OpenCV4入门系列教程90:轮廓拟合(直线、圆与椭圆)

索引地址:系列索引

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bool polynomial_curve_fit(std::vector<cv::Point>& key_point, int n, cv::Mat& A)
{
//Number of key points
int N = key_point.size();

//构造矩阵X
cv::Mat X = cv::Mat::zeros(n + 1, n + 1, CV_64FC1);
for (int i = 0; i < n + 1; i++)
{
for (int j = 0; j < n + 1; j++)
{
for (int k = 0; k < N; k++)
{
X.at<double>(i, j) = X.at<double>(i, j) +
std::pow(key_point[k].x, i + j);
}
}
}

//构造矩阵Y
cv::Mat Y = cv::Mat::zeros(n + 1, 1, CV_64FC1);
for (int i = 0; i < n + 1; i++)
{
for (int k = 0; k < N; k++)
{
Y.at<double>(i, 0) = Y.at<double>(i, 0) +
std::pow(key_point[k].x, i) * key_point[k].y;
}
}

A = cv::Mat::zeros(n + 1, 1, CV_64FC1);
//求解矩阵A
cv::solve(X, Y, A, cv::DECOMP_LU); //X*A = Y
return true;
}

int main()
{
//创建用于绘制的深蓝色背景图像
cv::Mat image = cv::Mat::zeros(480, 640, CV_8UC3);
image.setTo(cv::Scalar(100, 0, 0));

//输入拟合点
std::vector<cv::Point> points;
points.push_back(cv::Point(100., 58.));
points.push_back(cv::Point(150., 70.));
points.push_back(cv::Point(200., 90.));
points.push_back(cv::Point(252., 140.));
points.push_back(cv::Point(300., 220.));
points.push_back(cv::Point(350., 400.));

//将拟合点绘制到空白图上
for (int i = 0; i < points.size(); i++)
{
cv::circle(image, points[i], 5, cv::Scalar(0, 0, 255), 2, 8, 0);
}

//绘制折线
cv::polylines(image, points, false, cv::Scalar(0, 255, 0), 1, 8, 0);

cv::Mat A;

polynomial_curve_fit(points, 3, A);
std::cout << "A = " << A << std::endl;

std::vector<cv::Point> points_fitted;

for (int x = 0; x < 400; x++)
{
double y = A.at<double>(0, 0) + A.at<double>(1, 0) * x +
A.at<double>(2, 0)*std::pow(x, 2) + A.at<double>(3, 0)*std::pow(x, 3);

points_fitted.push_back(cv::Point(x, y));
}
cv::polylines(image, points_fitted, false, cv::Scalar(0, 255, 255), 1, 8, 0);

cv::imshow("image", image);

cv::waitKey(0);
return 0;
}

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