REArtGS: Reconstructing and Generating Articulated Objects via 3D Gaussian Splatting with Geometric and Motion Constraints
Authors: Di Wu
Liu Liu
Zhou Linli
Anran Huang
Liangtu Song
Qiaojun Yu
Qi Wu
Cewu Lu
Venue: NeurIPS 2025 poster ()
Keywords: Surface Reconstruction
3DGS
Embodied Intelligence
Primary area: applications
TL;DR: REArtGS

Abstract: Articulated objects, as prevalent entities in human life, their 3D representations play crucial roles across various applications. However, achieving both high-fidelity textured surface reconstruction and dynamic generation for articulated objects remains challenging for existing methods. In this paper, we present REArtGS, a novel framework that introduces additional geometric and motion constraints to 3D Gaussian primitives, enabling realistic surface reconstruction and generation for articulated objects. Specifically, given multi-view RGB images of arbitrary two states of articulated objects,  we first introduce an unbiased Signed Distance Field (SDF) guidance to regularize Gaussian opacity fields, enhancing geometry constraints and improving surface reconstruction quality. Then we establish deformable fields for 3D Gaussians constrained by the kinematic structures of articulated objects, achieving unsupervised generation of surface meshes in unseen states. Extensive experiments on both synthetic and real datasets demonstrate our approach achieves high-quality textured surface reconstruction for given states, and enables high-fidelity surface generation for unseen states. Project site: https://sites.google.com/view/reartgs/home.

REArtGS: Reconstructing and Generating Articulated Objects via 3D Gaussian Splatting with Geometric and Motion Constraints
Di Wu? Liu Liu st Zhou Linli', Anran Huang", Liangtu Song", Qiaojun Yu?, Qi Wu Cewu Lu
1 Hefei Institutes of Physical Science Chinese Academy of Sciences
2 University of Science and Technology of China
3 Hefei University of Technology
4 Shanghai Jiao Tong University
5 ByteDance
Email: wdcs@mail. wwt.cttcc.... edu. cn, liuliuGhfut edu. cn
Abstract
Articulated objects, prevalent entities in human life, their 3D representations play crucial roles across various applications. However, achieving both high-fidelity textured surface reconstruction and dynamic generation for articulated objects remains challenging for existing methods. this paper, we present REAnGS, a novel framework that introduces additional geometric and motion constraints to 3D Gaussian primitives, enabling realistic surface reconstruction and generation for articulated objects. Specifically, given multi-view RGB images of arbitrary two states of articulated objects, we first introduce an unbiased Signed Distance Field (SDF) guidance regularize Gaussian opacity fields, enhancing geome- try constraints and improving surface reconstruction quality. Then we establish deformable fields for 3D Gaussians constrained by the kinematic structures of articulated objects, achieving unsupervised generation of surface meshes in un- states. Extensive experiments both synthetic and real datasets demon- strate our approach achieves high-quality textured surface reconstruction for given states, and enables lighfiielity surface generation for unseen states. Project site: https://siten wwwssiitessogggeee.eeeeeooo comm/vieewreeartg///honne
Introduction
Articulated objects are ubiquitous our daily lives. Modeling articulated objects, i.e. mesh recon- struction and generation, holds significant importance in many fields including virtual and augmented reality [66] (3),, object manipulation [4) 31], robots [33 [7] and human-object interaction [37 [2]
Currently, the surface and shape reconstruction for articulated objects a non-trivial task due the challenges: firstly, articulated objects exhibit complicated and diverse geometric structures with a wide range of scales. Secondly, articulated objects possess varied kinematic structures, and the static surface meshes generated from vanilla 3D reconstruction methods fail to meet practical interaction requirements. Under this circumstance, PARIS (14) attempts use multi-view images from two states for articulated object dynamically reconstruction with neural implicit radiance fields. Nevertheless, PARIS lacks geometric constraints, leading shape-radiance ambiguity and additional errors for motion analysis.
* "oorrespondigg author Project leader
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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In recent years, 3D Gaussian Splatting (3DGS) [TO] achieves realistic and real-time novel view synthesis through explicit representa- tion with 3D Gaussian primitives. Some subse- quent works have expanded 3DGS to surface re- construction (42
Iupurs
Recon.
Generation
Unseen StIee
Stut
Mesa
End Soez
Tranned Mash
8 I and dynamic reconstruc- 13 4 However, existing DDGS-based surface reconstruction methods typically suffer from insufficient geometric constraints [42] or impose constraints by restricting the shapes of Gaussian primitives g 6), leading noisy surface reconstruction results. On the other hand, current dynamic reconstruction methods via 3DGS tend to input motion time and spatial positions into neural networks to obtain the de-
tion 38
Figure 1: Given multi-view RGB images of ar- ticulated objects from two arbitrary states, our REARGS enables high-quality textured surface mesh reconstruction and generation for unseen states.
formed positions of Gaussian primitives [38] 4]. Consequently, these methods require continuous supervision throughout the entire motion, which limits their ability to generate surface meshes in unseen states. In general, introducing 3DGS as a ready-to-use technique into articulated object surface reconstruction and generation still not feasible and remains a challenging task.
In this paper, to address the aforementioned issues and make full advantage of 3DGS, we propose REArIGS, a novel approach that Reconstructs and gEnerates high-quality texture-rich mesh surfaces for Articulated objects via 3D Gaussian Splatting, only taking multi-view RGB images from two arbitrary states. Specifically, unlike most 3DGS methods based the opacity field, which may lead to noisy surface extraction due to the non-strict linearity of the opacity field, we first introduce the Signed Distance Function (SDF) field facilitate geometry learning. Then we propose geometry constraint which encourages the SDF values of the Gaussian primitives approach zero when their opacity values reach the maximum, achieving unbiased guidance of the SDF field over the opacity field. In this way, we can take advantage of the strong linearity of the SDF field to explicitly establish connection between Gaussian opacity field and the scene surface, which significantly enhances geometric learning and reduces artifacts.
Subsequently, we employ the optimized Gaussian primitives as an accurate geometry initialization for dynamic surface generation. Due to the absence of intermediate states, we leverage the kinematic structures of articulated objects model time-continuous Gaussian deformable fields in unsuper- vised fashion, and constrain the deformable fields using learnable motion parameters. Concretely, we propose a heuristic method for unsupervised part segmentation and formulate the deformable fields of dynamic parts via the motion parameters. Our REAnGS is evaluated on PartNet-Mobility 3d and
AKB-48 [15] object repositories, ranging from synthetic real-worke data. Extensive experiments demonstrate that our REArtGS outperforms existing state-of tafee-of-theaat methods in articulated object surface reconstruction and generation tasks, as shown in Fig.
In summary, our main contributions can be summarized as follows: (1) We propose REARGSS, a novel framework introducing 3DGS to conduct high-quality textured surface reconstruction and time-continuous generation for articulated objects, only using multi-view images from two arbitrary states. (2) Our REANGS exploits unbiased SDF guidance for 3D Gaussian primitives to enhance geometric constraints for improving reconstruction quality, and also establishes the deformable fields constrained by kinematic structures of articulated objects to generate unseen states in unsupervised manner. (3) We incorporate REAnGS into various scenes ranging from synthetic to the real-world data across many different articulation categories. The extensive experimental results demonstrate that our approach significantly outperforms SOTAs in both mesh reconstruction and generation tasks.
2 Related Work
2.1 Articulated Object Shape Reconstruction
Object surface reconstruction is well-established problem for understanding the full geometric shape of objects. Some works introduce to encode continuous functions that model the objects using 30 and occupancy 200] To achieve both geometry and
Signed Distance [24 22 radiance 21 motion analysis in a single forward, Ditto 9 and REACTÓ 29 propose to generate shapes at
27
unseen states from pair observations. Specifically, PARIS 14 alleviates the 3D data requirement

