图像处理（六）：二值化

二值化：设置一个阈值，图像灰度值如果小于这个阈值，就将对应灰度值设置为0，反之，保留。

按照设置阈值的方式：

1、固定阈值：预先设置的固定阈值；

2、自适应阈值：通过某种算法对图像像素进行处理，自动计算出最佳的阈值；

固定阈值就不多说了，太简单了！这里说一下自适应阈值，最经典的要数大津法（OTSU），将图像直方图用某一灰度分成两组，将分割后两组间方差对应的灰度值设置为最佳阈值，具体原理可以参考博客：点击打开链接，该博客也有对应代码，代码写的更加简洁明了。

步骤如下：

1）直方图统计0~255对应像素的数目；

2）将0,1，...，244,255依次设置为阈值，计算分组后两组的均值及方差；

3）找寻最大方差对应的分割阈值即为最佳阈值；

代码如下：

#include <opencv2/opencv.hpp>#include <iostream>using namespace cv;using namespace std;int main(){Mat src = imread("1.jpg");Mat gray_ori;cvtColor(src, gray_ori, CV_BGR2GRAY);Mat gray, gray_OTSU;gray_ori.copyTo(gray);gray_ori.copyTo(gray_OTSU);// 1、fixed thresholdint thr = 30;int i, j;for (i = 0; i < gray.rows - 1; i++)for (j = 0; j < gray.cols - 1; j++){if (gray.at<uchar>(i, j) < thr){gray.at<uchar>(i, j) = 0;}}// 2、OTSU// 2.1、直方图统计int hist[256] = { 0 };for (i = 0; i < gray_ori.rows - 1; i++)for (j = 0; j < gray_ori.cols - 1; j++){hist[gray_ori.at<uchar>(i, j)]++;}// 2.2、计算系数int s = 0;int hist_cum[256] = { 0 };float hist_coeff[256] = { 0 };for (i = 0; i < 256; i++)   // 累计统计{s += hist[i];hist_cum[i] = s;hist_coeff[i] = 1.0 * s / (gray_ori.rows * gray_ori.cols);//cout << hist_coeff[i] << endl;}// 2.3、计算加权值s = 0;int hist_cum_Add[256] = { 0 };for (i = 0; i < 256; i++)   {s += i * hist[i];hist_cum_Add[i] = s;//cout << hist_cum_Add[i] << endl;}// 2.4、计算均值float hist_mean[256] = { 0 };float hist_mean_l[256] = { 0 };float hist_mean_r[256] = { 0 };for (i = 0; i < 256; i++) {if (hist_cum[i] == 0){hist_mean_l[i] = 0;}else{hist_mean_l[i] = hist_cum_Add[i] / hist_cum[i];}hist_mean_r[i] = (s - hist_cum_Add[i]) / (gray.rows * gray.cols - hist_cum[i]);hist_mean[i] = hist_coeff[i] * hist_mean_l[i] + (1 - hist_coeff[i]) * hist_mean_r[i];}// 2.5、计算方差float sigma[256] = { 0 };for (i = 0; i < 256; i++)   {sigma[i] = hist_coeff[i] * (hist_mean_l[i] - hist_mean[i]) * (hist_mean_l[i] - hist_mean[i]) +(1 - hist_coeff[i]) * (hist_mean_r[i] - hist_mean[i]) * (hist_mean_r[i] - hist_mean[i]);}// 2.6、获取最佳阈值float temp = 0;int index = 0;for (i = 0; i < 256; i++)   {if (temp < sigma[i]){temp = sigma[i];index = i;}}cout << "best threshold is: " << index << endl;// 进行阈值滤波for (i = 0; i < gray_OTSU.rows - 1; i++)for (j = 0; j < gray_OTSU.cols - 1; j++){if (gray_OTSU.at<uchar>(i, j) < index){gray_OTSU.at<uchar>(i, j) = 0;}}imshow("gray", gray);imshow("OTSU", gray_OTSU);waitKey();return 0;}

运行效果如下：

刚才又看了一种迭代阈值法，具体步骤如下：

1、以图像均值初始化 best_thr；

2、利用best_thr将图像中像素分为两组：Group1和Group2;

3、计算Group1和Group2对应的均值u1和u2；

4、重新选择阈值：best_thr = （u1 + u2）/ 2.0；

重复2~4，直到u1和u2不再发生变化。

代码如下：

#include <opencv2/opencv.hpp>#include <vector>using namespace cv;using namespace std;int main(){Mat src = imread("1.jpg");Mat gray;cvtColor(src, gray, CV_BGR2GRAY);int i, j;double sum = 0;double best_thr = 0;for (i = 0; i < gray.rows; i++)for (j = 0; j < gray.cols; j++){sum += gray.at<uchar>(i, j);}// 以图像像素均值来初始化阈值best_thr = sum / (gray.rows * gray.cols);vector<Point> Lows;vector<Point> Higs;bool flag = true;float u1 = 0, u2 = 0;float s1 = 0, s2 = 0;while (flag){Lows.clear();Higs.clear();// 获取分割后的两个部分for (i = 0; i < gray.rows; i++)for (j = 0; j < gray.cols; j++){if (gray.at<uchar>(i, j) < best_thr){Lows.push_back(Point(i, j));}else{Higs.push_back(Point(i, j));}} // end fors1 = 0;u1 = 0;for (i = 0; i < Lows.size(); i++){s1 += gray.at<uchar>(Lows[i].x, Lows[i].y);}u1 = s1 / Lows.size();s2 = 0;u2 = 0;for (i = 0; i < Higs.size(); i++){s2 += gray.at<uchar>(Higs[i].x, Higs[i].y);}u2 = s2 / Higs.size();cout << "u1: " << u1 << " u2: " << u2 << endl;// 迭代的终止条件：u1和u2都不再变化if (abs(best_thr - (u1 + u2) / 2.0) < 0.1){flag = false;}else{best_thr = (u1 + u2) / 2.0;}cout << best_thr << endl;}// end whilecout << best_thr << endl;for (i = 0; i < gray.rows; i++)for (j = 0; j < gray.cols; j++){if (gray.at<uchar>(i, j) < best_thr){gray.at<uchar>(i, j) = 0;}}imshow("iteration", gray);waitKey();return 0;}

效果如下：