Mining and Transferring Feature-Geometry Coherence for Unsupervised Point Cloud Registration
Authors: KeZheng Xiong
Haoen Xiang
Qingshan Xu
Chenglu Wen
Siqi Shen
Jonathan Li
Cheng Wang
Venue: NeurIPS 2024 poster (2024)
Keywords: Unsupervised Point Cloud Registration
Deep Learning
Computer Vision
Primary area: machine_vision
TL;DR: A novel unsupervised point cloud registration method for large-scale outdoor scenes.

Abstract: Point cloud registration, a fundamental task in 3D vision, has achieved remarkable success with learning-based methods in outdoor environments. Unsupervised outdoor point cloud registration methods have recently emerged to circumvent the need for costly pose annotations. However, they fail to establish reliable optimization objectives for unsupervised training, either relying on overly strong geometric assumptions, or suffering from poor-quality pseudo-labels due to inadequate integration of low-level geometric and high-level contextual information. We have observed that in the feature space, latent new inlier correspondences tend to cluster
around respective positive anchors that summarize features of existing inliers. Motivated by this observation, we propose a novel unsupervised registration method termed INTEGER to incorporate high-level contextual information for reliable pseudo-label mining. Specifically, we propose the Feature-Geometry Coherence Mining module to dynamically adapt the teacher for each mini-batch of data during training and discover reliable pseudo-labels by considering both high-level feature representations and low-level geometric cues. Furthermore, we propose Anchor-Based Contrastive Learning to facilitate contrastive learning with anchors for a robust feature space. Lastly, we introduce a Mixed-Density Student to learn density-invariant features, addressing challenges related to density variation and low overlap in the outdoor scenario. Extensive experiments on KITTI and nuScenes datasets demonstrate that our INTEGER achieves competitive performance in terms of accuracy and generalizability.

Mining and Transferring Feature-Geometry Coherence for Unsupervised Point Cloud Registration
Kezheng Xiong Haoen Xiang Qingshan Xu', Chenglu Wen Siqi Shen
Jonathan Li Cheng Wangth
"Fujan Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University, China.
'Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry Education of China, Xiamen University, China.
*Nnyyang Technological University, Singapore. Universityy of Waterloo, Waterloo, Canada {xi orinnnkezeeng.o www.nnianngnne...m............on @stu. xmu edu cn
{clwen, siqishen, cwang) 0xmu edu. cn qingshan xuêntu. edu. edu.sg, juml @wwaterloo.cc. ca
Oxmu.
Abstract
Point cloud registration, fundamental task in 3D vision, has achieved remark- able success with learning-based methods in outdoor environments. Unsupervised outdoor point cloud registration methods have recently emerged to circumvent the need for costly pose annotations. However, they fail establish reliable optimiza- tion objectives for unsupervised training, either relying on overly strong geometric assumptions, suffering from poor-quality pseudo-labels due inadequate in- tegration of low-level geometric and high-level contextual information. We have observed that in the feature space, latent new inlier correspondences tend cluster around respective positive anchors that summarize features of existing inliers. Mo- tivated by this observation, we propose a novel unsupervised registration method termed INTEGER to incorporate high-level contextual information for reliable pseudo-label mining. Specífically, we propose the Feature-Geone Geomery Coherence Mining module to dynamically adapt the teacher for each mini-batch of data dur- ing training and discover reliable pseudo-labels by considering both high-level feature representations and low-level geometric cues. Furthermore, propose Anchor-Based Contrastive Learning to facilitate contrastive learning with anchors for robust feature space. Lastly, we introduce Mixed-Density Student to learn censity-invarian features, addressing challenges related to density variation and low overlap in the outdoor scenario. Extensive experiments KITTI and nuScenes datasets demonstrate that our INTEGER achieves competitive performance in terms of accuracy and generalizability. [Code Release]
Introduction
Point cloud registration is a fundamental task in autonomous driving and robotics. It aims to align two partially overlapping point clouds with rigid transformation. Learning-bass based methods have achieved remarkable success in outdoor point cloud registration [155]. PCAM[]] pioneered the integration of low-level geometric and high-level contextual information, inspiring subsequent works(2H51 However, these supervised methods suffer from poor generalizability and reliance on costly pose
*Corresooding author
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Inliers/Outliers w.r.t Anchors 4 Samples in Feature Space tSN Visualization
Our Proposed Method
Reliable & Effective Optimization Objectives
ABCont
IR% of Corr. Pseudo Label
+ +-40%
Inliers (Outliers) tends to cluster around positive (negative) anchors feature space
Far
Near
Outlier
Pos. Anchor Neg. Anchor
2
5
10
20
30
Inlier
Distance to the Nearest Anchor
Frame Distance (m)
Figure 1: (1) Motivation: new inliers (outliers) tend to cluster around latent positive (negative)
anchors that represent existing inliers (outliers) in the feature space, respectively. (2) Perfor- mance: pseudo-labels from INTEGER are more robust and accurate than the previous state-of-the-an [2]
annotations 6688, underscoring the need for unsupervised methods to address these challenges in real-world applications.
Despite recent progress 12] in unsupervised registration methods, the task remains challenging and underexplored, especially in outdoor scenarios where LiDAR point clouds are large-scale and complexly distributed. Some methods [ optimize photometric and depth consistency, limiting their applicability to indoor scenarios where RGB-D data and differentiable rendering are feasible. Others 13 [4] learn global alignment and neighborhood consensus, but struggle with low overlap frameworks, achieving promising results in outdoor scenarios [12] [5]. However, they rely solely on geometric cues to mine and filter pseudo-labels, neglecting the complementarity of high-level contextual information feature space. Their partiality results in incomplete scene perception, leading to noisy and suboptimal optimization objectives.
and density variation in outdoor settings. Recent advances resort to perudd-label-baseee
have benefited from integrating both low- level and high-level information. In point cloud registration, as illustrated in Fig. (Left), we observe that potential inliers (outliers) tend to cluster around positive (negative) anchors that summarize the features of existing inliers (outliers) in the feature space, respectively. This suggests that high- level contextual information adept at discovering inliers from a global perspective of the scene. Meanwhile, low-level geometric cues have proven effective in rejecting outliers[13] (3]. Inspired by this, we propose a novel method, termed INTEGER, which adopts a to mINe and Transfer Mature-GEoomety cohe for unsupervised point cloud registration.
Various 2D [16 17 and 3D vision tasks 20 2
framework
Specifically, our method starts by initializing teacher with synthetic pairs generated from each point cloud scan, and then transfers to real point cloud pairs with a teacher-student framework. Building Coherence Mining (FGCM) module for
upon our observations, we introduce the the teacher, which first adapts the teacher to each mini-batch of real data to establish a denoised feature space. Reliable pseudo-labels, including correspondences and anchors, are then generated based on our key observation by iteratively mining potential inliers based on their similarity to anchors and rejecting outliers via spatial compatibility [21. These robust pseudo- labels mined by FGCM not only accurately include inlier correspondences as shown in Fig. (Right), but also aggregate effective representations of inliers and outliers from the teacher. We refer to this characteristic as coherence. To further enhance robustness and transfer feature-geometry coherence to the student, we propose Anchor-Bass Based Contrastive Learning (ABCont) for contrastive learning with anchors. Mcanwhile, design succinct and efficient Mixed-Density Density Student (MDS) for the student to learn density-inven invariant features using teacher's anchors, overcoming density variation and low overlap in distant scenarios.
We extensively evaluate our method on two large-scale outdoor datasets, KITTI and nuScenes. By exploiting feature-geome geometry coherence for reliable optimization objectives, INTEGER outperforms existing unsupervised methods by considerable margin. even performs competitively compared to state-of-the-art supervised methods, especially in distant scenarios. To the best of our knowledge, our approach is the first to integrate both low-level and high-level information for producing lseudo-labels of unsupervised point cloud registration. Overall, our contributions threefold:

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We propose INTEGER, a novel method to exploit low-level and high-level information for unsu- pervised point cloud registration, achieving superior performance in complex outdoor scenarios.
We introduce FGCM and MDS for the teacher and student, respectively, to mine reliable pseudo- labels and learn density-invariany features.
We design ABCont to mitigate pseudo-label noise and facilitate contrastive learning with anchors for a robust feature space.
2
Related Works
Supervised Registration. There are two categories of supervised registration approaches:
Correspondence-based methods 264 4 27 28 3 first extract point correspondences and then estimate the transformation with robust pose estimators. In contrast, direct registration methods extract global feature vectors and regress the transformation directly with neural network. Recently, a series of works [2 have tackled distant point cloud registration, which is crucial for real-world applications.
29 31
Unsupervised Registration. Previous researches in unsupervised registration mainly focus indoor scenes. B BOOC[[]] suggests that random 2D CNNs generate robust image correspondences for supervising 3D registration networks. Meanwhile, render-based methods ( 10] leverage differ- entiable renders as the supervision signal of 3D registration. However, these methods are restricted to RGB-D input. To address this, Mei et al.
33 enforce consistencies between Gaussian Mixture Models for unsupervised training. using only point cloud as input. Shen et al. [13] introduce an inlier evaluation method based on neighborhood consensus. However, its performance drops when the overlap is low. SGP proposes a teacher-student framework for self-supervised learning from hand-crafted feature descriptors. [Y introduces progressive training and spatial filtering to adapt the model to distant point cloud pairs gradually, demonstrating promising results in outdoor scenarios.
Robust Pose Estimators. Pose estimators evaluate inliers and estimate poses from input correspon- dence sets. Traditional methods such as RANSAC suffer from inefficiencies. Learning- based methods(35|37) learn predict inliers and poses using neural networks. However, they require training and are thus constrained to supervised settings. To address this, non-parametric methods have emerged. Chen al. (2 introduced SC*-measurement for robust inlier selection. Graph-based methods such as MAC[3] and 22) approximate maximal cliques for fast and accurate inlier evaluation.
3 Methodology
Problem Formulation. Given two point clouds P [p:} E mR3 and Q= {q:} E Rax3 the goal of point cloud registration is to uncover the rigid transformation T (R. that perfectly aligns P to Q, where R SO(3) is the rotation matrix and t E IR3 the translation vector. When the two point clouds are acquired at a large distance d such when d E 50m]. the registration task faces the challenges of low overlap and density variation 32 learn density-invariant features.
38
Therefore, it crucial to
Overall Pipeline. INTEGER adopts a two-stage training scheme and a teacher-student framework. Training of INTEGER consists of two stages: First, we initialize the teacher with synthetic data. Then, we train a student model on real data with the reliable pseudo-labels mined by the teacher. The overall pipeline and proposed modules are illustrated in Fig. 2 During teacher-student training. FGCM first dynamically adapts the teacher model 0 to data-specific teacher & designated for the current mini-batch, and then mines reliable pseudo-labels with the adapted teacher. Next, the MDS learns density-invarian features by learning to match regular and sparse views of point cloud pairs supervised by pseudo-labels mined by ø. A pseudo-label Z (,, A,,AA contains correspondences C, Ć to supervise dense matches and sparse matches, respectively. The feature-space positive and negative anchors. denoted respectively by A4 and A_, serve overall representatives of inliers and outliers in the feature space. For a correspondence (1-) (p. q,) e C, the correspondence features are
3

