Questions about extrinsics in JSON files

[xiaominzhen]

Hello: I see in your code that the extrinsics read directly from the JSON file cannot be used directly to projecting coordinate (u; v) in the front-view to the corresponding point in BEV by (u, v, 1) = K(intrinsics)·E(extrinsics)· (x, y, z, 1), but needs to be transformed first:

Then take the inverse of it:

Why is it needed this extra transformation for the external parameter? Why not just put the transformed external parameters in the JSON file?
In addition, I would like to ask you another question. If I want to get the coordinates in the camera coordinate system, can I directly use the transformed E· (x, y, z, 1) to get the coordinates?
Looking forward to your answer ~ thank you very much

[dyfcalid]

The camera extrinsic matrix from the JSON file is the standard representation which transforms the coordinates from the camera coordinate system to the vehicle coordinate system. The annotation of lane coordinates from the JSON file are under the camera coordinate system.
But particularly, we will represent the 3D lane coordinates under the ground coordinate system for the model to predict, which is consistent with 3D-LaneNet and Gen-LaneNet, so we add some extra transformation based on the extrinsics in the code.
And the P_g2im matrix in the second picture can finally transform the coordinates from the ground coordinate system to the image pixel coordinate system.
The origin of the ground coordinate system is located on the ground plane, with the y-axis pointing forward, the x-axis pointing right, and the z-axis pointing up. See the following figure from Gen-LaneNet.