局部歸一化 (Local Normalization)
Posted on Wed 29 August 2018 in Digital Image Processing
簡介
局部歸一化的目標是使影像亮度的 mean 與 variance 在局部相鄰區域趨於一致，用來改善不均勻照明或是遮蔽的影響。
實作
對原始影像\(f(x,y)\)的 local normalization 可以寫成：
$$g(x)=\frac{f(x,y)-m_{f}(x,y)}{\sigma_f(x,y)},$$
其中
- \(m_f(x,y)\)是\(f(x,y)\)的 local mean 估算值
- \(\sigma_f(x,y)\)是 local variance 的估算值
- \(g(x,y)\)是輸出影像。
local mean 與 variance 的估算通過 Gaussian filter，\(\sigma_1\)與\(\sigma_2\)是 Gaussian window size，用來控制 local mean 與 local variance，通常\(\sigma_2\)應該大於\(\sigma_1\)。
範例
%matplotlib inline
import scipy as sp
import skimage.filters as fil
import matplotlib.pyplot as plt
from skimage.color import rgb2gray
from skimage.data import camera
from skimage import img_as_float
def local_norm(img, sigma_1, sigma_2):
local_mean = fil.gaussian(img, sigma_1)
numerator = img - local_mean
local_variance = fil.gaussian(numerator**2, sigma_2)
denominator = local_variance**(0.5)
output = numerator / denominator
output = output + abs(output.min())
output = output / output.max()
return output
img = img_as_float(camera())
img = img / img.max()
sigma_1 = 4
sigma_2 = 40
normalized = local_norm(img, sigma_1, sigma_2)
plt.figure()
plt.title('Original image')
plt.imshow(img, 'gray')
plt.figure()
plt.title('Normalized image')
plt.imshow(normalized, 'gray')
plt.show()