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Sell Sell-Adaption
Tealure-Geometry Clustering
# Stop Gradients
Sujure anissaBBll
DC) Downsample
Teacherd
FGCM
goreespndence Seed Progosal
P.0 P
EMA
Spatial
Anchor- Based
Compatiblity Filtering
Clustering
MDS
Knowledgr Transfer
Student
Network
Fg..F
Pseudo
Labels
Samples
Hard
Anchors
Feature- Geetmery Coherence Mining
Mixed-Density Student
Figure 2: The Overall Pipeline. FGCM(See. 3.2) first adapt the teacher model to a data-specific
teacher for the current mini-batch, and then mine reliable pseudo-labels. Next, MDS(See. (.4] learns density-invariant features from pseudo-labels. ABCont(Sec. (3.3) is applied for adapting the teacher and transferring knowledge to the student in the feature space.
defined as F(..) = F.P F.. Then, the positive and negative anchors At, A are computed as the average the respective features inliers C. and outliers C_
A+
1 C+1 (P.9))EC+
F A_
Σr F(
C+
(P..)))CC_
ABCont is applied to effectively learn a robust student guided by anchors from the teacher. Progressive training [12 adopted gradually train the student adapt pairs of distant point clouds.
3.1 Synthetic Teacher Initialization
To initialize teacher model, Liu et al. [22 assume that two consecutive frames approximately have no relative transformation and pretrain the teacher with the identity transformation. However, the errors introduced in such approximation lead to suboptimal initial teachers. To address this, inspired by existing efforts (39 44), we instead pretrain the teacher with synthetic pairs generated from each partially overlap fragments for each scan. We additionally apply periodic sampling 339 to remove points periodically with respect random center, simulating the irregular sampling of LiDAR. Please refer to the Appendix for visualization of synthetic pairs.
real scan. Specifically, we follow PointContrast [40] generate
3.2 Feature-Geometry Coherence Mining
With the teacher initialized on syn- thetic pairs, our goal is to provide reliable supervision for the student. Despite efforts to ensure an effective initialization, a distribution discrep- ancy persists between synthetic and real data. Hence, we introduce train- only FGCM. As is depicted in Fig. [ FGCM starts with Correspondence
Per-Batch Self-Adaption
Hard Samples
FGCM
Loss
Teacher
Teacher
Data
Pseudo
FGCM
Loss
Labels
Seed Proposals for Co using a sim- ple similarity threshold. Subsequently. Geouerry Clustering extends from C by mining additional reliable correspondences and anchors, which serve effective optimization objec- tives.
Hard Samples
Teacher
MDS
Anchors
Teacher-Student Knowledge Transfer
Figure 3: The two-pass usage of the proposed FGCM.
As is illustrated in Fig. for each mini- we use FGCM in two-pass manner. In the first forward pass, we perform Per-Batch Self-Adaption on the teacher model 0 to establish a denoised feature space, yielding a data-specific teacher Φ. In the second forward pass, the adapted teacher and FGCM are used to mine reliable pseudo-labels I, which are then used to train the student, achieving Seacher-Studert Knowledge Transfer.

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Algorithm 1: Peature-Geometry Clustering
Input:
Initial correspondence seed proposals Co Compute initial U?. Uº and anchors A+, A- with Eq. for to mar maa_iterr jiters do
Generate unclassified correspondences Cu - FealureMatching (U', Uº)
Select Chyp- with top-k St satisfying St > Se based on Eq. Update C t- 1- C Clop-
// Anchor Clustering
Filter C with spatial compatibility to produce Ci ci.
// Spatial Compatibility
Filtering
Update UP. U and A4, A_ with Eq.
if c c or | =|c- ---- then
break
return C, A4, A_
Feomeryy Clustering. Feature-Geonen Clustering is central to the FGCM, designed to extend initial correspondence proposals by integrating both high-level feature representations and low-level geometric cues. It iteratively includes speculative inliers based on feature-space clustering, followed by outlier rejection with spatial compatibility filtering. We empirically adopt SC*-PCR (2) for spatial compatibility filtering. Our experiments show that our method is agnostic to the choice of spatial compatibility measures.
To discover latent correspondences in the feature space, it is necessary to measure the similarity between putative correspondences and anchors. Inspired by Xia et al. [41), we compute the feature similarity using both Euclidean distance and cosine similarity. Specifically, for a correspondence (Ps, 9,) C with its features (((.)) The similarity 8 and St w.r.t. respective anchors A4 and A_ is computed as:
5 = iminDD((A,,Fg (i.))) Dc )) S. = min F( De F(.)) (1d)) }} (2)
where Dg(F1. F2)=11mmn(LLaf) FF..F2).. 1) and Dc(F1, = (cos(F1, F2)+ /2 are normalized Euclidean distance and cosine similarity, respectively.
The algorithm is detailed in Alg. [ Given correspondence set Ci at i-th iteration, we define unclassi- fied points UP. U in P and Q as:
U <PDDEPND (C), U = (qiq e @^ (+, #C}
Then, the algorithm takes an iterative approach, starting from the given initial correspondence set C": during the jth iteration, it (1) generates putative correspondences from UP and U via feature matching: (2) expands C--1 with top-k similar correspondences to positive anchors measured by S., yielding C:; (3) filters the expanded correspondence set with spatial compatibility and updates anchors based Eq. [ (4) updates UP, U and A4. A_ according to Eq. 3 The iteration stops when the number of inliers and outliers converges, or the maximum iteration is reached.
With ample accurate correspondences included in C, we can then estimate a more accurate transfor- mation T and compute ć using nearest neighbor search (NN-search) with T. We do not directly apply Alg. for sparse pairs because, downsampled views, the features become less descriptive hindering feature-based approaches.
38
Throughout the iterations in Alg. [ positive and negative anchors gradually aggregate representative and discriminative features of inliers and outliers, respectively. In the first forward pass, noise exists due distributional discrepancies, leading the rejection of some correspondences by spatial compatibility. These rejected correspondences are hard samples: ambiguous correspondences that are closer to positive anchors in the feature space but are more likely to be outliers. We leverage these hard samples for teacher self-adaptation by applying the InfoNCF(42) loss, guiding the teacher distinguish them from the positive anchors. This step results in the adapted teacher é, which produces more discriminative features for the current
Per-Batch Sell-Adaption.
5

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Focusing only on hard samples for self-adaptation is more efficient than simply using all correspon- dences for self-adaptation. Hard samples capture the key ambiguities in the feature space while introducing only limited number of pairwise relationships. This defines a clear and reliable opti- mization objective for self-adaptation. contrast, self-adaption with all correspondences not only slows down the training, but also introduces too many drready-distinguishabl pairwise relationships, diluting the focus on feature-space ambiguity and thus hindering effective adaptation.
Teacher-Student Knowledge Transfer. After Per-Batch Self-Adaption, the feature space of the adapted teacher & is expected to contain less noise. Consequently, the positive and negative anchors become sufficiently representative and discriminative now, enabling effective guidance for the student to learn a robust feature space. For Teacher-Studens correspondences and anchors from the adapted teacher ABCont. Unlike existing methods [2] that rely solely on correspondences, our approach directly bridges the teacher and student in the feature space via anchors, providing clear and effective optimization objective for the student.
Knowledge Transfer, we utilize both the
train the student using the proposed
3.3 Anchor-Based Contrastive Learning
Contrastive learning has been widely adopted to train reg- istration models [3 24
Recently, a surge of research various tasks involves anchor-based proxy- based approaches to facilitate contrastive learning due to their robustness against inconsistency and noise in the fea-
20].
Spmpil Based
Anchor Basd
ture space 45 41, superiority in generalizability (46) and ability to learn discriminative features (7). There-
Pos. Samples Neg. Samples
Inevitable Noise
Pos. Anchor Neg. Anchor
fore, we design ABCont to leverage positive and negative anchors to facilitate effective contrastive learning with where noise and outliers are inevitable. As shown in Fig. with anchor- based representations, ABCont sets up convergence target that is more robust against label noise. Moreover, it more efficient because the number of additionally- inn.oluucddd pairwise relationships is reduced[46)
Pseudo Labels
Figure 4: Toy Example for ABCont. Anchor-based methods introduce fewer pairwise relationships and are robust against inevitable label noise.
the pseudo-labes
free+t Specifically, we propose the ABCont loss LABCOm - Lreg Aeor where Ccom is the anchor-based correspondence loss, weighted by hyperparameter Acor to complement the registration loss Leg originally used by the feature extractors. The student's 's feature matching results can be classified into inliers C+ and outliers C_ based on the pseudo-labels from the teacher. Then, anchors A_. from the teacher designated as a universal inlier and universal outlier, resulting in augmented inliers and outliers:
C c4 Usg(A.), e = sg(AA))
where sg(-) denotes the stop-gradient operator, preventing gradients from flowing back the teacher. Following existing efforts/A1]40) we sample np correspondences randomly and formulate L as contrastive learning problem to distinguish inliers from outliers. InfoNCE [2)
loss then applied to
these correspondence features:
exp(33)
log exp( + exp((Bh)
Thp 1=1
where S and 3 are the distance between the th positive correspondence and the jth negative correspondence, respectively. ABCont is pivotal in transferring feature-geometry coherence from the teacher to the student: the accurate pseudo-labels for correspondences, combined with anchors, enable the student to learn discriminative features efficiently. Anchors from the teacher impose direct constraints on the student's feature space, encouraging the student to replicate the teacher's feature-space matchability. This leads to more effective transfer of ceature-geometry coherence.
3.4 Mixed-Density Student
The density of LiDAR point clouds varies greatly with the distance to the sensor, posing challenges for matching distance point clouds effectively[33. (38). To address this, it is crucial for student model

