目錄

• • 使用低通頻率域濾波器平滑圖像
  • • 理想低通濾波器(ILPF)
    • 高斯低通濾波器(GLPF)
    • 巴特沃斯低通濾波器
    • 低通濾波的例子

使用低通頻率域濾波器平滑圖像

理想低通濾波器(ILPF)

在以原點為中心的一個圓內(nèi)無衰減地通過所有頻率，而在這個圓外“截止”所有的頻率的二維低通濾波器。

$$H(u,v)=\{\begin{array}{ll}1,& D(u,v)\le D_0\\ 0,& D(u,v)>D_0\end{array}\text{\hspace{1em}(4.111)}$$

$$D(u,v)=[(u?P/2{)}^2+(v?Q/2{)}^2{]}^{1/2}\text{\hspace{1em}(4.12)}$$

$D_0$是一個正常數(shù)，控制圓的大小

def idea_low_pass_filter(source, center, radius=5):"""create idea low pass filter param: source: input, source imageparam: center: input, the center of the filter, where is the lowest value, (0, 0) is top left corner, source.shape[:2] is center of the source imageparam: radius: input, the radius of the lowest value, greater value, bigger blocker out range, if the radius is 0, then allvalue is 0return a [0, 1] value filter"""M, N = source.shape[1], source.shape[0]u = np.arange(M)v = np.arange(N)u, v = np.meshgrid(u, v)D = np.sqrt((u - center[1]//2)**2 + (v - center[0]//2)**2)D0 = radiuskernel = D.copy()kernel[D > D0] = 0kernel[D <= D0] = 1return kernel def plot_3d(ax, x, y, z):ax.plot_surface(x, y, z, antialiased=True, shade=True)ax.view_init(20, 60), ax.grid(b=False), ax.set_xticks([]), ax.set_yticks([]), ax.set_zticks([]) # 理想低通濾波器 ILPF from mpl_toolkits.mplot3d import Axes3D import numpy as np from matplotlib import pyplot as plt from matplotlib import cmcenter = img_ori.shape ILPF = idea_low_pass_filter(img_ori, center, radius=50)# 用來繪制3D圖 M, N = img_ori.shape[1], img_ori.shape[0] u = np.arange(M) v = np.arange(N) u, v = np.meshgrid(u, v)fig = plt.figure(figsize=(21, 7)) ax_1 = fig.add_subplot(1, 3, 1, projection='3d') plot_3d(ax_1, u, v, ILPF)ax_2 = fig.add_subplot(1, 3, 2) ax_2.imshow(ILPF,'gray'), ax_2.set_xticks([]), ax_2.set_yticks([])h = ILPF[img_ori.shape[0]//2:, img_ori.shape[1]//2] ax_3 = fig.add_subplot(1, 3, 3) ax_3.plot(h), ax_3.set_xticks([0, 50]), ax_3.set_yticks([0, 1]), ax_3.set_xlim([0, 320]), ax_3.set_ylim([0, 1.2])plt.tight_layout() plt.show()

總圖像能量$P_T$是對填充零后圖像的功率譜的各個分量在點$(u,v)$處求和得到。
$$P_T=\sum _{u=0}^{P?1}\sum _{v=0}^{Q?1}P(u,v)\text{\hspace{1em}(4.113)}$$

半徑為$D_0$的圓將包含$a$%的功率
$$a=100[\sum _{u=0}\sum _{v=0}P(u,v)/P_T]\text{\hspace{1em}(4.114)}$$

def mask_ring(img_ori, d=10):ILPF_1 = idea_low_pass_filter(img_ori, img_ori.shape, radius=d)ILPF_2 = idea_low_pass_filter(img_ori, img_ori.shape, radius=d-1)ILPF = ILPF_1 - ILPF_2return ILPF # 測試模型 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0441(a)(characters_test_pattern).tif', -1) M, N = img_ori.shape[:2]# 填充 fp = pad_image(img_ori, mode='reflect')radius = [10, 30, 60, 160, 460] mask = np.zeros(fp.shape) for i in range(len(radius)):mask += mask_ring(fp, d=radius[i])plt.figure(figsize=(16, 8)) plt.subplot(1, 2, 1), plt.imshow(img_ori, cmap='gray'), plt.xticks([]), plt.yticks([]) plt.subplot(1, 2, 2), plt.imshow(mask, cmap='gray'), plt.xticks([]), plt.yticks([]) plt.tight_layout() plt.show()

