用更优的低通滤波器提升3D重建精度。
Revisiting 3D Reconstruction Kernels as Low-Pass Filters
- 从信号处理角度重看3D重建，将采样周期性扩展视为核心挑战。
- 引入Jinc核实现理想低通特性，有效分离高低频成分。
- 提出调制核，在空间效率与频域保真间取得更好平衡。
3D重建旨在从离散2D像素中恢复连续3D信号。本文从信号处理视角重新审视该问题，指出离散采样引起的周期性频谱扩展是根本挑战。传统3D重建核如高斯、指数函数和学生t分布虽具低通特性，但非理想，导致高频分量与低频分量在离散信号频谱中重叠。为此，本文引入Jinc核，其在截止频率处瞬时降为零，符合理想低通滤波器特征。由于Jinc核在空间域衰减缓慢，进一步提出调制核以兼顾空间效率与频域保真度，实验验证了其优越的渲染性能。
原文摘要 · Abstract (English)
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.
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