*Note that there is an entire SciPy subpackage, scipy.ndimage, devoted to image processing. This example serves simply to illustrate the syntax and format of NumPy's two-dimensional FFT implementation.*

The two-dimensional DFT is widely-used in image processing. For example, multiplying the DFT of an image by a two-dimensional Gaussian function is a common way to blur an image by decreasing the magnitude of its high-frequency components.

The following code produces an image of randomly-arranged squares and then blurs it with a Gaussian filter.

import numpy as np import pylab # image size, square side length, number of squares ncols, nrows = 120, 120 sq_size, nsq = 10, 20 # The image array (0=background, 1=square) and boolean array of allowed places # to add a square so that it doesn't touch another or the image sides image = np.zeros((nrows, ncols)) sq_locs = np.zeros((nrows, ncols), dtype=bool) sq_locs[1:-sq_size-1:,1:-sq_size-1] = True def place_square(): """ Place a square at random on the image and update sq_locs. """ # valid_locs is an array of the indices of True entries in sq_locs valid_locs = np.transpose(np.nonzero(sq_locs)) # pick one such entry at random, and add the square so its top left # corner is there; then update sq_locs i, j = valid_locs[np.random.randint(len(valid_locs))] image[i:i+sq_size, j:j+sq_size] = 1 imin, jmin = max(0,i-sq_size-1), max(0, j-sq_size-1) sq_locs[imin:i+sq_size+1, jmin:j+sq_size+1] = False # Add the required number of squares to the image for i in range(nsq): place_square() pylab.imshow(image) pylab.show() # Take the 2-dimensional DFT and centre the frequencies ftimage = np.fft.fft2(image) ftimage = np.fft.fftshift(ftimage) pylab.imshow(np.abs(ftimage)) pylab.show() # Build and apply a Gaussian filter. sigmax, sigmay = 10, 10 cy, cx = nrows/2, ncols/2 x = np.linspace(0, nrows, nrows) y = np.linspace(0, ncols, ncols) X, Y = np.meshgrid(x, y) gmask = np.exp(-(((X-cx)/sigmax)**2 + ((Y-cy)/sigmay)**2)) ftimagep = ftimage * gmask pylab.imshow(np.abs(ftimagep)) pylab.show() # Finally, take the inverse transform and show the blurred image imagep = np.fft.ifft2(ftimagep) pylab.imshow(np.abs(imagep)) pylab.show()

The original and blurred images appear on the lefthand side here, with their Fourier Transforms on the right.