原理
直方圖均衡化是一種通過使用圖像直方圖，調整對比度的圖像處理方法；通過對圖像的強度（intensity）進行某種非線性變換，使得變換后的圖像直方圖為近似均勻分布，從而，達到提高圖像對比度和增強圖片的目的。普通的直方圖均衡化采用如下形式的非線性變換:
設 f 為原始灰度圖像，g 為直方圖均衡化的灰度圖像，則 g 和 f 的每個像素的映射關系如下：
其中，L 為灰度級，通常為 256，表明了圖像像素的強度的范圍為 0 ~ L-1;
pn 等於圖像 f 中強度為 n 的像素數占總像素數的比例，即原始灰度圖直方圖的概率密度函數；
fi,j 表示在圖像 f 中，第 i 行，第 j 列的像素強度；gi,j 表示在圖像 g 中，第 i 行，第 j 列的像素強度.
Python 實現
#!/usr/bin/env python # -*- coding: utf8 -*-
""" # Author: klchang # Date: 2018.10 # Description: histogram equalization of a gray image. """
from __future__ import print_function import numpy as np import matplotlib.pyplot as plt def histequ(gray, nlevels=256): # Compute histogram
histogram = np.bincount(gray.flatten(), minlength=nlevels) print ("histogram: ", histogram) # Mapping function
uniform_hist = (nlevels - 1) * (np.cumsum(histogram)/(gray.size * 1.0)) uniform_hist = uniform_hist.astype('uint8') print ("uniform hist: ", uniform_hist) # Set the intensity of the pixel in the raw gray to its corresponding new intensity
height, width = gray.shape uniform_gray = np.zeros(gray.shape, dtype='uint8') # Note the type of elements
for i in range(height): for j in range(width): uniform_gray[i,j] = uniform_hist[gray[i,j]] return uniform_gray if __name__ == '__main__': fname = "320px-Unequalized_Hawkes_Bay_NZ.png" # Gray image
# Note, matplotlib natively only read png images.
gray = plt.imread(fname, format=np.uint8) if gray is None: print ("Image {} does not exist!".format(fname)) exit(-1) # Histogram equalization
uniform_gray = histequ(gray) # Display the result
fig, (ax1, ax2) = plt.subplots(1, 2) ax1.set_title("Raw Image") ax1.imshow(gray, 'gray') ax1.set_xticks([]), ax1.set_yticks([]) ax2.set_title("Histogram Equalized Image") ax2.imshow(uniform_gray, 'gray') ax2.set_xticks([]), ax2.set_yticks([]) fig.tight_layout() plt.show()
原始圖片 320px-Unequalized_Hawkes_Bay_NZ.png
結果顯示
參考資料
[1]. Histogram_equalization - Wikipedia. https://en.wikipedia.org/wiki/Histogram_equalization
[2]. Histogram Equalization. https://www.math.uci.edu/icamp/courses/math77c/demos/hist_eq.pdf