourier-transformed input image 2.
Number of elements: ImageFFT2 == ImageFFT1 || ImageFFT2 == 1
ImageCorrelation (output_object) image(-array) → object (complex)
Result in the frequency domain.
Example🔗
(HDevelop)
* Compute the auto-correlation of an image.
get_image_size(Image,Width,Height)
rft_generic(Image,ImageFFT,'to_freq','none','complex',Width)
correlation_fft(ImageFFT,ImageFFT,Correlation)
rft_generic(Correlation,AutoCorrelation,'from_freq','n','real',Width)
Result🔗
correlation_fft 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>:).
If necessary, an exception is raised.
Combinations with other operators🔗
Combinations
Possible predecessors
fft_generic, fft_image, rft_generic
Possible successors
fft_generic, fft_image_inv, rft_generic
Alternatives
Module🔗
Foundation