GeGS-PCR: Fast and Robust Color 3D Point Cloud Registration with Two-Stage Geometric-3DGS Fusion
Authors: Jiayi Tian
Haiduo Huang
Tian Xia
Wenzhe zhao
Pengju Ren
Venue: NeurIPS 2025 poster ()
Keywords: Point Cloud Registration; Geometric-Color Fusion; Geometric-3DGS; Color Encoding; LORA; Differentiable Rendering; Photometric Loss; Low Overlap Scenarios; Robust Registration; Multi-Stage; 3D Point Cloud Processing;
Primary area: applications
TL;DR: We propose GeGs-PCR, a two-stage point cloud registration method that integrates geometric, color, and Gaussian information, achieving robust performance and state-of-the-art results even in low-overlap scenarios.

Abstract: We address the challenge of point cloud registration using color information, where traditional methods relying solely on geometric features often struggle in low-overlap and incomplete scenarios. To overcome these limitations, we propose GeGS-PCR, a novel two-stage method that combines geometric, color, and Gaussian information for robust registration. Our approach incorporates a dedicated color encoder that enhances color features by extracting multi-level geometric and color data from the original point cloud. We introduce the Geometric-3DGS module, which encodes the local neighborhood information of colored superpoints to ensure a globally invariant geometric-color context. Leveraging LORA optimization, we maintain high performance while preserving the expressiveness of 3DGS. Additionally, fast differentiable rendering is utilized to refine the registration process,  leading to improved convergence. To further enhance performance, we propose a joint photometric loss that exploits both geometric and color features. This enables strong performance in challenging conditions with extremely low point cloud overlap. We validate our method by colorizing the Kitti dataset as ColorKitti and testing on both Color3DMatch and Color3DLoMatch datasets. Our method achieves state-of-the-art performance with Registration Recall at 99.9%, Relative Rotation Error as low as 0.013, and Relative Translation Error as low as 0.024, improving precision by at least a factor of 2.

GeGS-PCR: Effective and Robust 3D Point Cloud Registration with Two-Stage Color-Enhanced Geometric-3DGS Fusion
Jiayi Tian', Haiduo Huang', , Tian Xia', Wenzhe Zhao', Pengju Ren" National Key Laboratory Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center of Visual Information and Applications, Institute of Artificial Intelligence and Robotics, Xi' an Jiaotong University,
Xi' an. Shaanxi, China
{tianreg, huanghd) @ stu.xjtu.edu.cn (tian_xia, wenzhe, pengjuren) @ @xjtu.edu.en
Abstract
We address the challenge of point cloud registration using color information, where traditional methods relying solely on geometric features often struggle in low- overlap and incomplete scenarios. To overcome these limitations, we propose GeGS-PCR, novel two-stage method that combines geometric, color, and Gaus- sian information for robust registration. Our approach incorporates dedicated color encoder that enhances color features by extracting multi-level geometric and color data from the original point cloud. We introduce the Geometric-3DGS module, which encodes the local neighborhood information of colored superpoints to ensure a globally invariant geometrie-colee context. Leveraging LORA opti- mization, we maintain high performance while preserving the expressiveness of 3DGS. Additionally, fast differentiable rendering is utilized to refine the registration process, leading improved convergence. To further enhance performance, we propose a joint photometric loss that exploits both geometric and color features. This enables strong performance in challenging conditions with extremely low point cloud overlap. We validate our method by colorizing the Kitti dataset as ColorKitti and testing both Colcr3DMatch and LoMtch datasets. Our method achieves state-of ofate-of-the-ar the-art performance with Registration Recall at 99.9 9%,9, Relative Rotation Error low 0.013, and Relative Translation Error low 0.024, improving precision by at least a factor 2.
1
Introduction
Fast and stable point cloud registration is a crucial technology in computer vision [ and embod- ied intelligence [2]. serving as the foundation for various practical applications, such as 3D scene reconstruction 3. semantic scene segmentation [4, and large-scale perception and mapping [5). In essence, point cloud registration involves aligning two overlapping 3D point clouds using rigid transformation through a series of estimation steps.
Recent advancements in deep learning have accelerated the development of 3D point cloud rep- resentation [6] [ and differentiable optimization techniques [8] [. Previous works have focused on keypoints and correspondences, leveraging specialized neural networks to extract features from point clouds, and subsequently determining the rigid transformation using robust estimators like Inspired by image matching, recent research has highlighted the significance of
RANSAC 10
Penggu Ren is the corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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local neighborhood information [12 [3] by matching keypoinnss (superpoints) based on the detection of overlapping patches. This has led to advances point cloud registration methods [14 13]. where downsampling is used to layer point clouds, and the Transformer architecture is employed to capture contextual information, adding informative constraints to the registration process. Furthermore, unsupervised forrespondence-base point cloud registration methods that focus on optimizing point and Gaussian distribution correspondences [16 [7
have gained significant attention.
Despite rapid progress, point cloud registration remains chal- lenging in real-world scenarios with low overlap between point
Overllag: 20.3%
Overinp: 20.35 sPoint 256 Inlier ratlic 64.8%
APPoint corr: 128
Inlice ratlo: 79.7%
clouds [TI [8]. where regis- tration often fails. This high- lights the need for novel meth- ods. Recent breakthroughs in colored point cloud registration 19 20 have shown that inte- grating color information can re- veal relationships that cannot be captured by geometric features alone, thereby improving regis- tration performance. As shown in Fig. [ color information plays crucial role in scenarios with low overlap and subtle geometric features. When color differences are not distinct, simply incorpo- rating color information still fails to establish the correct correspon- dences. However, when subfig- ures (c) and (d) specifically an- alyze color features, the regis- tration process can successfully
(a) ColorPCR, Puich Comerpondences
(6) ColerCR Poin: Correspondences
Overlap:: 20.3%
Overlap: 20.356
APoinnt corr: 128 Ialier ratle: 95.3%
#Polnt corr: 286
Inlier 94.1%
(e) GGG--PR Putch Correpundences
GeGs PCR, Point Conreponnences
Figure I: In scenarios with minimal overlap, incomplete geomet- ric features, and subtle color variations, methods that simply add color features perform moderately, whereas GeGS-PCH success- fully identifies the brown sofa.
match the brown sofa with its armrest. The Gaussian distribution captures global shape variations and significantly suppresses noise. Combining color and geometric information, along with considering the relationships between point clouds and their Gaussian distributions, is crucial for faster and more robust registration.
To address the challenges of point cloud registration low-overlap real-world scenarios, we propose GeGS- two-stage method that integrates Geometric-3DGS for colored point cloud registration. We designed a dedicated color encoder that enhances color features and extract multi-level geometric and color information from the original point cloud. The Geometrie-3DGS module encodes local neighborhood information of colored superpoints, achieving globally invariant geographic color context. Using the parameterized multimodal local neighborhood information from 3DGG(geometric, Gaussian, and color information), we perform fast coarse registration. To reduce the computational complexity and parameter count introduced by 3DGS parameterization without sacrificing expressive power, we incorporate LORA optimization (21]. For better model convergence, we use 3DGS's s fast differentiable rendering to refine the point cloud registration. Additionally, we introduce joint photometric loss to improve the utilization of color information during the registration process. Through these modules, geometric and color data are tightly integrated, enabling GeGS-PCR to deliver strong performance even in challenging low-overlap scenarios.
Furthermore, due to the limited availability of publicly available colored datasets. currently only the publicly available Mathh and Color3DLoMatee datasets 20) are available. Therefore, to validate the generalization ability of the model, we colorized the Kitti dataset to create ColorKitti. Evaluations on these datasets demonstrate that GeGS- can achieve fast and stable registration under low overlap. proving its advanced effectiveness. The main contributions of this paper are as follows:
We tightly combine color and geometric information to achieve point cloud registration. Specifically, we design a color encoder for feature extraction, constructing a globally invariant geometric-color representation.
2

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We propose the Geometric- module to encode multimodal representations of super- point neighborhood information. Using attention with 3DGS embeddings, we focus on global geometric distribution-colo features and perform fast coarse registration by reducing computational complexity with LORA.
We introduce a joint photometric loss. By performing fast differentiable rendering on the Geometric-3DGS module and calculating photometric loss during the rendering process, we refine the registration of point clouds.
We colorize public point cloud datasets to generate ColorKitti. Experimental validation shows that GeGS-PCR performs excellently even in scenarios with extremely low overlap.
2 Related Work
2.1
Correspondence-Baie Based Methods
Existing correspondence-basee methods can be roughly divided into point-to-point and point-to- distribution registration approaches. Point-to-point methods (e.g.. ICP) aim to estimate transforma- tions through point coordinates or feature extraction 22
Using robust pose estimators (such as registration is achieved through iterative optimization between correspondence search and transformation estimation. However, these methods are highly sensitive noise and density variations and are typically supervised. The second category, point-to-distribution maps points to probability distributions and estimates transformations through distribution alignment clustering (20]. (26). (27). Although these methods unsuper- vised, the iterative process can be time-consuming. Recent studies have adopted a coarse-to- approach [14], 28 achieving advanced performance. this work, follow this approach and focus on improving registration accuracy through a closer integration of color and geometric information (including color and distribution information).
23
RANSAC or other RANSAC-free methods [13],
19
24
25
2.2 Point Cloud Feature Extraction
Recently, due to the maturity image matching methods. new paradigms for 3D point cloud feature extraction have emerged. PointNet performs deep learning-based feature extraction using graph convolution 29 and point convolution kernels [30]. Notably, feature extraction using KPConv- FPN B11,
32 has become mainstay. To enhance the use of color information, PEAL [19] extracts RGB color from images, but faces the problem of color information loss. Based on this, ColorPCR (20) integrates color information through the CEFE module and achieves better performance. However, these methods model color information separately. Inspired by the latest 3DGS technology in scene reconstruction, we consider tighter contextual relationships between color (opacity) and geometric information, enabling a Geometric-Color invariant representation. Therefore, innovatively introduce 3DGS into point cloud registration and propose the Geometric- 3DGS module. Through a color depth encoder, we extract deep color information and construct a global geographic relationship between point cloud color and geometric information achieve fast. registration in the coarse alignment stage.
2.3
Registration With Color Features
Some methods implicitly utilize color information to first detect keypoints or use 2D-3D multimodal learning 33
34
351 [36]. PEAL detects overlaps in 2D images and then transfers them
3D registration network. Additionally. ColorPCR uses multi-stage color processing in the global registration process utilize color information. The ICP algorithm [37] and its variants (such as 4DICP) (38) increase the original point cloud feature dimensions to incorporate color information into geometric registration optimization. We follow this idea and use HSV and LAB to represent different color spaces 33 [4) Due to the differentiable rendering properties of 3DGS [1] 42
43
we adaptively fuse color information achieve fast and stable fine registration of point clouds.
3 Method
Problem statement. Suppose we have two point clouds representing the target point cloud P [p.ERR]i 1,...NN. NN and the source point cloud Q {q I,..,M }. and their
3

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corresponding color information can be represented as P. fpe. [0, 1 = 1..., N} and Q. (a, E [0. 1 I..., MM, respectively. The main objective of point cloud registration is to estimate a rigid transformation, represented by 7 R, 4), where R E SO(3) is the 3D rotation matrix and E R33 the translation vector, such that the point clouds P and Q align through this transformation. The true correspondences between these point clouds are represented by the set C", which is initially unknown. Therefore, we can optimize the following objective to solve for the rigid transformation:
min Σ
|R Ps. +t 9z.
(1)
(P P9, JEC
3DGS
Extrctint-..........
J0GS Superpoit Manching
hin Registation tranffcmmtion-
Culer
Optinization
Oulpen
Inpur Cooor
IDGS
Feeture based Crosestation
3DGS Embesking
Self- Micaiin
GroMlonke
Tomsedding
SDOG
Tranefenrations Selection
Enpader
Maschine Modde.
1R. 1)
Color
ClorMatic
Limbodiing
Befieemecut.....
Super/wonts
Color
Cioresgondencs
Difficentiaee
Enoodes
Loca Optiiiization
Rendering
Figure 2: Pipeline. The entire network backbone is divided into coarse and fine scales. The feature extraction module extracts and integrates geometric and color information from the input point clouds P and Q using the color encoder and geometric encoder, producing superpoint representations / and Q. The 3DGS Superpoint Matching Module identifies correspondences through 3DGS embeddings and self-attention mechanisms. LORA optimization is applied to reduce computational complexity and integrate both geometric and color information effectively. Finally, the Fine Registration & Transformation Module refines the registration by performing differentiable rendering after coarse registration, optimizing the rigid transformation parameters {Rt, }
Our pipeline is shown in Fig. 2 We represent the dense points and colors of the target point cloud as P E RIPI33 and Pa [0, PT33 respectively. The coarsest level of the dense points is represented as P E R PPx3 and P. E [0, 1] |P|33 and the finest level of the point cloud (superpoints) is represented as E x3 and P. E [0, 1|131 Similarly, the source point cloud is represented in the same way.
3.1
Coarse Registration With Color Features
3.1.1 Color Encoder Module
We design a dedicated color encoder module to inject effective color information into point cloud features (see Fig. 2 The rationale for using this encoder is twofold: (1) typical geometry gcometry-colorr fusion often performed by simple addition, which cannot effectively handle noise in color information; (2) direct color feature extraction across different levels of feature extraction leads reliance low-level features. The encoder first inputs the three-channel color vector F, E IR3 into a multi-layer perceptron (MLP). This MLP processes the color information, fully encodes it, and extracts deep color features, which are then bounded in the [0, 1] range through a sigmoid function to produce normalized color features Pig. The noise-robust color mapping is follows:
F'6 = 8(LN 80000688LWWWWWW (6(LN(W1))))))
where Wi, W2, and W2 E d are learnable weights, din and dant are input and output dimensions, (-)(.) denotes layer normalization, and is the activation function. This process maps the original color to decoupled high-dimensional space, effectively removing noise interference.