注：功率計算不太正確

#功率計算不太正確 # 填充 fp = pad_image(img_ori, mode='constant') # 中心化 fp_cen = centralized_2d(fp) # 正變換 fft = np.fft.fft2(fp_cen) spectrum = spectrum_fft(fft) # spectrum = np.log(1 + spectrum) PT = spectrum.sum()ILPF = idea_low_pass_filter(fp, fp.shape, D0=10)fh = fft * ILPF spectrum = spectrum_fft(fh) # spectrum = np.log(1 + spectrum) P = spectrum.sum() print(f"Power is -> {100*(P / PT)}") Power is -> 3.269204251436661 def ilpf_test(img_ori, mode='constant', radius=10):M, N = img_ori.shape[:2]# 填充fp = pad_image(img_ori, mode='reflect')# 中心化fp_cen = centralized_2d(fp)# 正變換fft = np.fft.fft2(fp_cen)# 濾波器H = idea_low_pass_filter(fp, center=fp.shape, radius=radius)# 濾波HF = fft * H# 反變換ifft = np.fft.ifft2(HF)# 去中心化gp = centralized_2d(ifft.real)# 還回來與原圖像的大小g = gp[:M, :N]dst = np.uint8(normalize(g) * 255)return dst # 頻率域濾波過程 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0441(a)(characters_test_pattern).tif', -1)radius = [10, 30, 60, 160, 460]fig = plt.figure(figsize=(15, 10)) for i in range(len(radius)+1):ax = fig.add_subplot(2, 3, i+1)if i == 0:ax.imshow(img_ori, 'gray'), ax.set_title('Original'), ax.set_xticks([]), ax.set_yticks([])else:img = ilpf_test(img_ori, radius=radius[i-1])ax.imshow(img, 'gray'), ax.set_title("radius = " + str(radius[i-1])), ax.set_xticks([]), ax.set_yticks([]) plt.tight_layout() plt.show()

# 頻率域ILPF傳遞函數(shù)對應(yīng)的空間核函數(shù) img_temp = np.zeros([1000, 1000]) ILPF = idea_low_pass_filter(img_temp, img_temp.shape, radius=15) ifft = np.fft.ifft2(ILPF) ifft = np.fft.ifftshift(ifft) space = ifft.real * 1200 space_s = abs(space) # space_s = np.clip(space, 0, space.max()) space_s = normalize(space_s)hx = space[:, 500] hx = centralized_2d(hx.reshape(1, -1)).flatten()fig = plt.figure(figsize=(15, 5)) ax_1 = fig.add_subplot(1, 3, 1) ax_1.imshow(ILPF, 'gray'), ax_1.set_xticks([]), ax_1.set_yticks([])ax_2 = fig.add_subplot(1, 3, 2) ax_2.imshow(space_s, 'gray'), ax_2.set_xticks([]), ax_2.set_yticks([])ax_3 = fig.add_subplot(1, 3, 3) ax_3.plot(hx), ax_3.set_xticks([]), ax_3.set_yticks([])plt.tight_layout() plt.show()

高斯低通濾波器(GLPF)

$$H(u,v)=e^{?D^2(u,v)/2D_0^2}\text{\hspace{1em}(4.116)}$$
$D_0$是截止頻率。當(dāng)$D(u,v)=D_0$時，GLPF傳遞函數(shù)下降到其最大值1.0的0.607。

