Python中的缺口拒绝过滤
我正在尝试在 python 中为分配实现缺口拒绝过滤。我曾尝试使用 Rafael Gonzales 书中的陷波拒绝滤波器公式，但我得到的只是边缘检测图像。然后我尝试了理想的缺口拒绝，结果如下：
输入图像--我的程序的输出--预期输出
这是我的代码：
import cv2
import numpy as np
import matplotlib.pyplot as plt
def notch_reject_filter(shape, d0=9, u_k=0, v_k=0):
P, Q = shape
# Initialize filter with zeros
H = np.zeros((P, Q))
# Traverse through filter
for u in range(0, P):
for v in range(0, Q):
# Get euclidean distance from point D(u,v) to the center
D_uv = np.sqrt((u - P / 2 + u_k) ** 2 + (v - Q / 2 + v_k) ** 2)
D_muv = np.sqrt((u - P / 2 - u_k) ** 2 + (v - Q / 2 - v_k) ** 2)
if D_uv <= d0 or D_muv <= d0:
H[u, v] = 0.0
else:
H[u, v] = 1.0
return H
img = cv2.imread('input.png', 0)
img_shape = img.shape
original = np.fft.fft2(img)
center = np.fft.fftshift(original)
NotchRejectCenter = center * notch_reject_filter(img_shape, 32, 50, 50)
NotchReject = np.fft.ifftshift(NotchRejectCenter)
inverse_NotchReject = np.fft.ifft2(NotchReject) # Compute the inverse DFT of the result
plot_image = np.concatenate((img, np.abs(inverse_NotchReject)),axis=1)
plt.imshow(plot_image, "gray"), plt.title("Notch Reject Filter")
plt.show()
回答
- 我得到的只是边缘检测图像，因为您的实现是高通滤波器，它是中间的黑色圆圈，用作边缘检测器。
- 然后我尝试了理想的缺口拒绝如果您正确应用，这是正确的。
主要概念是过滤频域中不需要的噪声，噪声可以被视为白点，您的作用是通过将它们乘以频域中的黑色圆圈来抑制该白点（称为过滤）。
为了改善这个结果，添加更多陷波滤波器（H5，H6，...）来抑制噪声。
import cv2
import numpy as np
import matplotlib.pyplot as plt
#------------------------------------------------------
def notch_reject_filter(shape, d0=9, u_k=0, v_k=0):
P, Q = shape
# Initialize filter with zeros
H = np.zeros((P, Q))
# Traverse through filter
for u in range(0, P):
for v in range(0, Q):
# Get euclidean distance from point D(u,v) to the center
D_uv = np.sqrt((u - P / 2 + u_k) ** 2 + (v - Q / 2 + v_k) ** 2)
D_muv = np.sqrt((u - P / 2 - u_k) ** 2 + (v - Q / 2 - v_k) ** 2)
if D_uv <= d0 or D_muv <= d0:
H[u, v] = 0.0
else:
H[u, v] = 1.0
return H
#-----------------------------------------------------
img = cv2.imread('input.png', 0)
f = np.fft.fft2(img)
fshift = np.fft.fftshift(f)
phase_spectrumR = np.angle(fshift)
magnitude_spectrum = 20*np.log(np.abs(fshift))
img_shape = img.shape
H1 = notch_reject_filter(img_shape, 4, 38, 30)
H2 = notch_reject_filter(img_shape, 4, -42, 27)
H3 = notch_reject_filter(img_shape, 2, 80, 30)
H4 = notch_reject_filter(img_shape, 2, -82, 28)
NotchFilter = H1*H2*H3*H4
NotchRejectCenter = fshift * NotchFilter
NotchReject = np.fft.ifftshift(NotchRejectCenter)
inverse_NotchReject = np.fft.ifft2(NotchReject) # Compute the inverse DFT of the result
Result = np.abs(inverse_NotchReject)
plt.subplot(222)
plt.imshow(img, cmap='gray')
plt.title('Original')
plt.subplot(221)
plt.imshow(magnitude_spectrum, cmap='gray')
plt.title('magnitude spectrum')
plt.subplot(223)
plt.imshow(magnitude_spectrum*NotchFilter, "gray")
plt.title("Notch Reject Filter")
plt.subplot(224)
plt.imshow(Result, "gray")
plt.title("Result")
plt.show()