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to learn density-invariane invariant features, ensuring robust correspondences across varying point densities. Previous methods [22] 38 have sought density invariance through auxiliary reconstruction tasks or by identifying positive groups, but these techniques are either computationally expensive or depend on precise supervision. Xía al. [48] introduced simple yet effective technique for density invariance in object detection by using features from downsampled views. Inspired by this, we propose DixestDensity Student to learn density-invariant features from reliable correspondences.
Specifically, given point clouds P and Q, we compute their sparsely-downsampled views P and Q with increased voxel sizes. We then extract student's features (Fp, F. FQ) and (F Using features from point clouds of different density, we compute dense matches and sparse matches through matching respective features. We then apply ABCont both sets of matches, encouraging the extraction of similar features at corresponding spatial locations across point clouds of varying densities, thereby promoting density-invarian feature learning.
Loss Aggregation. LABCom both dense and sparse matches:
The student's overall training loss is aggregated as a weighted combination of
L (P.2) ABCont + A ABCooa
(P .2
(6)
where d is a weight for the sparse match.
Experiments
We mainly evaluate INTEGER two challenging public datasets: KITTI and nuScenes 77. Both datasets adhere to official splits. The evaluation protocol follows the standard setting of EYOC[[2] Please refer the appendix for more details of implementation and experimental settings.
we evaluate the registration performance using Relative Rotation Error (RRE), Relative Translation Error (RTE) and Registration Recall (RR). Related to the practical purpose of outdoor registration, we additionally report RR [d,, d2) and mean Registration Recall(mRR), RR& [di, .2) is registration recall w.r.t pairs with distance d E [di, d2), following 12]. mRR is defined as the average of RR d1, d2) for all [d1, d2). To measure the quality of correspondences in pseudo-label, epoch, denoted "tR @ 1s Epoch".
Metrics Following previous works
report Inlier Ratio(IR) of the teacher in the first
Baselines For supervised methods, We compare INTEGER with FCGF 24 44 D3Feat (50), (o5,Net(5]), and Geometric Transformer(Geo vised methods, we compare with RIENet and EYOC[12). Following Liu et al. 12] we report variant FCGF denoted as FCGF+C, which is FCGF trained with progressive training [12].
Predator 46
For unsuper-
4.1 Performance Comparison with State-of-the-Art
Quantitative results are presented in Table Our method outperforms existing unsupervised ap- proaches and achieving tate-of-the-ar performance across all datasets and demonstrates superior generalizability. Notably, our unsupervised approach maintains competitive performance compared to supervised methods and surpasses them in distant scenarios, highlighting its potential for real-world application.
Overall Performance Compared to existing methods, our approach excels in performance. RIENet, an end-to-end unsupervised registration method outdoor scenes, exhibits suboptimal performance, particularly in low-overlap scenarios and enviromments with low LiDAR resolution, such nuScenes. Both EYOC and INTEGER adopt a teacher-student framework for unsupervised training. However, method demonstrates superior accuracy across all evaluation metrics, overcoming challenges associated with pseudo-label discovery and the absence of feature-space knowledge transfer in EYOC.
Generalizability We assess generalizability on nuScenes using weights trained on KITTI Vari- ations LiDAR resolutions between nuScenes and KITTI may lead to different point densities, potentially degrading extracted features. Compared to existing unsupervised methods, our approach exhibits superior generalizability to unseen datasets. This superiority can attributed to INTEGER's design, which learns ceensity-ivvarine features.
7

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Table Comparisons with State-of-the-Art Methods. "V" in the column "U" denotes the methods are Unsupervised. Otherwise, they are supervised. The best unsupervised results are highlighted in bold. "enotes generalizability results from KITTI to nuScenes.
RR @d E
Dataset
Method
U
mRR
55 10)
[10, 20)
200, 30)
[30, 40)
[40, 50)
FCGF
77.4
98.4
95.3
86.8
69.7
36.9
FCGF+C
84.6
100.0
97.5
90.1
79.1
56.3
Predator
87.9
100.0
98.6
97.1
80.6
63.1
SpinNet
39.1
99.1
82.5
13.7
0.0
0.0
KITTI
D3Feat
66.4
99.8
98.2
90.7
38.6
4.5
CoFiNet
82.1
99.9
99.1
94.1
78.6
38.7
GranT.
42.2
100.0
93.9
16.6
0.7
0.0
EYOC
83.2
99.5
96.6
89.1
78.6
52.3
RIENet
50.7
96.3
72.1
38.2
24.4
22.6
Ours
84.0
99.5
97.1
89.6
79.6
54.2
FCGF
39.5
87.9
63,9
23.6
11.8
10.2
FCGF+C
59.3
96.2
85.1
59.6
35.8
20.0
nuScenes
Predator
51.0
99.7
72.2
52.8
16.2
14.3
EYOC
61.7
96.7
85.6
61.8
37.5
26.9
RIENet
47.1
96.5
57.9
36.6
25.8
18.9
Ours
63.1
97.1
86.9
62.9
39.6
29.4
KITTI
EYOC
55.3
96.2
75.6
58.7
26.6
19.7
RIENet
46.2
83.3
73.2
43.5
19.8
11.1
nuScenes
Ours
62.6
97.5
84.6
62.6
37.8
30.2
4.2 Analysis
Different Choices of Pose Estimator FGCM We contend contingent
that the robustness and efficacy of FGCM upon specific pose estimator. To substantiate this claim, we conduct experiments employing various robust pose estimators within FGCM. The results are detailed in Table For differ- ent robust pose estimators in FGCM module, we experiment PoinDDSC MAC[23), FastMAC and SC*-PCR(I]. The results demonstrate that the effectiveness of FGCM agnostic to choices of pose estimators, despite marginal perfor- mance discrepancies are observed. Given the iterative nature of FGCM, the efficiency of pose estimators holds paramount importance, as the module's runtime is proportional to pose estimation time. We choose SCR-PC for FGCM by default due to its superior balance in performance and efficiency.
Table 2: Different Pose Estimators in FGCM
Pose
IR@ 1st Epoch
Time
Estimators
(s)
PointDSC
81.3
1.13
MAC
80.1
28.2
FastMAC
79.3
0.67
SC²-PCR
81.2
0.75
Effectiveness of Self-Adaption for Discriminative Features. To further understand the effective- ness of self-adaption in FGCM, visualize the point-level feature distribution and correspondence- level similarity distribution in Fig. (Please refer to the Appendix for implementation details.). The representative samples taken from KITTI dataset. In Fig. 5 the smaller overlap regions of point-level feature distribution between points from inliers and outliers indicate the features of inliers and outliers distribute more distant, and thus, the features correspondence-leve similarity, inlier similarity should be distinct from outlier similarity to effec- tively differentiate between the two. With the self-adaption in FGCM, the data-specific teacher produces more discriminative features, resulting in a less noisy feature space conducive to the subsequent feature-based approach employed in FGCM.
more discriminative. For
We directly their official weights for evaluation.

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Feature Distribution Samples
Feature Similarity Distribution
of Inlier/Outlier Correspondences
Sample
Sample
0.B
0.8
Before
Inlier Pts (P).
Inlier Pts (P).
Adaptoo Adaption
1.25
Outller Pts (P).
Outlier Pts (P).
0.6
0.6
1.00
Inlier Pts (Q).
Inlier Pts (Q).
Pts (Q).
Pts (Q).
0.75
0.4
0.4
0.50
0.2
0.2
0.25
0.00
0.0
0.0
0.0
5-
1.0
15
Inlier
Outlier
0.0
0.3
Inlier Pts (P).
Inlier Pts (P).
Outlier Pts (P).
Outlier Pts (P).
After Adaptinn
Inlier Pts (Q).
Inlier Pts (Q).
After Adaption
Outlier Pts (Q).
Outlier Pts (Q).
0.1
0.0
1.5
1.0
1.5
0.0
0.5
1.0
1.5
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Inlier
Outlier
Figure 5: Before v.s. After Self-Adaption in FGCM: Point-wise Feature & Correspondence-wiss
Similarity Distribution indicate that the self-adaption results in more discriminative features.
4.3 Ablation Study
We conduct ablation studies to evaluate the efficacy of INTEGER on the KITTI dataset. We present mRR and registration errors in distant scenario where de [40, 50). Various alternative configurations INTEGER are compared Table Our method exhibits superior performance compared to alternatives, demonstrating the effectiveness of our design. This superiority may be at- tributed the features-geometry coherence: With FGCM, correspondences pseudo-labels possess discriminative features, facilitating effective knowledge transfer in feature space using ABCont.
Additionally, MDS significantly enhances performance in distant scenarios. The com- bination of Per-Batch Self-Adaption and Peature-Geomette Clustering in the FGCM module yields more substantial improve- ment than using either alone. The removal of Per-Batch Addftionttion marginally de- grades the quality of pseudo-labels, phasizing the importance of denoising the feature space. When synthetic teacher ini- tialization removed (w/o S.T.I), we em- ployed the same way EYOC pretrain the teacher. We find that synthetic teacher initialization greatly enhances the initial teacher's performance. Please refer to the Appendix for more qualitative results on generated synthetic pairs.
Table 3: Ablation Study of INTEGER. S.T.I denotes synthetic teacher initialization. PBSA and FGC denote Per-Batch Self-Adaption and Feature- -eaturry Clus- tering, respectively
UR @ 1st
d
[40, 50)
Methods
mRR
Epoch
RR
RRE
RTE
Full
81.2
84.0
54.2
1.1
0.54
ABCont
80.3
83.5
53.7
1.3
0.58
w/o PBSA
43.3
80.9
50.2
1.7
0.79
w/o FGC
67.6
82.8
52.7
0.61
w/o MDS
81.2
82.7
52.3
1.3
0.71
w/o S.T.I
71.9
83.7
53.7
1.2
0.55
Conclusion
In this paper, we present INTEGER, novel unsupervised method for point cloud registration that integrates low-level geometric and high-level contextual information for reliable pseudo-labels. Our method introduces Seature-Geometry Coherence Mining for dynamic teacher self-adaption and robust pseudo-label mining based on both feature and geometric spaces. Then, we propose Mixed-Densin Student learn density-inn density-invariant invariant features. We also introduce Anchor- Based Contrastive Learning

