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.

翻译：三维重建旨在从采样的离散二维像素中恢复三维信号，其目标是收敛于连续的三维空间。本文从信号处理的角度重新审视三维重建，将离散采样引起的周期性频谱延拓识别为根本性挑战。以往的三维重建核，如高斯函数、指数函数和学生t分布，均作为低通滤波器用于分离基带频谱。然而，其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混叠。为此，我们引入Jinc核，其在截止频率处具有瞬时降为零的幅度特性，对应于理想的低通滤波器。由于Jinc核在空间域存在衰减速度较慢的问题，我们进一步提出调制核以实现有效的平衡，并通过协调空间效率与频域保真度获得了优越的渲染性能。实验结果验证了我们提出的Jinc核与调制核的有效性。