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limitation and succeeds in reconstructing shape surface with only RGB images. Most recently. ArticulatedGS 7 and ArtGS [T8] introduce 3DGS achieve both the reconstruction and motion estimation of articulated objects. However, these methods still suffer from insufficient geometry constraints, which may lead to noisy surface mesh outputs. Therefore, our REArGS aims to address these issues, and proposes geometric and motion constrained 3DGS for this task.
2.2 Surface Reconstruction with 3DGS
3D Gaussain Splatting has become increasingly popular technique for surface reconstruction in recent years [T0 M 41 26]. GOF 42 establishes opacity fields of 3D Gaussians using ray- macing-based rendering, and extracts the surface meshes by the opacity level set. 2DGS [8] and PGSR [ seek transform 3D Gaussians into 2D flat representation, obtaining accurate normal distribution. Although improving the surface reconstruction quality, these methods still lack more reasonable geometry constraints. Several researchers attempt to integrate SDF representation with but these approaches commonly use SDF to regularize normals and guide the pruning 3D Gaussians, without substantial optimization of Gaussian opacity fields. Meanwhile, some works conduct dynamic reconstruction using 3DGS. Deformable 3DGS proposes deformation field to reconstruct dynamic scenes with 3D Gaussian primitives. 4DGS 4 leverages spatial-temporal structure encoder and multi-head Gaussian deformation decoder to derive the deformed 3D Gaussians at given time. However, these methods rely on complete supervision motion process, limiting their capacity for generating unseen states. The similar issues also occur in DGMesh 133 and REACTO [29]. We provide more analysis and comparison of the related works in
3D Gaussians 33 35 3
the
Appendix B
Reconstruction
Generation
Upacity
Readeriuu
Start State
F (depth)
Points
Pricanic
End State
Revolite a..
Regstarbed Qpuaity Fidcs
|A,P8
Dynamic Part Evaluation
Initial Dynamic Part
Final Dynamic Part
3D Gaussians
Operation flow
Gradient flow
Reconstruction
Surface
Figure 2: The overall pipeline of REAnGS. We introduce additional geometric and motion constraints for 3D Gaussian primitives, achieving high-quality surface mesh reconstruction and cime-continuous generation, with only multi-view images from arbitrary two states.
3 Method
The overall framework of our REAnGS is illustrated in Fig. 2 Taking multi-view RGB images from two arbitrary states s = 0, s = 1 of artieulated objects, we aim to achieve high-quality textured mesh reconstruction and generation at any unseen states between [0.
We first introduce SDF representation and propose an unbiased SDF regularization to enhance the geometry constraints of 3D Gaussian primitives. In this manner, we improve the reconstruction quality and yield dense point clouds at state subsequent dynamic reconstruction. Then we establish time-com mnee-contnuous deformable fields for 3D Gaussian primitives constrained by the kinematic structures of articulated objects. Given any state s, we can derive the deformed position of Gaussian primitives through the deformation fields in an unsupervised fashion. The details of our approach are elaborated below.
0, providing an accurate geometric prior for
3.1 Reconstruction with Unbiased SDF Guidance
3

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To better preserve the geometric features of Gaussian primitives, we use the ray-tracing basend 3DGS following GOF, which evaluates rendering contribution of Gaussian primitives directly without the 3D-to-2D projection step. However, the Gaussian primitives still suffer from insufficient geometric constraints. Coneretely, the opacity fields lack an explicit link with scene surface, which may lead to noisy outputs in surface reconstruction of articulated objects.
To address the limitation, we first introduce SDF representation to guide the geometry learning of Gaussian primitives. We utilize Multi-layer Perceptrons (MLP) with 8 hidden layers to learn the SDF values for spatial position inputs, and the scene surface can be represented by the zero- set:
AnS)
S= f R3 f(x) - =0}
(1)
Following Neus B32, we can derive the opacity ē for the center x; of Gaussian G, from learned SDF values:
The illustration unbiased SDF regular- ization. It can be observed that when approaches t", the absolute value of SDF |S] converges to zero with the unbiased SDF regularization.
Figure 3:
$ (f)() T (f (x++1))
.0
à: max
① (f (x4)
(2)
where & denotes Sigmoid function. [(xx+1) ] approximated as:
f(x(11) - = fx,) + f'xx)
(3)
where Ax RSr. R E R3x3 is the rotation matrix derived from Gaussian's 's quaternion, and E 3x3 is the diagonal matrix of Gaussian's scaling. is the normalized ray direction. Nevertheless, the SDF-opacity conversion is not directly applicable to the a blending rendering. This is because each 3D Gaussian primitive models a local density distribution, while Eq. 2 only maps the global positions to their opacity values and neglects the local properties of Gaussian primitives. Therefore, we define the opacity of Gaussian primitive combining the rendering contribution e proposed in GOF as:
o GEE (G.)
ô; max(e txx +xx)
(4)
Ô max (e
where OL, rz are the camera center and incident ray direction represented in the local coordinate system of Gaussian G., which can be acquired by local scaling matrix and rotation matrix of G,, The maximum value E (G,) occurs at ray depth t², expressed as follows:
(5)
r
The rendering equation based on or represented as:
C=
C II (1-ar) as))
(6)
where N is the number of Gaussian primitives involved in a-blending and is the color modeled with spherical harmonics. To leverage SDF constrain the geometric learning of Gaussian primitives. we first introduce a bell-shaped function & to modulate the transformation from SDF to opacity and replace the original Sigmoid activation function + in Eq. formulated as:
kx(()))
(x(f(x)) (1 f(x)))
where is learnable parameter that adjusts the function shape and we initially set it 0.1. Intuitively, the Gaussian primitive closer to the surface has higher opacity value.

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However, since & is determined solely by the Gaussian's 's center, -oinnligmmenn still exists between the maximum points of & and E, which can formulated as:
thias
argmax(0) argmax(E)
(8)
To mitigate this bias, we propose unbiased regularization for the SDF value at depth t" as following:
Lunbins = [I + +rr)]l
where o, r are the camera center and incident ray direction. Through the unbiased regularization, we encourage that when the rendering contribution of Gaussian primitive reaches its maximum value, the corresponding spatial position is close to the scene surface, as shown in Fig. 3 In this manner, the SDF representation is able to regularize the opacity fields without bias and facilitate more reasonable distribution of Gaussian primitives over scene surface. We provide more detailed elaboration and proof in the Appendix C.I
3.2 Mesh Generation with Motion Constraints
Due to the explicit representation of Gaussian primitives, we can acquire accurate dense point clouds from reconstruction, serving as initial geometry for mesh generation. Then establish time- continuous deformable fields for 3D Gaussians to infer the deformed position x, at state s. However, it is challenging to optimize the deformable fields for Gaussian primitives only with the supervision of two states. Accordingly, we exploit the kinematic structures of articulated objects to constrain the Gaussian deformation field. We first assume that the articulated motion only includes rotation and translation following PARIS. Then we employ a heuristic method to efficiently predict the joint type through movement trend of points, which elaborated in the Appendix C.3 For rotation joints, our learning objective is to determine their rotation axis and rotation angle. Specifically, we take the pivot point o, E IR& of the rotation axis and normalized quaternion q E TR learnable parameters, where the quaternion can be decoupled into the rotation axis a E R33 and rotation angle 0. For determine their translation directions and translation distances m. Similarly, we take the unit vector d E 123 representing the translation direction and the translation distance m as learnable parameters.
prismatic joints, our learning objective
Subsequently, we formulate the deformable fields through a canonical state. Given the rotation motion SO(3) E R3x3, define its canonical state as s* 0.5 and the rotation angle of state be expresses as:
(10)
where s E [0, 1] and 0 E 1- The angle- bounded parameterization is able to prevent the singularity in exponential coordinates when |0]] > æ. Using Rodrigues' rotation formula [25), the deformed position x, can be derived as following:
X, = (I + sin(O,) + (1 cos 0.)) (*)) (x o,) + +
(11)
where K is skew-symmetric matrix formed by the rotation rotation axis and 33x3 is unit matrix. Meanwhile, we align the local quaternions of 3D Gaussian primitives after rotation through quaternion multiplication.
For the prismatic motion m-d d E R:3, we take advantage the vector space structure Fuclidean ge- ometry by setting s* = 0. The deformed position x, can be naturally acquired by linear interpolation, formulated as:
X,
d
(12)
unlike rotation motion, this parameterization avoids singularities due to the flat Riemannian structure of 3
However, the deformable fields should be applied exclusively to movable Gaussian primitives. Consequently, the Gaussian primitives need to be segmented into dynamic and static parts. To address this challenge, we propose an unsupervised method for dynamic part segmentation. We first only input the multi-view images at the end state during warm-up training iterations, and then perform an initialization segmentation of the dynamic part. The segmentation criterion for the initial dynamic
5

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Input state
GOF
PARIS
ArGS
Ours
Ours (textured)
GT
Foldchair
ination
Laptop
Washer
Fridge
Figure 4: The qualitative result of surface reconstruction PartNer-Mobility dataset. We show both textured and non-textured meshes for the best comparison. components is represented as: A > 3. where | is the LI distance spatial position variation during the warm-up training, and 3 is its average value. Furthermore, the spatial transformation of the dynamic part should align with the learnable motion parameters. Hence the dynamic part among the Gaussian primitives is re-evaluated at certain intervals of iterations, where the criterion for revolute or prismatic joints is represented as:
0
S0
K
(13)
9m K
Im ml
where è, m are the rotation angle around axis and the translation distance respectively, yp the tolerance threshold which decreases as the number of iterations K increases.
be conveniently transferred multi-part articulated objects, through sequentially learning the segmentation masks and motions of each individual part. Please refer to our Appendix C.4 for more details.
Moreover, method
3.3 Optimization and Textured Mesh Extraction
Since the shapes of Gaussian primitives are not limited, the normal distributions Gaussian primitives are difficult to estimate accurately. However, Gaussian's 's normals should be parallel to the gradients of SDF an ideal case. We consequently introduce additional regularization to regularize the normals of Gaussian primitives by SDF representation, expressed follows:
Σ D. V f(x)) N
1
Lnormal
(14)
| [[((x))]
where n; represents the normal of Gaussian G,, which is calculated following GOF:
n; - 5 'T
(15)
where R is the rotation matrix encoded by Gaussian's quaternion and S is the scaling matrix. We also employ the Eikonal regularization term [5] to encourage SDF gradient direction perpendicular to the surface, represented
Leck Σ (IVf(())))l - 1)
(16)
The overall training objective L is formulated follows:
L L. + X Lunbias CnCoomal Az + XaLa
(17)