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for effective contrastive learning using anchors. Extensive experiments on two large-scale outdoor datasets validate our method's efficacy. Despite being unsupervised, achieves results comparable to state-of-the-an supervised methods and surpasses existing unsupervised methods, particularly in distant scenarios. Furthermore, our approach exhibits superior generalizability to unseen datasets.
Limitations.
The main limitations of the proposed method are twofold:
Our method is subject the quality of the teacher. If the teacher is inaccurate, the feature space may become too noisy, potentially impeding Feature-Geemeetr Clustering in FGCM, especially in distant scenarios. One potential remedy to devise more robust strategy for initializing the teacher.
Our method is slightly slower to obtain pseudo-labels compared to existing efforts [2 due to the proposed iterative method used in FGCM of the FGCM module. Future work may involve devising more efficient strategy for mining pseudo-labels.
Acknowledgements
This work was supported in part by the National Key R&D Program of China under Grant YFFO70664, the Fundamental Research Funds for the Central Universities (No. 20720220064).
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13

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A Appendix
A.1 Evaluation Protocol
we evaluate the registration performance using Relative Rotation Error (RRE). Relative Translation Error (RTE) and Registration Recall (RR). Related the practical purpose of outdoor registration, we additionally report RR@ d2) and mean Registration Reca RR@ [dj. d2) is registration recall w.r. pairs with distance d E [d1, d2), following [1]. mRR is defined as the average of RR@ [d1,d, d2) for all [d1, d2). ). To measure the quality of correspondences pseudo-labels, we report Inlier Ratio(IR) of the teacher in the first epoch, denoted "tIR @ 1dt Epoch".
Following previous works
43
38
Relative Rotation Error Relative rotation error is the geodesic distance in degrees between ground-truth and predicted rotation matrices:
(raceeR,,R..b -
RRE(Rp Rgt) = arccos
2
where Ryt and Rg denote the ground-truth and predicted rotation matrices, respectively.
Relative Translation Error Relative translation error is the Euclidean distance between ground- truth and predicted translation vectors:
RTE Egx) = 1|t, tgell2,
(8)
where to and Eyt are the ground-trune and predicted translation vectors, respectively.
Registration Recall The registration recall is defined as the fraction of point cloud pairs whose RRE and RTE are simultancously below the given thresholds (i.e.RRE and RTE < 2m for KITTI datasets):
RR
1 M
Σ
IRRE <TH A RTE, < Tr..
(9)
i=1
where T, and Ty are thresholds for RRE and RTE, respectively, and [:] is the Iverson bracket. We compute the mean RRE and RTE only for point cloud pairs that registered successfully, following
common practices [50 24 43 2 51).
Following existing efforts 12 we denote the registration recall w.r.t pairs with distance d E [d1, d2) as RR@ [d1, dz). With the set of distance intervals D {[5, 10), [10, 20), [20, 30), [30, 40), [40, 50)}. we define the mean registration recall as:
mRR
Σ d2)dD
RRØ (di,
(10)
A.2 Implementation Details
We introduce the implementation details of INTEGER in this section. Firstly, we describe the network architectures of FCGF and SC²-PCR, which we use by default to implement INTEGER. Then, we provide additional information about the implementation of FGCM. Finally, we provide the details of implementation of visualization in Fig. [ and Fig.
We adopt the popular FCGF[24) for the registration network in INTEGER. As depicted Fig. 6 the architecture incorporates Res-UNet structure and is implemented with sparse voxel convolution. It adopts three layers of skip connections with roughly symmetric encoder-decoder structure. Before used for registration, features are normalized onto the unit sphere after the last convolutional layer.
FCGF
14

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3D Conv 3 x 3,,256
ResBlock 256
3D ConvTr 3x 3
30 Conv 32,122
ReuBlock 128
ResBlock 128
3D ComuTr x 3,2,64
3D Conv 31,
ResBlock N
3D Canu 7 x 7.1332
3D 3 3x3.1333
Conv 32664
Resölock
Resölock
ComnTr x3264
Canv
Geometric Features
3x3x11N
Figure 6:
The Architecture of FCGE We use the same architecture as their official implementation (24]. It adopts three layers of skip connections with roughly symmetric encoder- decoder structure.
SC2-PCR SC2-PCR is robust pose estimator built upon the SC² measurement(21] For two correspondence c₂ (p:: qi) and Cy (P&: qi), Literatures prior Chen al. 21 utilized first-order spatial compatibility (SC) defined as:
(11) to measure the spatial compatibility between two correspondences, where Cry cy E and M E [|[| is the spatial compatibility matrix. To better distinguish inliers from outliers, Chen et al. 21 proposed a second-order spatial compatibility (SC*) using M M2, Thus, the SC scores for inliers will be skyrocketing and can easily be distinguished from outliers.
Mzy = lp: 1 |6 - q/12a
Built upon the SC² measurement, SC2-PCP first using spectral technique to extract most promis- ing seed correspondences and then iteratively refine the correspondences. The SC²-PCR is GPU- compatible and non-parametrri. Therefore, is efficient and has great generalizability for implement- ing our unsupervised method.
have to sample n. 1024 correspondences training with Cardest-Contrastive Loss. Thus, when FGCM mines more than n. correspondences randomly sample n. correspondences for training. However, in some cases, FGCM may fails to mine enough correspondences, resulting in less than n. correspondences. For effective training, we additionally perform a NN-search to complement the correspondences under such circumstance. This typically happens in very carly stages in training when the teacher model has not adequately adapted to real data yet, and very late stages when the overlap between point clouds is too low.
Details in FGCM Following existing efforts 24
in pseudo-labels,
Visualization in Fig. 1 and Fig. In Fig- I we visualize the features of points and anchors by projecting them into space using t-SNE 52]. Fig. we visualize the point-wise feature distribution and correspondence-wist similarity distribution. For point-level feature distribution, first project the point features into scalar space using (-SNE(52). Then, we estimate the probability density for points associated with inlier and outlier correspondences using Kernel Density Estimation (53 To estimate correspondence-lewe similarity distribution, we compute the Ly-distance in feature space between points in each correspondence and visualize the distribution of similarities for inliers and outliers. We use the sklear (54) library to implement t-SNE and KDE.
A.3 Training Details
To train INTEGER, we use the SGD optimizer with an initial learning rate of 0.3 and a weight decay of le We train INTEGER for 400 epochs with batch size of 8. The training process takes approximately 6 days on a single NVIDIA RTX 3090 GPU running at 1.70 GHz with 24 GiB of GPU memory.
A.4 Additional Experiments
15

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k 2|Cul
Max Iterations
82.2
82.5
R9% of Corr. in Pseudo Label
82.06
IR% of Corr. in Pseudo Label
81.97
81.99
82.06
82.06
82
81.95
82
82.06
81.8
81.74
81.82
81.5
81.6
81.32
81.52
80.96
81.44
81.2
80.5
A
0.1
0.2
0.3
0.4
0.5
0.6
0
100
200
300
400
(a) &
(h) Max Iterations
Figure Sensitivity of hyperparameters in FGCM module.
Hyperparameter Sensitivity in FGCM We evaluate the sensitivity of hyperparameters in FGCM, including the number & of putative correspondences enlarge C²-1 and the max number of iterations. The results are illustrated in Fig. [ The performance of INTEGER is relatively stable with respect to the hyperparameters, indicating
robustness our method to hyperparameter settings. For best performance, we set k = 0.4Cv and the max number of iterations to 100.
Table 4: Adaptability of INTEGER for Different Registration Networks
RR@d E
Network mRR
5, 10)
[10, 20)
(20,30)
[30, 40)
[40, 50)
FCGF
84.0
99.5
97.1
89.6
79.6
54.2
Predator
61.6
91.6
76.2
60.7
44.5
32.7
Adaptability to Different Registration Networks. We assess the adaptability of INTEGER by training it with different registration networks, namely Predator [43] and FCGF[24). The results presented in Table (indiiciee that INTEGER exhibits compatibility with diverse registration networks, underscoring its superior adaptability. However, we indeed observe that the performance gap between supervised and unsupervised settings widens when using Predator the registration network. This may be attributed to the more sophisticated architecture of Predator compared to FCGF, which may require accurate supervision signals for effective training. It will be our future work to improve the adaptability of INTEGER to more complicated registration networks.
Table 5: Additional Generalizability Results Compared with Supervised Methods. "/" in the column "U" denotes the methods are Unsupervised. Otherwise, they are supervised. The best unsupervised results are highlighted in bold. SerrTI-mnuSeens""ee denotes generalizability results from KITTI to nuScenes.
RR E
Dataset
Method
U
mRR
5, 10)
[10, 20)
(20,30)
[30,4] 40)
[40, 50)
FCGF
60.1
93.9
84.5
58.9
39.2
23.9
FCGF+C
60.3
95.9
84.5
61.1
35.8
24.1
KITTI
Predator
32.9
91.1
50.2
11.2
5.9
6.1
nuScenes
EYOC
55.3
96.2
75.6
58.7
26.6
19.7
RIENet
46.2
83.3
73.2
43.5
19.8
11.1
Ours
62.6
97.5
84.6
62.6
37.8
30.2
16

