原理

　　直方圖均衡化是一種通過使用影象直方圖，調整對比度的影象處理方法；通過對影象的強度（intensity）進行某種非線性變換，使得變換後的影象直方圖為近似均勻分佈，從而，達到提高影象對比度和增強圖片的目的。普通的直方圖均衡化採用如下形式的非線性變換:

　　設 f 為原始灰度影象，g 為直方圖均衡化的灰度影象，則 g 和 f 

　　其中，L 為灰度級，通常為 256，表明了影象畫素的強度的範圍為 0 ~ L-1;

　　p_n 等於影象 f 中強度為 n 的畫素數佔總畫素數的比例，即原始灰度圖直方圖的概率密度函式；

　　f_i,j 表示在影象 f 中，第 i 行，第 j 列的畫素強度；g_i,j 表示在影象 g 中，第 i 行，第 j 列的畫素強度.

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