具体的公式推导参见冈萨雷斯 《数字图像处理》
Otsu方法又称最大类间方差法,通过把像素分配为两类或多类,计算类间方差,当方差达到最大值时,类分割线(即灰度值)就作为图像分割阈值。Otsu还有一个重要的性质,即它完全基于对图像直方图进行计算,这也使他成为最常用的阈值处理算法之一。
算法步骤如下:
Otsu只有在直方图呈现双峰的时候才会有一个很好的效果,在直方图单峰或多峰的情况下效果不是很好,那就需要通过实际情况来选取其他的方法来得到预期的分割效果。
代码如下;
double Otsu_threshold(const cv::Mat& InputImage)
{
cv::Mat SrcImage = InputImage.clone();
CV_Assert(SrcImage.type() == CV_8UC1);
int rows = SrcImage.rows;
int cols = SrcImage.cols;
const int L = 256;
int N = rows * cols;
int n_i[L] = { 0 };
for (int i = 0; i < rows; ++i)
{
uchar* p = SrcImage.ptr<uchar>(i);
for (int j = 0; j < cols; ++j)
n_i[p[j]]++;
}
double pn_i[L];
for (int i = 0; i < L; ++i)
{
pn_i[i] = (double)n_i[i] / N;
}
cv::Mat mat_mean, mat_stddev;
double gray_mean, gray_sigma;
cv::meanStdDev(SrcImage, mat_mean, mat_stddev);
gray_mean = mat_mean.at<double>(0, 0);
gray_sigma = mat_stddev.at<double>(0, 0) * mat_stddev.at<double>(0, 0);
std::vector<double>sigma_ks(L);
for (int k = 0; k < L; ++k)
{
double p1 = 0.0;
double m_k = 0.0;
for (int i = 0; i <= k; ++i)
{
p1 += pn_i[i];
m_k += i * pn_i[i];
}
if (p1 == 0.0 || (1 - p1) == 0.0)
sigma_ks[k] = 0.0;
else
sigma_ks[k] = (gray_mean * p1 - m_k) * (gray_mean * p1 - m_k) / (p1 * (1 - p1));
}
double max_Sigma_k = 0.0;
std::vector<int>maxval_Ts;
double Threshold_T = 0;
for (int i = 0; i < sigma_ks.size(); ++i)
{
if (sigma_ks[i] > max_Sigma_k)
max_Sigma_k = sigma_ks[i];
}
for (int i = 0; i < sigma_ks.size(); ++i)
{
if (abs(max_Sigma_k - sigma_ks[i]) < 1e-8)
maxval_Ts.push_back(i);
}
for (int i = 0; i < maxval_Ts.size(); ++i)
Threshold_T += maxval_Ts[i];
return Threshold_T / maxval_Ts.size();
}
int main()
{
std::string path = "F:\\NoteImage\\Lena.jpg";
cv::Mat src = imread(path, cv::IMREAD_GRAYSCALE);
if (!src.data) {
std::cout << "Could not open or find the image" << std::endl;
return -1;
}
cv::Mat dst;
double thres1 = cv::threshold(src, dst, 0, 255, cv::THRESH_OTSU);
double thres2 = Otsu_threshold(src);
std::cout << "opencv = " << thres1 << " my = " << thres2;
cv::waitKey(0);
return 0;
}
处理结果:
与本博文有关的其他博文:
mask_otsu
自适应阈值Canny
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