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Inverse rendering of outdoor scenes from unconstrained image collections is a challenging task, particularly illumination/albedo ambiguities and occlusion of the illumination environment (shadowing) caused by geometry. However, there are many cues in an image that can aid in the disentanglement of geometry, albedo and shadows. Whilst sky is frequently masked out in state-of-the-art methods, we exploit the fact that any sky pixel provides a direct observation of distant lighting in the corresponding direction and, via a neural illumination prior, a statistical cue to derive the remaining illumination environment. The incorporation of our illumination prior is enabled by a novel `outside-in' method for computing differentiable sky visibility based on a neural directional distance function. This is highly efficient and can be trained in parallel with the neural scene representation, allowing gradients from appearance loss to flow from shadows to influence the estimation of illumination and geometry. Our method estimates high-quality albedo, geometry, illumination and sky visibility, achieving state-of-the-art results on the NeRF-OSR relighting benchmark. Our code and models can be found at https://github.com/JADGardner/neusky, Comment: Accepted to ECCV 2024

Inverse rendering is an ill-posed problem. Previous work has sought to resolve this by focussing on priors for object or scene shape or appearance. In this work, we instead focus on a prior for natural illuminations. Current methods rely on spherical harmonic lighting or other generic representations and, at best, a simplistic prior on the parameters. This results in limitations for the inverse setting in terms of the expressivity of the illumination conditions, especially when taking specular reflections into account. We propose a conditional neural field representation based on a variational auto-decoder and a transformer decoder. We extend Vector Neurons to build equivariance directly into our architecture, and leveraging insights from depth estimation through a scale-invariant loss function, we enable the accurate representation of High Dynamic Range (HDR) images. The result is a compact, rotation-equivariant HDR neural illumination model capable of capturing complex, high-frequency features in natural environment maps. Training our model on a curated dataset of 1.6K HDR environment maps of natural scenes, we compare it against traditional representations, demonstrate its applicability for an inverse rendering task and show environment map completion from partial observations. We share our PyTorch implementation, dataset and trained models at https://github.com/JADGardner/ns_reni, Comment: Project Repo - https://github.com/JADGardner/ns_reni. arXiv admin note: substantial text overlap with arXiv:2206.03858

Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving that they generate samples from the correct distribution - is crucial to the use of probabilistic programming languages for statistical modelling and inference. However, the typical denotational semantics of probabilistic programs is incompatible with deterministic notions of sampling. This is problematic, considering that most statistical inference is performed using pseudorandom number generators. We present a higher-order probabilistic programming language centred on the notion of samplers and sampler operations. We give this language an operational and denotational semantics in terms of continuous maps between topological spaces. Our language also supports discontinuous operations, such as comparisons between reals, by using the type system to track discontinuities. This feature might be of independent interest, for example in the context of differentiable programming. Using this language, we develop tools for the formal verification of sampler correctness. We present an equational calculus to reason about equivalence of samplers, and a sound calculus to prove semantic correctness of samplers, i.e. that a sampler correctly targets a given measure by construction., Comment: Extended version of LiCS 2023 paper