We propose a general method for deep learning based point cloud analysis, which is invariant to rotation on the inputs. Classical methods are vulnerable to rotation, as they usually take aligned point clouds as input. Principle Component Analysis (PCA) is a practical approach to achieve rotation invariance. However, there are still some gaps between theory and practical algorithms. In this work, we present a thorough study on designing rotation invariant algorithms for point cloud analysis. We first formulate it as a permutation invariant problem, then propose a general framework which can be combined with any backbones. Our method is beneficial for further research such as 3D pre-training and multi-modal learning. Experiments show that our method has considerable or better performance compared to state-of-the-art approaches on common benchmarks. Code is available at https://github.com/luoshuqing2001/RI_framework.
Point cloud classifiers with rotation robustness have been widely discussed in the 3D deep learning community. Most proposed methods either use rotation invariant descriptors as inputs or try to design rotation equivariant networks. However, robust models generated by these methods have limited performance under clean aligned datasets due to modifications on the original classifiers or input space. In this study, for the first time, we show that the rotation robustness of point cloud classifiers can also be acquired via adversarial training with better performance on both rotated and clean dat…
National University of Singapore（新加坡国立大学）；Temasek Laboratories（淡马锡实验室）
Despite the recent active research on processing point clouds with deep networks, few attention has been on the sensitivity of the networks to rotations. In this paper, we propose a deep learning architecture that achieves discrete $\mathbf{SO}(2)$/$\mathbf{SO}(3)$ rotation equivariance for point cloud recognition. Specifically, the rotation of an input point cloud with elements of a rotation group is similar to shuffling the feature vectors generated by our approach. The equivariance is easily reduced to invariance by eliminating the permutation with operations such as maximum or average. Our…
Xi’an Jiaotong University（西安交通大学）；Technical University of Munich（慕尼黑工业大学）；Google（谷歌）
In this paper we propose a rotation-invariant deep network for point clouds analysis. Point-based deep networks are commonly designed to recognize roughly aligned 3D shapes based on point coordinates, but suffer from performance drops with shape rotations. Some geometric features, e.g., distances and angles of points as inputs of network, are rotation-invariant but lose positional information of points. In this work, we propose a novel deep network for point clouds by incorporating positional information of points as inputs while yielding rotation-invariance. The network is hierarchical and re…
Singapore University of Technology and Design（新加坡科技设计大学）；The University of Tokyo（东京大学）；Hong Kong University of Science and Technology（香港科技大学）
Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks being trained with data augmented with rotations. In this paper, we introduce a novel convolution operator for point clouds that achieves rotation invariance. Our core idea is to use low-level rotation invariant geometric features such as distances and angles to design a convolution operator for point cloud learning. The well-known point ordering problem is …
Renmin University of China（中国人民大学）；Nanjing University of Science and Technology（南京理工大学）；Tsinghua University（清华大学）
Point cloud-based large scale place recognition is an important but challenging task for many applications such as Simultaneous Localization and Mapping (SLAM). Taking the task as a point cloud retrieval problem, previous methods have made delightful achievements. However, how to deal with catastrophic collapse caused by rotation problems is still under-explored. In this paper, to tackle the issue, we propose a novel Point Cloud-based Rotation-aware Large Scale Place Recognition Network (RPR-Net). In particular, to solve the problem, we propose to learn rotation-invariant features in three ste…
Point cloud analysis is an area of increasing interest due to the development of 3D sensors that are able to rapidly measure the depth of scenes accurately. Unfortunately, applying deep learning techniques to perform point cloud analysis is non-trivial due to the inability of these methods to generalize to unseen rotations. To address this limitation, one usually has to augment the training data, which can lead to extra computation and require larger model complexity. This paper proposes a new neural network called the Aligned Edge Convolutional Neural Network (AECNN) that learns a feature rep…
School of Computer Science, University of Sydney（悉尼大学计算机科学学院）
Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks for invariance have seldom been looked into. In this work, we review rotation invariance in terms of point cloud registration and propose an effective framework for rotation invariance learning via three sequential stages, namely rotation-invariant shape encoding, aligned feature integration, and deep feature registration. We first encode shape descriptors co…
