標(biāo)題

• • • 統(tǒng)計(jì)排序?yàn)V波器
    • • 中值、最大值、最小值、中點(diǎn) 濾波器
      • 修正阿爾法均值濾波器

統(tǒng)計(jì)排序?yàn)V波器

中值、最大值、最小值、中點(diǎn) 濾波器

$$\hat{f}(x,y)=\text{median}\{g(r,c)\}\text{\hspace{1em}(5.27)}$$
$$\hat{f}(x,y))=\text{max}\{g(r,c)\}\text{\hspace{1em}(5.28)}$$
$$\hat{f}(x,y)=\text{min}\{g(r,c)\}\text{\hspace{1em}(5.29)}$$
$$\hat{f}(x,y)=\frac{1}{2}[\text{max}\{g(r,c)\}+\text{min}\{g(r,c)\}]\text{\hspace{1em}(5.30)}$$

中值濾波器應(yīng)用廣泛，因?yàn)榕c大小相同的線性平滑濾波器相比，它能有效地降低某些隨機(jī)噪聲，且模糊度要小得多。對(duì)于單極和雙極沖激噪聲，中值濾波器的效果更好，但多次使用中值濾波器會(huì)使用圖像模糊。

最大值濾波器可用于找到圖像中的最亮點(diǎn)，或用于消弱與明亮區(qū)域相信的暗色區(qū)域。此外由于胡椒噪聲的值很低，因此可用這種濾波器來降低胡椒噪聲。

最小值濾波器用于找到圖像中的最暗點(diǎn)，或用于削弱與暗色區(qū)域的明亮區(qū)域。此外，還可通過最小運(yùn)算降低鹽粒噪聲。

中點(diǎn)濾波器是統(tǒng)計(jì)排序?yàn)V波器與平均濾波器的結(jié)合。它最適合于處理隨機(jī)分布的噪聲，如高斯噪聲或均勻噪聲。

修正阿爾法均值濾波器

$$\hat{f}(x,y)=\frac{1}{mn?d}\sum g(r,c)\text{\hspace{1em}(5.31)}$$

d的取值范圍是從$0到mn?1$。 當(dāng)$d=0$時(shí)，簡(jiǎn)化為算術(shù)平均濾波器。當(dāng)$d=mn?1$，那么為中值濾波器。$d$取其它值時(shí)，修正阿爾法濾波器適合于處理多種混合噪聲，如高斯噪聲和椒鹽噪聲。