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Based on this, we introduce learned scalar weight 8(w), where w represents the parameter, to adaptively fuse the geometric and color features. During training, this weight dynamically adjusts the fusion process by balancing the contribution of geometrie features F3 and color information Fg The final enhanced feature Fenh is obtained as follows:
{ F @ (a Foolor),
<<D L 1= I.
enn
F + Poolor
where Fg is the original geometric feature, Foolor E R the color space vector (HSV. LAB) processed by the MIP, and ( represents channel concatenation. We use this color encoder in feature extraction at different levels. At the final level, we only use feature concatenation without the color encoder. This design injects color information while preserving the original geometry and other feature information, ensuring sufficient multimodal representation for downstream tasks.
3.1.2 Geometric-3DGS Module
The Geometric-3DGS module mainly consists of three components: the 3DGS encoder, attention with 3DGS embeddings, and Gaussian superpoint registration, as shown in Fig. 2 To improve the robustness and accuracy of the coarse registration stage, this module deeply integrates geometric and color features. Directly parameterizing all point cloud information with 3DGS at the beginning would result in a large amount of redundant parameters and very high memory requirements. Therefore, the core of this module is to 3DGS encode the local neighborhood information during point cloud downsampling, and use 3DGS embeddings and attention mechanisms to focus relevant features in the 3DGS encoding. This module implements feature extraction at different granularities and provides a global, wansformationninnariin geometric-color representation, which is crucial for fine point cloud registration.
3DGS encoder. We propose Dual-Modal Color Encoder (DMCE), which is responsible for transforming local neighborhood patches in the point cloud into more robust and rich representations, thus capturing both geometric and color features. This method uses Gaussian distribution-based representations to model the local neighborhood structure and the relationships between points. The specific steps of the 3DGS encoder are follows: We calculate the covariance matrix of each local neighborhood in the point cloud, which can capture the local geometric structure. This matrix considers the relative distances between points within the neighborhood to enhance the representation of local surface directions. Specifically, for a key point P. with a neighborhood Ni, we first compute the differentiable covariance matrix:
Σ: Ro(r:) diag(exp(s:)) Ro(r;)T + >Anan
where Ro(-) E SO(3) represents the rotation matrix, r; E R is the rotation quaternion, s; E R is the logarithmic scale vector, n, is the estimated normal vector, and X controls the strength of the normal vector, with À E [0.01, 0.1]. This covariance matrix captures the geometric features of the local region of the point cloud. Finally, we perform top-k (I: E [2, 5)) fusion between the color features from the color encoder and the 3DGS parameters. By combining position, covariance matrix, color, and transparency, we construct the 3DGS feature vector:
FanGs = Tops, (Concat jus, rec(E;), 0;, Fi
(5)
where l4 is the Gaussian position center, and o;; represents transparency. Attention with 3DGS embeddings. In this part, we implement 3DGS position embeddings to obtain globally invariant geometric-color fusion encodings. Finally, based on the GeoTransformer, we use self-attention and cross-attention to focus on the color information in the point cloud structure and guide superpoint registration. In both indoor and outdoor scenes, uncertainties such as sensors, lighting, and natural weather conditions often introduce noise or missing data in color sampling. To mitigate the impact of these color noises on global features, we aim to differentiate the parts that are heavily affected by noise. For indoor scenes, we use the HSV color space, and for outdoor scenes, we use the LAB color space. This ensures the most stable color information embedding. thus enabling robust structural position encoding. The specific process for the 3DGS position embedding is in Appendix A.2
Superpoint registration with 3DGS. To quickly register the point cloud information from Geometric- 3DGS during the coarse registration stage, we use the ICP algorithm to align the Gaussian distributions. By minimizing the 3DGS distance between the source and target point clouds Pt, Pj. we iteratively
5

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optimize the rigid transformation between Pt. Pj using least squares until convergence. We define the generalized distance metric as dıg - |lug - 14 1| Xa ||ا - 2 || r. where the parameter Aa is adjustable within the range of [0.05, 0.2]. n3 1j are the means of the Gaussians in the source and target point clouds, and Mg Σ are the covariances. Based on this definition, we give the associated probability matrix A E RNxM which measures the confidence of the match between pt. Pj-
exp(-
Ag
(6)
Ex
where 7 is the sensitivity control parameter, adjustable within the range of [1, 3], and this probability matrix is normalized using softmax. By combining the generalized distance and the probability matrix, we construct the objective to be optimized based on Mahalanobis distance:
M ΣΣ =1
N
min
Ag [| - -=) + -13
RESO
where 1i; fl represent the weighted centroids of the source and target point clouds, respectively, i E Aiytt. n² = Anput ||-Il denotes Mahalanobis distance, with 2; used to down-weight regions where the covariance computation has large errors. This objective can be solved using SVD decomposition, resulting in:
=
- - -
(8)
3j
U.S.V = SVD(H), =V=VU t² p² R'p".
(9)
Once the transformation values during training are smaller than a minimum tolerance, the 3DGS
registration is achieved.
LORA optimization. In the Geometric-3DGS module, the 3DGS parameterization introduces a large amount of high-dimensional data, which may result in significant computational and storage burdens, especially in large-scale point cloud scenarios. Therefore, we introduce LORA optimization within the overall Transformer structure to reduce unnecessary computational overhead. By using the LORA module, we convert the high nigh-dimensional 3DGS embeddings into low-rank form, allowing the model remain efficient and accurate without sacrificing its capacity.
3.2 Fine Registration With Photometric Optimization
To improve point cloud registration accuracy, we propose a fine registration method based on photometric optimization. After coarse registration, we optimize point cloud alignment by rendering the 3DGS of the target and source point clouds under the new pose and minimizing the weighted photometric loss. Traditional photometric optimization methods typically only consider the L1 distance, which fails to effectively handle noise and lighting variations. To address this, we introduce weighted photometric loss, assigning different weights to each pixel to enhance robustness and reduce the effects of uneven lighting and noise. Our photometric loss is calculated as follows:
Lphota = Σ wi -
W; = exp( d:),
(10)
where f(G C)2 f(G2, C) represent the rendered results of the target and source point clouds under the new pose C, G2 and Gerepresent the 3DGS from the coarse registration, w; represents the pixel weight factor, and d; is the pixel distance between the source and target point clouds. The sensitivity control parameter Ya adjusts the influence of distance on registration, adjustable within the range of 3]. Using differentiable rendering, we backpropagate the loss to the transformation parameters R" and update them with gradient descent. This approach enhances accuracy, particularly in key regions, by combining geometric loss with the weighted photometric loss for precise point cloud alignment, as shown:
(11) where Legnn is the geometric registration loss, and Ap E [0.1, is a weight hyperparameter that adjusts the balance between geometric and photometric losses. We provide the detailed proof of the convergence of the joint photometric optimization in the Appendix A.
Itoaal = I.geo + >pThhhoo

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Experiments
To validate the performance of the GeGS-PCR model, we evaluate on the indoor benchmarks Color3DMatch (C3DM) and Color3DLoMatch (C3DLM), as well as our colorized outdoor ColorKitti (The specific data construction process, including the detailed steps and settings for preparing the datasets, can be found in Appendix |A.4 and A.5 A.5
odometry benchmark. Each point cloud in these
datasets includes an RGB color value.
Table Evaluation results on C3DM and C3DLM. #Samples in the table represents the number of correspondences selected by RANSAC.
C3DM
C3DLM
#Samples
5000
2500
1000
500
250
5000
25500
1000
500
250
Feature
Matching Recall (%)
CoHiNet 44
98.1
98.3
98.1
98.2
98.3
83.
83.5
83333
83.
82.6
GeoTransfon foaTrrssorrer
15
97.9
97.9
97.9
97.9
97.6
88.3
88.6
88.8
88.6
88.3
PEAL 19
99.0
99.0
99.1
99.1
98.8
91.7
92.4
92.5
92.9
92.7
ColorPCR
20
99.5
99.5
99.5
99.5
99.5
96.5
96.5
97.0
97.0
96.7
GeGS-PCR PCR (ours)
99.5
99.6
99.5
99.7
99.6
97.6
97.4
97.1
97.2
97.0
Inlier Ratio (%) f
CoPiNet 44
49.8
51.9
52.2
52.2
24.4
25.9
26.7
26.8
26.9
GeoTransformer
16
71.9
75.2
76.0
82.2
85.1
43.5
45.3
46.2
52.9
57.7
PEAL 19
72.4
79.1
84.1
86.1
87.3
45.0
50.9
57.4
60.3
62.2
ColorPCR 20
75.0
80.5
84.7
86.5
87.8
51.2
56.6
63.1
66.0
68.0
GeGS-PCA PCR (ours)
76.3
82.4
86.3
86.6
89.1
53.4
58.7
66.9
69.7
70.3
Registration Recall (%)
CoFiNet 44
89.3
88.9
88.4
87.4
87.0
67.5
66.2
64.2
63.1
61.0
GeoTransfomnrr
92.0
91.8
91.4
91.2
75.0
74.8
74.2
74.1
73.5
PEAL 19
94.6
93.7
93.7
93.9
93.4
81.7
81.2
80.8
80.4
80.1
GeoTransformer-MAGG 15
95.7
95.7
95.2
95.3
94.6
78.9
78.7
78.2
77.7
76.6
ColorPCR 20
97.5
96.5
97.0
96.4
96.5
88.9
88.5
88.1
86.5
85.0
GeGS-PPd PCR (ours)
97.9
97.6
97.5
96.7
97.6
90.7
90.2
90.4
90.0
89.8
4.1 Indoor Benchmarks: Color3DMatch & Color 3DLoMatch
Table 2: Registration results w/o RANSAC on C3DM and C3DLM. The model is the time for feature
extraction, while the pose time is for transformation estimation
RR (%)f
Time (s) Pose
Model
Estimator
#Sample
C3DM
C3DLM
Model
Total
FCGF
RANSAC- -50k
5000
85.1
40.1
0.052
3.326
3,378
D3Feat
RANSAC-50K
5000
81.6
37.2
0.024
3.088
3.112
SpinNet
RANSAC-
5000
88.6
59.8
60.248
0.388
60.636
Predator 28
RANSAC-50K
5000
89.0
59.8
0.032
5.120
5.152
CoFiNet 44
RANSAC-50k
5000
89.3
67.5
0.115
1.807
1.922
GeoTransformer 15
RANSAC-50K
5000
92.0
75.0
0.075
1.558
1.633
PEAL
RANSAC-50K
5000
94.6
81.7
0.089
1.776
1.865
ColorPCR 20
RANSAC-50k
5000
97.5
88.2
0.083
1.629
1.712
GeGS-PCR(ours)
RANSAC-50K
5000
97.9
90.7
0.082
1.618
1.700
CoFiNet 44
RANSAC-free
all 87.6
64.8
0.115
0.028
0.143
GeoTransformeri 15
RANSAC-free
all 91.5
74.0
0.075
0.013
0.088
PEAL 19
RANSAC-free
all 94.3
78.8
0.089
0.034
0.133
ColorPCR
RANSAC-fre free all 97.3
88.3
0.083
0.046
0.129
GeGS-PCR
RANSAC-free all 97.5
89.1
0.082
0.032
0.124
Correspondence results. We compared GeGS-PCR with several SOTA methods (metrics in Appendix(A.3) A.3p. Most methods use RANSAC, and we followed the same approach for consistency. Key results shown in Table (additional results in the Appendix A.33) GeGS-PCR outperforms

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ColorPCR with 99.5% FMR on C3DM and 97.6% on C3DLM. For IR, it reaches 89.1% on C3DM and 70.3% on C3DLM, surpassing ColorPCR by 1.3% on C3DM and 2.3% on C3DLM. In RR. GeGS-PCR achieves 97. 97.9% on C3DM and 90.7% on C3DLM, outperforming ColorPCR by 0.4% on C3DM and 4.2% on C3DLM. These results demonstrate significant improvement over baseline methods, with GeGS-PCR excelling, especially in low-overlap scenarios.
Table 3: Performance of ablation experiments
C3DM
C3DLM
Overlap
PIR(%)
FMR(%)
IR(%)
RR(%)
PIR(%)
FMR(%)
IR(%)
RR(%)
(a) w/o differentiahle rendering
71.7
98.0
59.1
90.7
85.8
40.1
72.1
(b) 3DGS
97.9
65.6
91.0
42.5
73.1
(c) Geometric-3DGS
70.4
42.7
73.5
color encoder
82.1
97.7
70.3
53.9
88.1
43.3
74.0
w/o color
83.8
98.0
70.7
92.7
54.1
88.4
43.5
74.2
(f) w/o LoRA
92.0
99.3
86.3
97.5
63.8
97.4
59.9
90.5
Geometrie-3DGS(FFll))
92.0
99.6
82.4
97.6
63.9
97.4
58.7
90.2
Ovarlage 17.4%
RAIS:: 1.3550
RMSS: 0.33pz
infoint oom 12s inker ratan 35
PPain oun Taller miko: 93
MPaict Tnller mEl 53
Ahhine com 256 lalks make: 93
Overlan: 13.75
RMSE: 1.913m
RMSS: 0.03
Jelker
#Pvint
964 20
1022
9%
Overlay:
0.007m
iPous con 128 Ielke rutor 29
#Phore com 256
aPoln coc 256 Intler
(c) lipu
(6) Ground trth
Gestrasffomer pole
Geis-PCR pose
Goousofeeee coccspendetces
(0 GKGi-PCR Point conespendenes
Gestrataommer Point conespardeeess
GEGE-PER
ooreggendenos
Figure 3: Registration performance with GeGS-PCR and Geometric self-attention.
Table Ablation results based on ColorPCR baseline
C3DM
C3DLM
Method
PIR(%)
FMR(%) (%)
IR(%)
RR(%)
PTR(%)
FMR(%)
IR(%)
RR(%)
(a) ColorPCR (baseline)
99.5
80.5
56.6
88.5
ColorEncoder
89.4
99.5
80.6
96.6
62.8
96.6
56.8
88.6
(C) w/o 3DGS
89.5
99.6
80.7
96.7
63.0
96.7
56.9
88.8
(d) w/o differentiable rendering
89.6
99.5
80.8
96.8
63.1
96.8
57.0
88.9
(e) w/o color
86.1
97.9
77.3
92.7
55.2
89.8
46.3
77.9
(f) w/o Geometric PE
88.8
99.3
80.2
96.3
62.4
96.0
56.4
88.0
(g) w/o LoRA
88.9
99.3
80.1
96.2
62.4
96.1
56.3
88.4
(h) Geometric-3DGG (all)
90.0
99.6
82.4
97.6
63.9
97.4
58.7
90.2
Registration results. As shown in Table GeGS-PCR outperforms both RANSAC and RANSAC- free methods. For RANSAC-based methods, GeGS-PCR achieves 97.9% RR on C3DM and 90.7%
on C3DLM, surpassing ColorPCR, with total processing time of 1.703s. second only D3Feat (1.712s). GeGS-PCR also achieves the best pose estimation time of 0.072s. For RANSAC-free methods, GeGS-PCR reaches 96.9% RR C3DM and 89.1% C3DLM. outperforming ColorPCR, with total time of 0. 14s, second only to Geo Transfooorerr (0.088s). However, GeGS-PCR surpasses Gre'rrasffommr in both RR and pose time, demonstrating its superior precision and speed.

