VENI: Variational Encoder for Natural Illumination

Inverse rendering is an ill-posed problem, but priors like illumination priors, can simplify it.Existing work either disregards the spherical and rotation-equivariant nature of illumination environments or does not provide a well-behaved latent space.We propose a rotation-equivariant variational autoencoder that models natural illumination on the sphere without relying on 2D projections.To preserve the SO(2)-equivariance of environment maps, we use a novel Vector Neuron Vision Transformer (VN-ViT) as encoder and a rotation-equivariant conditional neural field as decoder.In the encoder, we reduce the equivariance from SO(3) to SO(2) using a novel SO(2)-equivariant fully connected layer, an extension of Vector Neurons.We show that our SO(2)-equivariant fully connected layer outperforms standard Vector Neurons when used in our SO(2)-equivariant model.Compared to previous methods, our variational autoencoder enables smoother interpolation in latent space and offers a more well-behaved latent space.