Tangent Space Backpropagation for 3D Transformation Groups

Understand

We address the problem of performing backpropagation for computation graphs involving 3D transformation groups SO(3), SE(3), and Sim(3).

• 3D transformation groups are widely used in 3D vision and robotics, but they do not form vector spaces and instead lie on smooth manifolds.
• The standard backpropagation approach, which embeds 3D transformations in Euclidean spaces, suffers from numerical difficulties.
• We introduce a new library, which exploits the group structure of 3D transformations and performs backpropagation in the tangent spaces of manifolds.