def gauss_low_pass_filter(source, center, radius=5):"""create gauss low pass filter param: source: input, source imageparam: center: input, the center of the filter, where is the lowest value, (0, 0) is top left corner, source.shape[:2] is center of the source imageparam: radius: input, the radius of the lowest value, greater value, bigger blocker out range, if the radius is 0, then allvalue is 0return a [0, 1] value filter""" M, N = source.shape[1], source.shape[0]u = np.arange(M)v = np.arange(N)u, v = np.meshgrid(u, v)D = np.sqrt((u - center[1]//2)**2 + (v - center[0]//2)**2)D0 = radiuskernel = np.exp(- (D**2)/(2*D0**2))return kernel def plot_3d(ax, x, y, z):ax.plot_surface(x, y, z, antialiased=True, shade=True)ax.view_init(20, 60), ax.grid(b=False), ax.set_xticks([]), ax.set_yticks([]), ax.set_zticks([]) # 高斯低通濾波器 GLPF from mpl_toolkits.mplot3d import Axes3D import numpy as np from matplotlib import pyplot as plt from matplotlib import cmcenter = img_ori.shapeGLPF_10 = gauss_low_pass_filter(img_ori, center, radius=10) h_10 = GLPF_10[img_ori.shape[0]//2:, img_ori.shape[1]//2] GLPF_20 = gauss_low_pass_filter(img_ori, center, radius=20) h_20 = GLPF_20[img_ori.shape[0]//2:, img_ori.shape[1]//2] GLPF_40 = gauss_low_pass_filter(img_ori, center, radius=40) h_40 = GLPF_40[img_ori.shape[0]//2:, img_ori.shape[1]//2] GLPF_60 = gauss_low_pass_filter(img_ori, center, radius=60) h_60 = GLPF_60[img_ori.shape[0]//2:, img_ori.shape[1]//2]# 用來繪制3D圖 M, N = img_ori.shape[1], img_ori.shape[0] u = np.arange(M) v = np.arange(N) u, v = np.meshgrid(u, v)fig = plt.figure(figsize=(21, 7)) ax_1 = fig.add_subplot(1, 3, 1, projection='3d') plot_3d(ax_1, u, v, GLPF_60)ax_2 = fig.add_subplot(1, 3, 2) ax_2.imshow(GLPF_60,'gray'), ax_2.set_xticks([]), ax_2.set_yticks([])ax_3 = fig.add_subplot(1, 3, 3) ax_3.plot(h_10, label='$D_0=10$'), ax_3.set_xticks([0, 50]), ax_3.set_yticks([0, 1]), ax_3.set_xlim([0, 320]), ax_3.set_ylim([0, 1.2]) ax_3.plot(h_20, label='$D_0=20$') ax_3.plot(h_40, label='$D_0=40$') ax_3.plot(h_60, label='$D_0=60$') plt.legend(loc='best') plt.tight_layout() plt.show()

def glpf_test(img_ori, mode='constant', radius=10):M, N = img_ori.shape[:2]# 填充fp = pad_image(img_ori, mode=mode)# 中心化fp_cen = centralized_2d(fp)# 正變換fft = np.fft.fft2(fp_cen)# 濾波器H = gauss_low_pass_filter(fp, center=fp.shape, radius=radius)# 濾波HF = fft * H# 反變換ifft = np.fft.ifft2(HF)# 去中心化gp = centralized_2d(ifft.real)# 還回來與原圖像的大小g = gp[:M, :N]dst = np.uint8(normalize(g) * 255)return dst # 高斯低通濾波器在頻率域濾波的使用，這效果要比理想低通濾波器好很多，不會出現(xiàn)振鈴效應(yīng) img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0441(a)(characters_test_pattern).tif', -1)radius = [10, 30, 60, 160, 460]fig = plt.figure(figsize=(15, 10)) for i in range(len(radius)+1):ax = fig.add_subplot(2, 3, i+1)if i == 0:ax.imshow(img_ori, 'gray'), ax.set_title('Original'), ax.set_xticks([]), ax.set_yticks([])else:img = glpf_test(img_ori, mode='reflect', radius=radius[i-1])ax.imshow(img, 'gray'), ax.set_title("radius = " + str(radius[i-1])), ax.set_xticks([]), ax.set_yticks([]) plt.tight_layout() plt.show()

# 頻率域GLPF傳遞函數(shù)對應(yīng)的空間核函數(shù) img_temp = np.zeros([1000, 1000]) GLPF = gauss_low_pass_filter(img_temp, img_temp.shape, radius=15) ifft = np.fft.ifft2(GLPF) ifft = np.fft.ifftshift(ifft) space = ifft.real * 1200 space_s = abs(space) space_s = normalize(space_s)hx = space[:, 500] hx = centralized_2d(hx.reshape(1, -1)).flatten()fig = plt.figure(figsize=(15, 5)) ax_1 = fig.add_subplot(1, 3, 1) ax_1.imshow(GLPF, 'gray'), ax_1.set_xticks([]), ax_1.set_yticks([])ax_2 = fig.add_subplot(1, 3, 2) ax_2.imshow(space_s, 'gray'), ax_2.set_xticks([]), ax_2.set_yticks([])ax_3 = fig.add_subplot(1, 3, 3) ax_3.plot(hx), ax_3.set_xticks([]), ax_3.set_yticks([])plt.tight_layout() plt.show()

