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• • • • 均勻噪聲

均勻噪聲

均勻噪聲的PDF為
$$P(z)=\{\begin{array}{ll}\frac{1}{b?a},& a\le z\le b\\ 0,& \text{other}\end{array}\text{\hspace{1em}(5.13)}$$

均值和方差為
$$\bar{z}=\frac{a+b}{2}\text{\hspace{1em}(5.14)}$$
$${\sigma }^2=\frac{(b?a{)}^2}{12}\text{\hspace{1em}(5.15)}$$

def average_pdf(z, a=1, b=2):"""create average PDF, math $$P(z) = \begin{cases}\frac{1}{b-a}, & a\leq z \leq b \\ 0, & \text{other}\end{cases} $$param: z: input grayscale value of iamgeparam: a: uint, if image value. it could be float as well.param: b: uint, if image value. b > a, it could be float as well."""assert b > a, "b must greater than a"average = 1 / (b - a)average = np.where(z < a, 0, average)average = np.where(z > b, 0, average)return average

更正下面代碼，如果之前已經復制的，也請更正

def add_average_noise(img, mean=0, sigma=800):"""add average noise for imageparam: img: input image, dtype=uint8param: mean: noise meanparam: sigma: noise sigmareturn: image_out: image with average noise"""# image = np.array(img/255, dtype=float) # 這是有錯誤的，將得不到正確的結果，修改如下image = np.array(img, dtype=float)a = 2 * mean - np.sqrt(12 * sigma)b = 2 * mean + np.sqrt(12 * sigma)noise = np.random.uniform(a, b, image.shape)image_out = image + noiseimage_out = np.uint8(normalize(image_out)*255)return image_out # 均勻噪聲 a = 8 b = 9 z = np.linspace(0, 10, 200)z_ = (a + b) / 2 sigma = (b - a)**2 / 12print(f"z_ -> {z_}, sigma -> {sigma}")mean = average_pdf(z, a=a, b=b)plt.figure(figsize=(9, 6)) plt.plot(z, mean) plt.show() z_ -> 8.5, sigma -> 0.08333333333333333

# 均勻噪聲 # img_ori = np.ones((512, 512)) * 128 img_ori = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH05/Fig0503 (original_pattern).tif", 0) img_average = add_average_noise(img_ori, mean=10, sigma=150)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_average, 'gray', vmin=0, vmax=255), plt.xticks([]), plt.yticks([])plt.tight_layout() plt.show()

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

總結

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