最大熵阈值分割算法原理及实现

写在前面

前面介绍了OTSU算法，对于阈值分割法，不得不介绍另外一种较为突出的算法——最大熵阈值分割法（KSW熵算法）。

最大熵阈值分割法和OTSU算法类似，假设将图像分为背景和前景两个部分。熵代表信息量，图像信息量越大，熵就越大，最大熵算法就是找出一个最佳阈值使得背景与前景两个部分熵之和最大。

 

原理

由于和OTSU算法类似，所以原理上就不再赘述和推导，言简意赅。

         熵的公式：

                                                             

 

 

基于OpenCV实现 

#include <iostream>
#include <opencv2/core.hpp>
#include <opencv2/highgui.hpp>
#include <opencv2/imgproc.hpp>

int Max_Entropy(cv::Mat& src, cv::Mat& dst, int thresh, int p){
	const int Grayscale = 256;
	int Graynum[Grayscale] = { 0 };
	int r = src.rows;
	int c = src.cols;
	for (int i = 0; i < r; ++i){
		const uchar* ptr = src.ptr<uchar>(i);   
		for (int j = 0; j < c; ++j){   
			if (ptr[j] == 0)				//排除掉黑色的像素点
				continue;
			Graynum[ptr[j]]++;
		}
	}

	float probability = 0.0; //概率
	float max_Entropy = 0.0; //最大熵
	int totalpix = r*c;
	for (int i = 0; i < Grayscale; ++i){

		float HO = 0.0; //前景熵
		float HB = 0.0; //背景熵

	    //计算前景像素数
		int frontpix = 0;
		for (int j = 0; j < i; ++j){
			frontpix += Graynum[j];
		}
		//计算前景熵
		for (int j = 0; j < i; ++j){
			if (Graynum[j] != 0){
				probability = (float)Graynum[j] / frontpix;
				HO = HO + probability*log(1/probability);
			}
		}

		//计算背景熵
		for (int k = i; k < Grayscale; ++k){
			if (Graynum[k] != 0){
				probability = (float)Graynum[k] / (totalpix - frontpix);
				HB = HB + probability*log(1/probability);
			}
		}

		//计算最大熵
		if(HO + HB > max_Entropy){
			max_Entropy = HO + HB;
			thresh = i + p;
		}
	}

	//阈值处理
	src.copyTo(dst);
	for (int i = 0; i < r; ++i){
		uchar* ptr = dst.ptr<uchar>(i);
		for (int j = 0; j < c; ++j){
			if (ptr[j]> thresh)
				ptr[j] = 255;
			else
				ptr[j] = 0;
		}
	}
	return thresh;
}


int main(){
	cv::Mat src = cv::imread("I:\\Learning-and-Practice\\2019Change\\Image process algorithm\\Img\\tttt.png");
	if (src.empty()){
		return -1;
	}
	if (src.channels() > 1)
		cv::cvtColor(src, src, CV_RGB2GRAY);

	cv::Mat dst, dst2;
	int thresh = 0;
	double t2 = (double)cv::getTickCount();
	thresh = Max_Entropy(src, dst, thresh,10); //Max_Entropy
	std::cout << "Mythresh=" << thresh << std::endl;
	t2 = (double)cv::getTickCount() - t2;
	double time2 = (t2 *1000.) / ((double)cv::getTickFrequency());
	std::cout << "my_process=" << time2 << " ms. " << std::endl << std::endl;

	double  Otsu = 0;
	Otsu = cv::threshold(src, dst2, Otsu, 255, CV_THRESH_OTSU + CV_THRESH_BINARY);
	std::cout << "Otsuthresh=" << Otsu << std::endl;
	

	cv::namedWindow("src", CV_WINDOW_NORMAL);
	cv::imshow("src", src);
	cv::namedWindow("dst", CV_WINDOW_NORMAL);
	cv::imshow("dst", dst);
	cv::namedWindow("dst2", CV_WINDOW_NORMAL);
	cv::imshow("dst2", dst2);
	//cv::imwrite("I:\\Learning-and-Practice\\2019Change\\Image process algorithm\\Image Filtering\\MeanFilter\\TXT.jpg",dst);
	cv::waitKey(0);
}

 

效果

                               原图                                                            最大熵法                                                            Otsu

阈值及效率

 

发现最大熵法 的阈值会偏高，我在代码中加了一个偏置矫正因子p，可以适当调节。

 

参考：

https://blog.csdn.net/bendanban/article/details/47058355

https://blog.csdn.net/lz0499/article/details/64164477