# 不使用傳統(tǒng)方法 import cv2 import numpy as np import matplotlib.pyplot as pltimg_ic = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0429(a)(blown_ic).tif', 0) #直接讀為灰度圖像plt.figure(figsize=(15, 12)) plt.subplot(221),plt.imshow(img_ic,'gray'),plt.title('origial'), plt.xticks([]), plt.yticks([])#-------------------------------- fft = np.fft.fft2(img_ic) fft_shift = np.fft.fftshift(fft) amp_img = np.abs(np.log(1 + np.abs(fft_shift))) plt.subplot(222),plt.imshow(amp_img,'gray'),plt.title('IC FFT'), plt.xticks([]), plt.yticks([])#-------------------------------- glpf = gauss_low_pass_filter(img_ic, img_ic.shape, radius=20) plt.subplot(223),plt.imshow(glpf,'gray'),plt.title('mask'), plt.xticks([]), plt.yticks([])#-------------------------------- f1shift = fft_shift * glpf f2shift = np.fft.ifftshift(f1shift) #對新的進(jìn)行逆變換 img_new = np.fft.ifft2(f2shift)#出來的是復(fù)數(shù)，無法顯示 img_new = np.abs(img_new)#調(diào)整大小范圍便于顯示 img_new = (img_new-np.amin(img_new))/(np.amax(img_new)-np.amin(img_new)) plt.subplot(224),plt.imshow(img_new,'gray'),plt.title('GLPF'), plt.xticks([]), plt.yticks([])plt.tight_layout() plt.show()

巴特沃斯低通濾波器

$$H(u,v)=\frac{1}{1+[D(u,v)/D_0{]}^{2n}}\text{\hspace{1em}(4.117)}$$
$$D(u,v)=[(u?M/2{)}^2+(v?N/2{)}^2{]}^{1/2}$$

• 特點
  • 較高的$n$值來控制這個BLPF函數(shù)可逼近ILPF的特性
  • 較低的$n$值來控制這個BLPF函數(shù)可逼近GLPF的特性，同時提供從低頻到高頻的平滑過渡。
  • 可用BLPF以小得多的振鈴效應(yīng)來逼近ILPF函數(shù)的清晰度

def butterworth_low_pass_filter(img, center, radius=5, n=1):"""create butterworth low pass filter param: source: input, source imageparam: center: input, the center of the filter, where is the lowest value, (0, 0) is top left corner, source.shape[:2] is center of the source imageparam: radius: input, the radius of the lowest value, greater value, bigger blocker out range, if the radius is 0, then allvalue is 0param: n: input, float, the order of the filter, if n is small, then the BLPF will be close to GLPF, and more smooth from lowfrequency to high freqency.if n is large, will close to ILPFreturn a [0, 1] value filter""" epsilon = 1e-8M, N = img.shape[1], img.shape[0]u = np.arange(M)v = np.arange(N)u, v = np.meshgrid(u, v)D = np.sqrt((u - center[1]//2)**2 + (v - center[0]//2)**2)D0 = radiuskernel = (1 / (1 + (D / (D0 + epsilon))**(2*n)))return kernel def plot_3d(ax, x, y, z):ax.plot_surface(x, y, z, antialiased=True, shade=True)ax.view_init(20, 60), ax.grid(b=False), ax.set_xticks([]), ax.set_yticks([]), ax.set_zticks([]) # 巴特沃斯低通濾波器 BLPF from mpl_toolkits.mplot3d import Axes3D import numpy as np from matplotlib import pyplot as plt from matplotlib import cmcenter = img_ori.shapeBLPF_60_1 = butterworth_low_pass_filter(img_ori, center, radius=60, n=1) h_1 = BLPF_60_1[img_ori.shape[0]//2:, img_ori.shape[1]//2] BLPF_60_2 = butterworth_low_pass_filter(img_ori, center, radius=60, n=2) h_2 = BLPF_60_2[img_ori.shape[0]//2:, img_ori.shape[1]//2] BLPF_60_3 = butterworth_low_pass_filter(img_ori, center, radius=60, n=3) h_3 = BLPF_60_3[img_ori.shape[0]//2:, img_ori.shape[1]//2] BLPF_60_4 = butterworth_low_pass_filter(img_ori, center, radius=60, n=4) h_4 = BLPF_60_4[img_ori.shape[0]//2:, img_ori.shape[1]//2]# 用來繪制3D圖 M, N = img_ori.shape[1], img_ori.shape[0] u = np.arange(M) v = np.arange(N) u, v = np.meshgrid(u, v)fig = plt.figure(figsize=(21, 7)) ax_1 = fig.add_subplot(1, 3, 1, projection='3d') plot_3d(ax_1, u, v, BLPF_60_1)ax_2 = fig.add_subplot(1, 3, 2) ax_2.imshow(BLPF_60_1,'gray'), ax_2.set_xticks([]), ax_2.set_yticks([])ax_3 = fig.add_subplot(1, 3, 3) ax_3.plot(h_1, label='$n=1$'), ax_3.set_xticks([0, 50]), ax_3.set_yticks([0, 1]), ax_3.set_xlim([0, 320]), ax_3.set_ylim([0, 1.2]) ax_3.plot(h_2, label='$n=2$') ax_3.plot(h_3, label='$n=3$') ax_3.plot(h_4, label='$n=4$') plt.legend(loc='best') plt.tight_layout() plt.show()

