Gabor Fields: Orientation-Selective Level-of-Detail for Volume Rendering

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Gabor Fields: Orientation-Selective Level-of-Detail for Volume Rendering

Gabor Fields: Orientation-Selective Level-of-Detail for Volume Rendering

ACM Transactions on Graphics (SIGGRAPH 2026)

Jorge Condor1,*<br>Nicolai Hermann1,*<br>Mehmet Ata Yurtsever1<br>Piotr Didyk1

*Equal effort.<br>1Università della Svizzera italiana (USI), Lugano, Switzerland

Level-of-detail decomposition of a Gabor Field: frequency- and orientation-selectivity lets us mask particle collections at render time for continuous LOD, faster rendering, and a controllable bias–variance trade-off when sample cost matters. OpenVDB volumetric Bunny.

arXiv<br>Paper PDF<br>Code<br>Slides

Gaussian-based volumetric representations make physically based rendering<br>practical at a fraction of the memory and runtime cost of dense voxel grids,<br>but level-of-detail (LOD) remains inefficient: prefiltering or<br>mipmap-style Gaussians costs extra memory, requires re-fitting per level, and<br>can produce harsh transitions between LODs. We introduce Gabor Fields :<br>mixtures of primitive anisotropic Gabor kernels (Gaussian envelopes with<br>harmonic modulation). Since each kernel lives in a known frequency band,<br>filtering becomes a matter of pruning primitives . Combined with analytic line integrals and a<br>hierarchical fitting procedure, this yields continuous LOD, stochastic masking<br>along rays for cheaper single- and multiple-scattering traversal, and easy<br>integration within volumetric path tracing frameworks.

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TL;DR : an alternative to Gaussian kernels that achieves ~2 dB higher PSNR<br>at equal primitive count and renders up to ~1.4&times; faster at equal variance, provides<br>free runtime level-of-detail , and plugs into control-variate theory for even further<br>acceleration (an extra ~2&times; or more), all while keeping the two orders of magnitude compression<br>over voxel grids of Don't Splat your Gaussians.

The anisotropic Gabor kernel

Each anisotropic Gabor primitive is a Gaussian envelope with a cosine planar wave. A plain<br>Gaussian is a special case of the anisotropic Gabor where the<br>modulation frequency &omega; is zero. In the Fourier domain the kernel is two<br>symmetric lobes at &plusmn;&omega;, so unlike a Gaussian its spectrum is<br>concentrated in a specific frequency band and a specific orientation rather than<br>spilling across all frequencies.

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Gabor Fields

A Gabor Field is a single continuous decomposition: a low-pass, high-density<br>volume of Gaussians (zero-&omega; Gabors), plus a residual of Gabor<br>kernels carrying the higher frequencies. Since we can analytically compute each kernel's power spectrum, filtering<br>becomes simply removing the kernels that do not contribute meaningfully at the desired cutoff frequency.

Continuous LOD from a single asset

Gabor Fields enable filtering volumes in a completely continuous manner: as the frequency cutoff<br>shrinks, kernels are masked before tracing, making rendering faster, with<br>no popping, no re-fitting, and no extra storage (no mipmaps, no pyramids).

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Orientation selectivity and ray-space masking

Gabors are also directional. As a ray aligns with a kernel's wave direction, its<br>positive and negative lobes cancel and the contribution collapses. We exploit this<br>by splitting each frequency band into oriented, steerable sub-bands, so<br>kernels that cannot contribute to a ray are masked before any intersection.

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Contribution collapses as the ray aligns with &omega; (left); each frequency band splits into steerable, oriented sub-bands (right).

Gaussians as control variates

A Gabor Field stacks a low-frequency Gaussian base and a series of<br>higher-frequency Gabor residuals that layer together into the full signal, and the<br>base alone already carries most of the density. We can leverage this to accelerate rendering.

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The low-pass base is an ideal control variate . We develop a series of stochastic-analytic estimators,<br>where we always trace and analytically integrate the Gaussian base (~2% of the total primitives),<br>and at each sample stochastically select which Gabor residuals to include . Crucially,<br>every selected Gabor is still integrated in closed form : variance only comes from selecting<br>which kernels we trace against. That choice is free: we can<br>prioritise by frequency band, by contribution, or by perceptual importance (foveation-aware<br>or blue-noise style), accelerating rendering with little variance (absorbing mediums) or bias (scattering mediums).

The objective in the end is reducing the main bottleneck of primitive volume rendering: the<br>number of intersections per ray.

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