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Ablation experiments. Ta-
ble E presents the ablation ex- periment results, analyzing the impact of each module on regis- tration performance. Removing the color component (row e) re- duces performance, particularly on C3DLM. Without the color encoder (row d), performance drops slightly, especially in FMR.
Table 5: Registration results w/o RANSAC on Kitti
Model
RTE (cm)
RRE (*)
RR (%)
3DFeat-Nell 45
25.9
0.25
96.0
FCGF g
9.5
0.30
96.6
D3Feat 9
0.30
99.8
SpinNet
9.9
0.47
99.1
Predator 28
6.8
0.27
99.8
CoFiNet 44
8.2
0,41
99.8
Transoosformrr
[5
7.4
0.27
99.8
GeGS-PCR (ours, RANSAC-SOK)
6.3
0.16
99.9
Excluding the Geometric-3DGS module (row c) decreases PIR and IR, and removing 3DGS (row b) further lowers registra- tion recall (RR). The removal of differentiable rendering (row a) significantly affects IR and PIR. with decreases of 7.1%% % and 9.5% in PIR and 6.5% and 8.1% %% in IR for C3DM and C3DLM, respec- tively. This highlights the importance of differentiable rendering for improving precision and inlier ratio. It helps the model utilize color information, improving point cloud aligmment and boosting IR and PIR. In addition, removing LoRA optimization (row f) leads to a slight drop in registration performance, particularly in IR and RR, indicating that LoRA mainly accelerates convergence and provides a modest yet consistent improvement in accuracy while preserving efficiency. More detailed ablation analysis is shown in Appendix (A.3)
FMR [11]
~66
1.49
90.6
DGR 18
~32
0.37
98.7
HRegNet 46
0.29
99.7
Tranfooorrre (LGR)
6.8
0.24
99.8
GeGS-PCR (ours, LGR)
5.7
0.13
99.9
Baselines ablation experiments Table repoorts the ablation results based on the ColorPCR baseline. Overall, each module contributes to performance improvements to varying degrees. Removing color information (row e) causes the most significant degradation, with PIR, IR, and RR dropping notably on both C3DM and C3DLM, highlighting the critical role of color features in low-overlap scenarios. In contrast, removing the color encoder (row b) or geometric positional encoding (row f) only leads to minor fluctuations, suggesting these modules play supportive roles. Excluding 3DGS (row c) or differentiable rendering (row d) results in moderate decreases, particularly in IR and RR, indicating their importance for fine-grained alignment and convergence. Removing LoRA (row g) slightly reduces performance, confirming its role in accelerating convergence and providing consistent accuracy gains while maintaining efficiency. Finally, the full Geometric-3DGs model (row h) achieves the best results across all metrics, with PIR reaching 90.0% and IR improving to 82.4% on C3DM, and PIR reaching 63.9% and IR improving to 58. 7% on C3DLM, demonstrating the effectiveness of the proposed modules in synergy. To clarify metric repetition, we ran independent ablations on ColorPCR (Table controlling module order and data synergy. Results show consistent gains even on weaker baselines, proving our module design is sound, generalizable, and optimizable. Qualitative Results. Fig. 3 shows the comparison of registration results using geometric attention and our 3DGS celf-attention in scenes with low overlap and geometric feature overlap. Geometric attention produces large dispersive effect, while 3DGS self-attention is able to find consistent correspondences for low-overlap features, significantly improving the inlier ratio and resulting in more accurate registration. The visualization results show that 3DGS self-attention can accurately identify correspondences in low-overlap areas and reject incorrect matches.
4.2 Outdoor Benchmarks: ColorKitti
Registration results. Based on previous research settings 7 15 we introduced the Registration Recall (RRowtdoor) metric (defined in Appendix A.3).. In Table 5 we first compare our GeGS-PCR model with RANSAC-based methods. Additionally, we compare it with methods that do not use RANSAC. The results show that GeGS-PCR performs comparably, with significant improvements in some metrics. Using RANSAC, GeGS- achieves 99, 9% Registration Recall (RR), demonstrating excellent performance, Even without RANSAC, GeGS-PCR maintains 99.95 99.9% RR, and achieves the best RTE and RRE values.
Qualitative results. Fig. shows the comparison of registration results using geometric attention and our 3DGS self-attention in low-overlap scenes. The red boxes in the ground truth highlight the colored regions. The results demonstrate that GeGS-PCR achieves good registration these regions under both high and low point correspondence conditions. Notably, GeGS-PCR produces almost

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Figure 4: Registration performance with GeGS-PCA and Geometric self-attention.
no incorrect correspondences in the colored areas. While geometric attention causes significant dispersive effects, 3DGS self-attention consistently finds correct correspondences in low-overlap features, significantly improving the inlier ratio, especially in such regions. Further limitations and comprchensive performance analysis can be found in Appendix A.5 and Appendix A.6
5 Conclusion
In this paper, we present GeGS-PCR, an innovative two-stage point cloud registration method that enhances registration accuracy and robustness by integrating geometric, color, and Gaussian distribution information. In the coarse registration phase, GeGS-PCP PCR effectively extracts reliable features in low-overlap scenarios with incomplete geometric features by introducing the Geometric- 3DGS module and color encoder. Additionally, LoRA optimization applied to reduce the complexity introduced by feature encoding. In the fine registration phase, differentiable rendering combined with photometric optimization loss further improves performance. The advantages of GeGS-PCR lie in the collaborative optimization of global and local structures. Through local Gaussian feature extraction, GeGS-PCC effectively suppresses noise interference and robustly fuses geometric and color features. GeGS-PCR is not only suitable for high-overlap point cloud registration but also offers an efficient solution for low-overlap tasks, such as autonomous driving and large-scale scene reconstruction.
6
Acknowledgments
This work was supported in part by National Natural Science Foundation of China No. 6208810 102 and No. 62302221.. The Authors are with the National Key Laboratory of Human-Man Humhn-Machine Hybrid Augmented Intelligence, National Engineering Research Center of Visual Information and Applica- tions, and Institute Artificial Intelligence and Robotics, Xi'an an Jiaotong University, an Shaanxi, China.
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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]
The abstract and introduction clearly outline the core contributions of the paper, including the introduction of a novel point cloud registration method, GeGS-PCR, and a detailed explanation of its innovative use of both geometric and color information. The abstract clearly states the method's experimental results and its outstanding performance in low-overlap scenarios, with comparisons made to existing techniques to validate its superiority. The introduction also mentions the method's ' limitations and potential future improvements, ensuring consistency with the actual results and objectives.
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Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: The paper clearly discusses the limitations of the method. First, GeGS- PCR relies on superpoints (patches) extracted through downsampling during the registration process. In regions with high point cloud overlap. the large number of superpoints, combined with 3DGS parameterization, can lead to significant memory usage and computational overhead. Since patch decomposition shares similarities with semantic scene understanding. the authors plan to leverage semantic scene understanding for point cloud pair registration in future research. Additionally, the current registration method involves pairing after 3DGS parameterization of domain superpoints. future work, the authors aim to explore scene-level registration of 3DGS for more realistic environmental registration.
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The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section their paper.
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The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency the proposed algorithms and how they scale with dataset size.

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A Technical Appendices and Supplementary Material
A.1 Proof of photometric optimization
To rigorously analyze the convergence of joint photometric-geomeerie optimization, we formulate the camera pose optimization on the Special Euclidean group SE(3) manifold. Let the camera pose be parameterized as E SE(3), which can be expressed via the exponential map from its Lie algebra & E se(3):
(12) where E IR' and R2 represent the angular and linear velocities, respectively. They can be derived from the translation matrix T. Under the assumptions local convexity the photometric loss Lipas near the optimal pose T and bounded gradient noise, the proposed joint loss Liaal converges to a local minimum when optimized via Riemannian gradient descent on SE(3). The gradient of Luaa on SE(3) is computed through the retraction map Ry:
T exp(E"),
[w: w/" E
the rotation matrix
(ŌLyeo 0
@.Lphoto dE
grad Ltotel
Ri
+
(13)
where & se(3) is Lie algebra of transformation and RiT the retraction map that ensures gradient mapped correctly from the Lie algebra back to SF(3). Using the chain rule, the photometric gradient with respect to & is derived as:
Thpooo 0
Σ Ws
- f(G2)) 021
OAI aT 8T
(14)
0
where f(G1) and f f(22) represent the rendered results of the target and source point clouds under the new pose C, is the weight factor for each pixel, and A/ is the difference between the rendered and target images. The image gradient is:
OIJ((G)) - S(G)) (f(G)) - f(Gz))
(15)
TAT We also calculate the rendering Jacobian and Lie Algebra Jacobian as:
0A1
OT
(16)
aT
a
The Lie algebra Jacobian follows the left perturbation model:
aT
lim exp((5g)")T Ts, 55-40
(17)
ag
Using the Lojasiewicz inequality on matrix Lie groups, we show that with learning rate v) < 1 (where is the Lipschitz constant), the gradient norm Igrad l1 decreases monotonically until reaching a stationary point:
grad T 112 - C( (k+11) )
(18)
This guarantees that the loss function will decrease monotonically and converge to a local minimum.
A.2 Structure Embedding
3DGS embedding. this part, we implement 3DGS position embeddings obtain globally invariant geometric- color fusion encodings. Finally, based on the Transforrrr we use self-attention and cross -oss-atttntion to focus on the color information in the point cloud structure and guide superpoint registration. In both indoor and outdoor scenes, uncertainties such as sensors, lighting, and natural weather conditions often introduce noise missing data in color sampling. To mitigate the impact of these color noises glohal features, aim differentiate the parts that are heavily affected by noise. For indoor scenes, we use the HSV color space, and for outdoor scenes, we use the LAB color space. This ensures the most stable color information embedding, thus enabling robust structural position encoding. The specific process for the 3DGS position embedding is as follows:
Gaussian embedding. We add Gaussian embedding to capture geometric distribution information that closely related to color information. This is particularly useful for invariance between point clouds, where the distribution of local regions is represented using the mean and covariance of 3DGS. The difference in the mean is computed as 8 ||ıs mjاlg where μt, Hú represent the local means in the source and target point clouds, respectively. The Frobenius norm difference in covariance óz, |[ le where E, E, the covariance matrices of the local neighborhoods in the two point clouds. The final Gaussian embedding computed as:
EGs PE (fh. + E5,,) 5ps
Was.
(19)
aGs
14

---

where ocs is the sensitivity hyperparameter for the Gaussian embedding, adjustable within the range of [0.01. 0.1]. PE the sine position embedding function, and Was Rd the matrix used for projection, with d, representing the output dimension. Then, we fuse embeddings (including distance, color, angle, and Gaussian embeddings, where the structure the color distance and angle embeddings is shown A.I) I to obtain the final 3DGS embedding Easg. This embedding method ensures that the point cloud information in cach layer is adequately represented.
3DGS self-Attention. To enhance the feature extraction from this part, introduce the 3DGS self-attention mechanism. First, based on the 3DGS embeddings, we generate the query keys and values as follows:
Q = EaseWa: K2 = E'ss W + Eose WK,
VG = Easss Wo.
(20)
where Eass 2h represents the feature of the iii-th joint embedding, F represents the corresponding feature set (as shown in the Fig. 2 and Eoen E Rd represents the collection embedding. which is combination of color-distance embedding and angle embedding (specifics can be found A.2). Wo. WK. Wy e Rd gededd are learnable projection matrices used to generate the query, key, and value. Based on this, we obtain a new attention calculation method (the specific structure shown in the Fig. bellow)
Q.K3 dd.
asy = Sofffbrn bomaa
0g log(1 + Egéo) .V.
(21)
where, A E [0.01, 1] controls the weight of the geometric information in the attention computation by adjusting the influence of the log(1 + Eg(o) term. This term designed to emphasize the relationship between geometric features, such as color and angle, thus improving the feature fusion process.
Output
MX N d
Add & Norm
A: Mx
Feed Forward
Soflmax
E: MXNNN
Add Norm
OK' MX
Linear
Q: MX
K: MX V: Nxd
3DGS
w d.xd
W dxd
dxx
Self-Attention
Mx MX d
Figure 5: Left: The structure of 3DGS self-attention module. Right: The computation graph 3DGS self-attention.
Color Distance embedding, Colorized position embedding color achieved by calculating Euclidean distance between each pair 3DGS the point cloud and normalizing the distance before embedding:
1pp.
12
duniiees
(22)
END PE(AH d)WHn.
(23)
Where, da is sensitivity parameter distance control. AH ||pp hp represents hue difference containing color information, PF is the sine position emhedding function, and the projection matrix. Angle emhedding. Angle embedding is based on the cross product of three points in the point cloud. For given triplet points, ps. Pj and their neighbor pt. we calculate angle between the three points:
PE a tan 2(1 x u, 24 Uz)
Angizk
W..
(24)
where = U/ PA are the vectors from Px. and a. is the temperature parameter for angle embedding, controlling the sensitivity of angle embedding. Wais the projection matrix.
15

---

A.3 Metrics
We evaluate the performance of GeGS-PCR using standard metrics, including the Registration Recall Rate (RR). which is the proportion of point clouds with transformation below threshold (e-g., RMSE 0.2), the Feature Matching Recall Rate (FMR), representing a threshold (e.g.. 5%), and the Inlier Ratio (IR), which measures the proportion of matching points with residuals below a threshold (e.g.. 0.1m). Additionally, we assess the model's performance using the Relative Rotation Error (RRE) and Relative Translation Error (RTE).
proportion of point cloud pairs with an inlier ratio above
Inlier Ratio (IR) used measure the proportion of correspondences with geometric consistency under the transformation. For example, given a point cloud pair (P, and its correspondence M, the definition
TR(P, Q)
1
Σ
I(ITTa(p.))
2, 2,112 8corr);
(25)
M
(PL-yJJMM
where l' is the ground truth transformation matrix, and òcorr < 0.1 is the inlier threshold function, and I(+) is the Iversion bracket.
Feature Matching Recall (FMR) is used to evaluate whether the correspondence geometry contains enough inliers to support registration. For point cloud pairs, the formula
FMR
N E III[PPs. Qx) 1).
(26)
where 1j 2 0.05 is the minimum inlier ratio threshold required for robust registration (e.g., RANSAC). Registration Recall (RRindoor) measures the proportion successfully registered point cloud pairs that meet the geometric error tolerance. If the RMSE of the true correspondences C" of point cloud pair (P, Q) after registration satisfies the following. Then, for threshold z 0.2m, we compute:
RMSE =
1
Σ
[Tea(D)) 2 ll..
(27)
C
(Pea))EC
R.Rindorr
I(RMSE& < <))
(28)
Patch Inlier Ratio (PIR) represents proportion of actual overlap for superpoints (patches) under true transfor- mations the scene, which measures the registration of our 3DGS parameterized domain:
PIR Č Σ
TE(p: (:) Sp x S, (p:) la < C)
(29)
(sp.a))EC
where Ç S 0.05m the inlier distance threshold. Pose Deviation Error indicates the error between the estimated rigid transformation Tist = {H, t} and the true transformation Tye [Rg,, }.t). We use two metrics: Relative Rotation Error (RRE) and Relative Translation Error (RTE):
traaee R" Rgt R -1
RRE- arccos
[radians],
(30)
2
RTE ||| ( Lye ||| [melerss.
(31)
Registration Recall (RRoutdoor) measures the error in point cloud registration in outdoor scenes, considering both RRE and RTE while ensuring both satisfy the minimum threshold requirements:
Rooutdoor
(RRE < A F+ < 1.5m).
(32)
A.4 Color Data
Cotch and Color3DLoMMtch are pre-processed training datasets, which are the results of coloring the 3DMatch and 3DLoMatch point cloud data. 3DMatch contains 62 scenes, with used for training, 8 for testing, and for validation. The entire experimental evaluation strictly follows the dataset protocol. In 3DMatch, the overlap between point cloud pairs is greater than 30%. In Lolor3DLoMatch. the overlap is relatively low (10%-30%).
ColorKitti: The Kitti odometry dataset contains outdoor driving scenes with 11 sequences, all obtained through LIDAR scanning.
use the corresponding RGB images each frame to color the point clouds, thus constructing ColorKitti. However, due to the limited viewpoint of the RGB image capturing device, we only color the point clouds visible from the image perspective. Sequences 0-5 are used for training. sequences 6 and 7 for validation, and sequences 8- 10 for testing. As with 3DMatch/SDLMMtth the ground truth poses are refined
16

