Learning to predict reliable characteristic orientations of 3D point clouds
is an important yet challenging problem, as different point clouds of the same
class may have largely varying appearances. In this work, we introduce a novel
method to decouple the shape geometry and semantics of the input point cloud to
achieve both stability and consistency. The proposed method integrates
shape-geometry-based SO(3)-equivariant learning and shape-semantics-based
SO(3)-invariant residual learning, where a final characteristic orientation is
obtained by calibrating an SO(3)-equivariant orientation hypothesis using an
SO(3)-invariant residual rotation. In experiments, the proposed method not only
demonstrates superior stability and consistency but also exhibits
state-of-the-art performances when applied to point cloud part segmentation,
given randomly rotated inputs.

本文提出了一种新颖的方法，通过将输入的 3D 点云的形状几何与语义学分离，来实现特征取向的稳定性和一致性，该方法将形状几何基于 SO（3）等变学习和形状语义基于 SO（3）不变残差学习相结合，通过校准 SO（3）等变定向假设来获得最终的特征定向。在实验中，该方法不仅展现出卓越的稳定性和一致性，而且在给定随机旋转输入的点云部分分割时也表现出最新的性能。

通过不变残差学习稳定一致地预测三维特征方向

Stable and Consistent Prediction of 3D Characteristic Orientation via  Invariant Residual Learning

The ability to generate novel, diverse, and realistic 3D shapes along with
associated part semantics and structure is central to many applications
requiring high-quality 3D assets or large volumes of realistic training data. A
key challenge towards this goal is how to accommodate diverse shape variations,
including both continuous deformations of parts as well as structural or
discrete alterations which add to, remove from, or modify the shape
constituents and compositional structure. Such object structure can typically
be organized into a hierarchy of constituent object parts and relationships,
represented as a hierarchy of n-ary graphs. We introduce StructureNet, a
hierarchical graph network which (i) can directly encode shapes represented as
such n-ary graphs; (ii) can be robustly trained on large and complex shape
families; and (iii) can be used to generate a great diversity of realistic
structured shape geometries. Technically, we accomplish this by drawing
inspiration from recent advances in graph neural networks to propose an
order-invariant encoding of n-ary graphs, considering jointly both part
geometry and inter-part relations during network training. We extensively
evaluate the quality of the learned latent spaces for various shape families
and show significant advantages over baseline and competing methods. The
learned latent spaces enable several structure-aware geometry processing
applications, including shape generation and interpolation, shape editing, or
shape structure discovery directly from un-annotated images, point clouds, or
partial scans.

StructureNet 是一种基于层次图网络的生成模型，可以对以各种方式变形、修改的 3D 形状进行编码。它可以用于生成大量逼真的结构形状几何，也可以通过从未标记的图像、点云或部分扫描中直接发现形状结构，同时还能够用于形状生成、插值和编辑。