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Additional Generalizability Results. We provide additional generalizability results in Table For supervised methods, FCGF and its variants surprisingly gains improved performance by generalize from KITTI, which may be attributed to the lower resolution of LiDAR in nuScenes(64 beams, 100m range KITTI v.s. 32 beams, 70m range nuScenes), which may hinder training from scratch. This phenomenon is also observed by existing efforts [2]. Our method show superior generalizability even compared with supervised methods.
Real Scan
Synthetic Pair
(a) Sample from KITTI
Real Scan
Synthetic Pair
(b) Sample from nuScenes
Figure 8: Visualization of Generated Pairs in the Synthetic Pretraining Stage. The synthetic pair on the right is generated from a single real scan on the right. We additionally visualize the result of periodic sampling the top-right corner of synthetic pairs.
Qualitative Results on Synthetic Pairs. In the synthetic pretraining stage, generate synthetic
pairs from each real scan to train the teacher. We provide visualization on generated pairs in Fig. S The synthetic pair on the right is generated from single real scan the right. We additionally visualize the result of periodic sampling in the top-right corner of synthetic pairs. The periodic sampling strategy effectively simulates the irregular sampling of LiDAR point clouds. By randomly cropping the point clouds, the synthetic pairs are partially overlapped, which facilitates the training of the registration network.
17

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NeurIPS Paper Checklist
1. Claims
Question:
Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: It accurately reflects our contributions and scope. The scope of the paper is illustrated in Sec. We detail our method in Sec. Experimental validation are detailed in
Sec. 4
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The claims made should match theoretical and experimental results, and reflect how much the results be expected to generalize other settings.
is fine include aspirational goals as motivation long is clear that these goals are not attained by the paper.
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Question:
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Answer: [Yes]
Justification: It has been discussed the Appendix. Furthermore, we also mention the location to find this discussion of limitations in the Conclusion section (See. 5 for clarity.
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Question: For each theoretical result, does the paper provide the full of assumptions and complete (and correct) proof?
18