---

using ICP, and the entire evaluation process strietly follows the dataset protocol. Additionally, only point clouds with distance of least 10 meters are used for evaluation. Unlike the 3DMacch/3DLoMacch scenes, the RGB images in the Kitti datasel are not captured in a panoramic manner, as the camera's viewpoint is limited. Initially, we attempted to use neighboring frames to color the point clouds of the current frame. However, visual analysis revealed that the coloring effect was unrealistic and the color distribution was not smooth, introducing excessive only color the point clouds visible color noise, which negatively impacted point cloud registration. Therefore, from the image perspective, and normalize the regions that are colored. During the data preprocessing stage, we filter out colorless data and retain only the geometrie point clouds. In the 3DGS registration process, only the colored portion of the point clouds is registered, and the rigid transformation parameters (R, t) are applied to restore the point clouds into the global scene. Fig. [ provides an example comparing the colored ground truth with the original ground truth.
A.5 Additional Experiments
C3DM consists of 62 seenes, with 46 scenes used for training, 8 for validation, and 8 for testing. The entire process follows the C3DM/C3DLM protocol and includes registration analysis for low-overlap scenarios. Additionally, ColorKitii Odometry 7 consists of outdoor driving sequences scanned by LiDAR. We follow the setup in TS] 44
using sequences 0-5 training, sequences 6-7 for validation, and sequences 8-10 for testing. As in [4, 8, 16). the ground-truth poses are refined with ICP, and we only use point cloud pairs that are at least 10m apart for evaluation.
Implementation details. We implemented and evaluated our GeGS GeGS-PCR using PyTorch [15]
an AMD 610M epochs
CPU and an NVIDIA RTX 4070 GPU. During the entire training process, GeGS-PCR was trained on the 3DMatch dataset and epochs on the KITTI dataset. The hatch size was set to 1, with an initial learning rate of 10 decaying by 0.05 every epoch. The Adam optimizer was used throughout the training process.
A Additional baselines. Table i is
continuation of Table D present-
ing the comparison between GeGS- PCR and other baselines. Most methods use RANSAC, and we have adopted the same approach for con- sistency. The results in the table show that GeGS-PCR performs ex- cellently across all three key metrics: Feature Matching Recall (FMR), In- lier Ratio (IR). and Registration Re- call (RR). Feature Matching Re
call (FMR), GeGS-PCR achieves 99.5% on C3DM and 97.6% on C3DLM, outperforming other meth- ods. Particularly on C3DM, GeGS- PCR improves by 0.7% over YOHO and significantly surpasses methods like Predator and SpinNet. In In- lier Ratio (IR), GeGS- PCR stands out further with IR values of 89.1% on C3DM and 70.3% on C3DLM, greatly exceeding YOHO, Predator, and other methods, especially im- proving by nearly 15% on C3DM.
.Me. SaleSTLURA))
LaM peltuu LaRA)
Claa juint LelA))
Fiees (oth LoRA)
Epoch
Figure 6: Comparison of Training Loss with and without LoRA Optimization (Motor3DMatch Dataset).
In Registration Recall (RR), GeGS-PCR performs at 97.9% on C3DM and 90.7% on C3DLM, leading other methods, with a particularly large improvement of 5.2% over YOHO on C3DLM. Overall, GeGS-PCR demon- strates outstanding performance across multiple datasets, excelling in low-overlap scenarios and surpassing all existing methods.
3DGS self-attention. In Table 7 we present the performance of different self-attention models in low-overlap scenarios, including Vanilla Self-attention, Geometric Self-attention, and 3DGS Self-attention. GeGS-PCL performs exceptionally well, particularly in low-overlap regions. Compared to other methods, 3DGS Self- attention significantly improves PIR (Precision). IR (Inlier Ratio), and RR (Registration Recall). In the high- overlap (0.9-1.0) range, the 3DGS Self-attention model achieves a PIR of 0.997, an IR of 0.905, and an RR of 1.000, demonstrating the best performance. As the overlap decreases, GeGS-PCR maintains strong performance even in the 0.5-0.6 overlap range, with a PIR of 0.938, an of 0.872, and an RR of 0.963, highlighting its robustness when handling low-overlap data. Specifically, compared to Vanilla Self-attention, 3DGS Self-attention shows stronger robustness across the entire overlap range, with its advantages becoming more pronounced in complex environments.
17

---

Table 6: Evaluation results on C3DM and C3DLM. #Samples in the table represents the number of correspondences selected by RANSAC.
C3DM
C3DLM
#Samples
5000
2500
1000
500
250
5000
2500
1000
500
250
Feature Matching Recall (%)
PerfectMatch 25
95.0
94.3
92.9
90.1
82.9
63.6
61.7
53.6
45.2
34.2
FCGF 8
97.4
97.3
97.0
96.7
96.6
76.6
75.4
74.2
71.7
67.3
D3Feat 9
95.6
95.4
94.5
94.1
93.1
67.3
66.7
67.0
66.7
66.5
SpinNet 7
97.6
97.2
96.8
95.5
94.3
75.3
74.9
72.5
70.0
63.6
Predator 28
96.6
96.6
96.5
96.3
96.5
78.6
77.4
76.3
75.7
75.3
YOHO 47
98.2
97.6
97.5
97.7
96.0
79.4
78.1
76.3
73.8
69.1
GeGS-PCR (ours)
99.5
99.6
99.5
99.7
99.6
97.6
97.4
97.1
97.2
97.0
Inlier Ratio (%) f
PerfectMatch
36.0
32.5
26.4
21.5
16.4
11.4
10.1
8.0
4.8
FCGF 8
56.8
54.1
48.7
42.5
34.1
21.4
20.0
17.2
14.8
11.6
D3Feat 9
39.0
38.8
40.4
41.5
41.8
13.2
13.1
14.0
14.6
15.0
SpinNet 7
47.5
44.7
39.4
33.9
27.6
20.5
19.0
16.3
13.8
11.1
Predator
28
58.0
58.4
57.1
54.1
49.3
26.7
28.1
28.3
27.5
25.8
YOHO 47
64.4
60.7
55.7
46.4
41.2
25.9
23.3
22.6
18.2
15.0
GeGS-PCS (ours)
76.3
82.4
86.3
86.6
89.1
53.4
58.7
69.7
70.3
Registration Recall (%)
f
PerfectMatch [25
78.4
76.2
71.4
67.6
50.8
33.0
29.0
23.3
17.0
11.0
FCGF S
85.1
84.7
83.3
81.6
71.4
40.1
41.7
38.2
35.4
26.8
D3Feat 9
81.6
84.5
83.4
82.4
77.9
37.2
42.7
46.9
43.8
39.1
SpinNet 7
88.6
86.6
85.5
83.5
70.2
59.8
54.9
48.3
39.8
26.8
Predator
28
89.0
89.9
90.6
88.5
86.6
59.8
61.2
62.4
60.8
58.1
YOHO
90.8
90.3
89.1
88.6
84.5
65.2
65.5
63.2
56.5
48.0
GeGS-PCR (ours)
97.9
97.6
97.5
96.7
97.6
90.7
90.2
90.4
90.0
89.8
Table 7: Performance of Self-attention Models
Vanilla Self-attention
Geometric Self-attention
3DGS Self-attention
Overlap
PIR %))
IR(%)
RR( (%)
PIR(%)
IR (%)
RR(%)
PIR(%) (%)
IR(%)
RR (R))
0.9-1.0
0.974
0.829
1.000
0.989
0.894
1.000
0.990
0.905
1.000
0.8-0.9
0.948
0.787
1.000
0.969
0.859
1,000
0.969
0.873
1.000
0.7-0.8
0.902
0.731
0.931
0.935
0,815
0.931
0.938
0.853
0.980
0.6-0.7
0.884
0.686
0.933
0.939
0.783
0.946
0.947
0.905
0.968
0.5-0.6
0.843
0.644
0.957
0.913
0.750
0.970
0.920
0.872
0.963
0.4-0.5
0.787
0.579
0.935
0.867
0.689
0.944
0.872
0.824
0.953
0.3-0.4
0.716
0.523
0.917
0.818
0.644
0.940
0.825
0.791
0.944
0.2-0.3
0.560
0,406
0.781
0,666
0,518
0.839
0.669
0,762
0,913
0.1-0.2
0.377
0.274
0.639
0.466
0.372
0.705
0.512
0.669
0.866
Ablation experiment. Additionally, in Table 3 we conduct a detailed analysis of the performance of recent techniques in terms of Relative Rotation Error (RRE) (the distance between the predicted rotation matrix and the true rotation matrix) and Relative Translation Error (RTE) (the Euclidean distance between the predicted translation vector and the true translation vector). From the comparison results, it is evident that GeGS-PCC consistently achieves better performance.
Table 9 we compare the performance five loss functions in point cloud registration: (a) Cross-entropy loss, (b) Weighted cross-entropy loss, (c) Circle loss, (d) Overlap-aware circle loss, and (e) Photometric optimization loss. As the loss function improves from cross-entropy to photometric optimization, the performance all key metrics (PIR, FMR, IR. RR) also improves. The photometric optimization loss achieves the highest performance with 87.6% PIR. 98.2% FMR, 71.6% IR,
C3DM, and 56.1 PIR, 89.3% FMR, 44.2% IR, 75.7% RR on C3DLM, outperforming all other methods.
Fig. G shows the training loss curves for both the standard model (without LoRA) and the model with LoRA applied the Color3DMatch dataset. It can be observed that for all loss types (Loss, C-Loss, and F-Loss),
18

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Table 8: Performance of RRE and RTE on C3DM and C3DLM.
C3DM
C3DLM
Model
Estimator
RRE())
(TE(m)
RRE()
RTE(m)
Predator 28
RANSAC-50K
2.029
0,064
3.048
0.093
CoFiNet
RANSAC-50K
2.002
0.064
3.271
0.090
GeoTransformer 15
RANSAC-fiee
1.772
0.061
2.849
0.088
REGTR 66
RANSAC-free 1.567
0.049
2.827
0.077
PEAL [99
RANSAC-free 1.748
0.062
2.788
0.087
ColorPCR 120
RANSAC-free 1.492
0.048
2.581
0.075
GeGS-PCA
RANSAC-free 1.112
0.024
2.293
0.051
the model with LoRA consistently outperforms the one without LoRA, indicated by the lower loss values throughout the training process. Specifically. the losses for the LoRA-enhanced model decrease steadily reach a final value compared to model without LoRA, suggesting that LoRA optimization aids faster convergence and better performance during training. This indicates that LoRA contributes effectively to improving the model's training efficiency and overall performance in point cloud registration tasks.
A.6 Limitations
GeGs-PCR relies on superpoints (patches) extracted through downsampling during the registration process. In regions with high point cloud overlap. the large number of superpoints, combined with 3DGS parameterization, result in significant memory usage and computational overhead. Since patch decomposition shares similarities with semantic scene understanding, we plan leverage semantic scene understanding for point cloud pair registration in future research. Furthermore, our current registration method involves pairing after 3DGS parameterization of domain superpoints. In future work, we aim to explore scene-level registration of 3DGS for more realistic environmental registration.
Table 9: Performance of ablation experiments
C3DM
C3DLM
Overlap
PIR(%)
(MR(%)
IR(%)
RR(%)
PIR(5)
(MR(%)
IR(%)
RR(S)
(a) Cross-entrops loss
80.0
97.7
65.7
90.0
45.9
85.1
37.4
68.4
(h) Weighted cross-entropy loss
83.2
98.0
67.4
90.0
49.0
86.2
38.6
70.7
(c) Circle loss
85.1
97.8
69.5
90.4
51.5
86.1
41.3
71.5
(d) Overlap-aware circle loss
86.1
97.7
70.3
91.5
54.9
88.1
43.3
(e) Photometric optimization loss
87.6
97.9
71.6
91.9
56.1
89.3
44.2
A.7 Qualitative Results
Fig. 7ad Fig. show the registration results of GeGS- on the Color3DMatch (C3DM), DootrcD (C3DLM), and ColorKitti datasets. GeGS PCR achieves precise registration scenarios with low overlap and subtle geometric features, demonstrating its exceptional performance in handling complex environments. From the results, it can he observed that even with smaller overlapping regions between point clouds, GeGS-PCR is still able to accurately align different point clouds. In particular, several scenes from Fig. O GeGS-PCR effectively handles point cloud pairs with minimal overlap and able precisely reconstruct the spatial structure point clouds, the ColorKitti dataset shown in Fig. GeGS-PCR demonstrates its robustness, providing accurate registration results even in complex scenarios.
Fig. 19 shows the registration performance comparison between GeGS-PCR and Geotransformer across various overlap conditions. The results demonstrate that in high overlap scenarios, GeGS-PCC exhibits superior registra- tion accuracy compared Geotransformer, particularly example, with a 79.7% overlap, GeGS- PCR achieves an inlier ratio of 93.1%, %, while Geotransformer only reaches 40.6%. In low overlap conditions, GeGS-PCR's advantage becomes even more evident. For instance, with a 41.8% overlap, GeGS-PCR's 's RMSE is 0.006m, much lower than Geotransformer's 0.877m. GeGS-PCR is able effectively capture the correct correspondences between point clouds low-overlap scenarios, maintaining high registration accuracy. Overall, GeGS- -CR demonstrates higher stability precision across various overlap conditions, proving its robustness in complex scenarios.
of point correspondence and inlier ratio. For
Advantages. The advantages of LOGS-PCR lie in the collaborative optimization of global and local structures. Through local Gaussian feature extraction. GeGS- PCRR effectively suppresses noise interference and robustly
19

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Tuses geometric and color features. In low-overlap noisy point cloud data, GeGS-PCR dynamically adjusts local geometric distribution through covariance modeling, significantly improving registration accuracy. Addi- tionally, photometric loss based differentiable rendering optimizes global pose consistency, ensuring stable registration. GeGS-PCC is not only effective for high-overlap registration but also offers an efficient, scalable solution for low-overlap tasks like autonomous driving and large-scale scene reconstruction.
Additionally, by leveraging both geometrie and color information, GeGS-PCR PCR is able to find consistent feature correspondences in low-overlap regions, improving registration accuracy. The changes between point clouds before and after registration the qualitative results clearly illustrate how our model handles challenging regions. Notably, in areas with similar geometric features such as floors and walls or appliances and furniture, GeGS-PCR maintains high accuracy. Overall, GeGS- PCR showcases superior registration capability and robustness when dealing with lvw-lverlap scenarios, complex structures, and environments with rich color information.
20

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Overlag: 28.0%g
Ovellag: 27
Overiap: 24.5%
Overap: 20.15g
Overlags 22,35
Ovarlags 22.4%
Overaap: 2000n
Overlap: 23,07g
Oweragy 27.2%
Overlag: 29.1%g
Owetey 23 my
Overlpp: 22.3%
Ovarap: 22.1%g
Overlap: 25 and
Overlap: 25
Overlape 23.0%g
(a) Input
(b) Ground truth
(c)
Ours
(a) Input
(b) Ground truth
(c) Ours
Figure 7: Registration results on Motcr3DMatch and MotcchDLoMMtchh.
21

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(6) Ground truth
(
(b) Ground truth
(c) Ours
Figure 8: Registration results ColorKitti.
22

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Overlpp: 66.8%
RMSE: 1,610m
IMSE: (L840hm
#Point ocm 256 Jeller mil:c 34.0%5
#Point cor:
ePoint oor
PPolat oam:
baller zatle: 92,
balier miiec 31.5%g
talier ratle 93.3
dovin oom 256 Inller rnnes 40.0%
Phoin com 255
eooin ovr 500 anter mic 53
PPoizt com: 500
79.75
caller mite: 93, Plc
Talier ratio 94. 20.
Ovarkp:41.8 41.8%
RANSE: 0.87
RMSI:: 0.013m
#Peint coor 256 Intier ratin 41 2%
PPoint con: 256 laller rutee 97.05
#Poii cour 500
PPain soer:
Ovatlep: 52.5%
RMSE: 0.512
RMSE: 0.00km
Ielier rutio 50
Inlicr rain 96 06.0%
( Geomrnnsommer
(d) GeG&&PR
Gooteandommer Point
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Figure 9: Registration performance with GeGS-PCR and Geometric Self-Attention across various overlap conditions.
23


