How to determine world coordinates of a camera?

Question

I have a rectangular target of known dimensions and location on a wall, and a mobile camera on a robot. As the robot is driving around the room, I need to locate the target and

Answer 1

It took me forever to understand it, but the pose meaning is the rotation over each axes - x,y,z. It is in radians. The values are between Pie to minus Pie (-3.14 - 3.14)

Edit: I've might been mistaken. I read that the pose is the vector which indicates the direction of the camera, and the length of the vector indicates how much to rotate the camera around that vector.

Answer 2

You get the translation and rotation vectors from solvePnP, which are telling where is the object in camera's coordinates. You need to get an inverse transform.

The transform camera -> object can be written as a matrix [R T;0 1] for homogeneous coordinates. The inverse of this matrix would be, using it's special properties, [R^t -R^t*T;0 1] where R^t is R transposed. You can get R matrix from Rodrigues transform. This way You get the translation vector and rotation matrix for transformation object->camera coordiantes.

If You know where the object lays in the world coordinates You can use the world->object transform * object->camera transform matrix to extract cameras translation and pose.

The pose is described either by single vector or by the R matrix, You surely will find it in Your book. If it's "Learning OpenCV" You will find it on pages 401 - 402 :)

Looking at Your code, You need to do something like this

    cv::Mat R;
    cv::Rodrigues(rotation_vector, R);

    cv::Mat cameraRotationVector;

    cv::Rodrigues(R.t(),cameraRotationVector);

    cv::Mat cameraTranslationVector = -R.t()*translation_vector;

cameraTranslationVector contains camera coordinates. cameraRotationVector contains camera pose.