question about convert quaternion to yaw

[yustaub]

Hi, sir. I have got 3D bbox in nuscenes lidar coords and transform it to kitti lidar coords by kitti_to_nu_lidar_inv, and get box_lidar_kitti:

and I want to use nuscenes data in kitti lidar coordinate system to train some 3D detection model which don't support nuscenes dataset, but I have no idea about converting quaternion to yaw; In box_to_string, it converts quaternion to yaw in kitti image frame, and how to convert quaternion to yaw in kitti lidar frame? Can I use quaternion_yaw? Appreciate for your reply!

[holger-motional]

Please check
https://github.com/nutonomy/nuscenes-devkit/blob/master/python-sdk/nuscenes/scripts/export_kitti.py#L305

and specifically

nuscenes-devkit/python-sdk/nuscenes/utils/kitti.py

Line 314 in 568762b

quat_box = Quaternion(axis=(0, 1, 0), angle=yaw_camera) * Quaternion(axis=(1, 0, 0), angle=np.pi/2)

[yustaub]

thanks for your quick reply! but I can not figure out what it means quat_box = Quaternion(axis=(0, 1, 0), angle=yaw_camera) * Quaternion(axis=(1, 0, 0), angle=np.pi/2), and still have no idea about convert quaternion to yaw in kitti lidar coordiante system. Can you share some advice? @holger-nutonomy

[holger-motional]

The first part Quaternion(axis=(0, 1, 0), angle=yaw_camera) is the standard definition of yaw in nuScenes. We rotate around the vertical (y) axis by yaw degrees. The second part is the conversion from KITTI to nuScenes - a rotation of 90 degrees around the x axis. Understanding the different coordinate systems is often tricky, but it is very easy to just try out the different options and visualize the result. E.g. there are only 6 possible 90 degree rotations (around an axis), 2 for each axis, so you can just try each.

[yustaub]

Thank you, sir. sorry for my late reply, I will try it.

[yustaub]

Hello,
I understand that quaternion to yaw in nuscenes lidar coordinate system: v = np.dot(q.rotation_matrix, np.array([1, 0, 0])) yaw = np.arctan2(v[1], v[0]), I convert nuscenes lidar data to kitti lidar coordinates system and it is x front, y left, z up, about its converting quaternion to yaw, should be yaw = np.arctan2(v[0],-v[1])? Very appreciate for your reply. @holger-nutonomy

[holger-motional]

Unfortunately I don't remember the conventions of KITTI and don't have it installed to run some checks. You can see our conventions at https://www.nuscenes.org/public/images/data.png .

[yustaub]

There is another question that about quaternion condused me. kitti_to_nu_lidar = Quaternion(axis=(0, 0, 1), angle=np.pi / 2), as I known that in kitti, its lidar coordinate system is : x front, y left, z up, and in nuscenes, its lidar coordinate system is : x right, y front, z up, kitti_to_nu_lidar is rotate pi/2 around z axis, according to right-handed, x front will turn to x left, does the z axis point down? @holger-nutonomy

[holger-motional]

You can see whether z points up or down in https://www.nuscenes.org/public/images/data.png.
The circle with an X means downwards, the circle with a dot means upwards.
x right, y front, z up is correct for nuScenes.
KITTI: For your right hand, point the thumb forward, index finger left, middle finger up.
Go to nuScenes: rotate your hand by 90 degrees clockwise around the middle finger.

[yustaub]

from wiki, right hand rule is For right-handed coordinates the right thumb points along the Z axis in the positive direction and the curl of the fingers represents a motion from the first or X axis to the second or Y axis. When viewed from the top or Z axis the system is counter-clockwise., what I know about right hand rule is also this, and z is up in kitti lidar and nuscenes lidar, follow the right hand rule, x front z up in kitti lidar will turn to x left which is just opposite from x right in nuscenes, it confused me. If there are some errors, please tell me. Thanks!