def blpf_test(img_ori, mode='constant', radius=10, n=1):M, N = img_ori.shape[:2]# 填充fp = pad_image(img_ori, mode=mode)# 中心化fp_cen = centralized_2d(fp)# 正變換fft = np.fft.fft2(fp_cen)# 濾波器H = butterworth_low_pass_filter(fp, center=fp.shape, radius=radius, n=n)# 濾波HF = fft * H# 反變換ifft = np.fft.ifft2(HF)# 去中心化gp = centralized_2d(ifft.real)# 還回來與原圖像的大小g = gp[:M, :N]dst = np.uint8(normalize(g) * 255)return dst # 巴特沃斯低通濾波器在頻率域濾波的使用 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0441(a)(characters_test_pattern).tif', -1)radius = [10, 30, 60, 160, 460]fig = plt.figure(figsize=(15, 10)) for i in range(len(radius)+1):ax = fig.add_subplot(2, 3, i+1)if i == 0:ax.imshow(img_ori, 'gray'), ax.set_title('Original'), ax.set_xticks([]), ax.set_yticks([])else:img = blpf_test(img_ori, mode='reflect', radius=radius[i-1], n=2.25)ax.imshow(img, 'gray'), ax.set_title("radius = " + str(radius[i-1])), ax.set_xticks([]), ax.set_yticks([]) plt.tight_layout() plt.show()

空間域的一階巴特沃斯沒有振鈴效應(yīng)。在2階和3階濾波器中，振鈴效應(yīng)通常難以察覺，但更高階濾波器中的振鈴效應(yīng)很明顯。

# 頻率域GLPF傳遞函數(shù)對應(yīng)的空間核函數(shù) img_temp = np.zeros([1000, 1000]) BLPF = butterworth_low_pass_filter(img_temp, img_temp.shape, radius=15, n=25) ifft = np.fft.ifft2(BLPF) ifft = np.fft.ifftshift(ifft) space = ifft.real * 1200 space_s = abs(space) space_s = normalize(space_s)hx = space[:, 500] hx = centralized_2d(hx.reshape(1, -1)).flatten()fig = plt.figure(figsize=(15, 5)) ax_1 = fig.add_subplot(1, 3, 1) ax_1.imshow(GLPF, 'gray'), ax_1.set_xticks([]), ax_1.set_yticks([])ax_2 = fig.add_subplot(1, 3, 2) ax_2.imshow(space_s, 'gray'), ax_2.set_xticks([]), ax_2.set_yticks([])ax_3 = fig.add_subplot(1, 3, 3) ax_3.plot(hx), ax_3.set_xticks([]), ax_3.set_yticks([])plt.tight_layout() plt.show()

def frequen2spatial(filter):ifft = np.fft.ifft2(filter)ifft = np.fft.ifftshift(ifft)spatial = ifft.real * 1200spatial_s = abs(spatial)spatial_s = normalize(spatial_s)return spatial, spatial_s # 頻率域BLPF傳遞函數(shù)對應(yīng)的空間核函數(shù) img_temp = np.zeros([1000, 1000]) n = [1, 2, 5, 20]fig = plt.figure(figsize=(20, 10))for i in range(len(n)):# 這是顯示空間域的核ax = fig.add_subplot(2, 4, i+1)BLPF = butterworth_low_pass_filter(img_temp, img_temp.shape, radius=15, n=n[i])spatial, spatial_s = frequen2spatial(BLPF)ax.imshow(spatial_s, 'gray'), ax.set_xticks([]), ax.set_yticks([])# 這里顯示是對應(yīng)的空間域核水平掃描線的灰度分布ax = fig.add_subplot(2, 4, i+5)hx = spatial[:, 500]hx = centralized_2d(hx.reshape(1, -1)).flatten()ax.plot(hx, label=f'n = {n[i]}'), ax.set_xticks([]), ax.set_yticks([])ax.legend(loc='best', fontsize=14) plt.tight_layout() plt.show()

