標題

• • • • 椒鹽噪聲

椒鹽噪聲

如果$k$是一幅數字圖像中表示灰度值的比特數，則灰度值可能是$[0,2^k?1]$。椒鹽噪聲的PDF為：

$$P(z)=?\begin{array}{ll}{P}_s,& z=2^k?1\\ P_p,& z=0\\ 1?(P_s+P_p),& z=V\end{array}\text{\hspace{1em}(5.16)}$$

$0<V<2^k-1 $的任意整數

均值和方差為
$$\bar{z}=(0)P_p+K(1?P_s?P_p)+(2^k?1)P_s\text{\hspace{1em}(5.17)}$$
$${\sigma }^2=(0?\bar{z}{)}^2{P}_p+(K?\bar{z}{)}^2(1?P_s?P_p)+(2^k?1{)}^2{P}_s\text{\hspace{1em}(5.18)}$$

• 添加椒鹽噪聲的方法
  令$\eta (x,y)$表示是一幅椒鹽噪聲圖像，其密度值滿足式(5.16)。我們使用椒鹽噪聲污染圖像$f(x,y)$的方法為：
  在$f$中$\eta$為0的所有位置賦0，在$f$中$\eta$為$2^k?1$的所有位置賦$2^k?1$值，保留$f$中$\eta$為$V$的所有位置的值不變。

• 噪聲密度
  像素被鹽粒或胡椒噪聲污染的概率$P$為$P=P_s+P_p$。$P$稱為噪聲密度。

def salt_pepper_pdf(ps=0.1, pp=0.1):"""create salt and pepper PDF, math $$P(z) = \begin{cases} P_s, & z = 2^k -1 \\ P_p, & z=0 \\ 1-(P_s + P_p), & z=V \end{cases}$$param: z: input grayscale value of iamgeparam: v: float, while z = v, probability of other valuesparam: ps: float, probability of the saltparam: pp: float, probability of the pepper"""salt_pepper = np.zeros([3])salt_pepper[0] = pssalt_pepper[2] = ppsalt_pepper[1] = 1 - (ps + pp)return salt_pepper def add_salt_pepper(img, ps=0.01, pp=0.01):"""add salt pepper noise to imageparam: img: input image, uint8 [0, 255]param: ps: probability of salt noise, which is white noise, default is 0.01param: pp: probability of peper noise, which is black noise, default is 0.01return image with salt pepper noise, [0, 255]"""h, w = img.shape[:2]mask = np.random.choice((0, 0.5, 1), size=(h, w), p=[pp, (1-ps-pp), ps])img_out = img.copy()img_out[mask==1] = 255img_out[mask==0] = 0return img_out def add_salt_pepper_1(img, prob):output = np.zeros(img.shape, np.uint8)thres = 1 - probfor i in range(img.shape[0]):for j in range(img.shape[1]):rdn = np.random.random()if rdn < prob:output[i][j] = 0elif rdn > thres:output[i][j] = 255else:output[i][j] = img[i][j]return output # 椒鹽噪聲 z = np.array([0, 128, 255]) ps = 0.1 pp = 0.3 k = 8 z_ = 0 * pp + k * (1 - ps - pp) + (2**k - 1) * ps sigma = (0 - z_) ** 2 * pp + (k - z_) ** 2 * (1 - ps - pp) + (2**k -1) ** 2 * psprint(f"z_ -> {z_}, sigma -> {sigma}")salt_pepper = salt_pepper_pdf(ps=ps, pp=pp)plt.figure(figsize=(9, 6)) plt.bar(z, salt_pepper), plt.xticks([]), plt.yticks([]) plt.show() z_ -> 30.3, sigma -> 7076.301

# 椒鹽噪聲，可隨意控制胡椒與鹽粒的概率大小 # img_ori = np.ones((512, 512)) * 128 img_ori = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH05/Fig0503 (original_pattern).tif", 0)img_salt_pepper = add_salt_pepper(img_ori, ps=0.05, pp=0.02)plt.figure(figsize=(9, 6)) plt.subplot(121), plt.imshow(img_ori, 'gray', vmin=0, vmax=255), plt.xticks([]), plt.yticks([]) plt.subplot(122), plt.imshow(img_salt_pepper, 'gray', vmin=0, vmax=255), plt.xticks([]), plt.yticks([])plt.tight_layout() plt.show()

hist, bins = np.histogram(img_salt_pepper.flatten(), bins=255, range=[0, 255], density=True) bar = plt.bar(bins[:-1], hist[:])