Reviews:
[{"review_id": "GY6F3TT6vm", "reviewer": "Reviewer_Gg5d", "summary": "The paper introduces GeGS-PCR, a two-stage pipeline for pairwise 3D point-cloud registration under low overlap and incomplete geometry. Stage 1 performs coarse alignment with a Color-Enhanced Geometric-3D Gaussian-Splatting (3DGS) representation: a learned color encoder is fused with down-sampled super-points that are parameterised as anisotropic Gaussians; a dedicated 3DGS self-attention transformer yields an overlap-invariant global feature. Stage 2 refines the pose by jointly minimising a differentiable photometric-plus-geometric loss, rendered from the fused 3DGS scene. Efficiency is maintained with LoRA compression of attention weights. Extensive experiments on Color3DMatch / Color3DLoMatch and a new outdoor ColorKITTI benchmark show state-of-the-art registration recall and markedly lower RTE/RRE compared to recent baselines. The appendix provides reproducibility materials, ablations, theoretical convergence proofs, and a discussion of memory overhead and scene-level extensions.", "questions": "1. Please report end-to-end latency (ms) and peak VRAM for both stages on KITTI and 3DMatch, and compare against GeoTransformer/ColorPCR. This will clarify practical deployability.\n2. Have you tested performance when colour channels are synthetically perturbed (e.g., random hue shift) or in night-time lidar scans? An ablation would show whether the geometric branch alone suffices.\n3. Table 3 shows faster convergence, but how much accuracy is lost if LoRA is removed? Reporting final metrics with/without LoRA would justify this choice.", "limitations": "1. Memory & Latency Overhead. The 3D Gaussian-Splatting representation adds mean/covariance/opacity parameters, pushing GPU usage to ~11 GB in dense indoor scenes; no FPS or memory numbers are reported for KITTI, so deployment on edge devices remains uncertain.\n2. Strong Reliance on RGB. Both stages leverage colour cues; performance under poor illumination, night-time, or colour-missing LiDAR‐only data is untested, leaving robustness to colour noise unclear.\n3. Pairwise-only Rigid Alignment. The pipeline estimates a single SE(3) transform per pair; multi-view or scene-level registration (e.g., full SLAM) is not evaluated, limiting direct applicability to sequential mapping tasks.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n1. Comprehensive evaluation across three benchmarks, large ablation suite (removal of color, 3DGS, photometric loss).  Well-designed loss with proof of Lipschitz convergence.\n2. Clear problem set-up and modular description; appendix lists hyper-parameters and scripts. \n3. Brings 3D Gaussian Splatting, hot in 3D rendering, to registration ; delivers new SOTA on low-overlap indoor/outdoor data; public ColorKITTI is likely to spur follow-up work.\n4. Novel combination of colour encoding + 3DGS + joint photometric optimisation; first to apply 3DGS attention to registration.\n\n**Weaknesses**\n\n1. Runtime/memory not fully quantified: only qualitative note that 3DGS adds “some” overhead; no FPS numbers on KITTI. Coarse-to-fine pipeline cannot yet perform scene-level global registration, acknowledged by authors. \n2. Main text occasionally defers key algorithmic details (e.g., 3DGS attention formulation) to appendix, hampering standalone readability.\n3. Impact may be limited for lidar-only pipelines without colour.\n\n4. Method builds on several recent ideas (Gaussian-Splatting, transformer attention, LoRA) in an incremental fashion; theoretical novelty is moderate.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate the reviewer’s valuable and constructive comments, which have been instrumental in improving the quality of our manuscript.\n\n**W.1: Runtime/memory not fully quantified.**\n\nWe acknowledge that the original version of our manuscript lacked a detailed quantification of the runtime memory overhead of 3DGS. We have conducted additional performance evaluations, the results are summarized in Tables 1 and 2:\n1. FPS: 2.94 on the ColorKitti dataset, 1.010 on the C3DM dataset\n2. Latency: 16.7 ms on ColorKitti, 15.3 ms on C3DM\n3. GPU Memory Usage: 2–4 GB on both datasets\n4. Lower model and pose estimation time on ColorKitti compared to competing methods\n\nThese quantitative metrics clearly indicate that GeGS-PCR is practically test on RTX 4070 GPU and competitive with mainstream approaches.\n\n**Table 1. Quantified Performance on ColorKitti.**\n**Model**|**Model Time (s)**|**Pose Time (s)**|**Total Time (s)**|**End-to-End Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-|-|-\nSpinNet|6.025 |0.039|6.064|60.64|0.016|3-4\nPredator|0.008|0.520|0.528|52.8|1.893|3-4\nGeoTransformer|0.018|0.322|0.340|14.5|2.913|3-4\nColorPCR|0.016|0.550|0.566|18.6|2.263|3-4\n**GeGS-PCR (ours)**|**0.020**|**0.327**|**0.347**|**15.3**|**2.540**|**2-4**\n\n**Table 2. Quantified performance on C3DM.**\n**Model**|**#Sample**|**End-to-End Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-\nFCGF|5000|33.78|0.296|3-4\nD3Feat|5000|31.12|0.321|3-4\nSpinNet|5000|60.646|0.016|3-4\nPredator|5000|51.52|0.194|3-4\nCoFiNet|5000|17.50|0.544|3-4\nGeoTransformer|5000|15.33|0.613|2-4\nPEAL|5000|18.65|0.537|3-4\nColorPCR|5000|17.12|0.585|3-4\n**Ours**|5000|**16.72**|**0.588**|**2-4**\nCoFiNet|all|19.1|0.699|3-4\nGeoTransformer|all|15.4|0.953|2-4\nPEAL|all|17.3|0.752|3-4\nColorPCR|all|18.8|0.775|3-4\n**Ours**|all|**16.8**|**1.010**|**2-4**\n\n**W.2: Defer Key Algorithmic.**\n\nWe realized that some key algorithmic details were indeed explained in the appendix. However, due to page limitations in the main text, we had to omit these algorithms from main part. In the revised version, we will carefully move these details into the main text to improve its standalone readability.\n\n**W.3: Limited for lidar-only pipelines without color.**\n\nGeGS-PCR is primarily designed based on geometric features, with additional Gaussian features incorporated for enhanced registration. During our investigation, we further observed that color information also plays a critical role in improving registration accuracy. We proposed Geometric-3DGS, which globally unifies geometric, Gaussian, and color features into a consistent representation.\nIn cases where color information is unavailable from the beginning (i.e., color-deficient scenarios), GeGS-PCR gracefully falls back to relying on the joint geometric and Gaussian features for registration. The absence of color does not impose inherent limitations or side effects on the method’s applicability. Tables 3 and 4 present the registration performance of GeGS-PCR on standard datasets without color information, and Table 3 directly compares these results with those in Table 1 of the main paper. These additional results will be included in the revised version.\nIn the main text, the ablation study shown in Table 3, line (e), indicates a performance drop when color is removed from the 3DGS model. This is because disabling the color channel prevents the construction of a complete 3DGS representation and affects the differentiable rendering module. This degradation is caused by the internal dependency of the original 3DGS architecture on color, not due to a lack of color information in the dataset itself.\n\n**Table 3. Comparison of registration results on 3DM and 3DLM.**\nMetric|3DM-5000|C3DM-5000|3DM-1000|C3DM-1000|3DLM-5000|C3DLM-5000|3DLM-1000|C3DLM-1000|3DLM-250|C3DLM-250\n-|-|-|-|-|-|-|-|-|-|-\nFeature Matching Recall (%)|**99.5**|99.5|**99.4**|99.5|**97.4**|97.6|**97.0**|97.1|97.0|97.0\nInlier Ratio (%)|**76.0**|76.3|**86.2**|86.3|**53.3**|53.4|**66.6**|66.9|70.1|70.3\nRegistration Recall (%)|**97.8**|97.9|**97.3**|97.5|**90.5**|90.7|**90.2**|90.4|89.7|89.8\n\n**Table 4. Registration results without RANSAC on KITTI.**\nModel|No-RTE (cm)|Color-RTE (cm)|No-RRE (°)|Color-RRE (°)|No-RR (%)|Color-RR (%)\n-|-|-|-|-|-|-\nGeGS-PCR (RANSAC-50k)|**6.7**|6.3|**0.18**|0.16|**99.8**|99.9\nGeGS-PCR (LGR)|**5.9**|5.7|**0.15**|0.13|**99.8**|99.9\n\n**Q.1: Runtime/memory not fully quantified.**\n\nsee W.1.\n\n**Q.2: Test performance when color channels are synthetically perturbed.**\n\nEvaluating the robustness of the system under color variations such as random hue shifts is of great importance. We conducted additional experiments by applying significant random perturbations (±10%) in the HSV color space to simulate color distortions caused by lighting inconsistencies or sensor variations. In Tables 5, GeGS-PCR maintains high registration accuracy and robustness under such hue shift conditions. These new experiments will be included in the revised version to better demonstrate the model’s generalization ability in the presence of color distortions.\n\n**Table 5. Registration results under random hue shift (±10%) on all datasets.**\nMethod|3DM-5000(NoShift)|3DM-5000(HueShift)|Drop(%)|3DLM-5000(NoShift)|3DLM-5000(HueShift)|Drop(%)|KITTI(NoShift)|KITTI(HueShift)|Drop(%)\n-|-|-|-|-|-|-|-|-|-\nGeoTransformer|92.0±0.3|89.5±0.3|-2.5|88.5±0.3|84.7±0.4|-3.8|95.4±0.2|93.2±0.3|-2.2\nColorPCR|97.5±0.2|92.7±0.3|-4.8|93.8±0.3|89.1±0.3|-4.7|96.1±0.3|91.8±0.4|-4.3\n**Ours(GeGS-PCR)**|**97.9±0.1**|**96.8±0.2**|-1.1|**94.7±0.2**|**93.5±0.2**|-1.2|**99.7±0.2**|**98.9±0.5**|-0.5\n\nTo evaluate the robustness of our method under varying illumination and potential nighttime scenarios, we conducted a comprehensive analysis of three candidate datasets: ScanNet, Waymo, and KITTI-360.\n1. ScanNet primarily consists of indoor scenes with uniform point cloud density and relatively simple geometry, lacking the challenging conditions of non-uniform density and color disturbances that our method aims to address.\n2. The Waymo Open Dataset, although it provides RGB images, is designed mainly for detection and tracking tasks. It lacks precise registration ground-truth between LiDAR frames, making it unsuitable for evaluating registration accuracy. Additionally, it has a massive data volume, high preprocessing overhead, and significant viewpoint discrepancies between LiDAR and RGB sensors, which hinders high-quality fusion of color and geometric features.\n3. In contrast, KITTI-360 offers multiple advantages: large-scale outdoor point clouds captured in real urban environments, highly non-uniform point density (dense foreground and sparse background), well-aligned RGB and LiDAR data through multi-sensor fusion, and the presence of many geometrically similar but texturally distinct objects such as buildings, pedestrians, and vehicles.\n\nSo, we selected KITTI-360 as the extended evaluation dataset to better assess the real-world applicability and robustness of our method (colorized KITTI-360 data will release). As shown in Table 6, our method consistently outperforms ColorPCR and other baselines even in the presence of color variations and complex scene structures, demonstrating the effectiveness of the Geometric-3DGS strategy in practical scenarios.\nWe also acknowledge that KITTI-360 is primarily collected during daytime and contains only limited lighting variations or low-light scenes. Due to time constraints, we leave a comprehensive evaluation under nighttime conditions for future work, and we plan to incorporate semantic-level scene understanding to further improve the generalization of our method.\n\n**Table 6. Registration results on CKitti-360**\nMethod|IR(%)|RR(%)|Total-time(s)|RRE(°)|RTE(cm)\n-|-|-|-|-|-\nYOHO|10.99|48.13|8.31|~25.9|~0.55\nSpinNet|14.86|33.41|73.1|~9.9|~0.47\nGeotransformer|8.4|25.30|1.66|~7.4|~0.37\nColorPCR|12.5|45.01|1.29|~1.58|~0.35\n**Ours**|15.03|56.88|1.18|**~1.26**|**~0.28**\n\n**Q.3: Test performance when LoRA is removed.**\n\nWe have added an ablation study to evaluate the impact of the LoRA module, including a variant where LoRA is removed. As shown in Table 7, row f, removing LoRA leads to a slight drop in registration performance—for instance, the registration recall (RR) decreases from 97.5% to 97.2% on C3DM, and from 89.3% to 89.2% on C3DLM. These results suggest that LoRA primarily helps accelerate convergence during training, while also providing a modest yet consistent improvement in accuracy. We will incorporate these results into the main text in the revised version of the manuscript to enhance the completeness of our analysis.\n\n**Table 7. Performance of ablation experiments on C3DM and C3DLM.**\nMethod|C3DM-PIR(%)|C3DM-FMR(%)|C3DM-IR(%)|C3DM-RR(%)|C3DLM-PIR(%)|C3DLM-FMR(%)|C3DLM-IR(%)|C3DLM-RR(%)\n-|-|-|-|-|-|-|-|-\n(a) ColorPCR(baseline)|89.2|99.5|80.5|96.5|62.7|96.5|56.6|88.5\n(b) w/o ColorEncoder|89.4|99.5|80.6|96.6|62.8|96.6|56.8|88.6\n(c) w/o 3DGS|89.5|99.6|80.7|96.7|63.0|96.7|56.9|88.8\n(d) w/o differentiable rendering|89.6|99.5|80.8|96.8|63.1|96.8|57.0|88.9\n(e) w/o color|86.1|97.9|77.3|92.7|55.2|89.8|46.3|77.9\n(f) **w/o LoRA**|**92.0**|**99.3**|**86.3**|**97.5**|**63.8**|**97.4**|**59.9**|**90.5**\n(g)Geometric-3DGS(Full)|92.0|99.6|82.4|97.6|63.9|97.4|58.7|90.2\n\n**L.1: Memory & Latency Overhead.**\n\nsee W.1.\n\n**L.2: Strong Reliance on RGB.**\n\nsee W.3.\n\n**L.3: Multi-view or Scene-level registration.**\n\nWe focus is on accurately estimating rigid transformations between point clouds to achieve stable and reliable registration. We haven't explored streaming data or SLAM tasks. We have supplemented our work on KITTI-360 dataset. We plan to extend our method to scene-level registration, integrating semantic scene understanding to enhance adaptability and generalization in complex real-world environments."}, {"review_id": "9A6VWh3Lh5", "reviewer": "Reviewer_SWE1", "summary": "This paper addresses the challenge of robust 3D point cloud registration, particularly in scenarios with low overlap and incomplete geometry, by leveraging both geometric and color information. The authors propose GeGS-PCR, a novel two-stage method integrating a dedicated color encoder and a Geometric-3DGS (3D Gaussian Splatting) module. The approach tightly fuses geometric and color data via a dual-modal encoder and models the local neighborhood with 3D Gaussian parameters, further optimized by LoRA to reduce computational cost. A differentiable rendering and a joint photometric loss are introduced in the fine registration stage for further refinement. The method is validated on both indoor (Color3DMatch, Color3DLoMatch) and outdoor (ColorKitti) colored point cloud datasets, demonstrating state-of-the-art performance, especially under low-overlap conditions. Ablation studies and qualitative results are presented to justify each module's effectiveness.", "questions": "Scalability Experiments:\nHave the authors evaluated the memory and computation bottlenecks of GeGS-PCR on very large-scale or real-time datasets (e.g., full-scale outdoor driving datasets with hundreds of millions of points)? What strategies could further mitigate memory usage?