Largely due to their implicit nature, neural fields lack a direct mechanism
for filtering, as Fourier analysis from discrete signal processing is not
directly applicable to these representations. Effective filtering of neural
fields is critical to enable level-of-detail processing in downstream
applications, and support operations that involve sampling the field on regular
grids (e.g. marching cubes). Existing methods that attempt to decompose neural
fields in the frequency domain either resort to heuristics or require extensive
modifications to the neural field architecture. We show that via a simple
modification, one can obtain neural fields that are low-pass filtered, and in
turn show how this can be exploited to obtain a frequency decomposition of the
entire signal. We demonstrate the validity of our technique by investigating
level-of-detail reconstruction, and showing how coarser representations can be
computed effectively.

通过简单修改，我们可以获得经过低通滤波的神经场，并展示如何利用此技术获得整个信号的频率分解，从而有效地计算出更粗糙的表示形式。

BANF：用于详细层次重建的带限神经场模型

BANF: Band-limited Neural Fields for Levels of Detail Reconstruction

Increasing the accuracy of instance segmentation methods is often done at the
expense of speed. Using coarser representations, we can reduce the number of
parameters and thus obtain real-time masks. In this paper, we take inspiration
from the set cover problem to predict mask approximations. Given ground-truth
binary masks of objects of interest as training input, our method learns to
predict the approximate coverage of these objects by disks without supervision
on their location or radius. Each object is represented by a fixed number of
disks with different radii. In the learning phase, we consider the radius as
proportional to a standard deviation in order to compute the error to propagate
on a set of two-dimensional Gaussian functions rather than disks. We trained
and tested our instance segmentation method on challenging datasets showing
dense urban settings with various road users. Our method achieve state-of-the
art results on the IDD and KITTI dataset with an inference time of 0.040 s on a
single RTX 3090 GPU.

该研究论文提出了一种使用较粗表示方法的实例分割方法，以在保持实时性的前提下提高准确性，通过学习预测目标对象的近似覆盖范围，采用固定数量和不同半径的圆盘来表示每个对象，并使用二维高斯函数代替圆盘进行误差传播计算。该方法在具有各种道路用户的复杂城市环境下，在 IDD 和 KITTI 数据集上实现了最先进的结果，单个 RTX 3090 GPU 推断时间为 0.040 秒。