深度旋转不变点云聚类网络CluterNet：解决3D对象识别中的旋转不敏感问题

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"CluterNet: Deep Hierarchical Cluster Network with Rigorously Rotation-Invariant Representation for Point Cloud Analysis" 是一篇深入探讨3D对象识别领域中的重要研究论文。随着计算机视觉在三维点云分析中的应用日益广泛，传统的神经网络模型在处理3D旋转不变性问题上表现出了明显的脆弱性。许多现有方法依赖于大量的旋转增强数据来缓解这个问题，但这并不保证模型对旋转的固有不变性。该论文提出了一种创新的点云表示方法，即ClusterNet，它旨在解决这一问题。其核心在于设计了一个严格意义上的旋转不变表示，即使对于不同方向的相同点云，也能被统一且一致地编码。这种新颖的表示方式具有理论上的数学证明，确保了对旋转的严格不变性，使得模型能够不受输入点云朝向的影响，提高识别的稳健性。 ClusterNet的特点是条件信息损失最小，因为它保留了点云中的所有必要信息，仅去除了关于方向或姿态的信息。这使得模型在处理点云数据时，能够更加专注于形状和结构特征，而不会因为旋转变化导致误判。此外，通过深度层次的集群网络架构，ClusterNet还能捕捉到点云内部的复杂结构，并进行有效的聚类和分类，从而实现更准确的物体识别。为了实现这一目标，作者们可能采用了自编码器、卷积神经网络（CNN）或者图神经网络（GNN）等技术，结合旋转不变特征提取方法，如旋转不变特征池化（Rotation-Invariant Pooling，RIP）或局部特征匹配算法，以确保旋转不变性的同时保持点云的局部结构信息。总结来说，这篇论文不仅提出了一个重要的技术突破，还可能包含实验部分，展示了与现有方法在标准的3D基准数据集上的对比结果，以及在各种旋转场景下的性能提升。这对于推动3D计算机视觉，特别是3D物体识别领域的研究有着深远的影响，为后续工作提供了一个强有力的基础，促进了旋转不变的点云分析技术的发展。"

ClusterNet: Deep Hierarchical Cluster Network with Rigorously

Rotation-Invariant Representation for Point Cloud Analysis

Chao Chen

Guanbin Li

1∗

Ruijia Xu

Tianshui Chen

1,2

Meng Wang

Liang Lin

1,2

Sun Yat-sen University

DarkMatter AI Research

Hefei University of Technology

chench227@mail2.sysu.edu.cn, liguanbin@mail.sysu.edu.cn, xurj3@mail2.sysu.edu.cn

tianshuichen@gmail.com, wangmeng@hfut.edu.cn, linliang@ieee.org

Abstract

Current neural networks for 3D object recognition are

vulnerable to 3D rotation. Existing works mostly rely on

massive amounts of rotation-augmented data to alleviate

the problem, which lacks solid guarantee of the 3D rotation

invariance. In this paper, we address the issue by introduc-

ing a novel point cloud representation that can be mathe-

matically proved rigorously rotation-invariant, i.e., identi-

cal point clouds in different orientations are uniﬁed as a

unique and consistent representation. Moreover, the pro-

posed representation is conditional information-lossless,

because it retains all necessary information of point cloud

except for orientation information. In addition, the pro-

posed representation is complementary with existing net-

work architectures for point cloud and fundamentally im-

proves their robustness against rotation transformation. Fi-

nally, we propose a deep hierarchical cluster network called

ClusterNet to better adapt to the proposed representation.

We employ hierarchical clustering to explore and exploit

the geometric structure of point cloud, which is embed-

ded in a hierarchical structure tree. Extensive experimen-

tal results have shown that our proposed method greatly

outperforms the state-of-the-arts in rotation robustness on

rotation-augmented 3D object classiﬁcation benchmarks.

1. Introduction

Rotation transformation is natural and common in 3D

world, however, it gives rise to an intractable challenge for

3D recognization. Theoretically, since SO(3)

is an inﬁnite

∗

Corresponding author is Guanbin Li. This work was supported in part

by the State Key Development Program under Grant 2016YFB1001004,

in part by the National Natural Science Foundation of China under Grant

No.61602533 and No.61702565, in part by the Fundamental Research

Funds for the Central Universities under Grant No.18lgpy63. This work

was also sponsored by SenseTime Research Fund.

3D rotation group, denoted as SO(3), contains all rotation transforma-

tions in R

under the operation of composition.

group, a 3D object possesses rotated clones in inﬁnite atti-

tudes, thus a machine learning model is obliged to extract

features from an extremely huge input space. For exam-

ple, in 3D object classiﬁcation task, the category label of

an object is invariant against arbitrary rotation transforma-

tion in majority situations. However, from the perspective

of a classiﬁcation model, an object and its rotated clone are

distinct in input metric space, hence the model, such as neu-

ral network based methods, should have enough capacity to

learn rotation invariance from data and then approximate a

complex function that maps identical objects in inﬁnite atti-

tudes to similar features in feature metric space.

To alleviate the curse of rotation, a straightforward

method is to design a model with high capacity, such as a

deep neural network with considerable layers, and feed the

model with great amounts of rotation-augmented data [1]

based on a well-designed augmentation pipeline. Although

data augmentation is effective to some extent, it is computa-

tionally expensive in training phase and lacks solid guaran-

tee of rotation robustness. [11, 18] apply spatial transformer

network [5] to canonicalize the input data before feature ex-

traction, which improves the rotation-robustness of model

but still inherits all the defects of the data augmentation.

[16] proposes a rotation-equivariant network for 3D point

clouds using a special convolutional operation with local

rotation invariance as a basic block. The method attempts

to equip the neural network with rotation-symmetry. How-

ever, it is hard to guarantee the capacity of such network to

satisfy all rotation-equivariant constraints in each layer.

We address the issue by introducing a novel Rigorous

Rotation-Invariant (RRI) representation of point cloud.

Identical objects in different orientations are uniﬁed as a

consistent representation, which implies that the input space

is heavily reduced and the 3D recognization tasks become

much easier. It can be mathematically proved that the pro-

posed representation is rigorously rotation-invariant, and

information-lossless under a mild condition. Given any

data point in point cloud and a non-collinear neighbor ar-

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