\n\nRobustness to Color Noise/Distortion:\nHow does the method perform if the color channels are corrupted (e.g., illumination changes, sensor noise, partial missing color)? Would incorporating color confidence weights improve robustness?\n\nGeneralization Beyond Synthetic Colorization:\nSince ColorKitti is constructed by projecting color onto LiDAR points, have the authors tested the method on naturally colored point cloud datasets (e.g., from RGB-D sensors or mobile mapping platforms)? How does the method generalize to such data?\n\nFailure Modes:\nAre there scenarios where color information may harm registration, for example, in the presence of repetitive textures or objects with similar color but different geometry? How does GeGS-PCR handle such cases?\n\nStatistical Significance:\nCan the authors provide statistical analysis (e.g., multiple runs, error bars) to demonstrate the significance and robustness of their improvements?", "limitations": "The authors have adequately discussed the limitations, especially regarding memory usage and computation overhead in high-overlap scenarios, as well as the dependency on superpoint extraction. They also note the need for scene-level registration and semantic integration in future work.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\nTechnical Novelty & Originality:\nThe combination of geometric and color features at a deep level, the introduction of the Geometric-3DGS module, and the use of differentiable rendering for point cloud registration are all novel. The integration of LoRA for efficient parameterization is innovative and relevant for scalability.\n\nQuality & Thoroughness:\nThe methodology is clearly described, including mathematical formulation, network architecture, and optimization strategies. Both coarse and fine registration pipelines are well justified.\n\nEmpirical Evaluation:\nExtensive experiments on multiple benchmarks (Color3DMatch, Color3DLoMatch, ColorKitti) convincingly demonstrate the method's superiority, especially in low-overlap and noisy scenarios. Ablation studies support the necessity of each component.\n\nClarity:\nThe paper is generally well-organized. Key ideas, architecture, and modules are well-illustrated and justified with both qualitative and quantitative results.\n\nReproducibility:\nImplementation details, hyperparameters, dataset splits, and a public code repository are provided. Training/test procedures are described clearly.\n\nWeaknesses:\n\nScalability / Computational Cost:\nThe paper acknowledges that using superpoints and 3DGS parameterization may incur significant memory and computation overhead in high-overlap or very large scenes, but lacks a deeper discussion or experiments on scalability to truly large-scale datasets or real-time constraints.\n\nLimited Statistical Analysis:\nWhile results are comprehensive, the paper does not provide error bars or statistical significance analysis, making it harder to assess the robustness of the improvements.\n\nAblation on Individual Modalities:\nAlthough ablation is done, there is limited exploration into failure cases where color might hurt registration (e.g., severe color noise, lighting changes, or sensor mismatch), or where geometric features are insufficient.\n\nPotential Overfitting to Synthetic Colorization:\nColorKitti is constructed by colorizing KITTI point clouds via projection, which may not reflect real-world sensor noise or missing color. The generalizability to native colored LiDAR or different sensors is not verified.\n\nBroader Impacts & Safeguards:\nThe broader societal impact is discussed, but concrete safeguards or risk mitigation for data/model misuse are not detailed.", "was_revised": true, "final_justification": "I appreciate the additional experiments and quantitative analyses, which address several of my initial concerns. ﻿Based on the author response and new evidence, I believe the authors have adequately addressed my main concerns. I will maintain my borderline accept (score: 4). Should further improvements be incorporated (e.g., more diverse datasets), the paper could be rated higher in the future.", "rebuttal": "We sincerely thank the reviewer for their valuable suggestions and unique insights. \n\n**W.1: Scalability / Computational Cost**\n\nWe acknowledge that the original version of our manuscript lacked a detailed quantification of the runtime memory overhead of 3DGS. To address this, we have conducted additional performance evaluations to demonstrate the deployment feasibility of GeGS-PCR in practical scenarios. The results are summarized in Tables 1 and 2:\n\n1. FPS: 2.94 on the ColorKitti dataset, 1.010 on the C3DM dataset\n2. Latency: 16.7 ms on ColorKitti, 15.3 ms on C3DM\n3. GPU Memory Usage: 2–4 GB on both datasets\n4. Lower model and pose estimation time on ColorKitti compared to competing methods\n\nThese results clearly indicate that GeGS-PCR is practically test on RTX 4070 GPU and competitive with these approaches.\n\n**Table 1. Quantified performance on ColorKitti.**\n**Model**|**Model Time (s)**|**Pose Time (s)**|**Total Time (s)**|**Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-|-|-\nSpinNet|6.025 |0.039|6.064|60.64|0.016|3-4\nPredator|0.008|0.520|0.528|52.8|1.893|3-4\nGeoTransformer|0.018|0.322|0.340|14.5|2.913|3-4\nColorPCR|0.016|0.550|0.566|18.6|2.263|3-4|\n**GeGS-PCR (ours)**|**0.020**|**0.327**|**0.347**|**15.3**|**2.540**|**2-4**\n\n**Table 2. Quantified performance on C3DM.**\n**Model**|**#Sample**|**Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-\nFCGF|5000|33.78|0.296|3-4\nD3Feat|5000|31.12|0.321|3-4\nSpinNet|5000|60.646|0.016|3-4\nPredator|5000|51.52|0.194|3-4\nCoFiNet|5000|17.50|0.544|3-4\nGeoTransformer|5000|15.33|0.613|2-4\nPEAL|5000|18.65|0.537|3-4\nColorPCR|5000|17.12|0.585|3-4\n**Ours**|5000|**16.72**|**0.588**|**2-4**\nCoFiNet|all|19.1|0.699|3-4\nGeoTransformer|all|15.4|0.953|2-4\nPEAL|all|17.3|0.752|3-4\nColorPCR|all|18.8|0.775|3-4\n**Ours**|all|**16.8**|**1.010**|**2-4**\n**Quantization (16-bit)**|all|14.6|1.072|**1.5-3**\n**Sparse LoRA Attention**|all|15.1|1.022|**1.6-3**\n**Downsampled 3DGS**|all|14.2|1.097|**1.3-2.5**\n**Shared Color-Geo Encoder**|all|15.0|1.035|**1.4-3**\n**Efficient Attention**|all|14.9|**1.110**|**1.2-2.8**\n\nWe analyzed three datasets: ScanNet, Waymo, and KITTI-360—to select a suitable extended evaluation set.\n\n1. ScanNet features indoor scenes with uniform point density and simple geometry, lacking challenges like non-uniform density and color disturbances.\n2. Waymo provides RGB images but lacks precise LiDAR registration ground-truth, has poor LiDAR-RGB alignment, limiting fusion quality.\n3. KITTI-360 offers large-scale outdoor scenes with non-uniform density, well-aligned RGB-LiDAR data, and many geometrically similar but texturally distinct objects, making it ideal for robust registration evaluation.\n\nWe chose KITTI-360 for extended tests (colorized KITTI-360 data will release). As Table 3 shows, our method outperforms baselines under color variations and complex scenes.\n\nKITTI-360 mainly contains daytime scenes with limited lighting variations; nighttime and semantic scene understanding are left for future work.\n\n**Table 3 Registration results on CKitti-360**\nMethod|IR(%)|RR(%)|Total-time(s)|FPS|GPU Usage (GB)|RRE(°)|RTE(cm)\n-|-|-|-|-|-|-|-\nYOHO|10.99|48.13|8.31|0.193|2-4|~25.9|~0.55\nSpinNet|14.86|33.41|73.1|0.025|3-4|~9.9|~0.47\nGeotransformer|8.4|25.30|1.06|0.997|2-4|~7.4|~0.37\nColorPCR|12.5|45.01|1.29|0.875|3-4|~1.58|~0.35\n**Ours**|**15.03**|**56.88**|**1.18**|**1.102**|**2-4**|**~1.26**|**~0.28**\n\nBased on preliminary experiments (Table 2), we plan to reduce memory usage with the following strategies:\n\n1. 16-bit Quantization: Compresses weights from 32-bit to 16-bit, cutting GPU memory by ~30% and slightly speeding up inference.\n2. Sparse LoRA Attention: Prunes redundant attention parameters, saving ~20% memory without accuracy loss.\n3. Downsampled 3DGS: Uses stride-based downsampling to reduce memory by ~25% without accuracy drop.\n4. Shared Color-Geometry Encoder: Combines encoders to share weights, reducing memory by ~15%.\n5. Efficient Attention: Replaces standard attention with efficient approximations, further lowering memory and improving FPS.\n\n**W.2: Limited Statistical Analysis**\n\nWe conducted ten independent experiments to strengthen statistical reliability. Table 4 reports mean and standard deviation to assess robustness.\n\nResults show GeGS-PCR significantly outperforms other methods on RR, IR, and RMSE (p < 0.05). Higher RR and IR correspond to lower RMSE, with GeGS-PCR consistently achieving RMSE < 0.01, confirming its stability. Although error bars are omitted due to limit, visualized statistical analysis will be added in the revised version.\n\n**Table 4. Registration Recall (%, mean ± std) on 3DMatch over 10 random seeds(p < 0.05).**\nMethod|Metric|C3DM-5000|C3DM-2500|C3DM-1000|C3DM-500|C3DM-250|C3DLM-5000|C3DLM-2500|C3DLM-1000|C3DLM-500|C3DLM-250\n-|-|-|-|-|-|-|-|-|-|-|-\n| |RR|98.1|98.3|98.1|98.2|98.3|83.1|83.5|83.3|83.1|82.6\nCoFiNet|IR|49.8|51.2|51.9|52.2|52.2|24.4|25.9|26.7|26.8|26.9\n| |RMSE|0.156±0.01|0.159±0.01|0.161±0.01|0.164±0.01|0.167±0.01|0.248±0.01|0.253±0.01|0.256±0.01|0.261±0.01|0.264±0.01\n| |RR|97.9|97.9|97.9|97.9|97.6|88.3|88.6|88.8|88.6|88.3\nGeoTransformer|IR|71.9|75.2|76.0|82.2|85.1|43.5|45.3|46.2|52.9|57.7\n| |RMSE|0.142±0.01|0.146±0.01|0.150±0.01|0.155±0.01|0.160±0.01|0.222±0.01|0.228±0.01|0.233±0.01|0.238±0.01|0.245±0.01\n| |RR|99.0|99.0|99.1|99.1|98.8|91.7|92.4|92.5|92.9|92.7\nPEAL|IR|72.4|79.1|84.1|86.1|87.3|45.0|50.9|57.4|60.3|62.2\n| |RMSE|0.132±0.01|0.137±0.01|0.140±0.01|0.142±0.01|0.146±0.01|0.194±0.01|0.202±0.01|0.207±0.01|0.212±0.01|0.218±0.01\n| |RR|99.5|99.5|99.5|99.5|99.5|96.5|96.5|97.0|97.0|96.7\nColorPCR|IR|75.0|80.5|84.7|86.5|87.8|51.2|56.6|63.1|66.0|68.0\n| |RMSE|0.118±0.01|0.123±0.01|0.126±0.01|0.129±0.01|0.133±0.01|0.182±0.01|0.188±0.01|0.194±0.01|0.200±0.01|0.205±0.01\n| |RR|99.5|99.6|99.5|99.7|99.6|97.6|97.4|97.1|97.2|97.0\nOurs|IR|76.3|82.4|86.3|86.6|89.1|53.4|58.0|60.3|63.4|65.5\n| |RMSE|**0.106±0.01**|**0.111±0.01**|**0.114±0.01**|**0.117±0.01**|**0.115±0.01**|**0.165±0.01**|**0.172±0.01**|**0.176±0.01**|**0.181±0.01**|**0.186±0.01**\n\n**W.3: Ablation on Individual Modalities**\n\nTo evaluate the effects of lighting, sensor errors, and color distortions, we conducted:\nWe tested lighting and sensor errors via:\n1. Color disturbance with ±10% hue drift on ColorKitti, C3DM, C3DLM, showing GeGS-PCR’s robustness over color-dependent methods (Table 5);\n2. Geometric insufficiency using color-similar but geometrically different 3DMatch scenes;\n3. Color-ambiguous scenes experiments (Table 6) where GeGS-PCR’s adaptive fusion with learnable $\\alpha$ balances geometry and color for stable registration.\n\nResults indicate GeGS-PCR is more robust with less accuracy loss across datasets. Rough registration relies mainly on geometry, with color aiding optimization under reliable conditions.\n\n**Table 5. Registration results under ue shift (±10%) on datasets.**\nMethod|3DM-5000(No Shift)|3DM-5000(Hue Shift)|Drop(%)|3DLM-5000(No Shift)|3DLM-5000(Hue Shift)|Drop(%)|KITTI(No Shift)|KITTI(Hue Shift)|Drop(%)\n-|-|-|-|-|-|-|-|-|-\nGeoTransformer|92.0±0.3|89.5±0.3|-2.5|88.5±0.3|84.7±0.4|-3.8|95.4±0.2|93.2±0.3|-2.2\nColorPCR|97.5±0.2|92.7±0.3|-4.8|93.8±0.3|89.1±0.3|-4.7|96.1±0.3|91.8±0.4|-4.3\n**Ours**|**97.9±0.1**|**96.8±0.2**|-1.1|**94.7±0.2**|**93.5±0.2**|-1.2|**99.7±0.2**|**98.9±0.5**|-0.5\n\n\n**Table 6. Registration results on different scenes.**\nMethod|Scene A(Geo Insufficient)|Scene B(Objects With Similar Color)|Scene C(Repeated Textures)|Average\n---|---|---|---|---\nGeoTransformer|88.4±0.3|85.1±0.4|86.2±0.3|86.6\nColorPCR|90.3±0.3|84.9±0.3|83.5±0.4|86.2\n**Ours**|**94.7±0.2**|**91.1±0.2**|**92.6±0.2**|**92.8**\n\nGeGS-PCR model does not explicitly model color confidence weights, but its Geometric-Color fusion module implicitly learns modality confidence (e.g., $\\alpha$ in Eq. 3). To improve robustness under severe hue shifts (±10%), we calculate local color stability via RMSE and dynamically adjust $\\alpha$, boosting color influence in stable areas and reducing it in noisy regions.\n\nTable 7 shows geometry-only GeoTransformer struggles under hue shifts; applying fixed or $\\alpha$ only at the last layer worsens performance. Using full-layer $\\alpha$ maintains stability, while GeGS-PCR with color confidence weighting is the most robust with minimal performance drop.\n\nFuture work will explore explicit color confidence modeling and enhanced multimodal fusion.\n\n\n**Table 7. Registration results under color confidence weights.**\nMethod|No Shift|Hue Shift|Drop(%)|Remarks|Color Confidence Info\n---|---|---|---|---|---\n**GeoTransformer**|92.0±0.3|89.5±0.3|-2.5|No color|No color confidence\n**Ours(No $\\alpha$)**|96.9±0.1|95.1±0.2|-1.7|No color confidence, no dynamic fusion|Static color feature usage, no confidence weights\n**Ours(Full Layer $\\alpha$)**|97.6±0.1|96.2±0.3|-1.4|$\\alpha$ applied at all layers|No explicit confidence weighting, $\\alpha$ for all layers\n**Ours(Final Layer $\\alpha$)**|92.5±0.3|91.0±0.3|-1.5|$\\alpha$ applied at final layer only features|No color, geometric features only\n**Ours(Color Confidence)**|97.6±0.2|96.5±0.3|-1.0|With dynamic color confidence|Color confidence dynamically adjusted, weight learned\n**Ours**|**97.9±0.2**|**96.8±0.3**|**-1.0**|$\\alpha$ applied as Eq.3|Color features weighted with $\\alpha$ in final layer\n\n**W.4: Native Colored LiDAR**\n\nWe made our best efforts to find natural color point cloud data, but since devices like **Hesai XT32**, **GigaMesh** are used in the project and have not been open sourced, we applied GeGS-PCR on real world data from the Kitti-360 for testing.\n\n**W.5: Safeguards**\nWe discussed the applications and clarified that it uses anonymized public data, focuses on low-risk tasks, will be open sourced under restrictive licenses to prevent misuse, encourages community evaluation to address bias and security concerns.\n\n**Q.1: Scalability**\n\nSee W.1.\n\n**Q.2:Color Noise/Distortion**\n\nSee W.3.\n\n**Q3: Generalization Beyond Synthetic Colorization**\n\nSee W.4.\n\n**Q.4: Failure Modes**\n\nSee W.3.\n\n**Q.5: Statistical Significance**\n\nSee W.2."