Various recent methods attempt to implement rotation-invariant 3D deep
learning by replacing the input coordinates of points with relative distances
and angles. Due to the incompleteness of these low-level features, they have to
undertake the expense of losing global information. In this paper, we propose
the CRIN, namely Centrifugal Rotation-Invariant Network. CRIN directly takes
the coordinates of points as input and transforms local points into
rotation-invariant representations via centrifugal reference frames. Aided by
centrifugal reference frames, each point corresponds to a discrete rotation so
that the information of rotations can be implicitly stored in point features.
Unfortunately, discrete points are far from describing the whole rotation
space. We further introduce a continuous distribution for 3D rotations based on
points. Furthermore, we propose an attention-based down-sampling strategy to
sample points invariant to rotations. A relation module is adopted at last for
reinforcing the long-range dependencies between sampled points and predicts the
anchor point for unsupervised rotation estimation. Extensive experiments show
that our method achieves rotation invariance, accurately estimates the object
rotation, and obtains state-of-the-art results on rotation-augmented
classification and part segmentation. Ablation studies validate the
effectiveness of the network design.

本篇论文提出了一种基于离心参考帧的旋转不变网络，将点云坐标作为输入，并通过离心参考帧将局部点变换为旋转不变表示，再基于离散点提出了连续的三维旋转分布，并引入了基于注意力机制的下采样策略，通过学习长距离依赖关系进而实现无监督旋转估计，在旋转不变、对象旋转估计以及旋转增强分类和部分划分等方面取得了最先进的结果。

CRIN：基于离心参考系的旋转不变点云分析与旋转估计

CRIN: Rotation-Invariant Point Cloud Analysis and Rotation Estimation  via Centrifugal Reference Frame

Recent interest in point cloud analysis has led rapid progress in designing
deep learning methods for 3D models. However, state-of-the-art models are not
robust to rotations, which remains an unknown prior to real applications and
harms the model performance. In this work, we introduce a novel Patch-wise
Rotation-invariant network (PaRot), which achieves rotation invariance via
feature disentanglement and produces consistent predictions for samples with
arbitrary rotations. Specifically, we design a siamese training module which
disentangles rotation invariance and equivariance from patches defined over
different scales, e.g., the local geometry and global shape, via a pair of
rotations. However, our disentangled invariant feature loses the intrinsic pose
information of each patch. To solve this problem, we propose a
rotation-invariant geometric relation to restore the relative pose with
equivariant information for patches defined over different scales. Utilising
the pose information, we propose a hierarchical module which implements
intra-scale and inter-scale feature aggregation for 3D shape learning.
Moreover, we introduce a pose-aware feature propagation process with the
rotation-invariant relative pose information embedded. Experiments show that
our disentanglement module extracts high-quality rotation-robust features and
the proposed lightweight model achieves competitive results in rotated 3D
object classification and part segmentation tasks. Our project page is released
at: this https URL

本研究介绍了一种新颖的 Patch-wise Rotation-invariant 网格，通过 Feature Disentanglement 实现旋转不变性，并且 Propose 了一个 Rotation-Invariant Geometric Relation 来还原每个 Patch 的相对位姿信息，在 3D 模型分类和部分分割任务方面实现了有竞争力的结果。

PaRot: 基于特征解耦和姿态恢复的小块旋转不变网络

PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement  and Pose Restoration

Emerging from low-level vision theory, steerable filters found their
counterpart in prior work on steerable convolutional neural networks
equivariant to rigid transformations. In our work, we propose a steerable
feed-forward learning-based approach that consists of neurons with spherical
decision surfaces and operates on point clouds. Such spherical neurons are
obtained by conformal embedding of Euclidean space and have recently been
revisited in the context of learning representations of point sets. Focusing on
3D geometry, we exploit the isometry property of spherical neurons and derive a
3D steerability constraint. After training spherical neurons to classify point
clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate
the neurons and construct rotation-equivariant spherical filter banks. We then
apply the derived constraint to interpolate the filter bank outputs and, thus,
obtain a rotation-invariant network. Finally, we use a synthetic point set and
real-world 3D skeleton data to verify our theoretical findings. The code is
available at this https URL

该论文提出了一种可定向前馈的学习方法，利用球面神经元对点云进行分类，得到具有旋转等变性的滤波器组建网络，利用三角形基础来推导滤波器并构建旋转等变性的球形滤波器组。