---

where À is the weight of regularization and La is the depth distortion loss following [8] Le is defined as:
Le ALD SSIM (1 21
(18)
where CD-SSIM is proposed in 10 and &1 is the LI norm of the pixel loss.
Once the optimization converges, we adopt the TSDF fusion algorithm 23 to extract the textured mesh from Gaussian primitives. We utilize the a-blending rendering pipeline to obtain depth, opacity and RGB renderings for training views. Then we integrate these images into a voxel block grid (VBG) and extract triangle mesh from the VBG. The textures of surface meshes can be efficiently obtained leveraging the spherical harmonics and opacity of Gaussian primitives. Please refer to our Appendix C.3 for more detailed illustration.
Table Quantitative results for the surface reconstruction quality on PartNet-Mohine Mobility dataset. We bold the best results and underline the second best results. means we implement it without depth supervision for fair comparison.
Metrics
Mathod
Stapler
USB
Scissor
Fridge
Foldchair
Washer
Laptop
Oven
Storage
Mean
A-SDF X2
14,19
7.14
10.61
13.71
40.85
12.50
3.31
2.11
21.37
22.57
14.34
Ditto
2.38
2.09
1.70
2.16
6.80
7.29
42.04
2.51
3.91
7.19
CI(ws) L
PARIS
0.96
1,80
0.30
2.68
0.42
18.31
0.46
0.25
6.07
8.12
3.94
GOF
42
1.51
8,09
0.36
1.51
0.53
17.35
0.89
0.84
19.81
10.04
6.09
AnGS 18
2.77
1,36
0.75
2.01
0.41
20.59
0.63
9.00
4.75
REAnGS (Ouns
3.47
0.75
0.29
1.50
0.40
12:20
0.72
0.53
8.89
8.27
3,79
A-SDF 24
2,140
2,478
1,8055
1.001
2,080
T,590
5.630
2.418
2,751
4,077
2.677
Ditto
2.926
1,550
1,296
CD(s)
PARIS
2,077
3.812
2,807
0.370
1.209
3.869
2.855 858
1.025
2,873
2,903
2. 2,380
GOF
2,510
1.736
2,304
2.230
2.787
5.725
2.111
0.961
3,080
2.812
2.626
AnGS
2.949
1.704
2.438
2.031
1.148
1,157
REAnGS (Ouns)
2.186
1.433
2,291
0.475
0.018
1.204
2.596
0.038
0.784
1,350
1.236
A-SDF 24
0.041
0,035
0.034
0.019
0.053
0.046
0.224
0.001
0.010
0.015
0.054
Ditto
0.197
0.181
0.275
0.114
0.352
0.059
0.107
0.366
0.052
0.030
0.173
FL
PARIS 44
GOF
0.240
0.189
0,151
0.343
0.091
0.429
0.087
0.024
0.386
1.3966
0.533
0.031
0.033
0.036
0.227
0.253
AnGS 18
0.251
0.209
0.438
0.118
0.447
0.053
0.408
0.294
0.056
0.042
0.232
REAnGS (Ouxs)
0.256
0.307
0.598
0,168
0.502
0.069
0.488
0.419
0LIKS
0.066
0.294
1.113
Ditlo g
1.724
1.308
1.212
0.619
0.935
0.841
1.996
0.417
0,852
0.970
1.087
EMD L
PARIS
1.197
1.38.
0.637
0.426
0.778
1.660
1.823
0,706
1,200
1,046
1.055
1.643
1.075
1,058
1.181
0,394
1,241
0.959
AntS [8
1.921
0.677
0.934
0.637
0.506
1.154
11311
0,502
1.006
0.787
0.926
REAnGS (Ours)
1,060
0.847
1.078
0.485
0.097
0.777
1.112
0.111
0.627
0.755
0.695
Ours
(eextured)
Ours
PARIS
D-IDGS
Ours
(lextured)
Ours
PARIS
D-3DGSS
Figure 5: The qualitative results of surface generation at arbitrary unseen states on PartNet-Mobiliy dataset. We show both textured and non-textured meshes for best comparison. The states are sampled randomly.
7

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Table 2: Quantitative results for the surface generation quality PartNet-Mobility dataset. We bold the best results and underline the second best results. * means we implement it without depth supervision for fair comparison.
Metries
Method
Stupler
USB
Scissor
Fridge
Foldchair
Washer
Blade
Laptop
Oven
Stooage
Mecan
A-SDF
112.30
34,01
94.11
33.46
56.73
55.82
3.78
27.64
29.60
25.30
47.28
PARIS
14
2,09
14.51
12.81
2.64
10.42
18.30
01800
3.25
10.89
5.89
8.16
CD(ws)
D-3DGS
30.93
42.49
AnGS
18
2.34
1.72
0.68
2,05
0.52
20.59
0.63
1.00
8.78
10.97
4.92
REAnGS
(Ours)
2,60
1.68
01.4
2.21
0.41
14.80
0.59
3.65
8,11
6.48
4,10
A.SDI
5.166
3.668
7,050
7.794
5,224
PARIS 14
2,113
0.417
4,704
0.408
1.216
0.857
4.442
1.354
2,793
4.332
2.264
CDbs)
D-3DGS 38
9.589
1.544
0,891
0.165
1,147
3.218
0.168
0.449
3.773
3,100
2,434
AnGS 18
0,381
0.471
2.670
1.794
REAnGS (Ours)
3.651
0.487
0.127
0.464
0.420
1.617
0.414
0.298
2.129
1,020
1,063
A.SDF 22
0.007
0.0.4
0,056
0.012
0.021
0.023
0.168
0.001
0.010
0.004
0.034
PARIS
0.221
0.151
0,319
0.091
0.423
0.024
0.421
0.530
0.031
0.032
0.224
FL
D-5DGS
X8
0.064
0.180
0.125
0.073
0.168
0.195
0.233
0.131
0.022
0.023
0.121
AnGS 1X
0.264
0.255
0.125
0.460
0.055
0.426
0.292
0.045
0.244
REAnGS
(Ours)
0.254
0.215
0,577
0.186
0.465
0.052
0.509
0.608
0
0,050
0,298
A-DDF
2.123
0.951
0.955
L,606
1684
1.878
1.731
1,115
16200
L837
1.359
0,451
1.354
1.113
EMD
D-SDGS
X8
3.224
0.612
0.665
0.48
0.758
1.269
0.291
0.436
1.374
1,206
1,032
AnGS
2.207
0,562
0,412
0.563
0.525
1.171
0.631
0.724
1.299
0,750
0,8884
(Ours)
0:473
0.900
0.456
0.670
4 Experiments
4.1 Experimental Setting
Datasets. To evaluate the reconstruction quality of our method, we conduct surface reconstruction experiments on synthetic dataset PartNet-Mobility (34) and real-world dataset AKB-48 (15), an extremely rich repository of real-world articulated objects which exhibit a wide variety of geometries and textures. Please see the Appendix D.I for more details.
Metrics. Chamfer Distance (CD), Fi-score and Earth Mover's Distance (EMD) 43 are usually adopted as evaluation metries for surface quality. However, these methods typically focus the whole surface, endowing the unseen areas (such as the bottom of the object) with considerable weights during evaluation. This is unreasonable since tend be more concerned with the upper hemisphere regions of articulated objects. Therefore, we sample point clouds from the fragments between the rays cast by test cameras and the surface mesh to calculate EMD and CD, defined as CD (Is). We also evaluate the Fi-score and CD for the whole surface, defined as CD (ws), to comprehensively evaluate the surface quality. Note that the CD values are multiplied by 1000 and the distance threshold of F1-score is set to 0.4. The calculation of these metrics can be referred to in our Appendix D.4
All the experiments are conducted on a single RTX 4090 GPU. We also provide detailed implementa- tion of our approach and basclines in the Appendix D.2
4.2 Mesh Reconstruction Performance
We report the guantitative results of mesh reconstruction in Table. | and qualitative results shown in Fig. 4 Note that we implement AnGS without depth supervision for a fair comparison. As can be observed, our REArGS outperforms state-of-the-ard approaches in the mean across all metrics with 3.79, 1.236, 0.294 and 0.695 respectively. Compared to A-SDF [22] and Ditto [9] that exploits 3D inputs for articulated object surface reconstruction, our method still achieves higher reconstruction quality in the majority of categories. In terms of PARIS, GOF and ArtSS, our approach exhibits significantly smoother and clearer surfaces shown in Fig. benefiting from our enhanced geometric constraints.
4.3
Mesh Generation Performance
We report the quantitative results of mesh generation in Table. 2 and present the qualitative results Please refer to our Appendix for more qualitative results. Our REArGG achieves the best mean results across all metrics with 4.10, 1.063, 0.298 and 0.670. Compared to PARIS, our method exhibits smoother surface generation results, as shown in Fig. 5 It is mainly because PARIS lacks reasonable geometry initiation and directly utilizes the composite rendering, leading to the spatial
Fig. 55
overlap between the neural radiation fields of the start and end states. It can be also observed that
8

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our method is superior to ArtGS on most categories, shown in Fig. [0 the Appendix. This is primarily attributed our high-quality geometry initialization from the reconstruction stage, as well as the motion-constraine deformable fields to yield dynamic generation.
Besides, provide the part segmentation and joint parameter estimation results in the Appendix, D.5 and D.6 respectively.
Table 3: The ablation study of the unbiased SDF guidance
Table 4: The ablation study of motion constraints on PartNettMobiling dataset.
dataset.
w/ SDF w/ Unbiused Reg.
(D(sss
CD (ws)
CD (D(ss
F1
EMD
Settings
CD (ws)
CD (rs)
F1
EMD
5.56
2.252
1.921
0.250
0.273
1.366
w/o
18.65
2,270
0.200
1.105
3,79
1.236
0.294
0.695
w/ motion constraints
5.41
1.663
0.276
0.670
4.4
Ablation Studies
We conduct an ablation of the unbiased SDF guidance on PartNee-Mobility dataset to validate its effectiveness. The ablation setting and results are reported in Table. The quantitative results prove that both SDF guidance and the unbiased regulariza- tion of SDF indeed improve surface recon- struction quality. This primarily because the SDF representation establishes explicit geometric association between the opacity fields and scene surface through 4k. and the unbiased SDF regularization further op- timizes the distribution of Gaussian opacity fields.
Table 5: The quantitative results on real-world AKB- 48 dataset. We bold the best results and underline the second best results, * means we implement it without depth supervision for fair comparison.
Cangers
Medsal
CDreall
Racreamcire
CDiool
EMD
CD
Generati CDool:
EMDL
PARI5
6.63
1.611
0.90
0.843
1.00
2.331
0.306
1,05
REAntS
6.465
0,62
1-07
0135
1137
11577
0711
162
0.07
0.72
0,337
0.54
0.844
0.50
6.151
Schoor
AmtSs 1X
11:35
0.03
03551
1.50
11:88
140
6.21
FARRS [
2:55
1351
0.50
0303
45.83
1.51
6.39
1183
8,00
REAntSS
33.61
1568
1.33
AnDss
88.75
2467
0.138
1.42
11.31
1318
6.300
We also conduct an ablation study of the Mobility
Eyeglases
AndSS [B
27.00
1354
0351
0331
12.13
1.91
5.055
motion constraints on dataset and present the quantitative results in Table. For the baseline without mo- tion constraints, we employ three MLPs to learn the variations of spatial positions, scales, and quaternions respectively for Gaussian primitives, which is similar to D-3DGS. The significantly superior results demonstrate the effectiveness of the motion constraints.
089
6/H
1.51
1200
PARES L1]
6:
136
0.11
035
13:55
1.5
5.00
33A1
Iapuss
Reconeractoon
Geseurtinn
Figure 6: The qualitative results of surface reconstruction real-world AKB-48 [5] repository. We show both textured and non-textured meshes for two-part and multi-part articulated objects.
4.5 Generalization to the Real World
We conduct reconstruction and generation experiments in the real world to investigate the generaliza- tion capacity of our REAnGS. We report the quantitative results comparing with PARIS and ArtS in Table. and present the qualitative results in Fig. Our approach significantly outperforms PARIS and ArGSS in mean performance across all metrics. This demonstrates that our method exhibits strong generalization capability for real-world objects and enables high-quality surface reconstruction and generation as shown in Fig. 6

---

Conclusion and Future Work
We propose REArtGS, a novel framework that achieves high-quality textured mesh reconstruction and dynamic generation of articulated objects using only RGB views of two arbitrary states. We propose an unbiased SDF guidance to regularize Gaussian opacity fields and model the Gaussian deformation fields constrained by kinematic structures for generating meshes of unseen states. Experiments show the superior performance of our method on both synthetic and real-world data.
The limitations of REArtGS lie on the requirement of camera pose prior and challenges of objects with transparent materials. Future works will introduce relative pose estimation to alleviate the dependence on camera poses and employ physically-basee networks to model the transparent materials.
Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant 62302143, 62576130, and Anhui Province's Key Science and Technology Project 202423k09020007.
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18

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Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
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Please refer to our LLM policy for what should or should be described.
19

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Appendix
A Overview
In the appendix, we first provide a detailed comparison highlighting our advantages over related works in Sec. B Then we elaborately extend our method in Sec. Bec.[frrm the following four aspects: unbiased SDF guidance theory, textured mesh extraction, joint type prediction, and multi-joint mesh generation. In addition, more experimental details and results presented in Sec D Finally, provide our codes and video in Sec.
B Related Work, Extended
Recently several methods also attempt to integrate SDF representaion with 3D Gaussian primitives [39
2.35 3 [9] and have improved surface reconstruction quality. However, most approaches are limited to normal regularization and pruning strategy of Gaussian primitives through SDF representation [39
2 35 3. and the opacity of Gaussian primitives holds more essential role in the a-blending. In contrast, we leverage the unbiased SDF guidance to regularize Gaussian opacity fields, achieving substantial geometric constraints and enhancing geometric optimization. 3DGSR [19 directly obtains the opacity of Gaussian primitives through SDF-opacity conversion proposed in Neus [32 and also employs a bell-shaped activation function to control the distribution of SDF-opacity. Nevertheless, since the SDF network simply utilizes Gaussian's 's center as input, 3DGSR ignores the local features of Gaussian primitives. In comparison, approach combines the local rendering contributions with opF-opycity conversation results as Gaussian's 's opacity values, yielding more reasonable distribution of Gaussian opacity fields.
Most recently, ArtSS [8] also proposes mesh reconstruction method for articulated objects. Although demonstrating its effectiveness and robustness for mesh reconstruction, it relies on depth inputs, limiting its performance when the 3D supervision is unavailable. Moreover, it still lacks sufficient geometry constraints, leading to noisy results occasionally. In contrast, our REArGG only requires 2D RGB images as inputs and introduces additional geometry constraints, improving the mesh reconstruction quality.
C Methodology, Extended
C.1 Unbiased SDF Guidance for Gaussian Opacity Fields, Extended
As defined in the main draft, the opacity of Gaussian primitives combines with the rendering contribution e, formulated as:
0: θ;E
Ô: max (e- 120 oz)+
(19)
where X = Oz + ir X1, OL, ry represent the spatial position, camera center, and ray direction of Gaussian's 's local coordinate system respectively. attain its maximum value when t" as mentioned in the main draft. Ô; can be derived from 4, and the SDF-opacity conversation, where & is also defined in the main draft, formulated as:
k(x())
(x(f(x)) (1+ f(0))
(20)
Although the composite function è (f(x)) attains its maximum when f(x) 0. non-alignment still exists between the maximum points, formulated as:
argmax (ō (x (t)) A ft"
(21)
This mismatch leads to spatial deviation between å and e proposed in the main draft:
taiu = argmax(0) argmax (E)
(22)
20

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(X)
(b)
Figure 7: The distribution of l-e (a) and SDF-O, (b) without the unbiased SDF regularization.
As illustrated in the main draft (Fig. 3), the deviation thias results in disordered distribution of the Gaussian opacity fields. We also present their distributions without regularization for intuitive illustration in Fig. 7
To tackle the deviation, we propose an unbiased SDF regularization uubiia defined in the main draft:
Lunbins = [ + t²r)l1
(23)
We present the theorem and proof that Lumbius is capable of eliminating the deviation Ibiss in Theorem, and Proof. below.
Theorem Let f : IR3 + R be pereptonn (MLP) with smooth activation functions, and the spatial position be defined as x()) o ir with camera center o E TR3 and ray direction E R33 Let argmux(e) l". Consider the activation function D R - IR. defined by:
perceptron
(x(2) (1+ e
k >
0
(24)
If lim f(x(()) = 0, then the composite function Tt a I x(1) allains its maximum at 1 = 1", iee. (+ argmax(0) argmax(e) = O.
Proof
Define 2(t) = f(x(t)). Compute the first derivative:
dd d
kz
dz
dz
(1 (1+
he Re (1 + cko)2
2kc R ck2)
(1+ ekzj
kekt kkz)) (1+ekzys
der Setting ds
gives the unique critical point 0.
Evaluate the second derivative at z 0:
d2 k
2.2 k2 (1 4ekz 2kz
d=2
(1 + chzj
===
==
22 (-4)
222
4 < 0
16
For 0, de < 0; for 0, d4
0. This proves that the maximum value of Tu is attained when 2(t) = O. Given that lim f(x(t)) = and argmax(E) = t", it can be proved that
argmax(()) - argmax(s) =
21

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C.2 Textured Mesh Extraction, Extended
In this paper, we employ TSDF fusion 23 to extract textured meshes from the regularized Gaussian opacity fields. We first obtain multi-view RGB renderings through a-blending, where the opacity o and view-dependent spherical harmonics (SH) coefficients jointly modulate the color accumulation. These per-pixel blended colors are then projected into the voxel block grid (VBG), ensuring that high-opacity regions dominate the color field, while low-opacity areas are suppressed. Meanwhile, we acquire the multi-view depth renderings via a-blending and conduct filtration with minimum opacity threshold 0.5 as well as a maximum depth threshold 5,0. Then the filtered depth renderings similarly integrated into the VBG, After multi-view fusion, triangle mesh is extracted via Marching Cubes and vertex colors are directly sampled from the VBG's color fields. This process effectively bakes the fused texture into the extracted mesh.
In the early experiments, we also attempt to use SDF combined with Marching Tetrahedra to extract surface meshes, but this leads to a decline in surface quality. It is mainly because the SDF-opacity conversion only uses the center positions of Gaussian primitives for approximate calculation during training. Therefore, the SDF network only learns the spatial information at Gaussian's center, making challenging to handle dense sampling points in mesh extraction. In contrast, the a-blending in TSDF fusion incorporates the local information of the Gaussian primitives via Gaussian opacity fields, yielding higher-quality mesh results.
C.3 Joint Type Prediction
Given an articulated object with unknown kinematic structure, we first obtain two coarse point clouds Po and P1 using the multi-view images from two states so and 81 respectively, based on the proposed pipeline in Sec. 3.1 Note that it only takes few minutes since the training process only undergoes 3000 iterations. Then we use the Farthest Point Sampling (FPS) produce the sparse point clouds Po and Pi for Po and P1. For each point p; E Pü. we identify a point qi E Pi closest to it. Subsequently, we filter the dynamic points D with significant displacement through the distance between p and g, formulated as:
D = (pil llps q:ll > 7}
(25)
where 7 the dynamic threshold.
After that, we determine the motion type of the dynamic point set D through the variance ap of the displacement direction angle.
2
TD
1 D
Σ
arecos
Te:
Umean
Umeam
(26)
where Pi yi and Umean D Σ vs. Then we use threshold orot to predict the motion type, that is, the joint type of the articulated object. Concretely, determine the dynamic part prismatic joint if oD & rrot and as rotation joint unsatisfactory cases.
C.4 Mesh Generation of Multi-Pare Articulated Object
Mesh generation of multi-part articulated objects can be treated as straightforward extension of the two-part task for our approach. We can generate meshes for multi-part objects in unseen states through sequentially learning strategy. Specifically, given an articulated object with k dynamic parts Wda, we start with fixing parts (wdg...,Wdd, except for the dynamic part Wa, and the object can be decomposed the into dynamic part Wa, and static part W, (all the remaining points). After learning the motion and segmentation mask for way we sequentially perceive dynamic part w'y,, while the static part wa can be updated as: w, Wa, Way where Wd, denotes the remaining points except waz By parity of reasoning, we achieve learning all motions and segmentation masks for the parts, and the mesh generation results for any unseen state can be obtained using the proposed pipeline in Sec. 3.2
22

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D Experiments, Extended
D.1 Dataset
The PartNet-Mobility dataset [34] a synthetic dataset comprising articulated objects across 46 categories, characterized by a diverse scale and geometry. Following PARIS, we selected the same 10 categories for our experiments. Each category comprises 64 to 100 RGB views at two arbitrary states, which sampled randomly from their upper hemispheres. AKB-48 [T5] is real-world dataset containing an extensive collection of articulated objects scanned in real indoor scenes. We select categories with both two-part and multi-part objects and sample 100 RGB views two arbitrary states for each object.
D.2 Implementation
All the experiments are conducted on single RTX 4090 GPU. Our approach constitutes two-stage procedure to perform surface reconstruction and generation respectively. For the reconstruction stage, we train the 3D Gaussian primitives with SDF network for 3, 5,1000 iterations, which includes an warm-up phase consisting of 1,000 iterations for SDF initial learning. Then we employ the unbiased SDF regularization in 1,500 1,6000 iterations, use the SDF-normal regularization and Eikonal regularization during the entire training process. We perform the densification and pruning for 3D Gaussian primitives from 1,500 iterations to 16,000 iterations. The training time reconstruction stage is about 60 minutes.
For the generation stage, we leverage the 3D Gaussian primitives optimized from the reconstruction stage as initialization. We also set warm-up phase with 3,000 iterations to train 3D Gaussian primitives only using RGB images from the end state. Then we start to evaluate dynamic parts of the articulated object and apply the deformation fields to them. The total number of training iterations during the generation stage 30,000. The training time of the generation stage about 10 minutes and the total training time for surface generation from scratch is approximately 70 minutes.
D.3 Baselines
For the surface reconstruction experiments articulated objects, we define the start states of ar- ticulated objects reconstruction targets, and compare the reconstruction results with existing state-of-the-arr methods: A-SDF (22), Ditto (28), PARIS [14), GOF [42 and ArtGS [18). Note that implement ArtGS without depth supervision for a fair comparison. In particular, A-SDF uses sampled point clouds as inputs and Ditto requires both point clouds and united robotics description format (URDF) files of articulated objects. Following PARIS, we train A-SDF the 10 categories of the PartNet-Mobility dataset and employ the pretrained weights Ditto to conduct the comparison.
As for the surface generation experiments, compare the surface generation results with existing state-of-the-arr methods: A-SDF, PARIS, Deformable-3DGS (D-3DGS) [38) and ArGS [88. Since the ground truth point clouds of unseen states unavailable, we take the end states of the articulated objects as generation targets and generate surface meshes from the canonical states. Besides, all the methods employ point clouds (A-SDF) RGB images (PARIS, D-3DGS, ArGS, ours) from both start and end states as training inputs.
D.4 Metries, Extended
We employ CD (ws), CD (rs), F1-score, EMD the metrics of surface quality. We present the detailed calculation below.
The CD (ws) is defined the mean of the shortest distance between two point clouds, which can be formulated as following:
CD (ws)
1
Σ
min yeN₂
||x
211
N
xEN.
(27)
Σ
min
lyy
x
2₂
yE,
23

---

where N1. N2 represent the point number of output and ground truth respectively. The CD (rs) is calculated by the sampled point clouds from the fragments between the rays cast by test cameras and the surface mesh, shown as following:
CD (rs)
Σ
min
|| y
Nei
yENeg
xEN.
(28)
min xEN.
ly - x1
N
yEN
where N.., Na² denote the point number of sampled output and sampled ground truth respectively. Similarly, we adopt the same point cloud sampling method to calculate EMD score [43, which can be formulated as:
EMD (Na,: Nz2)
min d:N., -N
Σ DEN,1
||
(xx)l
(29)
N
where á is bijection to identify the optimal correspondence between two point clouds.
Start State
End State
GT
Ours
GT
Ours
Figure 8: The qualitative results of part segmentation. We set the dynamic parts to yellow and the static parts to blue.
Fl-score the harmonic mean between the precision P(d) and recall R(d) with distance threshold d = 0.4 in this paper, formulated as:
F = 2((d)R(d) P(d) + R(d)
(30)
D.5 Part Segmentation
We present the quantitative results of part reconstruction quality on PartNet-Mobility dataset in Table, [6] and provide the qualitative results of part segmentation in Fig. g Our method achieves
the best mean results both dynamic and static parts. It can be also observed that our REArGGS

---

successfully acquires accurate part decompositions, as shown in Fig. 8 This demonstrates that our approach is capable of perceiving motion, and enables accurate part segmentation using the simple yer effective heuristic method.
Table 6: Quantitative results for the part reconstruction quality on PartNet-Mobility dataset. CD-s and CD-m represent the CD results of static part and dynamic part respectively. We bold the best results and underline the second best results.
Metries
Method
Stapler
USB
Scissor
Fridge
Foldchair
Washer
Blade
Laptop
Oven
Storage
Mcan
Ditto
2.38
2.09
2.16
7.29
42.04
0.31
3,91
7.19
CD-s
PARIS
14
0.96
180
0.30
2.68
0.42
18.31
0.46
0.25
6.07
8.12
3.94
AnGS
2.05
0.57
2.03
20.97
0.44
0.76
9.20
13.51
5,31
REAnGS (Ours)
1.47
0.82
0.25
1.53
0.31
13.04
0.69
0.48
6.59
7.30
3.25
12.89
2.20
PARIS 18
0.85
0.89
0.23
1.13
0.53
0.27
5.13
0.14
0.41
20.67
3.06
CD-m.J
ArOS 18
1.17
2.15
REAnGS (Ours)
1.18
0.40
0.21
0.66
0.30
0.42
1.97
0.11
0.25
12.39
1.79
D.6 Joint Parameter Estimation
We also present the joint parameter estimation quantitative results in Table. 7 and qualitative results in Fig. to evaluate motion learning. Following PARIS [14) we compute the orientation error (Ang Err) between the predicted axis direction (a, in our method) and the ground truth, and evaluate position error (Pos Err) for revolute joints through the position difference of the pivot point (o, in our method). can be observed that our method achieves the best results, which demonstrates our superiority in motion learning and further demonstrates the high fidelity of our dynamic generation.
Fridge
Scissor
Stapler
Storage
USB
g
Figure 9: The qualitative results of joint parameter estimation. We show the textured mesh with red arrow representing joint axis.
Table Quantitative results for the joint parameter estimation on PartNet-Mooility dataset. Note that, denotes the absence results for prismatic joints. We bold the best results and underline the second best results.
Metries
Method
Slupler
USB
Scissur
Fridge
Foldchuir
Washer
Oven
Laplop
Blade
Storage
Mean
Diita
89.86
89.77
4,498
89.
89.35
89.31
0.955
3.124
6.319
79.54
54.22
PARIS
14
0.069
0.065
0.019
0.001
0.020
0.082
0.028
0.034
0.001
0.369
0.069
Ang
ArUS
18
0.062
0.034
0.039
0.038
0.048
0.081
0.066
0.052
0.072
0.020
0,051
REAnGGS (Ours)
0.042
0,059
0.010
0.006
0,013
0.067
0.031
0.012
0.005
0.201
0.045
Ditto
0.201
5,409
5.698
1.021
3,768
0.661
0.129
0.014
2.113
Eir
PARIS
44
0.006
0.000
0.000
0.002
0.004
0.020
0.083
0.001
0.005
ArCS
18
0.011
0.002
0.001
0.003
0.000
0.017
0.004
0.001
0.004
REAnGS (Ours)
0.002
0.000
0,000
0.000
0.006
0.011
0.004
0.003
0.003
D.7
Mesh Generation, Extended
To present our generation results more comprehensively. we provide the qualitative results in Fig. T0 corresponding Table. in the main draft. We generate surface meshes of the end state from the canonical state using the Gaussian deformation fields. It can be observed that our generated results still maintain smooth and high-quality surfaces, which proves the effectiveness of our method.
D.8 Computational Efficiency Analysis for Mesh Generation
present the detailed training time Sec. D.2 and also provide the qualitative inference time for mesh generation in Table. g It can be observed that our method achieves the highest computational
25

