CVPR 2026 Papers

Inverse rendering is an ill-posed problem, but priors such as illumination priors can help 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.

We present a general optimization-based framework for depth-preserving normal integration. Unlike existing methods that operate on surface orientations defined over regular grids, our approach introduces a unified graph-based formulation capable of integrating semi-differentiable surfaces on unstructured domains. Given a set of points uniformly sampled from a surface, we construct a directed, weighted graph that jointly parameterizes the surface geometry and pairwise point correlations. Surface depth is recovered by minimizing projected point-to-plane distances across the graph, and we attain this objective through variational inference. In our formulation, estimated surface normals serve as latent variables that encode local geometry via the posterior probabilities of a two-component Gaussian mixture, allowing depth discontinuities to be explicitly inferred from sampled triplet configurations. The unknowns are estimated in an alternating fashion, and we provide a geometric interpretation of this inference process by relating it to shape deformation. Experimental results show that the proposed method not only delivers superior performance on regularly gridded data, but also generalizes effectively to scattered points, which existing approaches do not directly support.