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Fft2 Two Dimensional Fft

This page is about the 2D FFT, also called FFT2 in certain libraries and programming environments.

In [2]:
img = Image.open("/home/leo/kekw.jpg").convert('L')
#img = img.resize((int(img.width / 4), int(img.height / 4)))
In [3]:
npimg = np.zeros((img.height, img.width))

for y in range(img.height):
    for x in range(img.width):
        npimg[y][x] = img.getpixel((x, y))

npimg = npimg / 256
img = npimg
plt.imshow(img, cmap="gray")
plt.colorbar()
Out [3]:
<matplotlib.image.AxesImage at 0x7fbbb7e92430>
Out [3]:
<matplotlib.colorbar.Colorbar at 0x7fbbb7e4d910>
Out:
<Figure size 900x600 with 2 Axes>
In [4]:
def fft_rows(img):
    fft_img = np.zeros(img.shape, dtype=np.complex_)
    
    for y in range(img.shape[0]):
        row = [img[y][x] for x in range(img.shape[1])]
        
        row_fft = np.fft.fft(row)
        
        for x, col in enumerate(row_fft):
            fft_img[y][x] = col
        
    return fft_img

img = fft_rows(img)

plt.imshow(np.abs(img), vmax=1)
plt.colorbar()
Out [4]:
<matplotlib.image.AxesImage at 0x7fbbb7dbdfd0>
Out [4]:
<matplotlib.colorbar.Colorbar at 0x7fbbb7d62370>
Out:
<Figure size 900x600 with 2 Axes>
In [5]:
def fft_cols(img):
    fft_img = np.zeros(img.shape, dtype=np.complex_)
    
    for x in range(img.shape[1]):
        row = [img[y][x] for y in range(img.shape[0])]
        
        row_fft = np.fft.fft(row)
        
        for y, col in enumerate(row_fft):
            fft_img[y][x] = col
        
    return fft_img

img = fft_cols(img)

plt.imshow(np.abs(img), vmax=2)
plt.colorbar()
Out [5]:
<matplotlib.image.AxesImage at 0x7fbbb7c834c0>
Out [5]:
<matplotlib.colorbar.Colorbar at 0x7fbbb7ca29d0>
Out:
<Figure size 900x600 with 2 Axes>
In [6]:
plt.imshow(np.fft.ifft2(img).real, cmap="gray")
plt.colorbar()
Out [6]:
<matplotlib.image.AxesImage at 0x7fbbb7c38520>
Out [6]:
<matplotlib.colorbar.Colorbar at 0x7fbbb7bd5820>
Out:
<Figure size 900x600 with 2 Axes>
In [7]:
shp = img.shape
img = img.flatten()

decim = 50

for i, x in enumerate(img):
    img[i] = int(x.real / decim) * decim + int(x.imag / decim) * decim * 1j

img = img.reshape(shp)

plt.imshow(np.fft.ifft2(img).real, cmap="gray")
plt.colorbar()
Out [7]:
<matplotlib.image.AxesImage at 0x7fbbb7b754f0>
Out [7]:
<matplotlib.colorbar.Colorbar at 0x7fbbb7b119d0>
Out:
<Figure size 900x600 with 2 Axes>
In [8]:
plt.imshow(np.abs(img), vmax=5)
plt.colorbar()
Out [8]:
<matplotlib.image.AxesImage at 0x7fbbb7aa66d0>
Out [8]:
<matplotlib.colorbar.Colorbar at 0x7fbbb7a42af0>
Out:
<Figure size 900x600 with 2 Axes>
In [9]:
np.max(img.real)/decim, np.min(img.real)/decim
np.max(img.imag)/decim, np.min(img.imag)/decim

#from collections import Counter
#Counter(img.real.flatten()/decim)
#Counter(img.imag.flatten()/decim)
Out [9]:
(4590.0, -1974.0)
Out [9]:
(645.0, -645.0)

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