---

Ours (textured)
Input States
D-3DGS
PARIS
ARGS
Blade
Scissor
Oven
Stapler
Storage
The qualitative results of surface generation on PartNet-Mobinn dataset. We employ the deformable fields to generate surface meshes at the end state from the canonical state.
Figure 10:
efficiency. This is mainly because of our efficient design for the learnable motion parameters, which obviates inference of deep networks.
Table 8: The qualitative results of inference time for mesh generation on PartNet-Mobility dataset.
The results derived from the average of more than ten inference times.
Method
Time (second)
Ditto
g
36
D-3DGS
40
PARIS 14
33
REAnGS (Ours)
21
D.9 Ablation Study, Extended
Table 9: The ablation study of canonical state setting on PartNet-Mobility dataset.
Joint
Canonical
CD (ws)
CD (TS)
EMD
0.0
0.717
0.250
Prismatic
0.5
5.69
1.203
0.242
0.608
1.0
6.10
1.304
0.236
0.591
0.0
5.93
1.352
0.266
0.637
Revolute
5.88
0,556
1.0
7.13
1.591
0.194
0.680
To evaluate the effectiveness of the canonical state selecting, we compare the surface generation quality under three settings of canonical state 0.0, 0.5, and 1.0 on PartNet-Mobilitt dataset. The quantitative results can be found in Table. 9 For prismatic joints, the surface reconstruction quality attains the highest when the canonical state is 0.0. It is mainly because the linear interpolation be performed more stably taking advantage the vector space structure Euclidean geometry.
As for revolute joints, setting canonical state 0.5 achieves the best surface generation quality. This can be mainly attributed the fact that canonical state 0.5 leads to the angle-bounded parameterization 0 E [-m/2, 2, π /2], which prevent the singularity in exponential coordinates when ||@|| >
26

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E
Reproducibility and Video
We provide our codes in http:://ggaauo.comm//tutttteeeee and present video to show more visualization results in httpa///s.....oooo....ooooaaaaaa
27