Rotation estimation of known rigid objects is important for robotic applications such as dexterous manipulation. Most existing methods for rotation estimation use intermediate representations such as templates, global or local feature descriptors, or object coordinates, which require multiple steps in order to infer the object pose. We propose to directly regress a pose vector from raw point cloud segments using a convolutional neural network. Experimental results show that our method can potentially achieve competitive performance compared to a state-of-the-art method, while also showing more…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Many recent works show that a spatial manipulation module could boost the performances of deep neural networks (DNNs) for 3D point cloud analysis. In this paper, we aim to provide an insight into spatial manipulation modules. Firstly, we find that the smaller the rotational degree of freedom (RDF) of objects is, the more easily these objects are handled by these DNNs. Then, we investigate the effect of the popular T-Net module and find that it could not reduce the RDF of objects. Motivated by the above two issues, we propose a rotation transformation network for point cloud analysis, called RT…
SHReg: Strictly Rotation-Equivariant Point Cloud Registration via Spherical Harmonics
College of Mathematics and Systems Science, Shandong University of Science and Technology（山东科技大学数学与系统科学学院）；School of Artificial Intelligence, Shandong Women’s University（山东女子学院人工智能学院）
Huazhong University of Science and Technology（华中科技大学）；Northwestern Polytechnical University（西北工业大学）；West Virginia University（西弗吉尼亚大学）
Point cloud analysis is a fundamental task in 3D computer vision. Most previous works have conducted experiments on synthetic datasets with well-aligned data; while real-world point clouds are often not pre-aligned. How to achieve rotation invariance remains an open problem in point cloud analysis. To meet this challenge, we propose a novel approach toward achieving rotation-invariant (RI) representations by combining local geometry with global topology. In our local-global-representation (LGR)-Net, we have designed a two-branch network where one stream encodes local geometric RI features and …
We propose a local-to-global representation learning algorithm for 3D point cloud data, which is appropriate to handle various geometric transformations, especially rotation, without explicit data augmentation with respect to the transformations. Our model takes advantage of multi-level abstraction based on graph convolutional neural networks, which constructs a descriptor hierarchy to encode rotation-invariant shape information of an input object in a bottom-up manner. The descriptors in each level are obtained from a neural network based on a graph via stochastic sampling of 3D points, which…
Point-cloud is an efficient way to represent 3D world. Analysis of point-cloud deals with understanding the underlying 3D geometric structure. But due to the lack of smooth topology, and hence the lack of neighborhood structure, standard correlation can not be directly applied on point-cloud. One of the popular approaches to do point correlation is to partition the point-cloud into voxels and extract features using standard 3D correlation. But this approach suffers from sparsity of point-cloud and hence results in multiple empty voxels. One possible solution to deal with this problem is to lea…
Technical University of Munich（慕尼黑工业大学）；The Hong Kong Polytechnic University（香港理工大学）；Tongji University（同济大学）
Registration is a fundamental but critical task in point cloud processing, which usually depends on finding element correspondence from two point clouds. However, the finding of reliable correspondence relies on establishing a robust and discriminative description of elements and the correct matching of corresponding elements. In this letter, we develop a coarse-to-fine registration strategy, which utilizes rotation-invariant features and a new weighted graph matching method for iteratively finding correspondence. In the graph matching method, the similarity of nodes and edges in Euclidean and…
Point cloud registration is a fundamental step for many tasks. In this paper, we propose a neural network named DetarNet to decouple the translation $t$ and rotation $R$, so as to overcome the performance degradation due to their mutual interference in point cloud registration. First, a Siamese Network based Progressive and Coherent Feature Drift (PCFD) module is proposed to align the source and target points in high-dimensional feature space, and accurately recover translation from the alignment process. Then we propose a Consensus Encoding Unit (CEU) to construct more distinguishable feature…
Chinese University of Hong Kong（香港中文大学）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；Tel Aviv University（特拉维夫大学）
