重新审视三维重建核作为低通滤波器
Revisiting 3D Reconstruction Kernels as Low-Pass Filters
把 3D 重建核（高斯、指数、Student's t）统一视为低通滤波器，用频域混叠解释重建模糊与高频丢失，并给出 Jinc 与调制核两种可直接替换现有 splatting/辐射场核的即插即用方案，对做新视角合成与高斯泼溅的人是一个可复用的核设计思路。
原文依据 Previous 3D reconstruction kernels, such as Gaussians, Exponential functions, and Student's t distributions, serve as the low pass filters to isolate the baseband spectrum.
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论三维重建旨在从采样得到的离散二维像素中恢复三维信号，目标是收敛到连续的三维空间。本文从信号处理的角度重新审视三维重建，指出由离散采样引起的周期性频谱延拓是其中的根本性挑战。此前的三维重建核，例如高斯、指数函数与 Student's t 分布，都充当隔离基带频谱的低通滤波器。然而，它们非理想的低通特性导致离散时间信号频谱中高频分量与低频分量发生重叠。为此，我们引入 Jinc 核，其幅值在截止频率处瞬时降为零，对应理想低通滤波器。由于 Jinc 核在空域中衰减速度较慢，我们进一步提出调制核以取得有效平衡，通过协调空间效率与频域保真度实现了更优的渲染性能。实验结果验证了 Jinc 核与调制核的有效性。
英文原文摘要 1154 字符
3D reconstruction is to recover 3D signals from the sampled discrete 2D pixels, with the goal to converge continuous 3D spaces.In this paper, we revisit 3D reconstruction from the perspective of signal processing, identifying the periodic spectral extension induced by discrete sampling as the fundamental challenge.Previous 3D reconstruction kernels, such as Gaussians, Exponential functions, and Student's t distributions, serve as the low pass filters to isolate the baseband spectrum.However, their unideal low-pass property results in the overlap of high-frequency components with low-frequency components in the discrete-time signal's spectrum.To this end, we introduce Jinc kernel with an instantaneous drop to zero magnitude exactly at the cutoff frequency, which is corresponding to the ideal low pass filters.As Jinc kernel suffers from low decay speed in the spatial domain, we further propose modulated kernels to strick an effective balance, and achieves superior rendering performance by reconciling spatial efficiency and frequency-domain fidelity.Experimental results have demonstrated the effectiveness of our Jinc and modulated kernels.