如何使过滤器在此代码中工作？

Question

I am trying to apply the Butterworth low pass filter on the image but for some reason the values in lpFilter is not copied in lpFilter_matrix I tried to do it with a nested loop but still didn't work and the values of lpFilter_matrix remained zero.

import cv2
import numpy as np
from matplotlib import pyplot as plt
image=cv2.imread(r"C:/Users/Admin/Pictures/eee.jpg",0)
image_float32=np.float32(image)
dft =cv2.dft(image_float32,flags=cv2.DFT_COMPLEX_OUTPUT)
dft_shift=np.fft.fftshift(dft)
magnitude_spectrum=np.log(cv2.magnitude(dft_shift[:,:,0],dft_shift[:,:,1]))

rows, cols = image.shape
crow, ccol = rows//2 , cols//2   
r, c = np.mgrid[0:rows:1, 0:cols:1]
c -= crow
r -= ccol    

d = np.sqrt(np.power(r, 2.0) + np.power(c, 2.0))
lpFilter_matrix = np.zeros((rows, cols, 2), np.uint8)
d0=10
n=2

lpFilter = 1.0 / (1 + np.power(d/d0, 2*n))
lpFilter_matrix[:, :, 0] = lpFilter
lpFilter_matrix[:, :, 1] = lpFilter           
fshift = dft_shift*lpFilter_matrix
f_ishift = np.fft.ifftshift(fshift)
img_back = cv2.idft(f_ishift)
img_back = cv2.magnitude(img_back[:,:,0],img_back[:,:,1])
plt.figure(figsize=(14,9))
plt.subplot(121)
plt.imshow(image, cmap = 'gray')
plt.title('Input Image')
plt.axis('off')
plt.subplot(122)
plt.imshow(img_back, cmap = 'gray')
plt.title('filtered Image')
plt.axis('off')

Answer 1

I think your issue is that your filter needs to be float and not 8-bit. So as I said in my comment, change this line.

lpFilter_matrix = np.zeros((rows, cols, 2), np.uint8) with lpFilter_matrix = np.zeros((rows, cols, 2), np.float32 )

So this works for me in Python/OpenCV.

Input:

import cv2
import numpy as np
from matplotlib import pyplot as plt

# read image as grayscale and convert to float
image=cv2.imread("lena.jpg",0)
image_float32=np.float32(image)

# do dft
dft =cv2.dft(image_float32,flags=cv2.DFT_COMPLEX_OUTPUT)
dft_shift=np.fft.fftshift(dft)

# get the magnitude
magnitude_spectrum=np.log(cv2.magnitude(dft_shift[:,:,0],dft_shift[:,:,1]))

# initialize filter and center it
rows, cols = image.shape
crow, ccol = rows//2 , cols//2   
r, c = np.mgrid[0:rows:1, 0:cols:1]
c -= crow
r -= ccol    

# make filter circular
d = np.sqrt(np.power(r, 2.0) + np.power(c, 2.0))
lpFilter_matrix = np.zeros((rows, cols, 2), np.float32)

# specify filter arguments
d0=10
n=2

# compute butterworth filter
lpFilter = 1.0 / (1 + np.power(d/d0, 2*n))
lpFilter_matrix[:, :, 0] = lpFilter
lpFilter_matrix[:, :, 1] = lpFilter 

# apply filter         
fshift = dft_shift*lpFilter_matrix

# do idft
f_ishift = np.fft.ifftshift(fshift)
img_back = cv2.idft(f_ishift)

# convert back to real output from complex
img_back = cv2.magnitude(img_back[:,:,0],img_back[:,:,1])

fig = plt.figure(figsize=(14,9))
plt.subplot(121)
plt.imshow(image, cmap = 'gray')
plt.title('Input Image')
plt.axis('off')
plt.subplot(122)
plt.imshow(img_back, cmap = 'gray')
plt.title('filtered Image')
plt.axis('off')
plt.show()
fig.savefig('lena_butterworth.jpg')
plt.close(fig)  

Results: