Rotation matrix to euler angles with opencv

Question

I am working on a project wich involves Aruco markers and opencv. I am quite far in the project progress. I can read the rotation vectors and convert them to a rodrigues matrix using rodrigues() from opencv.

This is a example of a rodrigues matrix I get:

[0,1,0;

1,0,0;

0,0,-1]

I use the following code.

Mat m33(3, 3, CV_64F);
Mat measured_eulers(3, 1, CV_64F);
Rodrigues(rotationVectors, m33);

measured_eulers = rot2euler(m33);

Degree_euler = measured_eulers * 180 / CV_PI;

I use the predefined rot2euler to convert from rodrigues matrix to euler angles. And I convert the received radians to degrees.

rot2euler looks like the following.

Mat rot2euler(const Mat & rotationMatrix)
{
    Mat euler(3, 1, CV_64F);

    double m00 = rotationMatrix.at<double>(0, 0);
    double m02 = rotationMatrix.at<double>(0, 2);
    double m10 = rotationMatrix.at<double>(1, 0);
    double m11 = rotationMatrix.at<double>(1, 1);
    double m12 = rotationMatrix.at<double>(1, 2);
    double m20 = rotationMatrix.at<double>(2, 0);
    double m22 = rotationMatrix.at<double>(2, 2);

    double x, y, z;

    // Assuming the angles are in radians.
    if (m10 > 0.998) { // singularity at north pole
        x = 0;
        y = CV_PI / 2;
        z = atan2(m02, m22);
    }
    else if (m10 < -0.998) { // singularity at south pole
        x = 0;
        y = -CV_PI / 2;
        z = atan2(m02, m22);
    }
    else
    {
        x = atan2(-m12, m11);
        y = asin(m10);
        z = atan2(-m20, m00);
    }

    euler.at<double>(0) = x;
    euler.at<double>(1) = y;
    euler.at<double>(2) = z;

    return euler;
}

If I use the rodrigues matrix I give as an example I get the following euler angles.

[0; 90; -180]

But I am suppose to get the following.

[-180; 0; 90]

When is use this tool http://danceswithcode.net/engineeringnotes/rotations_in_3d/demo3D/rotations_in_3d_tool.html

You can see that [0; 90; -180] doesn't match the rodrigues matrix but [-180; 0; 90] does. (I am aware of the fact that the tool works with ZYX coordinates)

So the problem is I get the correct values but in a wrong order.

Another problem is that this isn't always the case. For example rodrigues matrix:

[1,0,0;

0,-1,0;

0,0,-1]

Provides me the correct euler angles.

If someone knows a solution to the problem or can provide me with a explanation how the rot2euler function works exactly. It will be higly appreciated.

Kind Regards

Brent Convens

Two different euler rotations can represent the same rotation. Try to get the 3x3 matrix using the inverse conversion. — hiroki
It seems that you are in the case of singularities. As far as I know, it is not convenient to use rotation matrices for angles like 90 or 180 degrees (no matters if they are positive or negative) because you are at risk of singularities. And it quite looks like the formulas are wrong... have a look at this paper — marcoresk

mal mal · Accepted Answer · 2017-11-07T20:50:58

I guess I am quite late but I'll answer it nonetheless. Dont quote me on this, ie I'm not 100 % certain but this is one of the files ( {OPENCV_INSTALLATION_DIR}/apps/interactive-calibration/rotationConverters.cpp ) from the source code of openCV 3.3

It seems to me that openCV is giving you Y-Z-X ( similar to what is being shown in the code above )

Why I said I wasn't sure because I just looked at the source code of cv::Rodrigues and it doesnt seem to call this piece of code that I have shown above. The Rodrigues function has the math harcoded into it ( and I think it can be checked by Taking the 2 rotation matrices and multiplying them as - R = Ry * Rz * Rx and then looking at the place in the code where there is a acos(R(2,0)) or asin(R(0,2) or something similar,since one of the elements of "R" will usually be a cos() or sine which will give you a solution as to which angle is being found.

Rotation matrix to euler angles with opencv

2 Answers