# 一些重要的概率密度函數 a = 2 b = 8z = np.linspace(0, 10, 200)gaussian = gauss_pdf(z) rayleigh = rayleigh_pdf(z, a=a, b=b) ireland = ireland_pdf(z, a=a, b=b-6) exponent = exponential_pdf(z, a=a) average = average_pdf(z, a=a, b=b)#=============椒鹽============= ps = 0.2 pp = 0.3 salt_pepper = salt_pepper_pdf(ps=ps, pp=pp)show_list = ['gaussian', 'rayleigh', 'ireland', 'exponent', 'average', 'salt_pepper']fig = plt.figure(figsize=(16, 8))for i in range(len(show_list)):ax = fig.add_subplot(2, 3, i+1)if i == 5:z = np.array([0, 100, 255])ax.bar(z, eval(show_list[i]), width=2), ax.set_xticks([0, 100, 255]), ax.set_yticks([0, eval(show_list[i]).max() ])ax.set_xlim(-1, 257), ax.set_ylim([0, eval(show_list[i]).max() + 0.05]), ax.set_title(show_list[i])else:ax.plot(z, eval(show_list[i])), ax.set_xticks([0, 10]), ax.set_yticks([0, eval(show_list[i]).max() ])ax.set_xlim(0, 10), ax.set_ylim([0, eval(show_list[i]).max() + 0.05]), ax.set_title(show_list[i]) plt.tight_layout() plt.show()

一般重要噪聲的例子

• 高斯噪聲

  • 由電子電路及（光照不足和/或高溫引起的）傳感器噪聲等因素導致的

• 瑞利噪聲

  • 有助于表征距離成像中的噪聲現象

• 指數和伽馬密度

  • 在激光成像中廣泛應用

• 沖激噪聲

  • 出現在成像期間的快速瞬變（如開關故障）

• 均勻密度

  • 是對實際情況最起碼的描述

# 一些重要的噪聲 img_ori = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH05/Fig0503 (original_pattern).tif", 0)img_gauss = add_gaussian_noise(img_ori, mu=0, sigma=0.05) img_rayleigh = add_rayleigh_noise(img_ori, a=1) img_gamma = add_gamma_noise(img_ori, scale=2) img_exponent = add_exponent_noise(img_ori, scale=3) img_average = add_average_noise(img_ori, mean=10, sigma=1.5) ps = 0.05 pp = 0.02 img_salt_pepper = add_salt_pepper(img_ori, ps=ps, pp=pp)show_list = ['img_gauss', 'img_rayleigh', 'img_gamma', 'img_exponent', 'img_average', 'img_salt_pepper']fig = plt.figure(figsize=(14.5, 20))for i in range(len(show_list)):if i >= 3:# 顯示圖像ax = fig.add_subplot(4, 3, i + 3 + 1)ax.imshow(eval(show_list[i]), 'gray'), ax.set_xticks([]), ax.set_yticks([]), ax.set_title(show_list[i].split('_')[-1])# 對應圖像的直方圖ax = fig.add_subplot(4, 3, i + 1 + 6)hist, bins = np.histogram(eval(show_list[i]).flatten(), bins=255, range=[0, 255], density=True)bar = ax.bar(bins[:-1], hist[:]), ax.set_xticks([]), ax.set_yticks([]),else:# 顯示圖像ax = fig.add_subplot(4, 3, i + 1)ax.imshow(eval(show_list[i]), 'gray'), ax.set_xticks([]), ax.set_yticks([]), ax.set_title(show_list[i].split('_')[-1])# 對應圖像的直方圖ax = fig.add_subplot(4, 3, i + 1 + 3)hist, bins = np.histogram(eval(show_list[i]).flatten(), bins=255, range=[0, 255], density=True)bar = ax.bar(bins[:-1], hist[:]), ax.set_xticks([]), ax.set_yticks([]),plt.tight_layout() plt.show()

總結

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6 - 椒盐噪声的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。