Defining an Action of SO(d)-Rotations on Projections of d-Dimensional Objects: Applications to Pose Inference with Geometric VAEs

Legendre, N, Dao Duc, K., Miolane, N.

GRETSI Conference (2022).

Recent advances in variational autoencoders (VAEs) have enabled learning latent manifolds as compact Lie groups, such as SO(d). Since this approach assumes that data lies on a subspace that is homeomorphic to the Lie group itself, we here investigate how this assumption holds in the context of images that are generated by projecting a d-dimensional volume with unknown pose in SO(d).