使用二维 FFT 对图像模糊处理

import numpy as np
import matplotlib.pyplot as plt

# 图像大小，正方形边长，正方形数量
ncols, nrows = 120, 120
sq_size, nsq = 10, 20

# The image array (0=background, 1=square) and boolean array of allowed places
# 添加一个正方形，使其不接触另一个或图像的边
image = np.zeros((nrows, ncols))
sq_locs = np.zeros((nrows, ncols), dtype=bool)
sq_locs[1:-sq_size-1:,1:-sq_size-1] = True

def place_square():
    """ 在图像上随机放置一个正方形并更新 sq_locs. """
    # valid_locs is an array of the indices of True entries in sq_locs
    valid_locs = np.transpose(np.nonzero(sq_locs))
    # 随机选择一个这样的条目，并将其添加到左上角
    # 角落里有;然后更新 sq_locs
    i, j = valid_locs[np.random.randint(len(valid_locs))]
    image[i:i+sq_size, j:j+sq_size] = 1
    imin, jmin = max(0,i-sq_size-1), max(0, j-sq_size-1)
    sq_locs[imin:i+sq_size+1, jmin:j+sq_size+1] = False

# 将所需的正方形数量添加到图像中
for i in range(nsq):
    place_square()
plt.imshow(image)
plt.show()

# Take the 2-dimensional DFT and centre the frequencies
ftimage = np.fft.fft2(image)
ftimage = np.fft.fftshift(ftimage)
plt.imshow(np.abs(ftimage))
plt.show()


# Build and apply a Gaussian filter.
sigmax, sigmay = 10, 10
cy, cx = nrows/2, ncols/2
x = np.linspace(0, nrows, nrows)
y = np.linspace(0, ncols, ncols)
X, Y = np.meshgrid(x, y)
gmask = np.exp(-(((X-cx)/sigmax)**2 + ((Y-cy)/sigmay)**2))

ftimagep = ftimage * gmask
plt.imshow(np.abs(ftimagep))
plt.show()

# Finally, take the inverse transform and show the blurred image
imagep = np.fft.ifft2(ftimagep)
plt.imshow(np.abs(imagep))
plt.show()

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