Convolution and Correlation.py

import numpy as np
import matplotlib.pyplot as plt
from scipy import ndimage
from scipy import signal

a = np.ones((20, 20)) * 0

a[5, 5] = 1
a[10, 10] = 1
a[15, 15] = 1

a = ndimage.gaussian_filter(a, 1)


s = np.zeros((3, 3))
s[1, 1] = 1

s = ndimage.gaussian_filter(s, 1)
s[0, :] = -0.1

print(a.shape, s.shape)

c = signal.correlate(a, s, mode='valid')
d = signal.convolve(a, s, mode='valid')

plt.subplot(221).imshow(a)
plt.title('$f$')
plt.subplot(222).imshow(s)
plt.title('$h$')
plt.subplot(223).imshow(d)
plt.title('convolve:\nblend $h$ into $f$')
plt.subplot(224).imshow(c)
plt.title('correlate:\nwhich pixel in $f$ looks like $h$')
plt.tight_layout()
plt.show()