使用時(shí)需要選取合適的$d$值，才能得到比較好的結(jié)果，不同的值差別也很大。

# 中值、最大值、最小值、中點(diǎn) 濾波器 def median_filter(image, kernel):"""median filter, math: $$\hat{f}(x, y) = \text{median} \{g(r,c)\}$$param: image: input image for denoisingparam: kernel: input kernel, actually only use kernel shape, just want to keep the format as mean filterreturn: image after median filter"""height, width = image.shape[:2]m, n = kernel.shape[:2]padding_h = int((m -1)/2)padding_w = int((n -1)/2)# 這樣的填充方式，可以奇數(shù)核或者偶數(shù)核都能正確填充image_pad = np.pad(image, ((padding_h, m - 1 - padding_h), \(padding_w, n - 1 - padding_w)), mode="edge")image_result = np.zeros(image.shape)for i in range(height):for j in range(width):temp = image_pad[i:i + m, j:j + n]image_result[i, j] = np.median(temp)return image_resultdef max_filter(image, kernel):"""max filter, math: $$\hat{f}(x, y)) = \text{max} \{g(r,c)\}$$param: image: input image for denoisingparam: kernel: input kernel, actually only use kernel shape, just want to keep the format as mean filterreturn: image after max filter"""height, width = image.shape[:2]m, n = kernel.shape[:2]padding_h = int((m -1)/2)padding_w = int((n -1)/2)# 這樣的填充方式，可以奇數(shù)核或者偶數(shù)核都能正確填充image_pad = np.pad(image, ((padding_h, m - 1 - padding_h), \(padding_w, n - 1 - padding_w)), mode="constant", constant_values=0)img_result = np.zeros(image.shape)for i in range(height):for j in range(width):temp = image_pad[i:i + m, j:j + n]img_result[i, j] = np.max(temp)return img_resultdef min_filter(image, kernel):"""min filter, math: $$\hat{f}(x, y) = \text{min} \{g(r,c)\}$$param: image: input image for denoisingparam: kernel: input kernel, actually only use kernel shape, just want to keep the format as mean filterreturn: image after min filter"""height, width = image.shape[:2]m, n = kernel.shape[:2]padding_h = int((m -1)/2)padding_w = int((n -1)/2)# 這樣的填充方式，可以奇數(shù)核或者偶數(shù)核都能正確填充image_pad = np.pad(image, ((padding_h, m - 1 - padding_h), \(padding_w, n - 1 - padding_w)), mode="edge", )img_result = np.zeros(image.shape)for i in range(height):for j in range(width):temp = image_pad[i:i + m, j:j + n]img_result[i, j] = np.min(temp)return img_resultdef middle_filter(image, kernel):"""middle filter, math: $$\hat{f}(x, y) = \frac{1}{2}\big[\text{max}\{g(r,c)\} + \text{min}\{g(r,c)\} \big]$$param: image: input image for denoisingparam: kernel: input kernel, actually only use kernel shape, just want to keep the format as mean filterreturn: image after middle filter"""height, width = image.shape[:2]m, n = kernel.shape[:2]padding_h = int((m -1)/2)padding_w = int((n -1)/2)# 這樣的填充方式，可以奇數(shù)核或者偶數(shù)核都能正確填充image_pad = np.pad(image, ((padding_h, m - 1 - padding_h), \(padding_w, n - 1 - padding_w)), mode="edge")img_result = np.zeros(image.shape)for i in range(height):for j in range(width):temp = image_pad[i:i + m, j:j + n]img_result[i, j] = int(temp.max()/2 + temp.min()/2)return img_result # 中值、最大值、最小值、中點(diǎn) 濾波器處理胡椒噪聲 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0508(a)(circuit-board-pepper-prob-pt1).tif', 0) #直接讀為灰度圖像kernel = np.ones([3, 3]) img_median = median_filter(img_ori, kernel=kernel) img_max = max_filter(img_ori, kernel=kernel) img_min = min_filter(img_ori, kernel=kernel) img_middle = middle_filter(img_ori, kernel=kernel)plt.figure(figsize=(15, 10))plt.subplot(231), plt.imshow(img_ori, 'gray'), plt.title('Original'), plt.xticks([]), plt.yticks([]) plt.subplot(232), plt.imshow(img_median, 'gray'), plt.title('Median filter'), plt.xticks([]), plt.yticks([]) plt.subplot(233), plt.imshow(img_max, 'gray'), plt.title('Max filter'), plt.xticks([]), plt.yticks([]) plt.subplot(234), plt.imshow(img_min, 'gray'), plt.title('Min filter'), plt.xticks([]), plt.yticks([]) plt.subplot(235), plt.imshow(img_middle, 'gray'), plt.title('Middle filter'), plt.xticks([]), plt.yticks([]) plt.tight_layout() plt.show()

