I'm currently trying to discover the 3D position of a projector within a real world coordinate system. The origin of such a system is, for example, the corner of a wall. I've used Open Frameworks addon called ofxCvCameraProjectorCalibration
that is based on OpenCV functions, namely calibrateCamera and stereoCalibrate methods. The application output is the following:
camera intrisic matrix (distortion coeficients included);
projector intrisic matrix (distortion coeficients included);
camera->projector extrinsic matrix;
My initial idea was, while calibration the camera, place the chessboard pattern at the corner of the wall and extract the extrinsic parameters ( [RT] matrix ) for that particular calibration.
After calibrating both camera and projector do I have all the necessary data to discover the position of the projector in real world coordinates? If so, what's the matrix manipulation required to get it?
Related
I have a laser giving out range data and a monocular camera attached on top of it which is used for detection and tracking. I have the intrinsic calibration parameters of the camera. I want to establish a correspondence between the camera data and laser data. Is there any known method to get the extrinsic calibration matrix?? The end goal is to use x,y of the detected object from the camera and z (or depth) of the detected object from the laser.
Thank you in advance.
Not sure if the question is still open, in this repo you'll find some Matlab code to get the extrinsic between an 1D laser range finder (or altimeter) and a monocular camera:
https://github.com/RiccardoGiubilato/1d-lidar-cam-calib
required are pairs of images of a plane with a printout of a checkerboard and "1-D" associated ranges from the altimeter.
Knowing the rotations and translations of two cameras in world coordinates (relative to some known point), how would I calibrate my stereo system?
In OpenCV the normal approach is to use a calibration pattern in front of both cameras to get point correspondences. These points are used in stereoCalibrate which calculates the rotation matrix R and translation vector T (and the fundamental matrix F). In the next step the stereo rectification can be done to row-align images of both cameras with stereoRectify. stereoRectify needs R and T to calculate the homographies for the perspective transform of the images and also calculates the Q-matrix for translating disparity to depth.
Giving the situation that R and T in the world coordinate system are already known (known is the rotation around the z-Axis (floor-ceiling or yaw angle in aeronomy) and the rotation around the axis perpendicular to the camera view (pitch angle)), in which coordinate system should they be given to stereoRectify? What I mean with that is that there is the coordinate system of Camera1, of Camera2, and the (or one) world coordinate system.
The computation of the essential matrix E can be done with R * S where S is the skew-symmetric matrix of T and the fundamental matrix F with M_r.inv().t() * E * M_l.inv() following LearningOpenCV 3 from Kaehler and Bradski (M_r and M_l are the camera intrinsics of the right and left camera respectively). Here the question on R and T is the same. Is it the rotation from one camera to the other in world coordinates or e.g. in the coordinate system of one camera?
A sketch of the involved coordinate systems can be found here:
How is the camera coordinate system in OpenCV oriented?, however it is still unclear for me how exactly R and T should be calculated.
The question is not terribly clear, but...
IIUC you know the extrinsic parameters of both cameras, ergo their relative pose, but not the intrinsic ones. Therefore you still need to calibrate the cameras' intrinsics.
Knowing the relative pose of the cameras simply allows you to calibrate the intrinsics of the two cameras independently. Whether this is a simplification for your procedure or not depends on your particular setup.
Note that, unless you have inferred the extrinsics you have from a separate, image-based procedure, you should hardly trust their values - especially if they are derived by some sort of CAD model of your rig. The reason is that, unless your cameras have quite low resolution, pixel-level accuracy is likely to be much finer than what the manufacturing tolerances of your rig would account for.
This is a question about terminology used in computer graphics and vision. I want to construct a camera projection matrix, using 2D to 3D correspondences. From these correspondences I create a camera object. I am using a class in a library to represent the camera. It takes the following parameters:
// R is the orientation of the camera expressed in a world coordinate frame
// t is the position of the camera expressed in a world coordinate frame
The first part of my question is: are R and t, as defined above, the extrinsic parameters satisfying x=K[R|t]X? Or do they need to be converted (for example, transpose(R) is the extrinsic orientation, and -transpose(R)*t for position).
