Maximum Entropy Encoding of Energy-Weighted Spherical Moments

A new rendering technique tackles a familiar problem in lighting pipelines: how to store directional energy compactly without introducing negative lobes or unstable reconstructions. The approach encodes non-negative Monte Carlo path samples as energy-weighted directional features, then uses a maximum-entropy closure to rebuild a positive irradiance distribution from a small set of moments.

The core representation keeps total energy, the first directional moment, and the traceless second moment, giving a 1+3+5 statistic set that stays linearly additive and rotationally covariant. In the full formulation, the reconstructed density takes the form p(r,u) ∝ exp(-β r g(u)), with directional probability and angular energy density proportional to g^-3 and g^-4. When the minimum of g stays positive, the reconstruction is normalizable and strictly non-negative.

For developers, the practical appeal is obvious: fewer artifacts from negative irradiance, better behavior on strongly directional lighting, and a path to compact storage that still supports analytic moment matching, inverse sampling, and closed-form diffuse response in some subfamilies. The paper also spells out realizability domains and LUT-friendly reconstruction for a coaxial five-parameter variant, which makes it easier to imagine integration into real-time or offline lighting systems.

On 981 Poly Haven HDRI 2K scenes plus three Debevec probes, the five-parameter MaxEnt variant won 78.7% of scenes against stored QZH and reduced mean luminance RMSE by 15.8%. Full second-order SH-2 still had the lowest overall error,...