用点云混合高斯提升神经场压缩效率，重建质量不降。
Lagrangian Hashing for Compressed Neural Field Representations
- 在即时NGP的哈希表中嵌入带影响场的点，融合网格与点表示优势。
- 新损失函数引导高斯点向需更高精度区域迁移，优化资源分配。
- 压缩后重建效果媲美原始模型，适合高效神经场存储与推理。
我们提出拉格朗日哈希（Lagrangian Hashing），一种结合快速训练神经辐射场方法（如InstantNGP）与基于带特征点表示方法（如3D Gaussian Splatting或PointNeRF）优点的神经场表示。通过将点表示引入InstantNGP的分层哈希表的高分辨率层，实现信息高效编码。由于这些点具有影响场，该表示可被解释为存储于哈希表中的高斯混合模型。我们设计了一种损失函数，促使高斯点向需要更多表示预算的区域移动以更充分表达。主要发现是，该表示可在不牺牲质量的前提下，实现信号的更紧凑重构。
原文摘要 · Abstract (English)
We present Lagrangian Hashing, a representation for neural fields combining the characteristics of fast training NeRF methods that rely on Eulerian grids (i.e.~InstantNGP), with those that employ points equipped with features as a way to represent information (e.g. 3D Gaussian Splatting or PointNeRF). We achieve this by incorporating a point-based representation into the high-resolution layers of the hierarchical hash tables of an InstantNGP representation. As our points are equipped with a field of influence, our representation can be interpreted as a mixture of Gaussians stored within the hash table. We propose a loss that encourages the movement of our Gaussians towards regions that require more representation budget to be sufficiently well represented. Our main finding is that our representation allows the reconstruction of signals using a more compact representation without compromising quality.
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