Most 3D shape completion approaches rely heavily on partial-complete shape
pairs and learn in a fully supervised manner. Despite their impressive
performances on in-domain data, when generalizing to partial shapes in other
forms or real-world partial scans, they often obtain unsatisfactory results due
to domain gaps. In contrast to previous fully supervised approaches, in this
paper we present ShapeInversion, which introduces Generative Adversarial
Network (GAN) inversion to shape completion for the first time. ShapeInversion
uses a GAN pre-trained on complete shapes by searching for a latent code that
gives a complete shape that best reconstructs the given partial input. In this
way, ShapeInversion no longer needs paired training data, and is capable of
incorporating the rich prior captured in a well-trained generative model. On
the ShapeNet benchmark, the proposed ShapeInversion outperforms the SOTA
unsupervised method, and is comparable with supervised methods that are learned
using paired data. It also demonstrates remarkable generalization ability,
giving robust results for real-world scans and partial inputs of various forms
and incompleteness levels. Importantly, ShapeInversion naturally enables a
series of additional abilities thanks to the involvement of a pre-trained GAN,
such as producing multiple valid complete shapes for an ambiguous partial
input, as well as shape manipulation and interpolation.

本研究提出了一种新的 3D 形状自动完成方法 ShapeInversion，它采用了生成性对抗网络（GAN）和无监督学习方法，无需配对数据，可实现对模型的形状操纵和插值。在测试中，该方法在特定于域的测试数据上表现出色，同时表现出对现实世界下不同形式和不完整程度的偏见现象具有鲁棒性。

通过 GAN 反推进行无监督的三维形状补全

Unsupervised 3D Shape Completion through GAN Inversion

Implicit surface representations, such as signed-distance functions, combined
with deep learning have led to impressive models which can represent detailed
shapes of objects with arbitrary topology. Since a continuous function is
learned, the reconstructions can also be extracted at any arbitrary resolution.
However, large datasets such as ShapeNet are required to train such models. In
this paper, we present a new mid-level patch-based surface representation. At
the level of patches, objects across different categories share similarities,
which leads to more generalizable models. We then introduce a novel method to
learn this patch-based representation in a canonical space, such that it is as
object-agnostic as possible. We show that our representation trained on one
category of objects from ShapeNet can also well represent detailed shapes from
any other category. In addition, it can be trained using much fewer shapes,
compared to existing approaches. We show several applications of our new
representation, including shape interpolation and partial point cloud
completion. Due to explicit control over positions, orientations and scales of
patches, our representation is also more controllable compared to object-level
representations, which enables us to deform encoded shapes non-rigidly.

本文提出了一种基于 patch 的中层面向对象表示方法，将不同类别对象的相似性建模在 patch 级别，使模型更具有通用性，并且提出了一种新的在规范空间中学习 patch 表示的方法，该表示方法对物体的类别不敏感，在训练时只需要较少的数据集，在形状插值和局部点云完成等应用上也有良好的效果。

PatchNets：基于局部块的通用深度隐式 3D 形状表征

PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape  Representations

This paper proposes a learning-based framework for reconstructing 3D shapes
from functional operators, compactly encoded as small-sized matrices. To this
end we introduce a novel neural architecture, called OperatorNet, which takes
as input a set of linear operators representing a shape and produces its 3D
embedding. We demonstrate that this approach significantly outperforms previous
purely geometric methods for the same problem. Furthermore, we introduce a
novel functional operator, which encodes the extrinsic or pose-dependent shape
information, and thus complements purely intrinsic pose-oblivious operators,
such as the classical Laplacian. Coupled with this novel operator, our
reconstruction network achieves very high reconstruction accuracy, even in the
presence of incomplete information about a shape, given a soft or functional
map expressed in a reduced basis. Finally, we demonstrate that the
multiplicative functional algebra enjoyed by these operators can be used to
synthesize entirely new unseen shapes, in the context of shape interpolation
and shape analogy applications.

本文提出了一种基于学习的框架来从实际操作符编码的小型矩阵中重建三维形状，并引入了一种名为 OperatorNet 的新型神经网络，该网络以表示形状的一组线性操作符作为输入，并生成其 3D 嵌入。我们展示了这种方法在同一问题的纯几何方法中具有明显的优势，并演示了如何使用这些操作符合成全新的未见过的形状，并将其应用于形状插值和类比应用中。