I am obtaining R and t using openCV's solvePnP function. The function returns R and t as follows:
rvec – Output rotation vector (see Rodrigues() ) that, together with tvec , brings points from the model coordinate system to the camera coordinate system.
tvec – Output translation vector.
The second part of my question is, based on the descriptions above, are the outputs equivalent to my camera's extrinsic parameters, or do they also need to be transformed (as previously defined)?
The camera projection matrix is typically defined as P = K [R|t], where R and t are the extrinsics, and not the camera orientation and location in the world coordinates.
As to what solvePnP returns, you would have to read its documentation, or try it out and see.
slovepnp takes image points(in image coordinate), object points(in model/world coordinate) and camera intrinsic, then output rvec/tvec, with which we could construct model to camera transform. in opengl, usually called this modelview matrix.
computers are difficult to get knowledge of the environment, we usually use easy-detect features like AR marker and calibration board and take it as world coordinate as well as model coordinate if you would like to call it in a opengl way. In these scene, camera's extrinsic do expressed in a world coordinate frame.
you could check the code of chapter 2 and chapter 3(AR things) of the book mastering opencv and get a good knowledge and practical code of these.
How do you stereo cameras so that the output of the triangulation is in a real world coordinate system, that is defined by known points?
OpenCV stereo calibration returns results based on the pose of the left hand camera being the reference coordinate system.
I am currently doing the following:
Intrinsically calibrating both the left and right camera using a chess board. This gives the Camera Matrix A, and the distortion coefficients for the camera.
Running stereo calibrate, again using the chessboard, for both cameras. This returns the extrinsic parameters, but they are relative to the cameras and not the coordinate system I would like to use.
How do I calibrate the cameras in such a way that known 3D point locations, with their corresponding 2D pixel locations in both images provides a method of extrinsically calibrating so the output of triangulation will be in my coordinate system?
Calculate disparity map from the stereo camera - you may use cvFindStereoCorrespondenceBM
After finding the disparity map, refer this: OpenCv depth estimation from Disparity map
I've 4 ps3eye cameras. And I've calibrated camera1 and camera2 using cvStereoCalibrate() function of OpenCV library
using a chessboard pattern by finding the corners and passing their 3d coordinates into this function.
Also I've calibrated camera2 and camera3 using another set of chessboard images viewed by camera2 and camera3.
Using the same method I've calibrated camera3 and camera4.
So now I've extrinsic and intrinsic parameters of camera1 and camera2,
extrinsic and intrinsic parameters of camera2 and camera3,
and extrinsic and intrinsic parameters of camera3 and camera4.
where extrinsic parameters are matrices of rotation and translation and intrinsic are matrices of focus length and principle point.
Now suppose there's a 3d point(world coordinate)(And I know how to find 3d coordinates from stereo cameras) that is viewed by camera3 and camera4 which is not viewed by camera1 and camera2.
The question I've is: How do you take this 3d world coordinate point that is viewed by camera3 and camera4 and transform it with respect to camera1 and camera2's
world coordinate system using rotation, translation, focus and principle point parameters?
OpenCV's stereo calibration gives you only the relative extrinsic matrix between two cameras.
Acording to its documentation, you don't get the transformations in world coordinates (i.e. in relation to the calibration pattern ). It suggests though to run a regular camera calibration on one of the images and at least know its transformations. cv::stereoCalibrate
If the calibrations were perfect, you could use your daisy-chain setup to derive the world transformation of any of the cameras.
As far as I know this is not very stable, because the fact that you have multiple cameras should be considered when running the calibration.
Multi-camera calibration is not the most trivial of problems. Have a look at:
Multi-Camera Self-Calibration
GML C++ Camera Calibration Toolbox
I'm also looking for a solution to this, so if you find out more regarding this and OpenCV, let me know.