2D Discrete Fourier Transform (DFT) and its inverse.
Calculates 2D DFT of an image and recreates the image using inverse 2D DFT.
Computation is slow so only suitable for thumbnail size images.
Python, 57 lines
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | # 2D Discrete Fourier Transform (DFT) and its inverse
# Warning: Computation is slow so only suitable for thumbnail size images!
# FB - 20150102
from PIL import Image
import cmath
pi2 = cmath.pi * 2.0
def DFT2D(image):
global M, N
(M, N) = image.size # (imgx, imgy)
dft2d_red = [[0.0 for k in range(M)] for l in range(N)]
dft2d_grn = [[0.0 for k in range(M)] for l in range(N)]
dft2d_blu = [[0.0 for k in range(M)] for l in range(N)]
pixels = image.load()
for k in range(M):
for l in range(N):
sum_red = 0.0
sum_grn = 0.0
sum_blu = 0.0
for m in range(M):
for n in range(N):
(red, grn, blu, alpha) = pixels[m, n]
e = cmath.exp(- 1j * pi2 * (float(k * m) / M + float(l * n) / N))
sum_red += red * e
sum_grn += grn * e
sum_blu += blu * e
dft2d_red[l][k] = sum_red / M / N
dft2d_grn[l][k] = sum_grn / M / N
dft2d_blu[l][k] = sum_blu / M / N
return (dft2d_red, dft2d_grn, dft2d_blu)
def IDFT2D(dft2d):
(dft2d_red, dft2d_grn, dft2d_blu) = dft2d
global M, N
image = Image.new("RGB", (M, N))
pixels = image.load()
for m in range(M):
for n in range(N):
sum_red = 0.0
sum_grn = 0.0
sum_blu = 0.0
for k in range(M):
for l in range(N):
e = cmath.exp(1j * pi2 * (float(k * m) / M + float(l * n) / N))
sum_red += dft2d_red[l][k] * e
sum_grn += dft2d_grn[l][k] * e
sum_blu += dft2d_blu[l][k] * e
red = int(sum_red.real + 0.5)
grn = int(sum_grn.real + 0.5)
blu = int(sum_blu.real + 0.5)
pixels[m, n] = (red, grn, blu)
return image
# TEST
# Recreate input image from 2D DFT results to compare to input image
image = IDFT2D(DFT2D(Image.open("input.png")))
image.save("output.png", "PNG")
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