This PyTorch SE3 composition layer implementation is being inspired by Torch gvnn .
Thanks for the advice from Ankur Handa @ankurhanda (https://github.com/ankurhanda)(The author of gvnn).

Please cite

@misc{JackyLiuSE3comp18,
  author = {Tse-An (Jacky) Liu},
  doi = {10.5281/zenodo.1304166},
  title = {se3comp pytorch},
  year = {2018},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/HTLife/se3comp_pytorch}}
}

SE3 composition layer

Purpose: Compose global pose Tg with related pose xi

• Tg is a SE3 pose represented with 7 parameters (x, y, z, ww, wx, wy, wz)
• xi is a se3 pose represented with 6 parameters (rho1, rho2, rho3, omega_x, omega_y, omega_z)
• Tutorial of lie group SE3: http://ethaneade.com/lie.pdf

Txi: 4x4 Matrix of the exponential mapping of xi (lie.pdf Eqation.84) Tg_matrix: Tg represented in matrix form T_composed: The pose calculated by matrix multiplication of Txi and Tg_matrix

T_composed = Txi (dot) Tg_matrix

Some implementation story

In VINet[1], the author described a important structure called SE3 composition layer (Figure.2 in VINet). However, they do not describe this structure in detail. I found some related statement in [2] page.9(which is a journal paper from the same advisor). In this journal paper, I found that gvnn[3] might be their reference of implementing SE3 composition layer.

Unfortunately, the source code of gvnn is written by torch-lua. After taking the kind advice from Ankur Handa, I finished implementing this PyTorch SE3 composition layer.

Reference

• [1] R.Clark, S.Wang, H.Wen, A.Markham, andN.Trigoni, “VINet: Visual-Inertial Odometry as a Sequence-to-Sequence Learning Problem,” pp. 3995–4001, 2017.
• [2] S.Wang, R.Clark, H.Wen, andN.Trigoni, “End-to-end, sequence-to-sequence probabilistic visual odometry through deep neural networks,” Int. J. Rob. Res., 2017.
• [3] A.Handa, M.Bloesch, V.Pătrăucean, S.Stent, J.McCormac, andA.Davison, “Gvnn: Neural network library for geometric computer vision,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 9915 LNCS, pp. 67–82, 2016.