# 中值、最大值、最小值、中點(diǎn) 濾波器處理鹽粒噪聲 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0508(b)(circuit-board-salt-prob-pt1).tif', 0) #直接讀為灰度圖像kernel = np.ones([3, 3]) img_median = median_filter(img_ori, kernel=kernel) img_max = max_filter(img_ori, kernel=kernel) img_min = min_filter(img_ori, kernel=kernel) img_middle = middle_filter(img_ori, kernel=kernel)plt.figure(figsize=(15, 10))plt.subplot(231), plt.imshow(img_ori, 'gray'), plt.title('Original'), plt.xticks([]), plt.yticks([]) plt.subplot(232), plt.imshow(img_median, 'gray'), plt.title('Median filter'), plt.xticks([]), plt.yticks([]) plt.subplot(233), plt.imshow(img_max, 'gray'), plt.title('Max filter'), plt.xticks([]), plt.yticks([]) plt.subplot(234), plt.imshow(img_min, 'gray'), plt.title('Min filter'), plt.xticks([]), plt.yticks([]) plt.subplot(235), plt.imshow(img_middle, 'gray'), plt.title('Middle filter'), plt.xticks([]), plt.yticks([]) plt.tight_layout() plt.show()

# 中值、最大值、最小值、中點(diǎn) 濾波器處理高斯噪聲 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0507(b)(ckt-board-gauss-var-400).tif', 0) #直接讀為灰度圖像kernel = np.ones([3, 3]) img_median = median_filter(img_ori, kernel=kernel) img_max = max_filter(img_ori, kernel=kernel) img_min = min_filter(img_ori, kernel=kernel) img_middle = middle_filter(img_ori, kernel=kernel)plt.figure(figsize=(15, 10))plt.subplot(231), plt.imshow(img_ori, 'gray'), plt.title('Original'), plt.xticks([]), plt.yticks([]) plt.subplot(232), plt.imshow(img_median, 'gray'), plt.title('Median filter'), plt.xticks([]), plt.yticks([]) plt.subplot(233), plt.imshow(img_max, 'gray'), plt.title('Max filter'), plt.xticks([]), plt.yticks([]) plt.subplot(234), plt.imshow(img_min, 'gray'), plt.title('Min filter'), plt.xticks([]), plt.yticks([]) plt.subplot(235), plt.imshow(img_middle, 'gray'), plt.title('Middle filter'), plt.xticks([]), plt.yticks([]) plt.tight_layout() plt.show()

# 多次中值濾波器處理椒鹽噪聲 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0507(a)(ckt-board-orig).tif', 0) #直接讀為灰度圖像img_salt_pepper = add_salt_pepper(img_ori, ps=0.1, pp=0.1)kernel = np.ones([3, 3]) img_median_1 = median_filter(img_salt_pepper, kernel=kernel) img_median_2 = median_filter(img_median_1, kernel=kernel) img_median_3 = median_filter(img_median_2, kernel=kernel)plt.figure(figsize=(15, 10)) plt.subplot(231), plt.imshow(img_ori, 'gray'), plt.title('Original'), plt.xticks([]), plt.yticks([]) plt.subplot(232), plt.imshow(img_salt_pepper, 'gray'), plt.title('With salt pepper 0.1'), plt.xticks([]), plt.yticks([]) plt.subplot(233), plt.imshow(img_median_1, 'gray'), plt.title('1 time Median filter'), plt.xticks([]), plt.yticks([]) plt.subplot(234), plt.imshow(img_median_2, 'gray'), plt.title('2 times Median filter'), plt.xticks([]), plt.yticks([]) plt.subplot(235), plt.imshow(img_median_3, 'gray'), plt.title('3 times Median filter'), plt.xticks([]), plt.yticks([]) plt.tight_layout() plt.show()

