Compute major and minor axes of an ellipse from a covariance matrix.

getEllipseAxes.cpp

// Taken from http://www.visiondummy.com/2014/04/draw-error-ellipse-representing-covariance-matrix/

// previously defined
cv::Mat covmat;

// Get the eigenvalues and eigenvectors
cv::Mat eigenvalues, eigenvectors;
cv::eigen(covmat, eigenvalues, eigenvectors);

// Calculate the angle between the largest eigenvector and the x-axis
double angle = atan2(eigenvectors.at<double>(0,1), eigenvectors.at<double>(0,0));

//S hift the angle to the [0, 2pi] interval instead of [-pi, pi]
if (angle < 0) {
	angle += 2 * M_PI;
}

// Convert to degrees instead of radians
angle = 180 * angle / M_PI;

// Calculate the size of the minor and major axes
double halfmajoraxissize = scale_factor * sqrt(eigenvalues.at<double>(0));
double halfminoraxissize = scale_factor * sqrt(eigenvalues.at<double>(1));


// Return the oriented ellipse
// The -angle is used because OpenCV defines the angle clockwise instead of anti-clockwise
cv::Point2f mean; // need to define
return cv::RotatedRect(mean, cv::Size2f(halfmajoraxissize, halfminoraxissize), -angle);