Multilayer perceptrons (MLPs) have been successfully used to represent 3D
shapes implicitly and compactly, by mapping 3D coordinates to the corresponding
signed distance values or occupancy values. In this paper, we propose a novel
positional encoding scheme, called Spline Positional Encoding, to map the input
coordinates to a high dimensional space before passing them to MLPs, for
helping to recover 3D signed distance fields with fine-scale geometric details
from unorganized 3D point clouds. We verified the superiority of our approach
over other positional encoding schemes on tasks of 3D shape reconstruction from
input point clouds and shape space learning. The efficacy of our approach
extended to image reconstruction is also demonstrated and evaluated.

本研究提出了一种新颖的位置编码方案 (Spline Positional Encoding)，将输入坐标映射到高维空间，以帮助从无组织的 3D 点云中恢复带有细节的几何形状，从而进一步验证了该方法在 3D 形状重建和形状空间学习任务中的优势。同时，在图像重建方面也展示并评估了我们方法的功效。