问题
I am trying to determine camera position in world coordinates, relative to a fiducial position based on fiducial marker found in a scene.
My methodology for determining the viewMatrix is described here: Determine camera pose?
I have the rotation and translation, [R|t], from the trained marker to the scene image. Given camera calibration training, and thus the camera intrinsic results, I should be able to discern the cameras position in world coordinates based on the perspective & orientation of the marker found in the scene image.
Can anybody direct me to a discussion or example similar to this? I'd like to know my cameras position based on the fiducial marker, and I'm sure that something similar to this has been done before, I'm just not searching the correct keywords.
Appreciate your guidance.
回答1:
What do you mean under world coordinates? If you mean object coordinates then you should use the inverse transformation of solvepnp's result.
Given a view matrix [R|t], we have that inv([R|t]) = [R'|-R'*t], where R' is the transpose of R. In OpenCV:
cv::Mat rvec, tvec;
cv::solvePnP(objectPoints, imagePoints, intrinsics, distortion, rvec, tvec);
cv::Mat R;
cv::Rodrigues(rvec, rotation);
R = R.t(); // inverse rotation
tvec = -R * tvec; // translation of inverse
// camPose is a 4x4 matrix with the pose of the camera in the object frame
cv::Mat camPose = cv::Mat::eye(4, 4, R.type());
R.copyTo(camPose.rowRange(0, 3).colRange(0, 3)); // copies R into camPose
tvec.copyTo(camPose.rowRange(0, 3).colRange(3, 4)); // copies tvec into camPose
Update #1:
Result of solvePnP
solvePnP estimates the object pose given a set of object points (model coordinates), their corresponding image projections (image coordinates), as well as the camera matrix and the distortion coefficients.
The object pose is given by two vectors, rvec and tvec. rvec is a compact representation of a rotation matrix for the pattern view seen on the image. That is, rvec together with the corresponding tvec brings the fiducial pattern from the model coordinate space (in which object points are specified) to the camera coordinate space.
That is, we are in the camera coordinate space, it moves with the camera, and the camera is always at the origin. The camera axes have the same directions as image axes, so
- x-axis is pointing in the right side from the camera,
- y-axis is pointing down,
- and z-axis is pointing to the direction of camera view
The same would apply to the model coordinate space, so if you specified the origin in upper right corner of the fiducial pattern, then
- x-axis is pointing to the right (e.g. along the longer side of your pattern),
- y-axis is pointing to the other side (e.g. along the shorter one),
- and z-axis is pointing to the ground.
You can specify the world origin as the first point of the object points that is the first object is set to (0, 0, 0) and all other points have z=0 (in case of planar patterns). Then tvec (combined rvec) points to the origin of the world coordinate space in which you placed the fiducial pattern. solvePnP's output has the same units as the object points.
Take a look at to the following: 6dof positional tracking. I think this is very similar as you need.
来源：https://stackoverflow.com/questions/28402446/camera-frame-world-coordinates-relative-to-fiducial