Recently, many deep neural networks were designed to process 3D point clouds, but a common drawback is that rotation invariance is not ensured, leading to poor generalization to arbitrary orientations. In this paper, we introduce a new low-level purely rotation-invariant representation to replace common 3D Cartesian coordinates as the network inputs. Also, we present a network architecture to embed these representations into features, encoding local relations between points and their neighbors, and the global shape structure. To alleviate inevitable global information loss caused by the rotati…
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电子信息与电气工程学院）
Point cloud recognition is an essential task in industrial robotics and autonomous driving. Recently, several point cloud processing models have achieved state-of-the-art performances. However, these methods lack rotation robustness, and their performances degrade severely under random rotations, failing to extend to real-world scenarios with varying orientations. To this end, we propose a method named Self Contour-based Transformation (SCT), which can be flexibly integrated into various existing point cloud recognition models against arbitrary rotations. SCT provides efficient rotation and tr…
Rotation Perturbation Robustness in Point Cloud Analysis: A Perspective of Manifold Distillation
Shanghai Jiao Tong University（上海交通大学）；Shanghai Key Laboratory of Intelligent Sensing and Recognition（上海智能感知与识别重点实验室）；School of Sensing Science and Engineering（感知科学与工程学院）；Intelligent Photoelectric Sensing Institute（智能光电感知研究院）
In this paper, we propose a novel deep architecture tailored for 3D point cloud applications, named as SPE-Net. The embedded ``Selective Position Encoding (SPE)'' procedure relies on an attention mechanism that can effectively attend to the underlying rotation condition of the input. Such encoded rotation condition then determines which part of the network parameters to be focused on, and is shown to efficiently help reduce the degree of freedom of the optimization during training. This mechanism henceforth can better leverage the rotation augmentations through reduced training difficulties, m…
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 rot…
Litemaze；VinAI Research（VinAI 研究院）；VinUniversity（Vin 大学）；Hong Kong University of Science and Technology（香港科技大学）
Recent advances in deep learning for 3D point clouds have shown great promises in scene understanding tasks thanks to the introduction of convolution operators to consume 3D point clouds directly in a neural network. Point cloud data, however, could have arbitrary rotations, especially those acquired from 3D scanning. Recent works show that it is possible to design point cloud convolutions with rotation invariance property, but such methods generally do not perform as well as translation-invariant only convolution. We found that a key reason is that compared to point coordinates, rotation-inva…
Rotational Symmetry based Object Pose Estimation from Point Clouds in the Absence of Known 3D Models
Key Laboratory of Brain Machine Collaborative Intelligence of Zhejiang Province, School of Computer Science, Hangzhou Dianzi University（浙江省脑机协同智能重点实验室，杭州电子科技大学计算机学院）；Advanced Intelligent Manufacturing Research Group, the University of Nottingham Ningbo China（先进智能制造研究组，宁波诺丁汉大学）
Wuhan University（武汉大学）；The University of Hong Kong（香港大学）；Texas A&M University（得克萨斯农工大学）
In this paper, we propose a novel local descriptor-based framework, called You Only Hypothesize Once (YOHO), for the registration of two unaligned point clouds. In contrast to most existing local descriptors which rely on a fragile local reference frame to gain rotation invariance, the proposed descriptor achieves the rotation invariance by recent technologies of group equivariant feature learning, which brings more robustness to point density and noise. Meanwhile, the descriptor in YOHO also has a rotation equivariant part, which enables us to estimate the registration from just one correspon…
RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning
South China University of Technology（华南理工大学）；The University of Adelaide（阿德莱德大学）；The University of Western Australia（西澳大学）；The University of Sydney（悉尼大学）
Point cloud analysis without pose priors is very challenging in real applications, as the orientations of point clouds are often unknown. In this paper, we propose a brand new point-set learning framework PRIN, namely, Pointwise Rotation-Invariant Network, focusing on rotation-invariant feature extraction in point clouds analysis. We construct spherical signals by Density Aware Adaptive Sampling to deal with distorted point distributions in spherical space. In addition, we propose Spherical Voxel Convolution and Point Re-sampling to extract rotation-invariant features for each point. Our netwo…
Technical University of Munich（慕尼黑工业大学）；Meta Reality Labs（Meta现实实验室）；National University of Defense Technology（国防科技大学）；Shanghai Jiao Tong University（上海交通大学）；Siemens AG（西门子股份公司）
Successful point cloud registration relies on accurate correspondences established upon powerful descriptors. However, existing neural descriptors either leverage a rotation-variant backbone whose performance declines under large rotations, or encode local geometry that is less distinctive. To address this issue, we introduce RIGA to learn descriptors that are Rotation-Invariant by design and Globally-Aware. From the Point Pair Features (PPFs) of sparse local regions, rotation-invariant local geometry is encoded into geometric descriptors. Global awareness of 3D structures and geometric contex…
