pfft

Synopsis

Description

pfft computes the Fast Fourier Transform of the input complex image im_in1. The input complex image is composed of two images:

• im_in1 is the real part;
• im_in2 is the imaginary part.

The imaginary image must be at least empty (see pnewimage, psetcst).

The output complex images is also composed of two images:

• im_out1 is the real part of the transform;
• im_out2 is the imaginary part of the transform.

Fast Fourier Transform is a way of going from the spatial domain to the frequency domain:

• The spatial domain is the domain where each value at the coordinate (x,y) contains the intensity value of the related point (x',y') in the scene. The distance between 2 pixels corresponds to a real distance in the scene.

• The frequency domain is the domain where each value of the image at the coordinate F(u,v) contains a quantity such that the intensity values in the input image varies on a distance related to F. For example, suppose that the value at the related coordinate for frequency 0.1 is 20 (ie. 1 period every 10 pixels). It means that in the spatial domain of the related image, the intensity value varies from dark to clear on a distance of 10 pixels and the contrast between the dark and the clear values occupies 40 gray levels (2*20).

The Fourier transform of an image represents the likeness degree between the image seen as function f and the functions are sine and cosine with various frequencies. Each point represents a particular frequency in the spatial domain.

if N is the number of pixels.
F(u,v) = 1/(N*N) * Sigma(x){Sigma(y){ I(x,y)*exp(-i2PI((u*i)/N+(v*i)/N))}}

This equation can be interpreted as follows:
The value of the point (u,v) results from the multiplication of the spatial image with the various basis function. The basis functions are sine and cosine with increasing frequencies. F(0,0) represents the mean intensity of the image, whereas F(N-1,N-1) represents the higher frequency.

The size of the output images im_out1 and im_out1 is the same as the input images im_in1 and im_in2.

Inputs

• im_in1: a gray level image (the real part of the transform).
• im_in2: a gray level image with the same properties than im_in1 (the imaginary part of the transform).

Outputs

• im_out1: a gray level image (the real part of the transform).
• im_out2: a gray level image (the imaginary part of the transform).

Result

Returns SUCCESS or FAILURE.

Examples

Computes the magnitude of the Fast Fourier Transform of tangram.pan. The imaginary part (i1.pan) is null. (Use log transform dynamic in pvisu to display out.pan.):

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pfftshift i2.pan i3.pan i4.pan i5.pan
   pmodulus i4.pan i5.pan out.pan

See also

C++ prototype

Version française

Calcul de la Transformée de Fourier Rapide d'une image.