I am doing camera calibration from tsai algo. I got intrensic and extrinsic matrix, but how can I reconstruct the 3D coordinates from that inormation?
1) I can use Gaussian Elimination for find X,Y,Z,W and then points will be X/W , Y/W , Z/W as homogeneous system.
2) I can use the
OpenCV documentation approach:
as I know
If you got extrinsic parameters then you got everything. That means that you can have Homography from the extrinsics (also called CameraPose). Pose is a 3x4 matrix, homography is a 3x3 matrix, H defined as
H = K*[r1, r2, t], //eqn 8.1, Hartley and Zisserman
with K being the camera intrinsic matrix, r1 and r2 being the first two columns of the rotation matrix, R; t is the translation vector.
Then normalize dividing everything by t3.
What happens to column r3, don't we use it? No, because it is redundant as it is the cross-product of the 2 first columns of pose.
Now that you have homography, project the points. Your 2d points are x,y. Add them a z=1, so they are now 3d. Project them as follows:
p = [x y 1]; projection = H * p; //project projnorm = projection / p(z); //normalize
Hope this helps.