question about allocentric_to_egocentric

[yrj88351]

Hi, actually i have some problem with this (allocentric_to_egocentric).
I can't really understand how 'R_local_to_global' come from after i read code and paper.
Could you help recommend some knowledge material about this question? I would really appreciate that

I think it's something like 'alpha' observation angle in KITTI.(To get rot_y, we need to consider 'alpha' and ray angle.)
But i can't exact reason this process in DD3D. (allocentric_to_egocentric)

[sanmin0312]

I think this link can help you.

https://towardsdatascience.com/orientation-estimation-in-monocular-3d-object-detection-f850ace91411

[emc222]

I also want to know how allocentric_to_egocentric works, i tried to use this function to convert a quaternion which yaw=1.1035268306732178, pitch=0, roll=0 to its global angle yaw=0.599697574750902, pitch=0, roll=0 (this is computed by simplified method as mentioned above), and i get yaw_pitch_roll (1.1051701660724589, -0.503826789884737, 0.003403815156846349). The converted yaw doesn't match global yaw but i notice the pitch value very close to the difference between local yaw and global yaw groundtruth, more tries also prove this. So I wonder if different definition of coordinate influence the result of conversion?

[yudai-kato-aisin]

I also found allocentric_to_egocentric does not work when other than yaw angle is not zero.
Because the gram-shmit process compute orthogonal axis but it's not guranteed to be what we expected as x, y, z axis.

update:
I noticed local to global rotation assume roll angle is 0.
In this case, we can compute rotation angles using tranlation from orthogonal coordinate to sphere coordinate.

The below code is a snipet to show an example to recover angles from a vector.

import numpy as np
from scipy.spatial.transform import Rotation
 
# examle angles. roll should be zero.
pitch, yaw, roll = [66, 120, 0]
print("pitch, yaw, roll", pitch, yaw, roll)
 
rot_matrix = Rotation.from_euler("xyz", [pitch, yaw, roll], degrees=True).as_matrix()
 
# compute a ray represents allocentric-egocentric rotation
ray = rot_matrix @ [0, 0, 1]
 
def angle_in_sphere_coord(x, y, z):
    r = np.sqrt(x**2 + y**2 + z**2)
    theta = np.arccos(y / r) - np.pi / 2
    phi = - np.sign(z) * np.arccos(x / np.sqrt(x**2 + z**2)) + np.pi / 2
    return r, theta, phi
 
r, theta, phi = angle_in_sphere_coord(*ray)
print("theta, phi", np.degrees(theta), np.degrees(phi))

outputs:

pitch, yaw, roll 66 120 0
theta, phi 66.00000000000001 119.99999999999997