• 灰度图的直方图均衡化(Histogram Equalization)原理与 Python 实现


    原理

      直方图均衡化是一种通过使用图像直方图,调整对比度的图像处理方法;通过对图像的强度(intensity)进行某种非线性变换,使得变换后的图像直方图为近似均匀分布,从而,达到提高图像对比度和增强图片的目的。普通的直方图均衡化采用如下形式的非线性变换:

      设 为原始灰度图像,为直方图均衡化的灰度图像,则 和 的每个像素的映射关系如下:

     

      

      其中,为灰度级,通常为 256,表明了图像像素的强度的范围为 0 ~ L-1;

      p等于图像 中强度为 的像素数占总像素数的比例,即原始灰度图直方图的概率密度函数;

      fi,j 表示在图像 中,第 行,第 列的像素强度;gi,j 表示在图像 中,第 行,第 列的像素强度.

     

    Python 实现

    #!/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()

     原始图片 320px-Unequalized_Hawkes_Bay_NZ.png

    结果显示

    参考资料

    [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

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  • 原文地址:https://www.cnblogs.com/klchang/p/9872363.html
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