how do you calculate pose

[jeannotes]

hi, in your provided bevplace++_dataset.zip,
it seems that the pose are not equall to kitti official odometry pose, how to calculate,
I also check with semantic kitti, seems also not equal.
hope to get response from you, thank you

[zjuluolun]

The ground truth poses provided by the KITTI dataset are expressed in the camera coordinate frame. To align them with the LiDAR frame, we apply the extrinsic transformation using the following equation:
$$T_l = T_{lc}T_cT_{lc}^{-1},$$
where $$T_l,T_c$$ are the poses of LiDAR and camera, and $$T_{lc}$$ is the extrinsic matrix that convert points from the LiDAR frame to Camera frame.

[jeannotes]

@zjuluolun I get confused, what does

$$T_l = T_{lc} \cdot T_c \cdot T_{lc}^{-1}$$

what does this mean?
why not :

$$T_l = T_{lc}^{-1} \cdot T_c$$

[zjuluolun]

This is because the odometry poses in the KITTI dataset are defined with the world frame aligned to the camera at the initial timestamp, $$T_{c,0}=I$$, where $$c,0$$ refer to the camera and the timestamp.To compute the corresponding LiDAR odometry poses with the world frame aligned to the LiDAR origin, we consider the following relation $$T_{l,t}P = T_{cl}T_{c,t}T_{lc}P$$, which expresses how a point $$P$$ in the local LiDAR frame is transformed to the LiDAR world frame using the camera odometry poses and the extrinsic matrix between LiDAR and camera. Sovling the equation leads to $$T_l=T_{lc}T_cT_{lc}^{-1}$$.

[BK-Snowball]

Thank you very much for your excellent work on BEVPlace++! I would like to ask a question: Is the KITTI true value of bevplace++_dataset.zip calculated using KITTI odometry? I transformed the true value of kitti odometry into the radar coordinate system through the calib file. The result seems to be different from the value provided in the compressed package. I don’t know which step caused the problem.