完成巴特沃斯滤波器

Butterworth.py

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+import cv2 as cv
+import numpy as np
+
+def filter(img, D0, W=None, N=2, type='lp', filter='butterworth'):
+    '''
+    频域滤波器
+    Args:
+        img: 灰度图片
+        D0: 截止频率
+        W: 带宽
+        N: butterworth和指数滤波器的阶数
+        type: lp, hp, bp, bs即低通、高通、带通、带阻
+        filter:butterworth、ideal、exponential即巴特沃斯、理想、指数滤波器
+    Returns:
+        imgback：滤波后的图像
+    '''
+ 
+    #离散傅里叶变换
+    dft=cv.dft(np.float32(img),flags=cv.DFT_COMPLEX_OUTPUT)
+    #中心化
+    dtf_shift=np.fft.fftshift(dft) 
+ 
+    rows,cols=img.shape 
+    crow,ccol=int(rows/2),int(cols/2) #计算频谱中心
+    mask=np.ones((rows,cols,2)) #生成rows行cols列的2纬矩阵
+    for i in range(rows):
+        for j in range(cols):
+            D = np.sqrt((i-crow)**2+(j-ccol)**2)
+            if(filter.lower() == 'butterworth'):
+                if(type == 'lp'):
+                    mask[i, j] = 1/(1+(D/D0)**(2*N))
+                elif(type == 'hp'):
+                    mask[i, j] = 1/(1+(D0/D)**(2*N))
+                elif(type == 'bs'):
+                    mask[i, j] = 1/(1+(D*W/(D**2-D0**2))**(2*N))
+                elif(type == 'bp'):
+                    mask[i, j] = 1/(1+((D**2-D0**2)/D*W)**(2*N))
+                else:
+                    assert('type error')
+            elif(filter.lower() == 'ideal'): #理想滤波器
+                if(type == 'lp'):
+                    if(D > D0):
+                        mask[i, j] = 0
+                elif(type == 'hp'):
+                    if(D < D0):
+                        mask[i, j] = 0
+                elif(type == 'bs'):
+                    if(D > D0 and D < D0+W):
+                        mask[i, j] = 0
+                elif(type == 'bp'):
+                    if(D < D0 and D > D0+W):
+                        mask[i, j] = 0
+                else:
+                    assert('type error')
+            elif(filter.lower() == 'exponential'): #指数滤波器
+                if(type == 'lp'):
+                    mask[i, j] = np.exp(-(D/D0)**(2*N))
+                elif(type == 'hp'):
+                    mask[i, j] = np.exp(-(D0/D)**(2*N))
+                elif(type == 'bs'):
+                    mask[i, j] = np.exp(-(D*W/(D**2 - D0**2))**(2*N))
+                elif(type == 'bp'):
+                    mask[i, j] = np.exp(-((D**2 - D0**2)/D*W)**(2*N))
+                else:
+                    assert('type error')
+            
+    fshift = dtf_shift*mask
+ 
+    f_ishift=np.fft.ifftshift(fshift) 
+    img_back=cv.idft(f_ishift) 
+    img_back=cv.magnitude(img_back[:,:,0],img_back[:,:,1]) #计算像素梯度的绝对值
+    img_back=np.abs(img_back)
+    img_back=(img_back-np.amin(img_back))/(np.amax(img_back)-np.amin(img_back))
+ 
+    return img_back

Filtering_Butterworth.py

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+import cv2
+import numpy as np
+import matplotlib.pyplot as plt
+plt.rcParams['font.sans-serif'] = ['simHei']
+plt.rcParams['axes.unicode_minus'] = False
+from Butterworth import filter
+
+# 读取照片
+image_characterTestPattern2 = cv2.imread("file/characterTestPattern2.jpg", cv2.IMREAD_GRAYSCALE)
+
+# 利用巴特沃斯滤波器进行处理
+image_characterTestPattern2_Butterworth1 = filter(image_characterTestPattern2, 10, type='lp')
+image_characterTestPattern2_Butterworth2 = filter(image_characterTestPattern2, 100, type='lp')
+image_characterTestPattern2_Butterworth3 = filter(image_characterTestPattern2, 1000, type='lp')
+
+# 展示图像
+plt.subplot(2,2,1)
+plt.imshow(image_characterTestPattern2, cmap='gray')
+plt.title('原图')
+plt.axis('off')
+
+plt.subplot(2,2,2)
+plt.imshow(image_characterTestPattern2_Butterworth1, cmap='gray')
+plt.title('D0 = 10')
+plt.axis('off')
+
+plt.subplot(2,2,3)
+plt.imshow(image_characterTestPattern2_Butterworth2, cmap='gray')
+plt.title('D0 = 100')
+plt.axis('off')
+
+plt.subplot(2,2,4)
+plt.imshow(image_characterTestPattern2_Butterworth3, cmap='gray')
+plt.title('D0 = 1000')
+plt.axis('off')
+
+plt.tight_layout()
+plt.show()