def modified_alpha_mean(image, kernel, d=0):"""modified alpha filter, math: $$$$\hat{f}(x, y) = \frac{1}{mn - d} \sum g(r,c)$$param: image: input image for denoisingparam: kernel: input kernel, actually only use kernel shape, just want to keep the format as mean filterparam: d : input int, which is from 0 to m * nreturn: image after modified alpha filter"""height, width = image.shape[:2]m, n = kernel.shape[:2]padding_h = int((m -1)/2)padding_w = int((n -1)/2)# 這樣的填充方式，可以奇數(shù)核或者偶數(shù)核都能正確填充image_pad = np.pad(image, ((padding_h, m - 1 - padding_h), \(padding_w, n - 1 - padding_w)), mode="edge")img_result = np.zeros(image.shape)for i in range(height):for j in range(width):temp = np.sum(image_pad[i:i + m, j:j + n] * 1)img_result[i, j] = temp / (m * n - d)return img_result # 修正阿爾法濾波器處理高斯噪聲 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0507(b)(ckt-board-gauss-var-400).tif', 0) #直接讀為灰度圖像kernel = np.ones([3, 3])img_median = median_filter(img_ori, kernel=kernel) img_max = max_filter(img_ori, kernel=kernel) img_min = min_filter(img_ori, kernel=kernel) img_alpha_d_1 = modified_alpha_mean(img_ori, kernel, d=1) img_alpha_d_05 = modified_alpha_mean(img_ori, kernel, d=0.5)plt.figure(figsize=(15, 10)) plt.subplot(231), plt.imshow(img_ori, 'gray'), plt.title('Original'), plt.xticks([]), plt.yticks([]) plt.subplot(232), plt.imshow(img_median, 'gray'), plt.title('Median filter'), plt.xticks([]), plt.yticks([]) plt.subplot(233), plt.imshow(img_max, 'gray'), plt.title('Max filter'), plt.xticks([]), plt.yticks([]) plt.subplot(234), plt.imshow(img_min, 'gray'), plt.title('Min filter'), plt.xticks([]), plt.yticks([]) plt.subplot(235), plt.imshow(img_alpha_d_1, 'gray'), plt.title('Modified alpha d=1'), plt.xticks([]), plt.yticks([]) plt.subplot(236), plt.imshow(img_alpha_d_05, 'gray'), plt.title('Modified alpha d=0.5'), plt.xticks([]), plt.yticks([]) plt.tight_layout() plt.show()

# 修正阿爾法濾波器處理高斯噪聲+椒鹽噪聲 img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0507(a)(ckt-board-orig).tif', 0) #直接讀為灰度圖像img_uniform = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0512(a)(ckt-uniform-var-800).tif', 0) img_salt_pepper = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0512(b)(ckt-uniform-plus-saltpepr-prob-pt1).tif', 0) kernel = np.ones([5, 5])img_geometric_mean = geometric_mean(img_salt_pepper, kernel=kernel) img_dst = img_salt_pepper - img_geometric_mean img_median = median_filter(img_salt_pepper, kernel=kernel) img_modified_alpha = modified_alpha_mean(img_salt_pepper, kernel=kernel, d=1)plt.figure(figsize=(15, 10))plt.subplot(231), plt.imshow(img_ori, 'gray'), plt.title('Original'), plt.xticks([]),plt.yticks([]) plt.subplot(232), plt.imshow(img_uniform, 'gray'), plt.title('Uniform noise'), plt.xticks([]),plt.yticks([]) plt.subplot(233), plt.imshow(img_salt_pepper, 'gray'), plt.title('Uniform plus salt pepper'), plt.xticks([]),plt.yticks([]) plt.subplot(234), plt.imshow(img_dst, 'gray'), plt.title('Geometric mean'), plt.xticks([]),plt.yticks([]) plt.subplot(235), plt.imshow(img_median, 'gray'), plt.title('1 time Median filter'), plt.xticks([]),plt.yticks([]) plt.subplot(236), plt.imshow(img_modified_alpha, 'gray'), plt.title('Modified alpha mean d=6'), plt.xticks([]),plt.yticks([]) plt.tight_layout() plt.show()

總結(jié)

以上是生活随笔為你收集整理的第5章 Python 数字图像处理(DIP) - 图像复原与重建10 - 空间滤波 - 统计排序滤波器 - 中值、最大值、最小值、中点、修正阿尔法均值滤波器的全部?jī)?nèi)容，希望文章能夠幫你解決所遇到的問題。

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