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.
我们提出了Lagrangian Hashing，这是一种神经场的表示方法，结合了基于欧拉网格的快速训练NeRF方法（如InstantNGP）与那些使用带有特征点来表示信息的方法（如3D高斯分裂或PointNeRF）的特点。我们通过将基于点的表示引入InstantNGP层次化哈希表的高分辨率层中实现这一目标。由于我们的点带有影响域，这种表示可以解释为存储在哈希表中的高斯混合体。我们提出了一种损失函数，鼓励这些高斯向需要更多表示预算的区域移动，以确保这些区域能够得到充分表示。我们的主要发现是，这种表示方法能够在不损失质量的情况下，使用更加紧凑的表示来重建信号。