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.

翻译：基于高斯函数的表示方法已能以远低于常规离散体素分布的内存成本实现高效的基于物理的体渲染。然而，若干遗留问题阻碍了其广泛应用。经典体素网格的优势之一在于能够轻松构建层次化表示，无论是通过存储体素多级渐远纹理，还是选择性剪裁已有层次化体素网格的分支。此类策略在需要较低细节层次时能减少渲染时间并消除走样现象。为基于高斯的体数据构建类似策略并非易事。直接解决方案（如预滤波或计算多级渐远式表示）会导致内存需求增加或需对每个层级单独进行昂贵的重新拟合。此外，这类方案无法保证不同层级间平滑过渡。为突破这些限制，我们提出Gabor场——一种由Gabor核函数构成的定向选择性混合模型，能够以零成本实现连续频率滤波。通过选择性剪裁基元来降低资产的频率成分，直接提升渲染性能。除滤波功能外，我们证明了在每次光线递归中从不同频率和方向随机采样，能够遮蔽体数据的显著部分，从而在单次散射与多次散射场景中加速光线遍历过程。进一步地，受程序化体数据启发，我们提出一种将程序化云层作为Gabor噪声调制高斯函数进行高效设计与渲染的应用方案。