New Info: When exchanging Window1 with Window2, the results of CC exchange are as well. Meaning the left image CC_gsignal will look like the current cc_fftwtools and vice versa.
Edit: As per @OverLordGoldDragon's request, I add below a Python version using Scipy as well as FFT approach:
import numpy as np
import matplotlib.pyplot as plt
from numpy.fft import fft, ifft, fft2, ifft2, ifftshift
from PIL import Image
from scipy import signal
Window1 =array([[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 1., 1., 1., 0., 0.],
[0., 0., 1., 1., 1., 0., 0., 0.],
[0., 0., 1., 1., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]])
Window2 = array([[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 1., 1., 1., 1., 0., 0., 0.],
[0., 1., 1., 1., 0., 0., 0., 0.],
[0., 1., 1., 1., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 1., 1.],
[0., 0., 0., 0., 0., 0., 1., 1.]])
corr_scipy = signal.correlate2d(Window1, Window2, boundary='fill', mode='full')
def cross_correlate_2d(x, h):
h = ifftshift(ifftshift(h, axes=0), axes=1)
return ifft2(fft2(x) * np.conj(fft2(h))).real
# no zero padding
corr_fft = cross_correlate_2d(Window1, Window2)
fig = plt.figure(figsize=(8, 8))
fig.add_subplot(1,2, 1); plt.imshow(corr_scipy, cmap='turbo')
fig.add_subplot(1,2, 2); plt.imshow(corr_fft, cmap='turbo')
plt.show()