Reviews:
[{"review_id": "lNZWLQmVK9", "reviewer": "Reviewer_E8MT", "summary": "This paper propose REArtGS, a method for reconstructing articulated objects from multi-view RGB images captured at two different states. The approach uses 3D Gaussian Splatting enhanced with unbiased-SDF regularization to generate high-quality surface meshes.\n\nThe key innovation is an \"unbiased SDF guidance\" that regularizes the Gaussian opacity fields, addressing insufficient 3D constraints in the reconstruction. The method learns kinematic parameters (translation and rotation) during optimization, enabling it to estimate the articulation model and generate intermediate poses between the two input states. Experiments on synthetic PartNet-Mobility and real-world AKB-48 datasets show REArtGS outperforms existing methods like PARIS.", "questions": "- **Inadequate  Evaluation**: Why are the critical kinematic parameter results (Ang Err, Pos Err) and part-level evaluations (CD-m, CD-s) relegated to the supplementary material when these metrics are fundamental for articulated object reconstruction? Additionally, why is ArtGS excluded from the kinematic parameter comparison in Table 7, given that it's a strong baseline for articulated object modeling? Moving kinematic evaluation to the main paper and including comprehensive comparison with ArtGS across all metrics would demonstrate the method's true performance against state-of-the-art approaches.\n\n- **Questionable Technical Novelty Claims**: The \"unbiased SDF regularization\" is presented as a core contribution, but GOF already proposed using SDF regularization for 3D Gaussian learning. How does your approach fundamentally differ from GOF's method beyond applying it to articulated objects? What specific technical innovations justify this as a primary contribution rather than an engineering application?  Clear demonstration of novel technical components beyond existing SDF-Gaussian integration, or honest repositioning of the work as an engineering contribution with appropriate claims.\n\n- **Single-Part Limitation Acknowledgment**: The method appears fundamentally restricted to objects with one movable part, yet this critical limitation is not clearly stated in the main paper. Honest acknowledgment of the single-part restriction in the main paper, with discussion of its implications and potential solutions, would improve the paper's transparency and help readers understand its scope.", "limitations": "No acknowledgment that the method is fundamentally limited to objects with one movable part. Additionally, when the number of movable parts increases, reconstructing articulated objects from two states will be more challenging due to the occlusion between these parts.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "- REArtGS demonstrates superior performance over existing methods on standard benchmarks, outperforming approaches like DITTO and PARIS on PartNet-Mobility and AKB-48 datasets. \n- The method produces high-quality textured meshes and shows good real-world generalization, even in cluttered environments. \n- Ablation studies validate the contribution of key components like SDF regularization.\n# Weaknesses\n- **Insufficient evaluation.** For articulated objects reconstruction, kinematic parameters are as the same significant as part meshes. However, I found that the authors put the evaluation results of kinematic parameters (Ang Err) and part meshes (CD-m) in the supplementary and ignore a strong baseline ArtGS. The authors need to explain the reason.\n- **Insufficient Technical Innovation.** While the \"unbiased SDF regularization\" is highlighted as a core contribution, it is not an innovation proposed by the authors.  Using unbiased SDF regularization for 3D Gaussian learning has been proposed by GOF and this paper apply this for articulated objects reconstruction. I recognize the engineering contribution of this paper but it't not enough to be a core contribution.\n- **Single-Part Restriction.** The method is limited to objects with only one movable part.", "was_revised": true, "final_justification": "Thanks to the author for the detailed rebuttal and supplementary experiments, which resolved most of my concerns, I have revised the final rating to 4", "rebuttal": "We sincerely appreciate your valuable comments. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time.  We earnestly look forward to the subsequent discussions with you.\n\n**1. Question on Insufficient Evaluation**\n\nThank you for your insightful opinions. We also recognize the significance of joint parameters and part-level meshes for articulated objects. However, as the main topic of this paper is the surface reconstruction and generation of articulated objects, we moved the evaluation results of joint parameter and part-level mesh results to the Appendix taking the page limitation into consideration. Additionally, the surface generation results presented in the main draft are essentially high-dimensional mappings of part-level meshes. Realistic surface generation already indicates accurate part-level mesh extraction.\n\nAs for not comparing the joint parameter and part-level mesh evaluation results of ArtGS, it is because ArtGS is essentially a method based on RGBD image inputs, while our method uses RGB images. We have already demonstrated in the main draft that our method outperforms ArtGS in surface reconstruction and generation when using the same RGB image inputs on both synthetic and real-world data. In kinematic parameter evaluation results of the supplementary material, we are more concerned with the comparison to PARIS, which also only uses RGB image inputs. Following your valuable suggestions, we have added  quantitative comparisons of joint parameter estimation and part-level mesh reconstruction between our method and ArtGS. To ensure a fair comparison, we train ArtGS using the same RGB image inputs as our approach. The results are presented below. The experimental results demonstrate that our method outperforms ArtGS in joint estimation and part-level mesh reconstruction.\n\n**Quantitative comparison of joint parameter estimation:**\n| Metrics       | Method         | Stapler |  USB  | Scissor | Fridge | Foldchair | Washer |  Oven  | Laptop | Blade  | Storage |  Mean  |\n|---------------|----------------|---------|-------|---------|--------|-----------|--------|--------|--------|--------|---------|--------|\n| Ang Err ↓     | ArtGS      | 0.062  | **0.034**  |  0.039 |  0.038 |   0.048  | 0.081  | 0.066 | 0.052  |  0.072 | **0.020**  | 0.051  |\n|               | REArtGS (Ours) | **0.042**   | 0.059 | **0.010**   | 0.006  | **0.013**     | **0.067**  | 0.031  | **0.012**  | 0.005  | 0.201   | **0.045**  |\n| Pos Err ↓       |ArtGS      | 0.011   | 0.002 |  0.001  | 0.003  |   0.000   | 0.017  |   0.004| **0.001**  | -      | -       | 0.004  |\n|               | REArtGS (Ours) | **0.002**   | **0.000** | **0.000**   | **0.000**  | 0.006     | **0.011**  | 0.004  | 0.003  | -      | -       | **0.003**  |\n\n**Quantitative comparison of part-level mesh reconstruction:**\n| Metrics       | Method         | Stapler |  USB  | Scissor | Fridge | Foldchair | Washer |  Blade  | Laptop | Oven  | Storage |  Mean  |\n|---------------|----------------|---------|-------|---------|--------|-----------|--------|--------|--------|--------|---------|--------|\n| CD-s ↓       | ArtGS      |  3.45 |  2.05 | 0.57  |  2.03 |   **0.16**  |  20.97 | **0.44** | 0.76 | 9.20  |  13.51 | 5.31  |\n|               | REArtGS (Ours) | **1.47**   | **0.82** | **0.25**   | **1.53**  | 0.31     | **13.04**  | 0.69  | **0.48**  | **6.59**  | **7.30**   | **3.25**  |\n| CD-m ↓    |  ArtGS      |   2.78 | 1.17 |  0.67  | 1.43  |    0.57  |  2.82 | **1.80**  | 0.99  |  2.12 | **7.18** | 2.15 |\n|               | REArtGS (Ours) | **1.18**   | **0.40** | **0.21**   | **0.66**  | **0.30**     | **0.42**  | 1.97  | **0.11**  | **0.25**    | 12.39    | **1.79**  |\n\n\n**2. Clarification on Technical Novelty**\n\nWe sincerely appreciate your dedicated efforts in the research of the relevant works. To our best knowledge, our method first innovatively introduce the unbiased SDF regularization, establishing a connection between SDF and the Gaussian opacity field. \n\n**It is important to clarify that GOF is an opacity-based 3DGS method.** SDF is not incorporated throughout its entire  process and its mesh extraction solely relies on an opacity level set. Given that opacity cannot explicitly represent the relationship between 3D Gaussian primitives and the scene surface, the opacity-based method typically yields surface mesh results with artifacts distant from the surface.\n\nBesidse, integrating SDF into 3DGS poses a significant challenge. This is because 3DGS is fundamentally a discrete point-based rendering pipeline, while SDF is a continuous implicit function representation. Existing works, such as GSDF and 3DGSR, merely utilize SDF guidance for normal constraint and the pruning of Gaussian primitives and fall short of futher regularizing the opacity of 3D Gaussians, which serves as the core attribute in $\\alpha$-blending.\n\nIn contrast, our unbiased SDF regularization encourages the alignment of the Gaussian opacity field with SDF. Specifically, when the opacity reaches its maximum value, it drives the SDF value at the corresponding position to approach zero. This ensures that Gaussians near the surface exhibit high opacity values, eliminating artifacts away from the surface. Therefore, the unbiased SDF regularization effectively addresses the limitations of the opacity field in geometric representation and forms the core innovation of our method.\n\nNote the TSDF fusion method mentioned in GOF's paper is distinct from the neural SDF representation and is designed for   mesh extraction with discrete volume representations. Its SDF values are simply constructed through multi-view depth image fusion when extracting the mesh, rather than a continuous representation learned from the network.\n\n**3. Clarification on Single-Part Limitation**\n\nWe sincerely appreciate your thorough consideration of our method. Our method is capable of effectively dealing with articulated objects exhibiting multiple movable parts. **We have already presented the high-quality reconstruction and generation results of an articulated object with three movable parts at the fourth row of Figure 6 in the main draft.** Moreover, we have elaborated in detail on the generation pipeline for articulated objects with multiple movable parts in Appendix C.4. We have put the details with italics below for your quick reference.\n\n*Mesh generation of multi-part articulated objects can be treated as a straightforward extension of the two-part task for our approach. We can generate meshes for multi-part objects in unseen states through a sequential learning strategy.  Specifically, given an articulated object with $k$ dynamic parts $\\omega\\_{d_k}$ , we start by fixing all dynamic parts $\\omega\\_{d\\_{2}}, ..., \\omega\\_{d\\_{k}}$ except $\\omega\\_{d\\_1}$ . The object is then decomposed into two parts: a dynamic part $\\omega\\_{d\\_1}$ and a static part $\\omega_s$ (comprising all remaining points). After learning the motion and segmentation mask for $\\omega\\_{d\\_1}$ , we sequentially process the next dynamic part $\\omega\\_{d\\_2}$—with the static part updated as:  $\\omega\\_s = \\hat{\\omega}\\_{d\\_2} - \\omega\\_{d\\_1}$ ,  where $\\hat{\\omega}\\_{d\\_2}$ denotes the remaining points excluding $\\omega\\_{d\\_2}$ .  By parity of reasoning, we extend this process to learn the motions and segmentation masks for all $k$ dynamic parts. Finally, mesh generation for any unseen state of the multi-part object is achieved using the pipeline proposed in Sec. 3.2.*\n\n\nRegarding the occlusion among multiple parts, the two-stage multi-view image inputs can mutually complement their respective unseen regions. Specifically, since the Gaussian primitives in the reconstruction stage undergo further optimization in the generation stage, the images from each viewpoint in both stages can act as valid rendering supervisions for 3D Gaussian primitives. This allows our method to make full use of the multi-viewpoint images from the two stages to refine the Gaussian primitives. Please refer to the response to Reviewer BVdL for details. Consequently, in most scenes, the two-stage multi-view image inputs are adequate to effectively mitigate the occlusion problem among multiple parts."}, {"review_id": "RXPsVyXkTG", "reviewer": "Reviewer_zVCD", "summary": "The authors propose a solution to surface reconstruction and generation for articulated objects by coupling geometric and motion constraints to 3D Gaussian primitives.\nGiven multi-view RGB images of arbitrary two states of articulated objects, the method utilizes an unbiased Signed Distance Field (SDF) guidance to regularize Gaussian opacity fields. \nIt then establishes deformable fields for 3D Gaussians, constrained by the kinematic structures of articulated objects, thereby achieving unsupervised generation of surface meshes in unseen states.", "questions": "What is the effect of the diversity of the two views on surface reconstruction quality? Does the method require the two surfaces to be very distinct, and would the surface reconstruction suffer if the images are close?