前景背景分割——ostu算法的原理及实现 OpenCV (八）

实验结果

代码实现

#include<opencv2/opencv.hpp>
#include<iostream>
using namespace std;
using namespace cv;
//计算图像灰度直方图
Mat calcgrayhist(const Mat& image)
{Mat histogram = Mat::zeros(Size(256, 1), CV_32SC1);//图像宽高int rows = image.rows;int cols = image.cols;for (int i = 0; i < rows; i++){for (int j = 0; j < rows; j++){int index = int(image.at<uchar>(i, j));histogram.at<int>(0, index) += 1;}}return histogram;
};//OTSU
int OTSU(const Mat& image, Mat& OTSU_image)
{int rows = image.rows;int cols = image.cols;Mat histogram = calcgrayhist(image);//归一化直方图Mat normhist;histogram.convertTo(normhist, CV_32FC1, 1.0 / (rows * cols), 0.0);//计算累加直方图和一阶累积矩Mat zeroaccumulate = Mat::zeros(Size(256, 1), CV_32FC1);Mat oneaccumulate = Mat::zeros(Size(256, 1), CV_32FC1);for (int i = 0; i < 256; i++){if (i == 0){zeroaccumulate.at<float>(0, i) = normhist.at<float>(0, i);oneaccumulate.at<float>(0, i) = i * normhist.at<float>(0, i);}else{zeroaccumulate.at<float>(0, i) = zeroaccumulate.at<float>(0, i - 1)+ normhist.at<float>(0, i);oneaccumulate.at<float>(0, i) = oneaccumulate.at<float>(0, i - 1)+ i * normhist.at<float>(0, i);}}//计算间类方差Mat variance = Mat::zeros(Size(256, 1), CV_32FC1);float mean = oneaccumulate.at<float>(0, 255);for (int i = 0; i < 255; i++){if (zeroaccumulate.at<float>(0, i) == 0 || zeroaccumulate.at<float>(0, i) == 1)variance.at<float>(0, i) = 0;else{float cofficient = zeroaccumulate.at<float>(0, i) * (1.0 -zeroaccumulate.at<float>(0, i));variance.at<float>(0, i) = pow(mean * zeroaccumulate.at<float>(0, i)- oneaccumulate.at<float>(0, i), 2.0) / cofficient;}}//找到阈值；Point maxloc;//计算矩阵中最大值minMaxLoc(variance, NULL, NULL, NULL, &maxloc);int otsuthreshold = maxloc.x;threshold(image, OTSU_image, otsuthreshold, 255, THRESH_BINARY);return otsuthreshold;
};int main()
{Mat img, gray_img, dst;img = imread("E:\\workspace\\opencv_study\\example\\1.jpg");imshow("img", img);cvtColor(img, gray_img, COLOR_BGR2GRAY);imwrite("1_gray.bmp", gray_img);imshow("gray_img", gray_img);OTSU(gray_img, dst);imshow("otsu image", dst);imwrite("ostu.bmp", dst);waitKey(0);return 0;
};

实现原理

Otsu算法（大津法或最大类间方差法）使用的是聚类的思想，把图像的灰度数按灰度级分成2个部分，使得两个部分之间的灰度值差异最大，每个部分之间的灰度差异最小，通过方差的计算来寻找一个合适的灰度级别来划分。 所以可以在二值化的时候采用otsu算法来自动选取阈值进行二值化。otsu算法被认为是图像分割中阈值选取的最佳算法，计算简单，不受图像亮度和对比度的影响。因此，使类间方差最大的分割意味着错分概率最小。

从L个灰度级遍历t，使得t为某个值的时候，前景和背景的方差最大， 则 这个 t 值便是我们要求得的阈值。

其中，方差的计算公式如下：
g=wo * (uo - u) * (uo - u) + w1 * (u1 - u) * (u1 - u)

[ 此公式计算量较大，可以采用：
g = wo * w1 * (uo - u1) * (uo - u1) ]

