Point set is a flexible and lightweight representation widely used for 3D
deep learning. However, their discrete nature prevents them from representing
continuous and fine geometry, posing a major issue for learning-based shape
generation. In this work, we turn the discrete point sets into smooth surfaces
by introducing the well-known implicit moving least-squares (IMLS) surface
formulation, which naturally defines locally implicit functions on point sets.
We incorporate IMLS surface generation into deep neural networks for inheriting
both the flexibility of point sets and the high quality of implicit surfaces.
Our IMLSNet predicts an octree structure as a scaffold for generating MLS
points where needed and characterizes shape geometry with learned local priors.
Furthermore, our implicit function evaluation is independent of the neural
network once the MLS points are predicted, thus enabling fast runtime
evaluation. Our experiments on 3D object reconstruction demonstrate that
IMLSNets outperform state-of-the-art learning-based methods in terms of
reconstruction quality and computational efficiency. Extensive ablation tests
also validate our network design and loss functions.

本研究使用 IMLS 将点云转化为光滑曲面，进而结合深度神经网络进行图形生成，实现了从点云到光滑曲面再到形状生成的流程，实验表明该方法在重建质量和计算效率方面优于当前最先进的学习方法。

基于深度隐式移动最小二乘函数的三维重构

Deep Implicit Moving Least-Squares Functions for 3D Reconstruction

Recent deep networks that directly handle points in a point set, e.g.,
PointNet, have been state-of-the-art for supervised learning tasks on point
clouds such as classification and segmentation. In this work, a novel
end-to-end deep auto-encoder is proposed to address unsupervised learning
challenges on point clouds. On the encoder side, a graph-based enhancement is
enforced to promote local structures on top of PointNet. Then, a novel
folding-based decoder deforms a canonical 2D grid onto the underlying 3D object
surface of a point cloud, achieving low reconstruction errors even for objects
with delicate structures. The proposed decoder only uses about 7% parameters of
a decoder with fully-connected neural networks, yet leads to a more
discriminative representation that achieves higher linear SVM classification
accuracy than the benchmark. In addition, the proposed decoder structure is
shown, in theory, to be a generic architecture that is able to reconstruct an
arbitrary point cloud from a 2D grid. Our code is available at
this http URL

本文提出了一个新的端到端深度自编码器来解决点云上无监督学习的挑战，其中在编码器端强制进行了基于图的增强以促进 PointNet 的局部结构，并且通过新颖的基于折叠的解码器将一个规范化的 2D 网格变形到点云的底层 3D 对象表面上，从而实现了低重建误差。