目录
使用低通频率域滤波器平滑图像理想低通滤波器(ILPF)高斯低通滤波器(GLPF)巴特沃斯低通滤波器低通滤波的例子使用低通频率域滤波器平滑图像
理想低通滤波器(ILPF)
在以原点为中心的一个圆内无衰减地通过所有频率，而在这个圆外“截止”所有的频率的二维低通滤波器。
H(u,v)={1,D(u,v)≤D00,D(u,v)>D0(4.111)H(u, v) = \begin{cases} 1, &D(u, v) \leq D_0 \\0, &D(u, v) > D_0\end{cases} \tag{4.111}H(u,v)={1,0,D(u,v)≤D0D(u,v)>D0(4.111)
D(u,v)=[(u−P/2)2+(v−Q/2)2]1/2(4.12)D(u, v) = \big[(u - P/2)^2 + (v - Q/2)^2 \big]^{1/2} \tag{4.12}D(u,v)=[(u−P/2)2+(v−Q/2)2]1/2(4.12)
D0D_0D0是一个正常数，控制圆的大小
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([])
# 理想低通滤波器 ILPFfrom mpl_toolkits.mplot3d import Axes3Dimport numpy as npfrom matplotlib import pyplot as pltfrom matplotlib import cmcenter = img_ori.shapeILPF = idea_low_pass_filter(img_ori, center, radius=50)# 用来绘制3D图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()
总图像能量PTP_TPT是对填充零后图像的功率谱的各个分量在点(u,v)(u, v)(u,v)处求和得到。
PT=∑u=0P−1∑v=0Q−1P(u,v)(4.113)P_T = \sum_{u=0}^{P-1} \sum_{v=0}^{Q-1}P(u, v) \tag{4.113}PT=u=0∑P−1v=0∑Q−1P(u,v)(4.113)
半径为D0D_0D0的圆将包含aaa%的功率
a=100[∑u=0∑v=0P(u,v)/PT](4.114)a = 100\Big[ \sum_{u=0} \sum_{v=0}P(u, v) /P_T \Big] \tag{4.114}a=100[u=0∑v=0∑P(u,v)/PT](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
# 测试模型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：功率计算不太正确
#功率计算不太正确# 填充fp = pad_image(img_ori, mode='constant')# 中心化fp_cen = centralized_2d(fp)# 正变换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 * ILPFspectrum = 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)# 正变换fft = np.fft.fft2(fp_cen)# 滤波器H = idea_low_pass_filter(fp, center=fp.shape, radius=radius)# 滤波HF = fft * H# 反变换ifft = np.fft.ifft2(HF)# 去中心化gp = centralized_2d(ifft.real)# 还回来与原图像的大小g = gp[:M, :N]dst = np.uint8(normalize(g) * 255)return dst
# 频率域滤波过程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()
# 频率域ILPF传递函数对应的空间核函数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 * 1200space_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()
高斯低通滤波器(GLPF)
H(u,v)=e−D2(u,v)/2D02(4.116)H(u,v) = e^{-D^2(u,v) / 2D_0^2} \tag{4.116}H(u,v)=e−D2(u,v)/2D02(4.116)
D0D_0D0是截止频率。当D(u,v)=D0D(u, v) = D_0D(u,v)=D0时，GLPF传递函数下降到其最大值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([])
# 高斯低通滤波器 GLPFfrom mpl_toolkits.mplot3d import Axes3Dimport numpy as npfrom matplotlib import pyplot as pltfrom 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]# 用来绘制3D图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)# 正变换fft = np.fft.fft2(fp_cen)# 滤波器H = gauss_low_pass_filter(fp, center=fp.shape, radius=radius)# 滤波HF = fft * H# 反变换ifft = np.fft.ifft2(HF)# 去中心化gp = centralized_2d(ifft.real)# 还回来与原图像的大小g = gp[:M, :N]dst = np.uint8(normalize(g) * 255)return dst
# 高斯低通滤波器在频率域滤波的使用，这效果要比理想低通滤波器好很多，不会出现振铃效应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()
# 频率域GLPF传递函数对应的空间核函数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 * 1200space_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()
# 不使用传统方法import cv2import numpy as npimport matplotlib.pyplot as pltimg_ic = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH04/Fig0429(a)(blown_ic).tif', 0) #直接读为灰度图像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 * glpff2shift = np.fft.ifftshift(f1shift) #对新的进行逆变换img_new = np.fft.ifft2(f2shift)#出来的是复数，无法显示img_new = np.abs(img_new)#调整大小范围便于显示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()
巴特沃斯低通滤波器
H(u,v)=11+[D(u,v)/D0]2n(4.117)H(u,v) = \frac{1} {1 + [D(u,v) / D_0]^{2n}} \tag{4.117}H(u,v)=1+[D(u,v)/D0]2n1(4.117)
D(u,v)=[(u−M/2)2+(v−N/2)2]1/2D(u,v) = [(u - M/2)^2 + (v-N/2)^2]^{1/2}D(u,v)=[(u−M/2)2+(v−N/2)2]1/2
特点 较高的nnn值来控制这个BLPF函数可逼近ILPF的特性较低的nnn值来控制这个BLPF函数可逼近GLPF的特性，同时提供从低频到高频的平滑过渡。可用BLPF以小得多的振铃效应来逼近ILPF函数的清晰度
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([])
# 巴特沃斯低通滤波器 BLPFfrom mpl_toolkits.mplot3d import Axes3Dimport numpy as npfrom matplotlib import pyplot as pltfrom 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]# 用来绘制3D图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)# 正变换fft = np.fft.fft2(fp_cen)# 滤波器H = butterworth_low_pass_filter(fp, center=fp.shape, radius=radius, n=n)# 滤波HF = fft * H# 反变换ifft = np.fft.ifft2(HF)# 去中心化gp = centralized_2d(ifft.real)# 还回来与原图像的大小g = gp[:M, :N]dst = np.uint8(normalize(g) * 255)return dst
# 巴特沃斯低通滤波器在频率域滤波的使用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()
空间域的一阶巴特沃斯没有振铃效应。在2阶和3阶滤波器中，振铃效应通常难以察觉，但更高阶滤波器中的振铃效应很明显。
# 频率域GLPF传递函数对应的空间核函数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 * 1200space_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
# 频率域BLPF传递函数对应的空间核函数img_temp = np.zeros([1000, 1000])n = [1, 2, 5, 20]fig = plt.figure(figsize=(20, 10))for i in range(len(n)):# 这是显示空间域的核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([])# 这里显示是对应的空间域核水平扫描线的灰度分布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()
低通滤波的例子
出下图，我们可以清晰看到不同的截止频率的核对图像的平滑效果。我们杺选择合适的核，以平滑图像，再加上其它图像处理技术，以达到想要的效果。
如下文字处理的例子，我们可以利用D0=20D_0=20D0=20，来平滑图像，再经过阈值处理，可以得到文字的蒙板。
# 高斯低通滤波器在印刷和出版业的应用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()
# 高斯低通滤波器在印刷和出版业的应用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()
# 高斯低通滤波器在印刷和出版业的应用，平滑后的图像看上去更柔和、更美观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()
# 高斯低通滤波器在卫星图像的应用，这里对图像的滤波的目的是尺可能模糊更多的细节，而保留可识别的大特征。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()
第4章 Python 数字图像处理(DIP) - 频率域滤波10 - 使用低通频率域滤波器平滑图像 - 理想 高斯 巴特沃斯低通滤波器