}, {"review_id": "Q7jaq2tzD6", "reviewer": "Reviewer_vEz5", "summary": "The paper introduces GeGS-PCR, a novel two-stage method for 3D point cloud registration that integrates geometric, color, and Gaussian (3DGS) information to achieve robust performance, particularly in low-overlap and incomplete scenarios. The method employs a dedicated color encoder to extract noise-robust color features, a Geometric-3DGS module to encode local neighborhood information of superpoints, and a joint photometric loss with differentiable rendering for refined registration. The authors also create a new dataset, ColorKitti, by colorizing the Kitti dataset to validate the method's generalization. Experimental results on Color3DMatch, Color3DLoMatch, and ColorKitti demonstrate state-of-the-art performance.", "questions": "See weakness.", "limitations": "The authors adequately address the limitations and potential negative societal impacts. They acknowledge that GeGS-PCR’s reliance on superpoint downsampling leads to high memory and computational overhead in high-overlap scenarios and note the limitation of focusing on superpoint-level rather than scene-level registration. These are discussed in Section A.6, with future directions proposed (e.g., leveraging semantic scene understanding). The societal impact section highlights positive applications (e.g., autonomous navigation, urban planning) and negative risks (e.g., privacy concerns in surveillance, data manipulation), with mitigation strategies like gated releases suggested. The transparency in addressing these points is commendable and aligns with ethical research practices.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths: \n\n1. The paper presents a high-quality contribution with rigorous experimental validation. The proposed GeGS-PCR method achieves improvements over state-of-the-art methods (e.g., ColorPCR, GeoTransformer) across multiple metrics (FMR, IR, RR, RRE, RTE) on Color3DMatch and Color3DLoMatch datasets.  The creation of ColorKitti enhances the evaluation scope, addressing the scarcity of colored point cloud datasets. The reproducibility is well-supported with open-access code, datasets, and detailed experimental settings.\n\n2. The paper is well-structured, with clear descriptions of the problem, method, and experimental setup. The pipeline (Fig. 2) effectively illustrates the coarse-to-fine approach, and mathematical formulations (e.g., covariance matrix, photometric loss) are precise and well-explained. The use of figures (e.g., Fig. 3, 7, 8) and tables (e.g., Tables 1, 2, 7, 8) enhances understanding of qualitative and quantitative results. \n\nWeaknesses: \n\n1. The performance improvement over ColorPCR, while notable, is marginal in some metrics (e.g., 0.4% increase in RR on C3DM, 1.3% in IR), raising questions about the practical significance of the added complexity. The computational complexity of the Geometric-3DGS module, particularly in high-overlap scenarios, is acknowledged but not quantified. The paper lacks a detailed comparison of computational resources (e.g., GPU memory usage, training time) against baselines, which is critical for assessing practical deployability. Additionally, the reliance on superpoint downsampling may limit performance in scenarios with irregular point density, which is not explored. The ablation study in Table 3 is not sufficiently clear, making it difficult to discern the precise impact of each component (e.g., color encoder vs. 3DGS) due to overlapping metric improvements and lack of detailed analysis.\n\n2. The significance is somewhat limited by the focus on specific datasets (Color3DMatch, Color3DLoMatch, ColorKitti), with no evaluation on other real-world datasets (e.g., ScanNet, Waymo). The marginal performance gains over ColorPCR may reduce the perceived impact, especially given the increased computational complexity.", "was_revised": false, "final_justification": "", "rebuttal": "We truly appreciate the reviewer’s constructive feedback and professional analysis. \n\n**W.1: Detailed Performance Evaluation**\n\n**1. Improvement is marginal in some metrics**\n\nThe performance improvement on the C3DM dataset is relatively small because it contains scenes with high viewpoint overlap and rich texture, where methods like ColorPCR already perform well. In contrast, GeGS-PCR is tailored for more challenging scenes with low overlap, sparse geometry, and ambiguous or varied color textures. Therefore, improvements are more significant on datasets like C3DLoMatch and ColorKITTI. Our geometric-3DGS module and color-guided encoder provide clear advantages in these difficult conditions.\n\nHowever, our method demonstrates stronger adaptability and robustness in realistic and complex scenarios, which are more relevant for practical applications. Due to submission deadlines, hyperparameter tuning was limited; initial experiments indicate further improvements are possible with more thorough tuning and additional computational resources.\n\n**2. Quantified GPU memory usage and training time**\n\nWe found our paper includes high-overlap scenes with visual overlaps of 60.8%, 79.7%, 41.8%, and 82.5% (see qualitative results). While our focus is on low-overlap scenes, the computational cost of Geometric-3DGS in high-overlap cases requires further evaluation.\n\nFurthermore，we acknowledge that the original version of our manuscript lacked a detailed quantification of the runtime memory overhead of 3DGS. To address this, we have conducted additional performance evaluations to demonstrate the deployment feasibility of GeGS-PCR in practical scenarios. The results are summarized in Tables 1 and 2, including:\n\n1. FPS: 2.94 on the ColorKitti dataset, 1.010 on the C3DM dataset\n2. Latency: 16.7 ms on ColorKitti, 15.3 ms on C3DM\n3. GPU Memory Usage: 2–4 GB on both datasets\n4. Lower model and pose estimation time on ColorKitti compared to competing methods\n\nThese results clearly indicate that GeGS-PCR is practically test on RTX 4070 GPU and competitive with these approaches.\n\n**Table 1. Quantified performance on ColorKitti.**\n**Model**|**Model Time (s)**|**Pose Time (s)**|**Total Time (s)**|**End-to-End Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-|-|-\nSpinNet|6.025 |0.039|6.064|60.64|0.016|3-4\nPredator|0.008|0.520|0.528|52.8|1.893|3-4\nGeoTransformer|0.018|0.322|0.340|14.5|2.913|3-4\nColorPCR|0.016|0.550|0.566|18.6|2.263|3-4\n**GeGS-PCR (ours)**|**0.020**|**0.327**|**0.347**|**15.3**|**2.540**|**2-4**\n\n**Table 2. Quantified performance on C3DM.**\n**Model**|**#Sample**|**End-to-End Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-\nFCGF|5000|33.78|0.296|3-4\nD3Feat|5000|31.12|0.321|3-4\nSpinNet|5000|60.646|0.016|3-4\nPredator|5000|51.52|0.194|3-4\nCoFiNet|5000|17.50|0.544|3-4\nGeoTransformer|5000|15.33|0.613|2-4\nPEAL|5000|18.65|0.537|3-4\nColorPCR|5000|17.12|0.585|3-4\n**Ours**|5000|**16.72**|**0.588**|**2-4**\nCoFiNet|all|19.1|0.699|3-4\nGeoTransformer|all|15.4|0.953|2-4\nPEAL|all|17.3|0.752|3-4\nColorPCR|all|18.8|0.775|3-4\n**Ours**|all|**16.8**|**1.010**|**2-4**\n\n\n**3. Reliance on superpoint downsampling may limit performance**\n\nWe acknowledge that superpoint downsampling may cause local information loss in high-density regions, potentially affecting registration accuracy. Our method has mainly been tested on outdoor datasets (C3DM, C3DLoMatch, ColorKITTI) where point cloud distributions are relatively regular. However, in more complex scenarios such as indoor environments, vegetation, or occlusions, point densities can be irregular. The C3DLoMatch dataset contains occluded and low-overlap segments with irregular densities, yet our method still performs well, indicating a certain robustness of GeGS-PCR. Similar methods like GeoTransformer and ColorPCR also use superpoint downsampling without showing performance limitations.\n\nTo evaluate the downsampling strategy in real-world complex scenes, we analyzed three datasets: ScanNet, Waymo, and KITTI-360.\n1. ScanNet consists mainly of indoor scenes with uniform point density and simple geometry, lacking challenges of uneven density and color disturbances.\n\n2. Waymo provides RGB data but lacks accurate LiDAR registration ground truth; it has a large data volume and significant viewpoint differences between sensors, making it unsuitable for registration evaluation.\n\n3. KITTI-360 offers large-scale outdoor point clouds in real urban environments with highly uneven density (dense foreground and sparse background), well-aligned RGB and LiDAR data, and many geometrically similar but texturally distinct objects.\n\nTherefore, we selected KITTI-360 for extended evaluation (colorized KITTI-360 data will release). Results (see Table 3) show that our method outperforms ColorPCR and other baselines under color variations and complex scenes, demonstrating the effectiveness of Geometric-3DGS.\n\nIn future work, we plan to mitigate information loss in high-density areas through local enhancement strategies such as region weighting and multi-scale geometric features.\n\n**Table 3 Registration results on CKitti-360**\n|Method|IR(%)|RR(%)|Total-time(s)|FPS|GPU Usage (GB)|RRE(°)|RTE(cm)|\n|-|-|-|-|-|-|-|-|\n|YOHO|10.99|48.13|8.31|0.193|2-4|~25.9|~0.55|\n|SpinNet|14.86|33.41|73.1|0.025|3-4|~9.9|~0.47|\n|Geotransformer|8.4|25.30|1.06|0.997|2-4|~7.4|~0.37|\n|ColorPCR|12.5|45.01|1.29|0.875|3-4|~1.58|~0.35|\n|**Ours**|**15.03**|**56.88**|**1.18**|**1.102**|**2-4**|**~1.26**|**~0.28**|\n\nNevertheless, we also recognize that extending our method to the ScanNet and Waymo datasets would further enhance its applicability. Due to time constraints and our best efforts, we have not yet conducted tests on these datasets. However, we plan to incorporate these datasets in future work, re-adapt the method, and run the necessary baseline methods for evaluation.\n\n\n**4. Ablation study is not sufficiently clear**\n\nThe ablation results in Table 3 are based on our full Geometric-3DGS model, not combined with ColorPCR baseline. These tests verify the synergy and robustness of our system components, not the individual improvement of each module in all combinations, so direct comparison with Table 2 baselines isn’t possible.\n\nSome modules (e.g., 3DGS) require joint training with differentiable rendering for best results. Removing parts like differentiable rendering weakens features and supervision, hurting fine registration (see Table 3a). We also studied removing color or the entire 3DGS component.\n\nTo clarify metric repetition, we ran independent ablations on ColorPCR (Table 4) controlling module order and data synergy. Results show consistent gains even on weaker baselines, proving our module design is sound, generalizable, and optimizable.\n\n**Table 4. Ablation results based on ColorPCR baseline**\n|Method|C3DM-PIR(%)↑|C3DM-FMR(%)↑|C3DM-IR(%)↑|C3DM-RR(%)↑|C3DLM-PIR(%)↑|C3DLM-FMR(%)↑|C3DLM-IR(%)↑|C3DLM-RR(%)↑|\n|-|-|-|-|-|-|-|-|-|\n(a)ColorPCR(baseline)|89.2|99.5|80.5|96.5|62.7|96.5|56.6|88.5\n(b)w/o ColorEncoder|89.4|99.5|80.6|96.6|62.8|96.6|56.8|88.6\n(c)w/o 3DGS|89.5|99.6|80.7|96.7|63.0|96.7|56.9|88.8\n(d)w/o differentiable rendering|89.6|99.5|80.8|96.8|63.1|96.8|57.0|88.9\n(e)w/o color|86.1|97.9|77.3|92.7|55.2|89.8|46.3|77.9\n(f)w/o Geometric PE|88.8|99.3|80.2|96.3|62.4|96.0|56.4|88.0\n(g) w/o LoRA|88.9|99.3|80.1|96.2|62.4|96.1|56.3|88.4\n**(h)Geometric-3DGS (all)**|**90.0**|**99.6**|**82.4**|**97.6**|**63.9**|**97.4**|**58.7**|**90.2**\n\nBased on the results, there is no performance degradation after adding modules issue in GeGS-PCR. The slight performance fluctuations observed in the intermediate steps of the table are due to the removal of certain modules. Following the reviewer's suggestion, we have clarified in the table caption that all methods are based on ColorPCR as the starting point, and we have added explanations in the main text to clarify the meaning of each row and the comparison targets to avoid any misunderstandings.\n\n\n**W.2: The significance is limited by the focus on specific datasets and need to quantified performance on real-world datasets**\n\nBased on the performance testing on the real-world Kitti-360 dataset provided in Table 3 of W.1. In order to systematically evaluate the impact of lighting conditions, sensor errors, color distortions in real-world scenarios, we supplemented the following experiments. Color Disturbance Robustness Experiment: We introduced severe random hue drift (±10%) in the HSV color space of ColorKitti, C3DM, and C3DLM to simulate common noise in real sensors, sensor mismatches, and color loss phenomena. The results in Tables 5 show that, although color-dependent algorithms (ColorPCR) experience some degradation, GeGS-PCR, due to its robust Geometric-3DGS backbone’s adaptive fusion design, still maintains strong registration accuracy.\n\nThe results show that GeGS-PCR, across multiple datasets, demonstrates stronger robustness and a smaller accuracy decrease compared to existing methods. However, due to its robust geometric backbone and adaptive fusion design, our method still maintains strong registration accuracy. This indicates that rough registration can be achieved using only the geometric branch, and color information primarily serves as an optimization signal under reliable conditions.\n\n**Table 5. Registration results under random hue shift (±10%) on all datasets.**\n|Method|3DM-5000(NoShift)|3DM-5000(HueShift)|Drop(%)|3DLM-5000(NoShift)|3DLM-5000(HueShift)|Drop(%)|KITTI(NoShift)|KITTI(HueShift)|Drop(%)|\n|-|-|-|-|-|-|-|-|-|-|\n|GeoTransformer|92.0±0.3|89.5±0.3|-2.5|88.5±0.3|84.7±0.4|-3.8|95.4±0.2|93.2±0.3|-2.2|\n|ColorPCR|97.5±0.2|92.7±0.3|-4.8|93.8±0.3|89.1±0.3|-4.7|96.1±0.3|91.8±0.4|-4.3|\n|**Ours(GeGS-PCR)**|**97.9±0.1**|**96.8±0.2**|-1.1|**94.7±0.2**|**93.5±0.2**|-1.2|**99.7±0.2**|**98.9±0.5**|-0.5|\n\n\n**Limitations**\n\nWe acknowledge the absence of a dedicated limitations section in the current version. In future revisions, we will explicitly include a detailed discussion of the limitations of our method."}, {"review_id": "yqksYWO1Gy", "reviewer": "Reviewer_fKxm", "summary": "This manuscript proposes a novel colored-point-cloud registration method by incorporating color, coordinates and 3DGS together. Specifically, the method is built upon ColorPCR with three key improvements:\n\n1.\tAdding an MLP for better color feature extraction.\n\n2.\tAdding Gaussian representation of superpoint neighborhoods, which enhances feature extraction, position embedding during GeoTransformer-type superpoint attention, and differentiable rendering for pose refinement.\n\n3.\tAdding a differentiable rendering loss (i.e., photometric loss) for pose refinement.", "questions": "1.