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Answer: [NA]
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5. Open access to data and code
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A.3
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Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
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Justification: It too computationally expensive for the proposed method. As shown in Sec. A.3 in the Appendix, our method currently requires a long training procedure. We
have demonstrated the robustness and reliability of the proposed method by conducting experiments on generalizability. Moreover, we have to note that a considerable amount of
existing research in point cloud registration 12 32 38 21 51 does not include results
on statistical significance, whereas a few 2 5 24 includes simple results such as variances for statistical results.
Guidelines:
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The answer NA means that the paper does not include experiments.
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Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics httph:tt////// httpp////eeerrpeec////////hhhhaa wtt.:hhhhhseiiieeeeeeneennee
Answer: [Yes]
Justification: We have read the code of ethics. Our research involves human subjects or participants, and the usage of KITTI and nuScenes datasets complies to their guidelines for privacy and ethical use cases. Information on reproducibility is provided in Sec. A. Sec.[A.2) and A.3. the Appendix. Our research point cloud registration currently involves no ethical considerations, and our usage of synthetic data adheres to ethical guidelines, because it is randomized, happens on-the-fly during training, and thus will not harm reproducibility.
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10. Broader Impacts
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Question:
Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: Our work performs positive socictal impact, such as its benefits for autonomous driving. We discuss it in Sec. [] We have not found negative societal impact yet for unsupervised point cloud registration.
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Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
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Justification: They are credited and cited properly in Sec. Release information on datasets has been included in their paper. KITTI uses CC BY-NC-SA 3.0 DEED, whereas nuScenes uses CC BY-NC-SA 4.0. We properly respect the license and terms of use. We also leverage official implementation for FCGF and Predator. We have cited their paper and their paper contains release information.
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According to the NeurlPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
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Reviews:
[{"review_id": "6HEqusjkN3", "reviewer": "Reviewer_Bwh6", "summary": "This paper focuses on unsupervised point cloud registration in 3D computer vision. To tackle the problem, it leverages the observation that in the feature space, points of latent new inlier correspondences tend to cluster around respective positive anchors. Based on that, this paper proposes a novel unsupervised registration method termed INTEGER to incorporate high-level contextual information for reliable pseudo-label mining. Extensive experiments were conducted on outdoor benchmarks including KITTI and nuScenes, which demonstrates the effectiveness of the proposed method.", "questions": "1. In Tab.1, why  there are fewer baseline methods on nuScenes compared to those on KITTI? As well as the  generalization test from KITTI to nuScenes?\n\n2. Although the title demonstrates that this paper focuses on outdoor scenes, the proposed method could also work on Indoor scenes. Why Indoor scenes are excluded? Could some experiments be added to further demonstrate the superiority of the proposed method?", "limitations": "Limitations have been dicussed.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper is well-written and well-organized;\n\n2. The observation w.r.t. the new inliers and positive anchors seems interesting and correct;\n\n3. The use of teacher-student networks is rational, and the design of Feature-Geometry Coherence Mining is novel.\n\n4. The experimental results are strong on outdoor scenes.", "weaknesses": "1. There are some problems in terms of figures. For example, Fig. 1 is not very easy to understand. As a teaser, it does not demonstrate the core idea of this paper very clearly. Fig. 2 and Fig.3 include too much content and make it hard to focus.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We first would like to thank the reviewer for giving us valuable comments.\n\n**W1:** *Problems with the figures. For example, Fig. 1 is not very easy to understand. Fig.2 and Fig.3 include too much content and make it hard to focus.*\n\n**A:** Thanks for pointing out the figure issues. A simplified version of Fig.2 is shown in **the PDF attachment of the general response**.  In Fig.1, we visualize the **feature space** by reducing the feature dimension to 2 with t-SNE. Here, we provide an explanation:\n\n- **Contour lines and colors in between** denote **the feature-space distance from a point to its nearest anchor**.\n- **The \"o\" and \"x\" markers** denote points forming inlier and outlier correspondence, respectively.\n-  From Fig.1, we can observe that **almost all points close to positive anchors in the feature space belong to inlier correspondences.**. The observation conforms to our key insight. \n\nWe will further improve the clarity of these figures in the revised version. Thank you for bringing this to our attention.\n\n---\n\n**Q2:** *Reasons for fewer baseline methods presented on nuScenes compared to those on KITTI, as well as the generalization test from KITTI to nuScenes.*\n\n**A:** We excluded some supervised baselines (e.g., GeoTransformer, CoFiNet, and Predator) in experimental results of nuScenes and generalization tests for two main reasons:\n- We aimed to align our experimental setup with previous research, such as EYOC, which similarly omits these baselines.\n- The omitted baselines are included in KITTI's results to demonstrate that ***state-of-the-art supervised methods fail when the overlap ratio is very low and density variation is huge.*** Since KITTI and nuScenes are both autonomous driving datasets and share similar challenges, we believe including these baselines may not significantly add to the completeness of our experiments.\n\nWe recognize the value of a comprehensive evaluation and have provided additional baselines in **part 1 of the general response**. Overall, these supervised SOTA methods still fail to perform on par with unsupervised counterparts with distant point cloud pairs. These experimental results will also be added to the revised version of our paper for clarity.\n\n---\n\n**Q3:** *Reasons indoor scenes are excluded? Additional experiments to further demonstrate the superiority of the proposed method?*\n\n**A:** We chose to focus on outdoor scenes for two reasons: (1) A rich set of unsupervised indoor registration methods have been proposed, and their performance is already on par with supervised indoor methods. Still, they **fail to tackle outdoor challenges** due to their reliance on RGB-D data, high overlap assumptions, and LiDAR data's sparsity in outdoor scenes. We aimed to extend the success of unsupervised methods to outdoor scenes, explicitly addressing the unique challenges of these scenarios, such as the varying point density of the same object in different scans, as often encountered in autonomous driving.  Given the very distinct applications and sensor characteristics (RGB-D cameras v.s. LiDARs), which may hinder a \"unified method\" from excelling in both indoor and outdoor environments, we only present the results on outdoor datasets in our paper. (2) Our method relies on progressive training (see Sec.3) and is designed to train with point cloud **sequences** that are commonly provided in outdoor autonomous driving datasets.\n\nWe acknowledge the significance of indoor scenes and have conducted additional experiments to explore our method's potential in these environments. Specifically, we tested generalization from the outdoor KITTI dataset to the indoor 3DMatch/3DLoMatch dataset, demonstrating that our framework, despite being unsupervised, outperforms the supervised FCGF by a significant margin (26.4% RR vs. FCGF's 19.7% RR). Please refer to **part 2 of the general response for details.**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "R8ciuNRFCD", "reviewer": "Reviewer_FNCk", "summary": "This submission proposes an unsupervised framework for point cloud registration. The key contribution is a two-stage training scheme, which first trains a teacher network on synthetic data that extract features in a density-invariant manner, and then trains a student network with pseudo label produced by the teacher net.", "questions": "In KITTI and nuScenes, as the data are scanned with limited degree of viewpoint freedom, can such method be applied to cases with significant rigid transformations? For example, in robotics, one may have to handle objects in varying poses randomly sampled in SE(3). If it is doable, could you please provide some insight/estimation on cost of the pre-training stage. \n\nMinor points: \n. L161, missing space.", "limitations": "The limitation discussion looks good to me.", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The submission is in general well structured. Similar to this type of works, it contains quite a few notations and architecture design details, which are presented in a relatively clear manner. \n\n2. The key insight, namely, \"points of latent new inlier correspondences tend to cluster around respective positive anchors...\" seems interesting and fresh to me (though I am not an expert in this area). \n\n3. The experimental performance looks competitive.", "weaknesses": "1. The key insight is more presented as an empirical observation, is there any chance that such can be justified in a more concrete way, even on some toy examples? \n\n2. I didn't find report on the training cost and inference efficiency in the submission.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We first would like to thank the reviewer for giving us valuable comments.\n\n**Q1:** *The key insight is more presented as an empirical observation, is there any chance that such can be justified in a more concrete way, even on some toy examples?*\n\n**A:** Thanks for your valuable comments. Fig.1 in our manuscript provides qualitative results concerning our key insight. We also conduct an additional simple quantitative experiment. For a sample pair from KITTI, we report the IR% of pseudo-labels at the first iteration in the FGC-Branch **under different thresholds based on the feature-space distance to positive anchors** in the following table. Features are normalized before calculating distances.\n\n||0.1|0.5|0.8|\n|-|-|-|-|\n|IR%|98.2|88.3|85.1|\n\nThe table shows that most inliers are close to positive anchors in feature space, and outliers are likely far away from positive anchors. This result conforms to our key insight. \n\nNotably, despite the high IR% of correspondences very close to anchors at the first iteration, **there are too few correspondences to supervise the student**, and some outliers still exist. This fact calls for our iterative design of FCEM to include potential inliers and update the anchors iteratively.\n\nWe will refine the presentation of our key insight by (1) providing detailed quantitative results that cover more pairs from both the KITTI and the nuScenes datasets and (2) adding some toy examples to Fig.1 in the revised version. \n\n---\n\n**Q2:** *Missing Report on the training cost and inference efficiency in the submission.*\n\n**A:** As an unsupervised registration network, our method's training cost and inference efficiency are highly dependent on the choice of registration network. For most experimental results with FCGF, the full training procedure takes approximately 76 hours. For the additional results with the Predator presented in the Appendix, the training procedure takes about 140 hours. The inference efficiency is the same as that of the registration network(0.16s for FCGF and 0.30s for Predator per pair) because our method does not introduce any **test-time** modules. We will add these details in the revised version. \n\n---\n\n**Q3:** *INTEGER applies to cases with significant rigid transformations. For example, object-level cases in robotics.* \n\n**A:** Although our work focuses on ***outdoor scene-level*** data rather than **object-level** data, we are willing to demonstrate the effectiveness of our method in scenarios involving significant rigid transformations. Specifically, we augment the rotation around the specified axis by a randomly-sampled angle between [a1,a2]°. \n\n- **Results with Augmented Z-axis Rotation on KITTI:** Transformation that has been presented in the training set.\n\nIn outdoor settings, the rotation around the Z-axis is the most common transformation. However, significant rotations as large as 180° are unseen in the model during training, which makes them a challenge.\n\nCompared to the supervised FCGF, our method has shown superior performance in terms of robustness against significant rigid transformations. Note that we follow the common practice of previous works to compute RRE and RTE only for pairs that are successfully registered. Therefore, RRE and RTE are not necessarily large even when RR% is very low. The results are as follows:\n\n**Ours**: \n||[-15,15]°|[-45,45]°|[-90,90]°|[-180,180]°|\n|-|-|-|-|-|\n|RRE(°)|0.25|0.28|0.28|0.33|\n|RTE(m)|0.13|0.14|0.14|0.16|\n|RR(%)|99.1|99.1|98.6|79.6|\n\nFCGF (supervised) trained on KITTI:\n||[-15,15]°|[-45,45]°|[-90,90]°|[-180,180]°|\n|-|-|-|-|-|\n|RRE(°)|0.36|0.38|0.39|0.44|\n|RTE(m)|0.46|0.42|0.43|0.25|\n|RR(%)|85.9|83.0|80.1|77.2|\n\n- **Results with Augmented X-axis Rotation on KITTI:** Transformation that **hasn't** been presented in the training set.\n\nIn outdoor settings, the rotation around the X-axis is almost absent from the dataset. Such transformations are thus considered a challenge for registration models, both in terms of generalization and robustness. In this case, we have observed that our method outperforms the supervised FCGF by a very large margin (+18.9 RR% at most), demonstrating the superior generalizability of our method. The results are as follows:\n\n**Ours**: \n||[-15,15]°|[-45,45]°|[-90,90]°|[-180,180]°|\n|-|-|-|-|-|\n|RRE(°)|0.49|0.51|0.84|1.28|\n|RTE(m)|0.15|0.28|0.25|0.30|\n|RR(%)|98.5|96.6|89.3|58.7|\n\nFCGF (supervised) trained on KITTI:\n||[-15,15]°|[-45,45]°|[-90,90]°|[-180,180]°|\n|-|-|-|-|-|\n|RRE(°)|0.91|0.93|1.01|1.23|\n|RTE(m)|0.49|0.52|0.51|0.48|\n|RR(%)|87.3|80.1|74.8|39.8|\n\nOverall, these results indicate that our method **can effectively handle cases with significant rigid transformations**, even when such transformations **are not adequately presented in the training dataset**.\n\nWe have acknowledged the importance of handling **object-level** data, such as ModelNet40. However, we are not able to conduct experiments on object-level datasets due to the lack of point cloud **sequences** in these datasets. Our method relies on progressive training (see Sec.3) and is designed to train with point cloud **sequences** provided in outdoor datasets. We will consider this in our future work.\n\n---\n\n**Q4:** *Insight/estimation on the cost of the pre-training stage.*\n\n**A:** For the KITTI dataset, we train the teacher for 30 epochs in the pretraining stage, which takes roughly the same time as teacher-student training. However, the time cost for a single epoch is longer because there are more point cloud pairs (we generate a synthetic pair for **every** frame in the training set). We will investigate the necessity and devise more efficient sampling strategies in our future work.\n\n---\n\n**Q5:** *Minor points: L161, missing space.*\n\n**A:** Thanks for pointing out it. We will correct it in the revised version.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "clKQ0abn0D", "reviewer": "Reviewer_SEpR", "summary": "This paper introduces an unsupervised framework for point cloud registration that generates reliable pseudo-correspondences using both low-level geometric and high-level contextual information. It employs a widely used teacher-student architecture and proposes Anchor-Based Contrastive Learning to facilitate robust feature space development through contrastive learning with anchors. Additionally, the paper introduces a Mixed-Density Student approach to learn density-invariant features, effectively addressing challenges associated with density variations and low overlap in outdoor scenarios.", "questions": "This paper introduces an unsupervised framework for point cloud registration that integrates both low-level geometric and high-level contextual information to generate reliable pseudo-labels. While the concept is promising, the manuscript could benefit from additional detail and clarification in several areas:\n1.\tSimilarity to Existing Methods: Some parts of the framework appears remarkably similar to the established EYOC method, thereby calling into question the novelty of this contribution.\n2.\tUsing low and high level information for mining pseudo-labels  is highlighted, yet the manuscript lacks a clear explanation of the specific mechanisms. If Spatial Compatibility Filtering is employed, it should be noted that this technique is already a component of EYOC.\n3.\tThe manuscript mentions pairs with distances [d1, d2], but it does not explain the impact of these distances for registration. A detailed explanation would enhance understanding of how these challenge the registration.\n4.\tDataset Differences and Overlap Ratios: The experimental section discusses the use of KITTI and nuScenes datasets. It is important to delineate the differences between these datasets, especially concerning their overlap ratios. Providing specific overlap ratios for these and other datasets would facilitate a more nuanced discussion of the framework's applicability and robustness across different scenarios.\n5.\tPerformance on Various Datasets: The framework's performance is evaluated on outdoor datasets like KITTI and nuScenes, but there is no discussion on its efficacy in indoor settings, such as with the 3DLoMatch dataset. Insights into performance in diverse environments would be particularly valuable, given the unique challenges posed by indoor scenarios.\n6.\tTraining Time: The manuscript omits details regarding the training duration. Including this information is essential for assessing the practicality of deploying this framework in real-world applications.\n7.\tComparative Analysis with EYOC: If EYOC also utilizes synthetic pretraining, a direct comparison with the proposed method under similar conditions is necessary. Such a comparative analysis would provide a fairer assessment of the proposed method's strengths and help highlight any genuine advancements.\n8.\tArchitecture Details for Predator:  Since Predator architecture employs cross-attention and a dual-branch structure but lacks clarity on how the network is divided into teacher and student components. This is non-trivial, and thus, more detailed explanations are required to understand its implementation and functionality fully.\n9.\tGeneralization to Indoor Environments: There is a need to assess how networks trained on outdoor datasets perform in indoor point cloud registration tasks. Evaluating the generalization capabilities of the framework would give insights into its versatility and effectiveness across different application settings.", "limitations": "The authors adequately addressed the limitations", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "This paper focuses on registering point clouds without relying on pose prior datasets to supervise model training. The observation that in the feature space, points of latent new inlier correspondences tend to cluster around respective positive anchors summarizing features of existing inliers is particularly interesting.