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

TL;DR

This work addresses the challenge of applying level-of-detail (LOD) techniques to Gaussian-based volumetric representations by introducing Gabor Fields, an orientation-selective, spectrally bounded mixture of Gaussian and Gabor kernels. It combines a 3D anisotropic Gabor kernel with a hierarchical, differentiable regression pipeline to distill voxel grids into compact, multi-band representations that support continuous LOD without extra memory, using analytic line integrals and stochastic rendering strategies to accelerate path tracing with multiple scattering. The key contributions include closed-form transmittance integrals for Gabor kernels, a regression framework that optimizes Gaussian bases plus Gabor residuals, and several acceleration techniques (stochastic Laplacian/path tracing, orientation-based masking, and adaptive clamping) that yield substantial speedups while maintaining quality. The approach enables efficient LOD, foveated rendering, motion blur, and procedural cloud authoring, with demonstrated compression and rendering performance improvements over prior Gaussian primitives and voxel-based methods, and lays groundwork for integration with radiance fields and wavelet-inspired representations.

Abstract

Gaussian-based representations have enabled efficient physically-based volume rendering at a fraction of the memory cost of regular, discrete, voxel-based distributions. However, several remaining issues hamper their widespread use. One of the advantages of classic voxel grids is the ease of constructing hierarchical representations by either storing volumetric mipmaps or selectively pruning branches of an already hierarchical voxel grid. Such strategies reduce rendering time and eliminate aliasing when lower levels of detail are required. Constructing similar strategies for Gaussian-based volumes is not trivial. Straightforward solutions, such as prefiltering or computing mipmap-style representations, lead to increased memory requirements or expensive re-fitting of each level separately. Additionally, such solutions do not guarantee a smooth transition between different hierarchy levels. To address these limitations, we propose Gabor Fields, an orientation-selective mixture of Gabor kernels that enables continuous frequency filtering at no cost. The frequency content of the asset is reduced by selectively pruning primitives, directly benefiting rendering performance. Beyond filtering, we demonstrate that stochastically sampling from different frequencies and orientations at each ray recursion enables masking substantial portions of the volume, accelerating ray traversal time in single- and multiple-scattering settings. Furthermore, inspired by procedural volumes, we present an application for efficient design and rendering of procedural clouds as Gabor-noise-modulated Gaussians.

Figures (14)

• Figure 1: Comparison of different LOD strategies for primitive-based volumetric representations. In each cell, we show the volume rendering and the corresponding power spectra of the Fourier Transform. Note how, in our method, Gabor Pruning and Gaussian Analytic, the spectra shrink for higher LOD levels. In our case, however, the higher levels consist of a substantially smaller number of primitives, while each level of Gaussian Analytic contains the same number of primitives. A simple Gaussian Pruning fails to create LOD levels with a low-pass characteristic.
• Figure 2: Top: 2D Gabor kernels in the spatial domain with different frequency magnitudes. Bottom: their respective power-spectrum representations. Gabor kernels exhibit directional attenuation, effectively modelling residuals in certain frequencies and orientations. As we clip their support to $3\sigma$, we can estimate at which orientations, relative to the integrating ray, their contribution decays enough to be considered (shaded area). In our work, we leverage this insight to extract performance by masking non-contributing Gabor kernels before an intersection query is even traced.
• Figure 3: Visualization of the integral over a plane of a 3D Gabor kernel at different rotations around the Y axis. As we can see, projected frequency and integral magnitude both depend on orientation. In the limit, integrating along its modulation plane causes destructive interference that attenuates the integral value significantly. Higher frequencies see their contributions decay even faster angularly, and to smaller integral magnitudes, as we show in our 2D example in Figure \ref{['fig:selectivity_spectral']}.
• Figure 4: Scalability evaluation of Gabor-based representations on the Tornado dataset. The primitive count ranged from 1,024 to 32,768, with an additional 768 base Gaussian primitives. PSNR was measured with respect to the original voxel grid, and runtime was averaged over 50 runs. Storage costs assume 32-bit floating-point precision without compression. Measured on an RTX 4090.
• Figure 5: Quality vs rendering time with the different stochastic-analytical estimators (see Appendix Table \ref{['tab:stochastic_sampling_strats']}). Starting from 1spp, each dot represents powers-of-two extra samples per pixel (1,2,4,8,etc).