Direct Optimization of a 3D Finite-Source Reflector via Neural-Network Parameterization
Authors: Roel Hacking, Lisa Kusch, Martijn Anthonissen, Wilbert IJzerman
Organizations: Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands · Signify, High Tech Campus 7, 5656 AE Eindhoven, The Netherlands
Abstract
We present a direct optimization method for three-dimensional freeform reflectors that transform the light of a finite-étendue source into a prescribed far-field angular intensity distribution. The reflector profile is represented by a small neural network (a multilayer perceptron), which is trained end-to-end through a differentiable ray-tracing objective. We furthermore parameterize the emission directions in gnomonic coordinates, and show how we use this to ensure that every emitted ray intersects the reflector. At each iteration, the network is converted to a bicubic spline representation for ray-tracing efficiency, and intersections with this smooth surface are solved by a damped Newton solve, with gradients computed via the implicit function theorem. The traced output distribution is compared with the desired target on a 'soft' histogram, under an H−1-type spectral weighting that emphasizes long-range transport of flux to improve convergence. Optimization is performed using a BFGS method with self-scaled Broyden updates and a plateau-perturbation rule to prevent stalling. The method converges reliably within seconds on a single GPU for all examples tested.
Recent advances in neural scene representations enable photorealistic novel-view synthesis, yet most methods remain tightly coupled to a single rendering paradigm, limiting their versatility and integration with conventional graphics workflows. We introduce Floating Radiance Networks (FlaRe), a neural scene representation combining explicit ray-traceable geometry with continuous neural radiance functions. A scene is represented by floating planar generalized Gaussian primitives, each carrying a compact latent descriptor of a local radiance field. A lightweight decoder shared across the scene maps this descriptor, local surface coordinates, and viewing direction to color and opacity. This formulation preserves the expressiveness of neural fields while providing an explicitly addressable structure that can be efficiently queried and manipulated. Hardware-accelerated primitive intersections enable interactive rendering and recursive ray-tracing, including reflections, refractions, transparency, and shadows. The same representation further supports primitive-level deformation, mesh extraction, and appearance stylization directly in its learned descriptor space. Experiments across standard reconstruction benchmarks demonstrate competitive rendering quality while using a compact set of primitives. Together, these results establish FlaRe as a versatile representation that brings high-fidelity neural rendering, ray-tracing, geometric manipulation, and appearance editing into a unified scene model. Source code is available online. Source code can be found at: https://github.com/KByrski/FlaRe
Krzysztof Byrski, Rafał Tobiasz, Grzegorz Wilczyński +5
We propose a neural formulation for estimating the appearance of complex luminaires. We focus on challenging luminaires with complex light transport (e.g., small emitters enclosed by multiple specular layers) that are difficult for (bidirectional) path tracing. To this end, we use light tracing to construct paths from emitters to the exit surfaces and formulate appearance estimation as a distribution learning problem. Specifically, we model the probability density function (pdf) of outgoing radiance on the exit surfaces using a large normalizing flow network, and recover the outgoing radiance as the product of the estimated pdf and flux. To enable efficient inference, we distill the learned appearance into a lightweight MLP that directly estimates radiance on the exit surfaces. We additionally train a sampling network for effective direct illumination computation from the luminaire, and a blending network to composite the luminaire into the scene. Our formulation makes it feasible to render challenging luminaires using low sample counts in arbitrary scenes.
We introduce a probabilistic splat-based radiance field framework that retains the fast rasterization and test-time efficiency of 3D Gaussian Splatting (3DGS) while replacing heuristic primitive manipulation with gradient-based optimization of a volumetric probability density. Rather than relocating, splitting, or culling Gaussians via hand-tuned densification (e.g., ADC), we treat primitive locations as samples drawn from a persistent, learnable density. We instantiate this density using a novel, memory-efficient multi-scale hierarchical grid that enables end-to-end gradient-based optimization. To stabilize the optimization, we derive an unbiased gradient estimator with control variates that markedly reduces variance. By allowing probability mass to flow to where the loss demands, our framework eliminates brittle priors and naturally explores the volume, achieving state-of-the-art reconstruction quality on mip-NeRF 360 while preserving 3DGS-level rendering speed.
Mia Gaia Polansky, George Kopanas, Stephan Garbin +2