\n\nThe FCEM adaptation of the teacher model to a data-specific teacher for the current mini-batch is intriguing. However, the procedure described in the manuscript is complex and challenging to follow. It seems that the teacher model is first updated using the current mini-batch dataset, then correspondences are selected to train the student, followed by an update of the teacher weights using Exponential Moving Average (EMA). This sequence raises questions about the efficiency and effectiveness of such a dynamic updating scheme.\nThe authors need to provide a clearer explanation of this process.", "weaknesses": "First limitation is that some parts of the framework appears remarkably similar to the established EYOC method, thereby calling into question the novelty of this contribution.\nBesides, the integration of different levels (low and high) of information for mining pseudo-labels  is highlighted as a distinguishing contribution, yet the manuscript lacks a clear explanation of the specific mechanisms. If Spatial Compatibility Filtering is employed, it should be noted that this technique is already a component of EYOC.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for the valuable comments. **For concerns about the efficiency and effectiveness of FCEM, please refer to the \"6. Efficiency and effectiveness of FCEM\" part in the general response.**\n\n**Q1:** *Similarity to EYOC.*\n\n**A:** Our method **significantly differs** from EYOC in several key aspects: (1) **Novel Insight:** We innovatively introduce a new perspective by demonstrating that inlier matches are closer to positive anchors than negative ones, which summarizes existing inlier and outlier features, respectively. (2) **Pseudo-Labeling with Multilevel Information:** Our innovative FCEM module dynamically adapts the teacher and integrates low-level geometric and high-level contextual information, whereas EYOC **only uses low-level geometric cues**. (3) **Robust Knowledge Transfer** We propose ABCont for effective and robust teacher-student knowledge transfer, which is not present in EYOC. (4) **Density Invariance:** We introduce MDS to explicitly address density variation in outdoor scenarios, a concern **overlooked by EYOC**. Experiments show that our method outperforms EYOC in two datasets by a considerable margin.\n\n---\n\n**Q2:** *Clarity on pseudo-labeling mechanisms and the use of Spatial Compatibility Filtering(SCF) in relation to EYOC.*\n\n**A:** We would like to clarify a potential misunderstanding. While SCF in GSA-Branch appears to be similar to EYOC regarding rejecting outliers, our intention **completely differs from EYOC**:  We aim to **improve the *teacher* for the current data batch**, whereas EYOC uses it for pseudo-label extraction for ***student***. Moreover, experiments(Sec4.2, L272-285) show that SCF can be implemented using other pose estimators rather than SC2-PCR estimators used by EYOC.\n\nMoreover, we **do not solely rely** on SCF to incorporate both low- and high-level information; this is achieved through the *entire* FCEM, particularly the FGC-Branch(Sec 3.3, L186-216). We iteratively identify latent inliers using feature-space anchors and exclude outliers via SCF. The contributions are novel and not found in EYOC. In our manuscript(L174-175), we cited EYOC to credit their work. We will add detailed discussions on the differences to EYOC in the revised version.\n\n---\n\n**Q3:**  *Impact of distances [d1, d2] on registration.*\n\n**A:** Our evaluation follows EYOC's existing protocol, focusing on pairs within distances [d1,d2], consistent with our method's design for autonomous driving data. The differences between frames, **indicated by the distance between them**, are crucial for demonstrating robustness and generalizability in real-world applications like collaborative perception. Increased distances mainly present two challenges:(1) Overlap Ratio: Increasing distances reduce overlap ratios, complicating the search for reliable correspondences. (2) Density Variation: Increasing distances often lead to significant point density variations, challenging feature matching without density-invariant features.\n\n---\n\n**Q4:** *Dataset Differences and Overlap Ratios.*\n\n**A:** **Fig.2 in the PDF attachment of the general response** illustrates the overlap ratios w.r.t distances between frames in KITTI and nuScenes datasets, indicating increasing distances reduce overlap ratios. Furthermore, KITTI and nuScenes differ in LiDAR resolution(64 LiDAR beams in KITTI and 32 LiDAR beams in nuScenes), resulting in denser point cloud data of the KITTI dataset. The sparsity of nuScenes point cloud data makes it more challenging for registration, especially for feature extraction.\n\n---\n\n**Q5:** *Performance on Various Datasets.*\n\n**Q9:** *Generalization to Indoor Environments.*\n\n**A:** We address Q5 and Q9 together here. We conduct additional experiments in **indoor**(3DMatch/3DLoMatch dataset) and **non-urban** environments(ETH dataset). Please refer to **parts 2 and 3 of the general response** for details.\n\n---\n\n**Q6:** *Lack of Training Time Details.*\n\n**A:** For most experimental results with FCGF, the full training procedure takes approximately 76 hours. For the additional results with the Predator presented in the Appendix, the training procedure takes about 140 hours. The inference efficiency is the same as that of the registration network(0.16s for FCGF and 0.30s for Predator per pair) because our method does not introduce any **test-time** modules. Please refer to **part 5 of the general response** for details.\n\n---\n\n**Q7:** *Direct Comparison with EYOC if it also uses synthetic pretraining.*\n\n**A:** EYOC **doesn't use** synthetic pretraining. Instead, it assumes minimal transformation between two consecutive LiDAR frames, using identity transformation as the ground truth for the teacher's pretraining. In contrast, our method employs synthetic pretraining to initialize the teacher, as detailed in Sec3.2(L149-156). Table 4 of the general response **shows that EYOC's assumption does not hold in real-world data**: it may introduce significant noise, leading to a suboptimal initial teacher of EYOC.\n\nFor direct comparison, we evaluate both methods using EYOC's **App**roximation approaches and **Syn**thetic-Pretraining.\n||App.|Syn.|\n|-|-|-|\n|EYOC|53.2|**54.0**|\n|**Ours**|71.9|**81.2**|\n\nOur method consistently outperforms EYOC even when initialized the same as EYOC. While synthetic pretraining benefits EYOC, the improvement is limited.\n\n---\n\n**Q8:**  *Clarification on Predator architecture and its use in the framework.*\n\n\n**A:** **Predator doesn't employ a dual-branch structure**. It consists of a **single-branch KPConv encoder-decoder structure** with an overlap-attention module in between, and we do not divide the architecture into teacher and student ***components**. Regarding Predator's results in the Appendix, we utilize the **entire** Predator model described in Predator's paper, pre-training it fully as the teacher, and then supervise the student with the **same** architecture. We will clarify this in the revised version.\n\n---", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Tq7IK51Vpq", "reviewer": "Reviewer_2VKD", "summary": "The paper introduces a new unsupervised outdoor point cloud registration method called INTEGER, which dynamically integrates high-level contextual information and low-level geometric information to generate reliable pseudo-labels, addressing the issue of poor performance in complex outdoor environments seen in previous methods reliant on geometric data. By incorporating the Feature-Geometry Coherence Mining module, Anchor-Based Contrastive Learning, and the Mixed-Density Student model, this method not only performs well in scenarios with significant variations in data density but also demonstrates its efficiency and generalizability on standard datasets like KITTI and nuScenes. Overall, the INTEGER method significantly improves in accuracy and generalizability, especially in handling complex and distant outdoor scenes, showing advantages that traditional methods struggle to match.", "questions": "Robustness of Initial Teacher Model:\nCould you elaborate on the strategies used for the initialization of the teacher model? Given the dependency of the INTEGER method on the quality of the initial teacher, understanding its robustness in adverse conditions or with suboptimal initialization would be informative.\nAre there specific conditions under which the initial model tends to fail, and how does this impact the overall registration accuracy?\nBroader Comparisons:\nThe paper currently compares INTEGER with a select group of methods. Could you include comparisons with additional state-of-the-art unsupervised methods that employ fundamentally different approaches? This could help in understanding the unique advantages or potential trade-offs of INTEGER.\nAdditionally, it would be beneficial if you could provide insights into the computational efficiency and scalability of INTEGER compared to both supervised and unsupervised counterparts.", "limitations": "The manuscript does discuss some technical limitations related to the initialization of the teacher model and the conditions under which the method may underperform. However, these discussions could be expanded to include:\nScalability: How does INTEGER scale with increasingly large datasets or more complex environments? Including a discussion on computational resources and runtime could provide a clearer scope of applicability.\nRobustness: More detailed exploration of robustness against different types of noise or outliers in point cloud data would be beneficial. Given the application domains of point cloud registration, such as autonomous driving and robotics, understanding these aspects is crucial.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "Originality:The INTEGER method demonstrates originality by innovatively combining high-level contextual and low-level geometric information for unsupervised point cloud registration. This method creatively addresses challenges in outdoor environments, where previous methods relying solely on geometric data often fail.\nQuality:The paper showcases high-quality research through detailed methodological execution and robust evaluations on standard benchmarks like KITTI and nuScenes. The proposed mixed-density student model, which learns density-invariant features, ensures robust performance across diverse scenarios.\nClarity:The manuscript is clearly written and well-organized, effectively communicating its core ideas, methodologies, and results. It uses figures and tables effectively to aid understanding, making it accessible to readers familiar with point cloud processing.\nSignificance:The work is highly significant, offering potential transformative impacts in autonomous driving and robotics by enhancing unsupervised point cloud registration in outdoor scenes. Its competitive performance against supervised methods highlights its practical relevance and potential to reduce reliance on labeled data.", "weaknesses": "Dependency on Initial Conditions\nThe INTEGER method's performance heavily relies on the quality of the initial teacher model. A poorly initialized teacher model could propagate errors and inefficiencies through the learning process. The paper could explore and discuss alternative strategies for more robust initializations or provide a more detailed analysis of how the initial conditions affect the overall performance. This would give readers a clearer understanding of the method's robustness and potential limitations in real-world scenarios.\nComparison with State-of-the-Art Methods\nWhile the paper presents comparisons with existing methods, the selection seems limited to those that are closely aligned with the proposed method's framework. Including a broader range of state-of-the-art methods, especially recent unsupervised learning approaches that use different paradigms, could help validate the strengths and uniqueness of INTEGER more convincingly. This comparison could also be extended to include a discussion on how INTEGER performs relative to these methods in terms of computational efficiency and scalability.\nDiscussion on Failure Cases and Limitations\nThe paper could benefit from a more thorough discussion of scenarios where INTEGER might underperform, such as extremely sparse point clouds or highly noisy environments. Understanding the method's limitations and potential failure cases would help in setting realistic expectations and could guide future research to address these specific challenges.\nGeneralizability Across Different Datasets\nWhile the paper tests INTEGER on KITTI and nuScenes, additional experiments on datasets from different domains or with different characteristics could help demonstrate the method's adaptability and robustness. Exploring performance on datasets with varying densities and noise levels would provide a more comprehensive evaluation of the method's effectiveness across diverse real-world conditions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We first would like to thank the reviewer for giving us valuable comments.\n\n**Q1:** *Robustness of Initial Teacher Model: the strategies used for teacher initialization and its robustness in adverse conditions or with suboptimal initialization.*\n\n**A:** The initialization strategy is detailed in Sec 3.2. We first split an input point cloud into two partially overlapping parts, apply a random rigid transformation to one part, and use it as the ground truth. To mimic real-world LiDAR scans, we employ a periodic sampling technique. We also apply commonly used data augmentations, such as random scaling and noise. Visualizations of the generated pairs are provided in Sec. A.5 (L594-600).\n\nThe performance of INTEGER indeed relies on the initial teacher. However, INTEGER remains robust even with suboptimal initialization. Our ablation study (Sec 4.3) shows that INTEGER maintains high-quality pseudo-labels, even with EYOC-style initialization (achieving 71.9% IR compared to EYOC's 53.2% IR). This superior robustness may be attributed to the proposed FCEM module, which dynamically adapts the teacher, enhancing it before mining pseudo-labels.\n\nTo further demonstrate the robustness, we have compared (1) a **F**ully-trained teacher, (2) a **U**nder-trained \n teacher, and (3) a **R**andomly-initialized teacher. We measured the Inlier Ratio of the teacher in the first epoch to assess the quality of pseudo-labels:\n\n||**F**|U|R|\n|-|-|-|-|\n|IR@1st Epoch|**81.2%**|72.1%|34.9%|\n\nWe observed only a **minor** performance drop when the teacher wasn't fully trained, and the randomly-initialized teacher performed only slightly worse than the **well-trained** EYOC. In this **very extreme** case, FCEM's adaptation process ensures that the teacher **still performs surprisingly well**, highlighting both the superiority of the FCEM design and the robustness of our method. We would also like to highlight that after training for several epochs, **the teacher's IR improves significantly**, with **minimal negative impact** on the student's convergence.\n\nIndeed, more complicated registration networks, such as Predator, **slightly** struggle with current initialization strategies. During training, they show suboptimal performance at the **beginning** of teacher-student training but **eventually catch up** after more training epochs, highlighting the superior effectiveness of the proposed FCEM module. We speculate that the complicated networks may suffer from overfitting the synthetic data. In further work, we will devise a better strategy to address this issue.\n\nRegarding adverse conditions, we plan to investigate common adverse conditions in autonomous driving scenarios, such as extreme weather, in our future work. This is a critical aspect of real-world applications that requires thorough investigation.\n\n---\n\n**Q2:** *Broader Comparisons: Additional SOTA unsupervised methods that employ fundamentally different approaches.*\n\n**A:** Our INTEGER focuses on **outdoor scenes**; only **a few unsupervised methods**, namely EYOC and RIENet, are applicable in this context. We ***have included both*** in our comparison (see Sec 4.1, Table 1). Among these unsupervised methods, RIENet takes a **fundamentally different approach**. Our INTEGER not only outperforms EYOC, but also suppresses RIENet by a large margin. \n\n---\n**Q3:** *Insights into computational efficiency and scalability of INTEGER compared to both supervised and unsupervised counterparts.*\n\n**A:** As mentioned in Limitations (Sec.A.1), our method is slightly slower to obtain pseudo-labels than EYOC because of the proposed iterative method used in the FGC-Branch of the FCEM module. However, with only 33% more time cost on KITTI, our INTEGER has **much more accurate** pseudo-labels with 28.1% higher IR (81.3% v.s. EYOC's 53.2%), and **considerable improvements** on RR% of very distant pairs. (54.2% v.s. EYOC's 52.3%). We show additional results for supervised baselines on the nuScenes dataset and generalizability tests in **part 2 in the general response**, which shows that our method has **better scalability than SOTA supervised and unsupervised methods.** Please refer to it for details.\n\n---\n\n**Q4:** *Scalability with increasingly large datasets or more complex environments and the discussion on computational resources and runtime; Generalizability Across Different Datasets.*\n\n**A:** \nOur method targets autonomous driving scenarios, so we tested it on KITTI and nuScenes, standard datasets in this field. These datasets vary in density, occlusion, and noise levels, enabling us to evaluate INTEGER's scalability and robustness.\n\nTo **further** demonstrate the scalability of INTEGER, we have also evaluated the performance of INTEGER on ETH, an outdoor dataset with **rural and forest scenes**, which are primarily unstructured and complex, differing from the urban environments of KITTI and nuScenes datasets. Moreover, we also conducted additional experiments in **indoor** scenes as requested by other reviewers. Please refer to **part 2 and 3 of the general response** for results. These results also show the superior generalizability of INTEGER.\n\n---\n\n**Q5:**  *Robustness against different types of noise or outliers.*\n\n**A:** In outdoor scenes, registration methods are often challenged by extremely low overlap and density variation, which introduces noise in correspondences, especially for distant pairs. Our method demonstrates superior robustness against these challenges, as shown in Sec 4.1, Table 1. \n\n---\n\n**Q6:**  *Discussion on Failure Cases and Limitations.*\n\n**A:**  The robustness of the proposed INTEGER against different types of noise and outliers, including the noise introduced by extreme weather, requires further investigation. These situations are particularly relevant for autonomous driving. We will discuss these limitations and future work in the conclusion.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We sincerely thank all reviewers for their careful, valuable, and insightful reviews. The reviewers acknowledge our work with good writing(Bwh6,FNCk,2VKD), novel design(Bwh6,SEpR), and competitive performance(Bwh6,FNCk,2VKD). We are particularly delighted to see that all reviewers recognize the novelty and correctness of the insight and the key observation of our method. We have conducted additional experiments to address the comments, and results are included in the PDF attachment. We describe new experiments in the PDF attachment and discuss the results most reviewers requested.