Shanghai Jiao Tong University（上海交通大学）；The Hong Kong University of Science and Technology（香港科技大学）；Qing Yuan Research Institute（清源研究所）；Shanghai Qizhi Research Institute（上海期智研究院）；AI Institute, Shanghai Jiao Tong University（上海交通大学人工智能研究院）
Point cloud analysis without pose priors is very challenging in real applications, as the orientations of point clouds are often unknown. In this paper, we propose a brand new point-set learning framework PRIN, namely, Point-wise Rotation Invariant Network, focusing on rotation invariant feature extraction in point clouds analysis. We construct spherical signals by Density Aware Adaptive Sampling to deal with distorted point distributions in spherical space. Spherical Voxel Convolution and Point Re-sampling are proposed to extract rotation invariant features for each point. In addition, we ext…
Many point cloud classification methods are developed under the assumption that all point clouds in the dataset are well aligned with the canonical axes so that the 3D Cartesian point coordinates can be employed to learn features. When input point clouds are not aligned, the classification performance drops significantly. In this work, we focus on a mathematically transparent point cloud classification method called PointHop, analyze its reason for failure due to pose variations, and solve the problem by replacing its pose dependent modules with rotation invariant counterparts. The proposed me…
RISurConv: Rotation Invariant Surface Attention-Augmented Convolutions for 3D Point Cloud Classification and Segmentation
School of Computing and Information Systems, Singapore Management University（新加坡管理大学计算与信息系统学院）；College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息与电子工程学院）
Chalmers University of Technology（查尔姆斯理工大学）；Umeå University（于默奥大学）
In this paper, we are concerned with rotation equivariance on 2D point cloud data. We describe a particular set of functions able to approximate any continuous rotation equivariant and permutation invariant function. Based on this result, we propose a novel neural network architecture for processing 2D point clouds and we prove its universality for approximating functions exhibiting these symmetries. We also show how to extend the architecture to accept a set of 2D-2D correspondences as indata, while maintaining similar equivariance properties. Experiments are presented on the estimation of es…
University of Hamburg（汉堡大学）；Tsinghua University（清华大学）
This paper addresses the task of estimating the 6 degrees of freedom pose of a known 3D object from depth information represented by a point cloud. Deep features learned by convolutional neural networks from color information have been the dominant features to be used for inferring object poses, while depth information receives much less attention. However, depth information contains rich geometric information of the object shape, which is important for inferring the object pose. We use depth information represented by point clouds as the input to both deep networks and geometry-based pose ref…
Ningbo Research Institute, Zhejiang University（浙江大学宁波研究院）；College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息与电子工程学院）；NingboTech University（浙大宁波理工学院）；VinAI；Hong Kong University of Science and Technology（香港科技大学）
3D point clouds deep learning is a promising field of research that allows a neural network to learn features of point clouds directly, making it a robust tool for solving 3D scene understanding tasks. While recent works show that point cloud convolutions can be invariant to translation and point permutation, investigations of the rotation invariance property for point cloud convolution has been so far scarce. Some existing methods perform point cloud convolutions with rotation-invariant features, existing methods generally do not perform as well as translation-invariant only counterpart. In t…
We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network, achieving invariance to both global shape transformations, and to local rotations on the level of patches or parts, useful when dealing with non-rigid objects. We achieve this by employing a spherical harmonics based kernel at different layers of the network, which is guaranteed to be invariant to rigid motions. We also introduce a more efficient pooling operation f…
Institute of Computer Science and Technology, Peking University（北京大学计算机科学技术研究所）
Point cloud analysis has drawn broader attentions due to its increasing demands in various fields. Despite the impressive performance has been achieved on several databases, researchers neglect the fact that the orientation of those point cloud data is aligned. Varying the orientation of point cloud may lead to the degradation of performance, restricting the capacity of generalizing to real applications where the prior of orientation is often unknown. In this paper, we propose the point projection feature, which is invariant to the rotation of the input point cloud. A novel architecture is des…
East China University of Science and Technology（华东理工大学）
