[Bug] relative_transformation returns wrong transformation

🐛 Bug

The function relative_transformation is not returning the correct relative transform given two random input transforms. We might have to take a look at compose_transformations and inverse_transformation too.

To Reproduce

Use this colab link: https://colab.research.google.com/drive/104_T6Jfqyq_cy3xTYd_Qo6g6dCYAiL8H?usp=sharing

or run:

Steps to reproduce the behavior:

import torch
import kornia as K

def to_homogeneous(x):
    x_out = torch.nn.functional.pad(x, (0, 0, 0, 1), "constant", 0.)
    x_out[..., -1, -1] += 1.
    return x_out

B = 1  # batch size
rtmat_a = torch.rand(B, 3, 4)
rtmat_b = torch.rand(B, 3, 4)

w_trans_a = to_homogeneous(rtmat_a)
w_trans_b = to_homogeneous(rtmat_b)
print("cam1")
print(w_trans_a)
print("cam2")
print(w_trans_b)

# compute relative motion using kornia with transpose
rtmat_ab = K.relative_transformation(w_trans_a[:, :3], w_trans_b[:, :3])
b_trans_a_kornia = to_homogeneous(rtmat_ab)

# compute relative motion using direct way
b_trans_a_torch = (w_trans_b).inverse() @ w_trans_a

# try to reconstruct cameras
print("rec cam1 kornia")
print(w_trans_b @ b_trans_a_kornia)

print("rec cam1 torch")
print(w_trans_b @ b_trans_a_torch)

print("rec cam2 kornia")
print(w_trans_a @ b_trans_a_kornia.inverse())

print("rec cam2 torch")
print(w_trans_a @ b_trans_a_torch.inverse())

Expected behavior

Environment

Please copy and paste the output from our environment collection script (or fill out the checklist below manually).

You can get the script and run it with:

wget https://raw.githubusercontent.com/pytorch/pytorch/master/torch/utils/collect_env.py
# For security purposes, please check the contents of collect_env.py before running it.
python collect_env.py

• PyTorch Version (e.g., 1.0):
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Additional context

[edgarriba]

gotcha - I think it’s worth having a utility function to create random orthogonal rotation matrices similar to scipy.stats.special_ortho_group https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.special_ortho_group.html

[thatbrguy]

gotcha - I think it’s worth having a utility function to create random orthogonal rotation matrices similar to scipy.stats.special_ortho_group https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.special_ortho_group.html

Yeah I think such a function would be nice to have in kornia for testing purposes