1. **More Supervised Baselines.**

We excluded some supervised baselines for **nuScenes dataset** and the **generalizability test** because:
- We aimed to align our experimental setup with previous work, such as EYOC, which similarly omits these baselines.
- The omitted baselines are included in KITTI's results to show that ***SOTA supervised methods fail with very low overlap and huge density variation***. Since KITTI and nuScenes are both autonomous driving datasets and share similar challenges, we believe including these baselines may not significantly add to the completeness of our experiments.

We have **included more** supervised baselines in **Table 1 of the PDF attachment**. Similar to KITTI's results, these supervised SOTA methods still fail to perform on par with unsupervised counterparts with distant point cloud pairs (within [40,50]m; see Table 1). This highlights the need for an unsupervised outdoor registration method with strong generalizability to handle distant point cloud pairs, which is crucial to real-world applications. We will include these results in the revised version for clarity.

---

2. **Reasons for Outdoor Scenes. Generalizability to Indoor Scenes.**

In our paper, we chose to focus on outdoor scenes because (1) A rich set of unsupervised indoor registration methods have been proposed, and they already perform on par with supervised indoor methods. Still, they **fail to tackle outdoor challenges** due to their reliance on RGB-D data, high overlap assumptions, and LiDAR data's sparsity in outdoor scenes. In this paper, we aimed to extend the success of unsupervised methods to outdoor scenes, explicitly addressing the unique challenges of these scenarios, such as the varying point density of the same object in different scans, as often encountered in autonomous driving.  Given the very distinct applications and sensor characteristics (RGB-D cameras v.s. LiDARs), which may hinder a "unified method" from excelling in both indoor and outdoor environments, we only present the results on outdoor datasets in our paper. (2) Our method relies on progressive training(see Sec.3) and is designed to train with point cloud **sequences** that are commonly provided in outdoor autonomous driving datasets.

However, we acknowledge the importance of indoor settings and provide results on **3DMatch/3DLoMatch** in **Table 3 in the PDF attachment**. Following SpinNet(CVPR 2021) and BUFFER(CVPR 2023), we report RR% for generalizability tests using weights trained on KITTI.

---

3. **ETH Dataset: Generalizability to Non-Urban Outdoor Environments.**

We **further** demonstrate the scalability of INTEGER by evaluating on ETH dataset, an outdoor dataset with **rural and forest scenes**, which are primarily unstructured and complex, differing from the urban environments of KITTI and nuScenes datasets.
Because ETH is too small for training from scratch, we directly evaluate performance using weights trained on the KITTI dataset. The results are shown in **Table 2 of the PDF attachment**. 

Overall, our method suppresses supervised FCGF in RR% by a large margin (58.06% v.s. 39.55%), demonstrating its superior generalizability. Moreover, our method also outperforms unsupervised EYOC by a considerable margin.

---

4. **Overlap w.r.t. Distance of KITTI and nuScenes.**

Our evaluation follows **EYOC's existing protocol**, focusing on pairs within distances [d1,d2], consistent with our method's design for autonomous driving data. The differences between frames, **indicated by the distance between them**, are crucial for demonstrating robustness and generalizability in real-world applications like collaborative perception. **Fig.2 in the PDF attachment** illustrates the overlap ratios w.r.t distances between frames in KITTI and nuScenes datasets, indicating **increasing distances reduce overlap ratios.**

---

5. **Training Cost and Computational Efficiency.**

As an unsupervised training framework, INTEGER's training cost is highly dependent on the choice of the registration network. For most experimental results with FCGF, the entire training takes ~76 hours. For results with Predator in the Appendix, the training takes ~140 hours.

The inference efficiency is the same as that of the registration network because our method does not introduce any **test-time** modules. We list the inference efficiency of FCGF and Predator on KITTI here for convenience:

|Method|Time(s)|
|-|-|
|FCGF|0.16| 
|Predator|0.30| 

We will add the results to the revised version.

---

6. **Efficiency and Effectiveness of FCEM.**

We have demonstrated the effectiveness in Sec 4.3, Table 3. In the ablation study, we validate the effectiveness with experiments on the two branches of FCEM.

As mentioned in Limitations (Sec.A.1), our method is slightly slower to obtain pseudo-labels than EYOC because of the proposed iterative method used in the FGC-Branch of the FCEM module. On average, our method takes ~12 minutes to *train* (i.e., validation time is not included) every epoch on KITTI, while EYOC takes about ~9 minutes. However, with only 33% more time cost on KITTI, our INTEGER has **much more accurate** pseudo-labels with 28.1% higher IR (81.3% v.s. EYOC's 53.2%), and **considerable improvements** on RR of very distant pairs. (54.2% v.s. EYOC's 52.3%). Therefore, our FCEM is efficient concerning **the trade-offs of time and performance**.

Meta-review: The paper focuses on unsupervised point cloud registration. To tackle the problem, it leverages the observation that in the feature space, points of latent new inlier correspondences tend to cluster around respective positive anchors. Based on that, this paper proposes a new unsupervised registration method termed INTEGER to incorporate high-level contextual information for reliable pseudo-label mining. Extensive experiments were conducted on outdoor benchmarks including KITTI and nuScenes, which demonstrates the effectiveness of the proposed method. The final recommendations from the reviewers were 1XWeak Accept, 2XBorderline Accept and 1XBorderline Reject.
Decision: Accept (poster)