概念

直方图均衡化是图像处理领域中利用图像直方图对对比度进行调整的方法，通过拉伸像素强度分布范围来增强图像对比度。

原理

• 均衡化指的是把一个分布 (给定的直方图) 映射 到另一个分布 (一个更宽更统一的强度值分布)，从而令强度值分布会在整个范围内展开。

• 要想实现均衡化的效果，映射函数应该是一个 累积分布函数 ( cumulative distribution function, cdf ) 。对于直方图$H(i)$，它的累积分布函数$H^{{}^{\prime }}(i)$：

  $H^{{}^{\prime }}(i)={\sum }_{j=0}^{i}H(j)$

  要使用其作为映射函数，我们必须对最大值为255 (或者用图像的最大强度值) 的累积分布 $H^{{}^{\prime }}(i)$ 进行归一化。

• 最后，我们使用一个简单的映射过程来获得均衡化后像素的强度值，假设原图为$I(x,y)$，均衡化后像素强度值$I^{{}^{\prime }}(x,y)$：

  $I^{{}^{\prime }}(x,y)=H^{{}^{\prime }}(I(x,y))$

代码实现

以 OpenCV 为例，其直方图均衡化函数为 equalizeHist()，代码实现如下：

/** @brief Equalizes the histogram of a grayscale image.

The function equalizes the histogram of the input image using the following algorithm:

- Calculate the histogram \f$H\f$ for src .
- Normalize the histogram so that the sum of histogram bins is 255.
- Compute the integral of the histogram:
\f[H'_i =  \sum _{0  \le j < i} H(j)\f]
- Transform the image using \f$H'\f$ as a look-up table: \f$\texttt{dst}(x,y) = H'(\texttt{src}(x,y))\f$

The algorithm normalizes the brightness and increases the contrast of the image.

@param src Source 8-bit single channel image.
@param dst Destination image of the same size and type as src .
 */
CV_EXPORTS_W void equalizeHist( InputArray src, OutputArray dst );

void cv::equalizeHist( InputArray _src, OutputArray _dst )
{
    CV_INSTRUMENT_REGION();

    CV_Assert( _src.type() == CV_8UC1 );

    if (_src.empty())
        return;

    CV_OCL_RUN(_src.dims() <= 2 && _dst.isUMat(),
               ocl_equalizeHist(_src, _dst))

    Mat src = _src.getMat();
    _dst.create( src.size(), src.type() );
    Mat dst = _dst.getMat();

    CV_OVX_RUN(!ovx::skipSmallImages<VX_KERNEL_EQUALIZE_HISTOGRAM>(src.cols, src.rows),
               openvx_equalize_hist(src, dst))

    CALL_HAL(equalizeHist, cv_hal_equalize_hist, src.data, src.step, dst.data, dst.step, src.cols, src.rows);

    Mutex histogramLockInstance;

    const int hist_sz = EqualizeHistCalcHist_Invoker::HIST_SZ;
    int hist[hist_sz] = {0,};
    int lut[hist_sz];

    EqualizeHistCalcHist_Invoker calcBody(src, hist, &histogramLockInstance);
    EqualizeHistLut_Invoker      lutBody(src, dst, lut);
    cv::Range heightRange(0, src.rows);

    if(EqualizeHistCalcHist_Invoker::isWorthParallel(src))
        parallel_for_(heightRange, calcBody);
    else
        calcBody(heightRange);

    int i = 0;
    while (!hist[i]) ++i;

    int total = (int)src.total();
    if (hist[i] == total)
    {
        dst.setTo(i);
        return;
    }

    float scale = (hist_sz - 1.f)/(total - hist[i]);
    int sum = 0;

    for (lut[i++] = 0; i < hist_sz; ++i)
    {
        sum += hist[i];
        lut[i] = saturate_cast<uchar>(sum * scale);
    }

    if(EqualizeHistLut_Invoker::isWorthParallel(src))
        parallel_for_(heightRange, lutBody);
    else
        lutBody(heightRange);
}

应用举例

C++ 代码如下：

#include "opencv2/imgcodecs.hpp"
#include "opencv2/highgui.hpp"
#include "opencv2/imgproc.hpp"
#include <iostream>

using namespace cv;
using std::cout;
using std::endl;

int main(int argc, char** argv)
{
    CommandLineParser parser(argc, argv, "{@input | wukong.png | input image}");
    Mat src = imread(samples::findFile(parser.get<String>("@input")), IMREAD_COLOR);
    if (src.empty())
    {
        cout << "Could not open or find the image!\n" << endl;
        cout << "Usage: " << argv[0] << " <Input image>" << endl;
        return EXIT_FAILURE;
    }

    // 转换为灰度图像
    cvtColor(src, src, COLOR_BGR2GRAY);

    Mat dst;
    // 直方图均衡化
    equalizeHist(src, dst);

    imshow("Source image", src);
    imshow("Equalized Image", dst);

    waitKey();

    return EXIT_SUCCESS;

}

Python 代码如下：

import cv2
import matplotlib.pyplot as plt

# 读取图像
img = cv2.imread('../data/wukong.png', cv2.IMREAD_COLOR)
# 转换为灰度图
src = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# 直方图均衡化
dst = cv2.equalizeHist(src)
# 显示原图和均衡化后的图
fig, axes = plt.subplots(2, 2, figsize=(18, 9))
axes[0, 0].imshow(src, cmap='gray')
axes[1, 0].imshow(dst, cmap='gray')
axes[0, 1].hist(src.ravel(), 256, [0, 256], color='#fc8403')
axes[1, 1].hist(dst.ravel(), 256, [0, 256], color='#fc8403')
# 显示直方图网格
axes[0, 1].grid(axis='y', linestyle='-.', alpha=0.5)
axes[1, 1].grid(axis='y', linestyle='-.', alpha=0.5)
# 设置标题
axes[0, 0].set_title('Original Image')
axes[1, 0].set_title('Equalized Image')
axes[0, 1].set_title('Histogram of Original Image')
axes[1, 1].set_title('Histogram of Equalized Image')
# 显示图表
plt.show()