使用直方图统计量增强图像

全局均值和方差
$${\mu }_n=\sum _{i=0}^{L-1}(r_i-m{)}^{n}p(r_i)\text{\hspace{1em}(3.24)}$$
$$m=\sum _{i=0}^{L-1}{r}_{i}p(r_i)\text{\hspace{1em}(3.25)}$$
$${\sigma }^2={\mu }_2=\sum _{i=0}^{L-1}(r_i-m{)}^{2}p(r_i)\text{\hspace{1em}(3.26)}$$

邻域均值和方差
令$S_{xy}$是以$(x,y)$为中心的一个规定大小的邻域
$$m_{S_{xy}}=\sum _{i=0}^{L-1}{r}_i{P}_{S_{xy}}(r_i)\text{\hspace{1em}(3.27)}$$
$${\sigma }_{S_{xy}}^2=\sum _{i=0}^{L-1}(r_i-m_{S_{xy}}{)}^2{P}_{S_{xy}}(r_i)\text{\hspace{1em}(3.28)}$$

$$g(x,y)=\{\begin{array}{ll}Cf(x,y),& k_0{m}_G\le m_{S_{xy}}\le k_1{m}_G\text{AND}{k}_2{\sigma }_G\le {\sigma }_{S_{xy}}\le k_3{\sigma }_G\\ f(x,y),& \text{others}\end{array}\text{\hspace{1em}(3.29)}$$

$k_0,k_1,k_2,k_3,C$选择的一些方法：
如果 我们的关注点是比平均灰度的1/4更暗的区域，那么选择$k_0=0,k_1=0.25$。如果我们的兴趣是增强那么对比度比较低的区域，则$k_2=0,k_3=0.1$。
满足条件的乘以一个规定常数$C$，增大（或减小）其相对于图像剩下部分的灰度。

下图像中$m_G=161,{\sigma }_G=103$，图像和待增强区域的最大灰度值分别是是228和10，最小值是为。我们希望增强后的特征的最大值与图像的最大值相同，因此选择$C=22.8$

def histogram_statistic(img_ori, grid_size = (3, 3), k0 = 0., k1 = 0.1, k2 = 0., k3 = 0.1, C = 22.8):"""Histogram statistic enhance local imageparam: input img_ori: uint8[0, 255] grayscal imageparam: grid size : size of the sliding window, default is [3, 3]"""m_G = np.round(np.mean(img_ori)).astype(int)sigma_G = np.round(np.std(img_ori)).astype(int)
#     max_img = img_ori.max()
#     min_img = img_ori.min()
#     img_roi = img_ori[12:120, 12:120]
#     max_roi = img_roi.max()
#     print(f'Global mean -> {m_G}, Global sigma -> {sigma_G}, Max -> {max_img}, Min -> {min_img}, ROI Max -> {max_roi}')img_dst = img_ori.copy()height, width = img_ori.shapem = grid_size[0]n = grid_size[1]for h in range(height):for w in range(width):temp = img_ori[h:h+m, w:w+n]temp_mean = np.round(np.mean(temp)).astype(int)temp_sigma = np.round(np.std(temp)).astype(int)if k0 * m_G <= temp_mean <= k1 * m_G and k2 * sigma_G <= temp_sigma <= k3 * sigma_G:temp = (C * temp)img_dst[h:h+m, w:w+n] = tempreturn img_dst

# 使用直方图统计增强局部图像
img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH03/Fig0326(a)(embedded_square_noisy_512).tif', 0)
m_G = np.round(np.mean(img_ori)).astype(int)
sigma_G = np.round(np.std(img_ori)).astype(int)
max_img = img_ori.max()
min_img = img_ori.min()
img_roi = img_ori[12:120, 12:120]
max_roi = img_roi.max()
print(f'Global mean -> {m_G}, Global sigma -> {sigma_G}, Max -> {max_img}, Min -> {min_img}, ROI Max -> {max_roi}')# ROI 区域的最小值是11， 228/11=20.72，即20.8，实现看起来效果也不错
img_dst = histogram_statistic(img_ori, C=20.8)plt.figure(figsize=(15, 6))
plt.subplot(1, 3, 1), plt.imshow(img_ori, cmap='gray', vmin=0, vmax=255), plt.title('Original')
plt.subplot(1, 3, 2), plt.imshow(img_dst, cmap='gray', vmin=0, vmax=255), plt.title(f'Histogram statistic')
plt.tight_layout()
plt.show()

Global mean -> 161, Global sigma -> 103, Max -> 228, Min -> 0, ROI Max -> 11