Rotation search and point cloud registration are two fundamental problems in robotics and computer vision, which aim to estimate the rotation and the transformation between the 3D vector sets and point clouds, respectively. Due to the presence of outliers, probably in very large numbers, among the putative vector or point correspondences in real-world applications, robust estimation is of great importance. In this paper, we present ICOS (Inlier searching using COmpatible Structures), a novel, efficient and highly robust solver for both the correspondence-based rotation search and point cloud r…
Technion – Israel Institute of Technology（以色列理工学院）；NVIDIA Research（英伟达研究院）
Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal -- it can approximate any equivariant function. In this paper we suggest a much simpler architecture, prove that it enjoys the same universality guarantees and evaluate its performance on Modelnet40. The code to reproduce our experiments is available at \url{https://github.com/simpleinvariance/UniversalNetwork}
Rotation-Adaptive Point Cloud Domain Generalization via Intricate Orientation Learning
South China University of Technology（华南理工大学）；Guangdong Engineering Center for Large Model and GenAI Technology（广东省大模型与生成式人工智能技术工程中心）；State Key Laboratory of Subtropical Building and Urban Science（亚热带建筑与城市科学国家重点实验室）；Ministry of Education Key Laboratory of Big Data and Intelligent Robot（大数据与智能机器人教育部重点实验室）；Singapore Management University（新加坡管理大学）
East China University of Science and Technology（华东理工大学）
Correspondence-based rotation search and point cloud registration are two fundamental problems in robotics and computer vision. However, the presence of outliers, sometimes even occupying the great majority of the putative correspondences, can make many existing algorithms either fail or have very high computational cost. In this paper, we present RANSIC (RANdom Sampling with Invariant Compatibility), a fast and highly robust method applicable to both problems based on a new paradigm combining random sampling with invariance and compatibility. Generally, RANSIC starts with randomly selecting s…
Recent years have witnessed the emergence and increasing popularity of 3D medical imaging techniques with the development of 3D sensors and technology. However, achieving geometric invariance in the processing of 3D medical images is computationally expensive but nonetheless essential due to the presence of possible errors caused by rigid registration techniques. An alternative way to analyze medical imaging is by understanding the 3D shapes represented in terms of point-cloud. Though in the medical imaging community, 3D point-cloud processing is not a "go-to" choice, it is a canonical way to …
Stanford University（斯坦福大学）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Lab（劳伦斯伯克利国家实验室）；Google（谷歌）
We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We demonstrate the capabilities of tensor field networks with tasks in geometry, physi…
Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances. Rigid patterns of point clouds can be reliably compared only by complete isometry invariants that can also be called equivariant descriptors without false negatives (isometric clouds having different descriptions) and without false positives (non-isometric clouds with the same description). Noise and motion in data motivate a search for invariants that are contin…
This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain conditions, the network feature naturally has the rotation-equivariance property. Rotation equivariance means that applying a specific rotation transformation to the input point cloud is equivalent to applying the same rotation transformation to all intermediate-layer quaternion features. Besides, the REQNN also ensures that the intermediate-layer features are inv…
Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study the relation between equivariance and invariance in 3D point convolutions. We show that using rotation-equivariant alignments, it is possible to make any convolutional layer rotation-invariant. Furthermore, we improve this simple alignment procedure by using the alignment themselves as features in the convolution, and by combining multiple alignments togeth…
Rotation moment invariants have been of great interest in image processing and pattern recognition. This paper presents a novel kind of rotation moment invariants based on the Slepian functions, which were originally introduced in the method of separation of variables for Helmholtz equations. They were first proposed for time series by Slepian and his coworkers in the 1960s. Recent studies have shown that these functions have an good performance in local approximation compared to other approximation basis. Motivated by the good approximation performance, we construct the Slepian-based moments …
The aim of this paper is to demonstrate that a state of the art feature matcher (LoFTR) can be made more robust to rotations by simply replacing the backbone CNN with a steerable CNN which is equivariant to translations and image rotations. It is experimentally shown that this boost is obtained without reducing performance on ordinary illumination and viewpoint matching sequences.