//实现方法1：
Source Code: https://blog.csdn.net/silent_gods/article/details/81046919
//将OTSU算法实现了一遍#include "opencv2/opencv.hpp"
#include "opencv2/highgui/highgui.hpp"#include <string>
#include <stdio.h>using namespace std;
using namespace cv;//#define Gamma 3//OTSU 函数实现
int OTSU(Mat srcImage) 
{int nCols = srcImage.cols;int nRows = srcImage.rows;int threshold = 0;//init the parametersint nSumPix[256];float nProDis[256];for (int i = 0; i < 256; i++){nSumPix[i] = 0;nProDis[i] = 0;}//统计灰度集中每个像素在整幅图像中的个数for (int i = 0; i < nRows; i++){for (int j = 0; j < nCols; j++){nSumPix[(int)srcImage.at<uchar>(i, j)]++;}}//计算每个灰度级占图像中的概率分布for (int i = 0; i < 256; i++){nProDis[i] = (float)nSumPix[i] / (nCols*nRows);}//遍历灰度级【0，255】，计算出最大类间方差下的阈值float w0, w1, u0_temp, u1_temp, u0, u1, delta_temp;double delta_max = 0.0;for (int i = 0; i < 256; i++){//初始化相关参数w0 = w1 = u0 = u1 = u0_temp = u1_temp = delta_temp = 0;for (int j = 0; j < 256; j++){//背景部分if (j <= i){w0 += nProDis[j];u0_temp += j*nProDis[j];}//前景部分else{w1 += nProDis[j];u1_temp += j*nProDis[j];}}//计算两个分类的平均灰度u0 = u0_temp / w0;u1 = u1_temp / w1;//依次找到最大类间方差下的阈值delta_temp = (float)(w0*w1*pow((u0 - u1), 2)); //前景与背景之间的方差(类间方差)if (delta_temp > delta_max){delta_max = delta_temp;threshold = i;}}return threshold;
}int  main()
{namedWindow("srcGray", 0);cvResizeWindow("srcGray", 640, 480);namedWindow("otsuResultImage", 0);cvResizeWindow("otsuResultImage", 640, 480);namedWindow("dst", 0);cvResizeWindow("dst", 640, 480);//图像读取及判断Mat srcImage;srcImage = imread("D:\\0604.png");if (!srcImage.data){return -1;}imshow("srcImage", srcImage);Mat srcGray;cvtColor(srcImage, srcGray, CV_RGB2GRAY);imshow("srcGray", srcGray);//调用otsu算法得到图像int otsuThreshold = OTSU(srcGray);cout << otsuThreshold << endl;//定义输出结果图像Mat otsuResultImage = Mat::zeros(srcGray.rows, srcGray.cols, CV_8UC1);//利用得到的阈值进行二值化操作for (int i = 0; i < srcGray.rows; i++){for (int j = 0; j < srcGray.cols; j++){//cout << (int)srcGray.at<uchar>(i, j) << endl;//高像素阈值判断if (srcGray.at<uchar>(i, j) > otsuThreshold){otsuResultImage.at<uchar>(i, j) = 255;}else{otsuResultImage.at<uchar>(i, j) = 0;}//cout <<(int)otsuResultImage.at<uchar>(i, j) << endl;}}imshow("otsuResultImage", otsuResultImage);waitKey(0);return 0;
}

参考资料

https://www.cnblogs.com/moon1992/p/5092726.html
https://blog.csdn.net/silent_gods/article/details/81046919
https://blog.csdn.net/u012005313/article/details/51945075
https://blog.csdn.net/liuzhuomei0911/article/details/51440305
https://blog.csdn.net/xiachong27/article/details/80572469
https://blog.csdn.net/u011574296/article/details/72829925
https://baike.baidu.com/item/otsu/16252828?fr=aladdin
https://www.cnblogs.com/uestc-mm/p/5366908.html
https://blog.csdn.net/baimafujinji/article/details/50629103