def dft(img):
height, width = img.shape[0], img.shape[1]
f = img
F = np.zeros((height, width, 1), np.float)
for u, v in product(range(0, height), range(0, width)):
for x, y in product(range(0, height), range(0, width)):
F[u, v] += f[x, y] * e ** (2 * pi * (u * x / height + v * y / width)) * (-1) ** (x + y)
return F
def high_frequency_emphasis(shape, D0, k1, k2):
height, width = shape
H = np.zeros((height, width), np.float)
for u, v in product(range(0, height), range(0, width)):
Duv = ((u - height / 2) ** 2 + (v - width / 2) ** 2) ** 0.5
H[u, v] = k1 + k2 * (1 - e ** (-1 * Duv ** 2 / (2 * D0 ** 2)))
return H
def butterworth_filter(shape, D0, n):
height, width = shape
A = 2 ** 0.5 - 1
H = np.zeros((height, width), np.float)
for u, v in product(range(0, height), range(0, width)):
Duv = ((u - height / 2) ** 2 + (v - width / 2) ** 2) ** 0.5
H[u, v] = 1 / (1 + A * (Duv / D0) ** (2 * n))
return H