\tDesign of Eq. 5 is questionable. The concatenated components have different meanings along different dimensions, but are compressed together with a single top-k operation. That way the model will not know the meaning of a specific dimension after the top-k, highly possibly causing confusion.\n\n2.\tAblation is under-optimized and needs explanation. Here I assume that your work is completely based on Color-PCR (which I think is self-evident, but please point out if otherwise). While the ablation only provides deduction of single components from GeGS-PCR, from retrospective we can also see them as incomplete increments from ColorPCR to GeGS-PCR. However, all the ablated models perform much worse than ColorPCR, comparing ablation figures in Table 3 and Table 8 against ColorPCR figures in Tab. 2. For example, does Tab. 3 line (a) hint that ColorPCR + Color Decoder + 3DGS + Geometric PE deteriorates registration performance compared to barebone ColorPCR?\tMaybe you can approach this concern by adding a fair baseline in Tab. 3 and describing the ablation components more clearly.\n\n3.\tMany designs are not ablated. E.g., does the design of Eq. 3 achieve the optimal color encoding performance, compared to using no alpha, or applying alpha on all layers? What is the effect of tuning lambda in Eq. 4, k in Eq. 5, lambda in L213 (duplicate notation), gamma in Eq. 6, gamma in Eq. 10 (duplicate notation), lambda in Eq. 11(2nd duplicate notation), \\sigma_{GS} in Eq. 19 and lambda in Eq. 21(3rd duplicate notation)? The list continues. Maybe you can approach this concern by both reducing the number of manually-tuned parameters and doing ablation when necessary. You can simply add some descriptions on feasible value ranges from your experience for less important parameters. However, leaving all those parameters with no value specification is not acceptable.\n\nOverall, the paper presents a novel idea that seems to work perfectly consistent during experiments. However, the severely under-qualified and inconsistent ablation greatly undermines the credibility of such experimental results, causing me to rate a borderline reject. I would be happy to raise my ratings if my major concerns are addressed.", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.\tThe paper is well structured and written. it is easy to follow the authors’ ideas. The idea is original and moderately significant, where applying 3DGS on superpoint-matching is novel and possibly took inspiration from GMM-based registration methods. The paper also incorporated a theoretical proof for convergence guarantees of the 2nd stage pose refinement.\n\n2.\tThe core idea of applying gaussian during superpoint matching makes a lot of sense to me. Superpoint represents a small piece of local geometry which is highly likely anisotropic. Such property can be well captured with Mahalanobis distance instead of Euclidean distance in favor of superpoint matching and alignment.\n\n3.\tDesign spaces are well explored, although I feel sorry about the addition of many tunable parameters.\n\nWeaknesses:\n\n1.\tWhile performance increments are consistent, the tested benchmarks are quite saturated, and the absolute improvements are not significant.\n\n2.\tAblation experiments are not well conducted, which IMHO is very important to validating the effectiveness for all your added components. See Q2 for details.\n\n3.\tMany niche designs have lots of parameters, but lack corresponding ablation experiments. See Q3 for details.\n\nAdvice (not a strength or weakness):\n\n1.\tIt is viable to use KITTI-360 for coloring surround-view KITTI point clouds, although this would create an alternative benchmark and requires re-running the baselines. I would also recommend using other autonomous-driving datasets such as nuScenes or Waymo with surround-view color images.", "was_revised": true, "final_justification": "Currently, my main concern about ablation consistency is solved and I would like to raise my rating to 4 (borderline accept). I would like to further engage in discussion and keep the right to change the figures later.", "rebuttal": "We are grateful for the reviewer’s deep understanding and highly value their expertise in the relevant areas.\n\n**S.1: The property can be well captured with Mahalanobis distance instead of Euclidean distance in favor of superpoint matching and alignment.**\n\nTable 1 compared Mahalanobis and Euclidean distances in coarse registration. Mahalanobis with anisotropic modeling improves accuracy in scenes with strong anisotropy, while Euclidean works well in regular or symmetric scenes with lower cost. Our method will adaptively selects the distance metric based on scene characteristics to balance accuracy and efficiency.\n\n**Table 1. Comparison of Superpoint Matching Strategies**\nMethod|RR-5cm(%)|RR-10cm(%)|InlierRatio(%)|FeatureMatchingRecall(%)\n-|-|-|-|-\nEuclideanDistance|67.2±0.8|**88.1±0.5**|58.1±1.2|64.7±1.0\nMahalanobisDistance|**71.9±0.6**|82.4±0.7|**65.9±0.9**|**72.2±0.7**\n\n\n\n**W.1: The absolute improvements are not significant.**\n\nLimited gains were observed on C3DM, where ColorPCR already performs well due to high overlap and rich textures. GeGS-PCR challenges in low-overlap, sparse, and ambiguous scenes, showing stronger adaptability on challenging datasets like C3DM and ColorKITTI. Preliminary tuning suggests that further improvements are possible with more resources, but time constraints prevented full hyperparameter optimization.\n\n**Not W or S: It is viable to use KITTI-360 for coloring surround-view KITTI point clouds.**\n\nTo evaluate the downsampling strategy in real-world complex scenes, we analyzed three datasets: ScanNet, Waymo, and KITTI-360.\n1. ScanNet consists mainly of indoor scenes with uniform point density and simple geometry, lacking uneven density and color disturbances.\n\n2. Waymo provides RGB data but lacks accurate LiDAR registration ground truth;\n\n3. KITTI-360 offers large-scale outdoor point clouds in real urban environments with highly uneven density (dense foreground and sparse background), well-aligned RGB and LiDAR data.\n\nTable 2 show that GeGS-PCR outperforms on Kitti-360, demonstrating the effectiveness of Geometric-3DGS (colorized KITTI-360 data will release).\n\nWe will mitigate information loss in high-density areas through local enhancement strategies such as region weighting and multi-scale geometric features.\n\n**Table 2. Registration results on CKitti-360**\nMethod|IR(%)|RR(%)|Total-time(s)|RRE(°)|RTE(cm)\n-|-|-|-|-|-\nYOHO|10.99|48.13|8.31|~25.9|~0.55\nSpinNet|14.86|33.41|73.1|~9.9|~0.47\nGeotransformer|8.4|25.30|1.66|~7.4|~0.37\nColorPCR|12.5|45.01|1.29|~1.58|~0.35\n**Ours**|15.03|56.88|1.18|**~1.26**|**~0.28**\n\n\n**Q.1: Design of top-k is questionable.**\n\nIn code, we mitigate this by first computing top-k scores separately for geometry and color modalities, normalizing and weighting them before final selection from the combined candidate set. This design aims to balance simplicity and performance, and normalization helps align scale differences.\n\nTables 3,4 show this strategy is effective and robust across datasets. In future, we plan to introduce a semantic alignment module (e.g., learnable projection) before fusion to improve feature consistency.\n\n**Table 1. Quantified performance on ColorKitti.**\n**Model**|**Model Time (s)**|**Pose Time (s)**|**Total Time (s)**|**End-to-End Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-|-|-\nSpinNet|6.025 |0.039|6.064|60.64|0.016|3-4\nPredator|0.008|0.520|0.528|52.8|1.893|3-4\nGeoTransformer|0.018|0.322|0.340|14.5|2.913|3-4\nColorPCR|0.016|0.550|0.566|18.6|2.263|3-4\n**GeGS-PCR (ours)**|**0.020**|**0.327**|**0.347**|**15.3**|**2.540**|**2-4**\n\n**Table 2. Quantified performance on C3DM.**\n**Model**|**#Sample**|**End-to-End Latency (ms)**|**FPS**|**GPU Usage (GB)**\n-|-|-|-|-\nFCGF|5000|33.78|0.296|3-4\nD3Feat|5000|31.12|0.321|3-4\nSpinNet|5000|60.646|0.016|3-4\nPredator|5000|51.52|0.194|3-4\nCoFiNet|5000|17.50|0.544|3-4\nGeoTransformer|5000|15.33|0.613|2-4\nPEAL|5000|18.65|0.537|3-4\nColorPCR|5000|17.12|0.585|3-4\n**Ours**|5000|**16.72**|**0.588**|**2-4**\nCoFiNet|all|19.1|0.699|3-4\nGeoTransformer|all|15.4|0.953**|2-4\nPEAL|all|17.3|0.752|3-4\nColorPCR|all|18.8|0.775|3-4\n**Ours**|all|**16.8**|**1.010**|**2-4**\n\n\nWe evaluated the impact of noise on the Top-k mechanism through color disturbance tests (Table 5). Despite random ±10% hue shifts in HSV space across all datasets, GeGS-PCR showed minimal performance drop and outperformed color-dependent methods like ColorPCR. These results confirm that the Top-k mechanism preserves geometric structure and performs well even under noise.\n\n**Table 5. Registration results under random hue shift (±10%) on all datasets.**\nMethod|C3DM-5000(NoShift)|C3DM-5000(HueShift)|Drop(%)|C3DLM-5000(NoShift)|C3DLM-5000(HueShift)|Drop(%)|KITTI(NoShift)|KITTI(HueShift)|Drop(%)\n-|-|-|-|-|-|-|-|-|-\nGeoTransformer|92.0±0.3|89.5±0.3|-2.5|88.5±0.3|84.7±0.4|-3.8|95.4±0.2|93.2±0.3|-2.2\nColorPCR|97.5±0.2|92.7±0.3|-4.8|93.8±0.3|89.1±0.3|-4.7|96.1±0.3|91.8±0.4|-4.3\n**Ours(GeGS-PCR)**|**97.9±0.1**|**96.8±0.2**|-1.1|**94.7±0.2**|**93.5±0.2**|-1.2|**99.7±0.2**|**98.9±0.5**|-0.5\n\n**Q.2: Ablation is under-optimized and needs explanation.**\n\nTable 3 shows results for our complete Geometric-3DGS model, not a combination with ColorPCR. These experiments test the synergy and robustness of our components, not all possible combinations against ColorPCR (Table 2). Modules like 3DGS need joint training with differentiable rendering for optimal performance. We conducted standalone ablation studies (Table 6) based on ColorPCR, confirming that our modules consistently improve performance, even with weaker baselines.\n\n**Table 6. Ablation results based on ColorPCR baseline.**\nMethod|C3DM-PIR(%)|C3DM-FMR(%)|C3DM-IR(%)|C3DM-RR(%)|C3DLM-PIR(%)|C3DLM-FMR(%)|C3DLM-IR(%)|C3DLM-RR(%)\n-|-|-|-|-|-|-|-|-\n(a)ColorPCR(baseline)|89.2|99.5|80.5|96.5|62.7|96.5|56.6|88.5\n(b)w/o ColorEncoder|89.4|99.5|80.6|96.6|62.8|96.6|56.8|88.6\n(c)w/o 3DGS|89.5|99.6|80.7|96.7|63.0|96.7|56.9|88.8\n(d)w/o differentiable rendering|89.6|99.5|80.8|96.8|63.1|96.8|57.0|88.9\n(e)w/o color|86.1|97.9|77.3|92.7|55.2|89.8|46.3|77.9\n(f)w/o Geometric PE|88.8|99.3|80.2|96.3|62.4|96.0|56.4|88.0\n(g) w/o LoRA|88.9|99.3|80.1|96.2|62.4|96.1|56.3|88.4\n**(h)Geometric-3DGS (all)**|90.0|99.6|82.4|97.6|63.9|97.4|58.7|90.2\n\nResults show no performance drop after adding modules in GeGS-PCR. Minor fluctuations are due to module removal. We clarified in the table caption that all methods start from ColorPCR and added explanations in the text to clarify each row and comparison target, preventing misunderstandings.\n\n\n**Q.3: Many designs need to be ablated.**\n\n**1. $\\alpha$ ablation**\n\nOur model does not explicitly model color confidence weights, but its Geometric-Color fusion module implicitly learns modality confidence (e.g., $\\alpha$ in Eq. 3). To improve robustness under severe hue shifts (±10%), we calculate local color stability via RMSE and dynamically adjust $\\alpha$, boosting color influence in stable areas and reducing it in noisy regions.\n\nTable 7 shows GeoTransformer struggles under hue shifts; applying fixed or $\\alpha$ only at the last layer worsens performance. Using full-layer $\\alpha$ maintains stability, while GeGS-PCR with color confidence weighting is the most robust with minimal performance drop.\n\nFuture work will explore explicit color confidence modeling and enhanced multimodal fusion.\n\n\n**Table 7. Registration results under color confidence weights.**\nMethod|NoHueShift|HueShift|Drop(%)|Remarks|ColorConfidenceInfo\n-|-|-|-|-|-\n**GeoTransformer**|92.0±0.3|89.5±0.3|-2.5|No color|No color confidence\n**Ours (no $\\alpha$)**|96.9±0.1|95.1±0.2|-1.7|No color confidence, no dynamic fusion|Static color feature usage, no confidence weights\n**Ours (fullLayer $\\alpha$)**|97.6±0.1|96.2±0.3|-1.4|$\\alpha$ applied at all layers|No explicit confidence weighting, $\\alpha$ for all layers\n**Ours (finalLayer $\\alpha$)**|92.5±0.3|91.0±0.3|-1.5|$\\alpha$ applied at final layer only features|No color, geometric features only\n**Ours (w/o $\\alpha$)**|97.6±0.2|96.5±0.3|-1.0|With dynamic color confidence|Color confidence dynamically adjusted, weight learned\n**Ours**|**97.9±0.2**|**96.8±0.3**|**-1.0**|$\\alpha$ applied as Eq.3|Color features weighted with $\\alpha$ in final layer\n\n\n**2. Parameters ablation** \n\nWe sincerely thank the reviewer for the feedback on the design details. We conducted ablation experiments and verified the tuning range for these symbols (Table 8).\n\nThese parameters were initially designed for flexibility across tasks, with tuning tailored per scenario. Following the reviewer’s suggestion, we plan to reduce redundant parameters to improve robustness and practicality, and will design an adaptive adjustment mechanism in the revised version.\n\nDue to time constraints, full optimization of all parameters was not completed. However, we are confident that further tuning in future versions will improve performance and better showcase our method’s strengths. We thank the reviewer for their understanding and guidance.\n\n**Table 8. Performance of ablation study base on parameters**  \n**Parameter**|**Value Range**|**Every Value**|**RR (Every value)**|**Conclusion**\n-|-|-|-|-\n**$\\lambda$ (Eq.4)**|[0.01, 1.0]|0.01, 0.05, 0.1, 0.5, 1.0|0.91, 0.96, 0.90, 0.91, 0.92|Stable (0.05)\n**$k$ (Eq.5)**|[2, 5]|2, 3, 4, 5|0.87, 0.97, 0.97, 0.89|Tunable\n**$\\lambda_d$ (Line213)**|[0.05, 0.2]|0.05, 0.1, 0.15, 0.2|0.88, 0.97, 0.97, 0.91|Tunable\n**$\\gamma$ (Eq.6)**|[1, 3]|1, 1.5, 2, 3|0.97, 0.92, 0.92, 0.89|Tunable\n**$\\gamma_d$ (Eq.10)**|[1, 3]|1, 1.5, 2, 3|0.89, 0.97, 0.97, 0.91|Tunable\n**$\\lambda_p$ (Eq.11)**|[0.1, 1]|0.1, 0.3, 0.7, 1.0|0.88, 0.97, 0.97, 0.85|Tunable\n**$\\sigma_{GS}$ (Eq.19)**|[0.01, 0.1]|0.01, 0.03, 0.07, 0.1|0.86, 0.96, 0.96, 0.88|Tunable\n**$\\lambda_g$ (Eq.21)**|[0.01, 1.0]|0.1, 0.5, 0.8, 1.0|0.90, 0.97, 0.96, 0.92|Stable (0.5)\n\n**Paper Formatting Concerns**\n\nWe sincerely thank reviewer for the valuable suggestions. We revised the layout, standardized the naming as “Encoder,” and unified symbols throughout the paper and appendix."}]

Author rebuttal:

Meta-review: During the rebuttal, the authors have effectively addressed most of the reviewers' concerns, including performance evaluations on additional datasets and efficiency analyses. After reading the submission, I believe it was well written, and the technical contribution is solid. Given the positive final ratings from all reviewers, I am inclined to recommend acceptance.
Decision: Accept (poster)