Python 上的卷积

Question

所以我想计算傅里叶变换图像和蒙版之间的卷积。

from scipy import fftpack
import numpy as np
import imageio
from PIL import Image, ImageDraw
import cv2
import matplotlib.pyplot as plt
import math
from scipy.ndimage.filters import convolve


input_image = Image.open('....image....')
input_image=np.array(input_image)
M,N = input_image.shape[0],input_image.shape[1]

FT_img = fftpack.fftshift(fftpack.fft2(input_image))

n = 2; # order value can change this value accordingly 


D0 = 60; # cut-off frequency can change this value accordingly 

# Designing filter 

u = np.arange(0, M)
idx = u > M/2
u[idx] = u[idx] - M
v = np.arange(0, N)
idy = v > N/2
v[idy] = v[idy] - N

V,U = np.meshgrid(v,u)

# Calculating Euclidean Distance 
D=np.linalg.norm(V-U) 

# determining the filtering mask 
H = 1/(1 + (D0/D)**(2*n)); 

# Convolution between the Fourier Transformed image and the mask 
G = convolve(H, FT_img)

当我运行此代码片段时，最后一行出现“运行时 error:filter 权重数组形状不正确。”错误。我的理解是 H 是浮点数而 FT_img 是数组所以我不能对它们进行卷积。但我不知道如何解决。我该如何解决这个问题？

Answer 1

为每个 (u, v) 计算距离 D 和滤波器 H 这将产生一个与输入图像大小相同的数组，将该数组（H 滤波器）与傅立叶域中的图像相乘将等效于卷积在Time域中，结果如下：

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

# Read Image as Grayscale
img = cv2.imread('input.png', 0)

# Designing filter 
#------------------------------------------------------
def butterworth_filter(shape, n=2, D0=60):
    '''
    n = 2; # order value can change this value accordingly 
    D0 = 60; # cut-off frequency can change this value accordingly 
    '''
    M, N = shape
    # Initialize filter with zeros
    H = np.zeros((M, N))

    # Traverse through filter
    for u in range(0, M):
        for v in range(0, N):
            # Get euclidean distance from point D(u,v) to the center
            D_uv = np.sqrt((u - M / 2) ** 2 + (v - N / 2) ** 2)
            # determining the filtering mask 
            H[u, v] = 1/(1 + (D0/D_uv)**(2*n))
    return H
#-----------------------------------------------------

f = np.fft.fft2(img)
fshift = np.fft.fftshift(f)
phase_spectrumR = np.angle(fshift)
magnitude_spectrum = 20*np.log(np.abs(fshift))
 
# Generate Butterworth Filter
H = butterworth_filter(img.shape)
# Convolution between the Fourier Transformed image and the mask
G = H * fshift
# Obtain the Result
result = np.abs(np.fft.ifft2(np.fft.ifftshift((G))))


plt.subplot(222)
plt.imshow(img, cmap='gray')
plt.title('Original')
plt.axis('off')

plt.subplot(221)
plt.imshow(magnitude_spectrum, cmap='gray')
plt.title('magnitude spectrum')
plt.axis('off')

plt.subplot(223)
plt.imshow(H, "gray") 
plt.title("Butterworth Filter")
plt.axis('off')

plt.subplot(224)
plt.imshow(result, "gray") 
plt.title("Result")
plt.axis('off')

plt.show()

Python 上的卷积

Convolution on Python

python

arrays

numpy

image-processing

convolution