低通濾波的例子

出下圖，我們可以清晰看到不同的截止頻率的核對圖像的平滑效果。我們杺選擇合適的核，以平滑圖像，再加上其它圖像處理技術(shù)，以達(dá)到想要的效果。
如下文字處理的例子，我們可以利用$D_0=20$，來平滑圖像，再經(jīng)過閾值處理，可以得到文字的蒙板。

# 高斯低通濾波器在印刷和出版業(yè)的應(yīng)用 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0419(a)(text_gaps_of_1_and_2_pixels).tif', -1)radius = [10, 30, 60, 90, 120]fig = plt.figure(figsize=(17, 10)) for i in range(len(radius)+1):ax = fig.add_subplot(2, 3, i+1)if i == 0:ax.imshow(img_ori, 'gray'), ax.set_title('Original'), ax.set_xticks([]), ax.set_yticks([])else:img = glpf_test(img_ori, mode='reflect', radius=radius[i-1])ax.imshow(img, 'gray'), ax.set_title("radius = " + str(radius[i-1])), ax.set_xticks([]), ax.set_yticks([]) plt.tight_layout() plt.show()

# 高斯低通濾波器在印刷和出版業(yè)的應(yīng)用 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0419(a)(text_gaps_of_1_and_2_pixels).tif', -1)radius = [10, 30, 60, 90, 120]fig = plt.figure(figsize=(17, 10)) ax = fig.add_subplot(1, 3, 1) ax.imshow(img_ori, 'gray'), ax.set_title('Original'), ax.set_xticks([]), ax.set_yticks([]) ax = fig.add_subplot(1, 3, 2) img = glpf_test(img_ori, mode='reflect', radius=20) ax.imshow(img, 'gray'), ax.set_title("radius = " + str(20)), ax.set_xticks([]), ax.set_yticks([]) ax = fig.add_subplot(1, 3, 3) ret, img_thred = cv2.threshold(img, 0, 255, cv2.THRESH_OTSU + cv2.THRESH_BINARY_INV) ax.imshow(img_thred, 'gray'), ax.set_title("Thred"), ax.set_xticks([]), ax.set_yticks([]) plt.tight_layout() plt.show()

# 高斯低通濾波器在印刷和出版業(yè)的應(yīng)用，平滑后的圖像看上去更柔和、更美觀 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0427(a)(woman).tif', -1)radius = [10, 50, 80, 130, 150]fig = plt.figure(figsize=(17, 10)) for i in range(len(radius)+1):ax = fig.add_subplot(2, 3, i+1)if i == 0:ax.imshow(img_ori, 'gray'), ax.set_title('Original'), ax.set_xticks([]), ax.set_yticks([])else:img = glpf_test(img_ori, mode='reflect', radius=radius[i-1])ax.imshow(img, 'gray'), ax.set_title("radius = " + str(radius[i-1])), ax.set_xticks([]), ax.set_yticks([]) plt.tight_layout() plt.show()

# 高斯低通濾波器在衛(wèi)星圖像的應(yīng)用，這里對圖像的濾波的目的是尺可能模糊更多的細(xì)節(jié)，而保留可識別的大特征。 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0451(a)(satellite_original).tif', -1)radius = [10, 20, 50, 80, 100]fig = plt.figure(figsize=(17, 10)) for i in range(len(radius)+1):ax = fig.add_subplot(2, 3, i+1)if i == 0:ax.imshow(img_ori, 'gray'), ax.set_title('Original'), ax.set_xticks([]), ax.set_yticks([])else:img = glpf_test(img_ori, mode='reflect', radius=radius[i-1])ax.imshow(img, 'gray'), ax.set_title("radius = " + str(radius[i-1])), ax.set_xticks([]), ax.set_yticks([]) plt.tight_layout() plt.show()

總結(jié)

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