【机器视觉学习笔记】大津法/Otsu最大类间方差法 最佳阈值处理（C++）

平台：Windows 10 20H2
Visual Studio 2015
OpenCV 4.5.3

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本文所用源码修改自C++ opencv 图片二值化最佳阈值确定（大津法,OTSU算法)——Sharon Liu

概念

        Otsu算法，也叫最大类间方差法，是1979年由日本学者大津提出的（所以也叫大津法），是一种自适应阈值确定的方法，一种全局的二值化算法。
        它是根据图像的灰度特性，将图像分为前景和背景两个部分。 当取最佳阈值时，两部分之间的差别应该是最大的。在Otsu算法中所采用的衡量差别的标准就是较为常见的最大类间方差。前景和背景之间的类间方差如果越大，就说明构成图像的两个部分之间的差别越大。
        当部分目标被错分为背景或部分背景被错分为目标，都会导致两部分差别变小。
        当所取阈值的分割使类间方差最大时，就意味着错分概率最小。

C++源码

OtsuThreshold

/******************************************************************************************
Function:       OtsuThreshold
Description:	图片二值化最佳阈值确定（大津法,OTSU算法)
Input:          src:原图片
Return:         阈值
******************************************************************************************/
int OtsuThreshold(Mat src)
{
     
	int threshold;

	try
	{
     
		int height = src.rows;
		int width = src.cols;

		//histogram  
		float histogram[256] = {
      0 };
		for (int i = 0; i < height; i++) 
		{
     
			unsigned char* p = (unsigned char*)src.data + src.step*i;
			for (int j = 0; j < width; j++) 
			{
     
				histogram[*p++]++;
			}
		}
		//normalize histogram  
		int size = height*width;
		for (int i = 0; i < 256; i++) 
		{
     
			histogram[i] = histogram[i] / size;
		}

		//average pixel value  
		float avgValue = 0;
		for (int i = 0; i < 256; i++) 
		{
     
			avgValue += i*histogram[i];
		}

		float maxVariance = 0;
		float w = 0, u = 0;
		for (int i = 0; i < 256; i++) 
		{
     
			w += histogram[i];
			u += i*histogram[i];

			float t = avgValue*w - u;
			float variance = t*t / (w*(1 - w));
			if (variance > maxVariance) 
			{
     
				maxVariance = variance;
				threshold = i;
			}
		}
	}
	catch (cv::Exception e)
	{
     
	}

	return threshold;
}
//————————————————
//版权声明：本文为CSDN博主「Sharon Liu」的原创文章，遵循CC 4.0 BY - SA版权协议，转载请附上原文出处链接及本声明。
//原文链接：https ://blog.csdn.net/sylsjane/article/details/80872744

主函数

图片路径根据实际情况调整，注意反斜杠是转义字符的开头，故“\”应替换为“\\”

int main(int argc, char * argv[])
{
     
	Mat Image = imread("D:\\Work\\OpenCV\\Workplace\\Test_1\\1.jpg", 0);

	int thresholdValue = OtsuThreshold(Image);
	cout << "类间方差为： " << thresholdValue << endl;

	Mat imageOutput;
	threshold(Image, imageOutput, thresholdValue, 255, CV_THRESH_BINARY);

	Mat imageOtsu;
	threshold(Image, imageOtsu, 0, 255, CV_THRESH_OTSU); //Opencv Otsu算法

	imshow("原图", Image);
	imshow("Output Image", imageOutput);
	imshow("Opencv Otsu", imageOtsu);

	waitKey(0);

	return 0;
}

效果

原图

效果

OpenCv自带的Otsu算法结果，与上图一致

完整源码

#include 
#include 
#include 

using namespace cv;
using namespace std;


/******************************************************************************************
Function:       OtsuThreshold
Description:	图片二值化最佳阈值确定（大津法,OTSU算法)
Input:          src:原图片
Return:         阈值
******************************************************************************************/
int OtsuThreshold(Mat src)
{
     
	int threshold;

	try
	{
     
		int height = src.rows;
		int width = src.cols;

		//histogram  
		float histogram[256] = {
      0 };
		for (int i = 0; i < height; i++) 
		{
     
			unsigned char* p = (unsigned char*)src.data + src.step*i;
			for (int j = 0; j < width; j++) 
			{
     
				histogram[*p++]++;
			}
		}
		//normalize histogram  
		int size = height*width;
		for (int i = 0; i < 256; i++) 
		{
     
			histogram[i] = histogram[i] / size;
		}

		//average pixel value  
		float avgValue = 0;
		for (int i = 0; i < 256; i++) 
		{
     
			avgValue += i*histogram[i];
		}

		float maxVariance = 0;
		float w = 0, u = 0;
		for (int i = 0; i < 256; i++) 
		{
     
			w += histogram[i];
			u += i*histogram[i];

			float t = avgValue*w - u;
			float variance = t*t / (w*(1 - w));
			if (variance > maxVariance) 
			{
     
				maxVariance = variance;
				threshold = i;
			}
		}
	}
	catch (cv::Exception e)
	{
     
	}

	return threshold;
}
//————————————————
//版权声明：本文为CSDN博主「Sharon Liu」的原创文章，遵循CC 4.0 BY - SA版权协议，转载请附上原文出处链接及本声明。
//原文链接：https ://blog.csdn.net/sylsjane/article/details/80872744

int main(int argc, char * argv[])
{
     
	Mat Image = imread("D:\\Work\\OpenCV\\Workplace\\Test_1\\1.jpg", 0);

	int thresholdValue = OtsuThreshold(Image);
	cout << "类间方差为： " << thresholdValue << endl;

	Mat imageOutput;
	threshold(Image, imageOutput, thresholdValue, 255, CV_THRESH_BINARY);

	Mat imageOtsu;
	threshold(Image, imageOtsu, 0, 255, CV_THRESH_OTSU); //Opencv Otsu算法

	imshow("原图", Image);
	imshow("Output Image", imageOutput);
	imshow("Opencv Otsu", imageOtsu);

	waitKey(0);

	return 0;
}