\n\nCan the method take more than two input images? Let's say $s_0=0$, $s_1=0.1$ and $s_2=1.0$, would that help the reconstruction quality or would it have any effect?", "limitations": "- The method requires accurate camera poses.\n- Rendering of objects with transparent materials and non-Lambertian surfaces are challenging.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strength**\n- The proposed method utilizes unbiased SDF guidance for 3D Gaussian primitives to enhance geometric constraints, thereby improving the reconstruction quality.\n- It learns deformable fields and generates unseen states by constraining the kinematic structures of articulated objects.\n- The method is evaluated on different synthetic and real datasets.\n\n**Weaknesses**\n- The method requires access to posed images as input.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for your recognition and encouragement of our method. The following is a point-to-point response to the questions you raised. If you have any other questions, please let us know at the first time. We sincerely look forward to the subsequent discussion with you.\n\n**1. The Effect of The Diversity of The Two-Stage Views**\n\nWe sincerely appreciate your professional review comments. Our approach exhibits remarkable robustness to the diversity of two-state views. Specifically, our method enable realistic surface mesh generation unless an articulated object undergoes extremely minimal rotation or translation.\n\nTo validate the robustness of our method on the diversity of two-state views, we have conducted ablation experiments on the rotation angles and translation distances in the second state for USB and storage of the PartNet-Mobility dataset.  Concretely, we adjust the rotation angle and translation distance of articulated object at the second state to different values, and then generates the surface mesh at $s=0$ from the canonical state. We report  the CD (ws) results below.\n\n|         | Storage |      |    |           | USB |            |\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n| 0.3m | 0.6m | 0.9m | |15°| 30°| 45°|\n|**7.43** | 7.71 | 7.48 ||1.43 | 1.52 | **1.35**|\n\nWe observe that the diversity of two-state viewpoints does not lead to a significant influence on the mesh generation results of our method. For the storage, even a smaller translation distance yields superior surface mesh generation. This demonstrates the robustness of our method against the diversity of two-state views.\n\n**2. Question on Taking More State Inputs**\n\nThank you for your valuable comment. This is an interesting question. During the generation stage, our method use the deformed Gaussians obtained from the deformable field to calculate the rendering loss with the image supervisions at corresponding state. Therefore, incorporating view inputs from additional states is equivalent to adding more image supervisions,  which can naturally enhance the surface mesh generation quality.\n\nWe also validate this analysis on the USB of PartNet-Mobility dataset. Specifically, we introduce additional view inputs at the state $s = 0.1$. As a result, the CD (ws) result of surface mesh generation improves significantly from 1.68 to 0.85. This proves that our method can improve the mesh generation quality through additional state view inputs.\n\nMoreover, we have demonstrated that views from different states mutually compensate for each other's unseen regions. For more details, kindly refer to our response to Reviewer BVdL.\n\n**3. Reliance on Camera Poses**\n\nThank you for your valuable feedback. In fact, camera pose estimation is now a ready-to-use technology. For multi-view images, our method can directly use Colmap to estimate the corresponding camera poses. The camera poses estimated by Colmap are sufficient for our method to achieve high-quality surface reconstruction and generation. In recent years, many excellent camera pose estimation methods have also been able to meet our requirements for camera poses, such as Reloc3r (Dong, 2024). Therefore, we believe that the reliance on camera poses does not constitute an intractable shortcoming, and we aim to introduce Reloc3r into our framework for camera pose estimation in the future work.\n\n**4. Rendering of Objects with Transparent Materials and Non-Lambertian Surfaces**\n\nThank you for the insightful comments. Transparent materials and non-Lambertian surfaces undoubtedly pose challenges in current 3D reconstruction due to their complex requirements for light modeling. However, several works attempt to address the reconstruction of transparent materials and non-Lambertian surfaces recently, and we are inspired by them. In the future works, we aim to introduce the Gaussian light field probes to encode both ambient light and specular refraction for transparent object reconstruction, following TransparentGS (Huang, 2025). Moreover, we consider the spectrum of a non-lambertian surface as a linear combination of the diffuse and specular components, and try to introduce the Dichromatic model in our framework for its reconstruction."}, {"review_id": "RhUO0tiU7q", "reviewer": "Reviewer_oBKh", "summary": "This paper aims to solve the problems of (1) 3D textured surface reconstruction of articulated objects from multiview RGB images (2) generating dynamic unseen motion states from a given start state to an end state both of which have multiview RGB images. The paper proposes a novel approach using unbiased Signed Distance Field (SDF) guidance for regularization of Gaussian opacity fields for solving the problem in (1). Reconstruction and Motion Generation results are demonstrated on a synthetic dataset and a real world dataset.", "questions": "1. What is $x_{i+1}$ in Eq. 2 ? In NeuS i refes to the index of the sampled point along the ray, in this case the how is the (i+1)th gaussian defined with respect to the ith Gaussian? \n\n2. How many input views are used for each of the two states (both source and target) ?  \n\n3. Lines 94-95 : Although improving the surface reconstruction quality, these methods still lack “more reasonable geometry constraints”. Exactly what is unrealistic or unreasonable about the geometric constraints in GOF, 2DGS and PGSR that this paper has improved?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n+ The paper attempts to solve a challenging intermediate state generation problem given multiview images of a only start and end state of an articulated object, and achieves geometry and texture generation of reasonably good quality on real world datasets and on multi-part articulated objects.\n+ The paper is well-written and easy to follow. \n+ The geometry reconstruction results on USB and Fridge in Fig.4 and the generation results in Fig. 5 clearly denote better geometric quality.\n\nWeaknesses :\n\n1. Originality : This paper reuses concepts and ideas from NeuS (Eq. 2), GOF (Eq. 3-5) and 3DGSR (bell-shaped function similar to Eq. 6).  SDF guidance for 3D Gaussian primitives has been done in 3DGSR. \n\n2. Results : \n- Fig 4 – The reconstruction quality of Washer and Laptop does not seem to be very good. \n- Missing Qualitative comparison with state-of-the-art methods on real-world dataset AKB-48. \n- Qualitative comparison with Ditto missing in Fig 4. \n- Qualitative ablation results needed to understand the significance of the proposed geometric constraints. \n- Quantitative / qualitative comparison of 3D reconstruction not done with 3DGSR, which also uses SDF along with 3DGS for unified surface and appearance modeling, and uses a similar bell-shaped function. \n \n\n3. Writing Ambiguity : Lines 94-95 : Although improving the surface reconstruction quality, these methods still lack “more reasonable geometry constraints”. \n\n \n\n4. Undefined notations: \n\n- $x_{i+1}$ in Eq. 2 not defined. \n\n - $x_L$ and $t$ in Eq. 3 are not defined.", "was_revised": true, "final_justification": "Thanking the authors for their detailed justification. Based on the authors' feedback, I have updated my final rating to 4.", "rebuttal": "We sincerely appreciate your valuable comments. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time. We sincerely look forward to the subsequent discussion with you.\n\n**1. Question on $x\\_{i+1}$ and Undefined Symbols**\n\nThank you for your insightful opinions. In fact, $x\\_{i+1}$ in this paper refers to the next sampled point along the ray. We calculate  $f(x\\_{i+1})$ through Taylor's first-order expansion, i,e, $f(x\\_{i+1}) =f(x\\_{i})+{f}'(x\\_{i}) \\Delta x$, where $\\Delta x = \\frac{z\\_{\\text{far}}-z\\_{\\text{near}}}{l} $. $z\\_{\\text{far}}$ and $z\\_{\\text{near}}$ are  the distances from the near and far cutting surfaces along the Z-negative axis to the viewpoint respectively. $l$ is set to 64. Note that we use the annealing $(1-\\frac{n}{N})(\\Theta (\\frac{1-r\\cdot f' (x\\_{i})}{2} ) )-\\frac{n}{N} (\\Theta (-r\\cdot {f}' (x\\_{i}) )$ to replace ${f}'(x\\_{i})$ in actual computation for adaptive transformation of view-normal angle, where $n$ and $N$ denote the current iteration and total iterations respectively. $r$ is the normalized ray direction.  $\\Theta$ is the ReLU activation Function.\nWe also apologize for the undefined symbols. $x\\_{L}$ and $t$ represent the spatial position of Gaussians local coordinate system and ray depth respectively.\n\n**2. Input View Setting**\n\nWe follow the same input settings as PARIS and ArtGS, using 64 multi-view images and 50 test images per stage. We have also supplemented an ablation study on the number of input images.  Due to character limitations, please refer to the rebuttal provided to Reviewer BVdL for details.\n\n**3. Question on the Geometry Constraints of GOF, 2DGS and PGSR**\n\nThank you for your feedback. 2DGS, PGSR, and GOF are all essentially based on the Gaussian opacity fields. Among them, 2DGS and PGSR attempt to facilitate the normal estimation by compressing 3D Gaussian primitives to 2D shapes. This geometric constraint is not reasonable as the restriction on the shape of Gaussian primitives leads to degraded performance in capturing detailed structures. On the other hand, GOF attempts to optimize the rendering process of 3DGS and approximates the Gaussian’s normal as the normal of the ray-Gaussian intersection plane. The approximation typically introduces normal estimation errors. Moreover, since Gaussian opacity field cannot explicitly define the scene surface, the opacity-based methods often extracts surface meshes with artifacts distant from the surface. Therefore, they still lack more reasonable geometric constraints. \n\nIn contrast, our method introduces SDF in 3D Gaussian primitives and leverages the gradients of SDF to accurately define the normals, instead of restricting the shapes of Gaussian primitives or using approximation strategy. And the unbiased regularization encourages Gaussians near the surface to exhibit a high opacity value, achieving more reasonable geometric constraints.\n\n**4. Clarification on Originality**\n\nWe sincerely appreciate your dedicated efforts in the research of the relevant works. We first clarify that this paper does not merely reuse the concepts from Neus, GOF, and 3DGSR. Instead, our REArtGS is the first framework that innovatively introduces SDF to regularize the Gaussian opacity field, which plays a core attribute in 3DGS rendering pipelne. \n\nAmong the existing methods, GOF is an opacity-based 3DGS method. The Eq. 3 and Eq. 5 in this paper fundamentally differ from GOF. Specifically, GOF solely determines the $\\alpha$-blending weight by the rendering contribution $\\varepsilon$, which fails to explicitly define the relationship between Gaussian primitives and the scene surface, leading to results with artifacts. In contrast, our method computes the $\\alpha$-blending weight based on both  SDF $\\sigma(f(x))$ and the rendering contribution $\\varepsilon$ (see Eq. 2, Eq. 3, and Eq. 5). The points with the maximum rendering contribution are aligned with the scene surface through the unbiased SDF regularization, enhancing surface reconstruction quality. Note that we quote Eq.4 for the detailed elaboration of the unbiased SDF regularization.\n\nAlthough 3DGSR also incorporates SDF with 3DGS, its $\\alpha$-blending weights purely depend on the SDF-derived opacity, which only utilizes Gaussians’ center as input and ignores their local features.  In contrast, our REArtGS integrates both local and global information through Eq. 2 and Eq. 3. Conretely, Eq. 3 combines the rendering contribution derived from local properties of Gaussian primitives with the SDF encoding global spatial position information.\n\nBesides, Neus is built upon a neural implicit continuous representation, allowing the continuous SDF to be seamlessly incorporated into its rendering pipeline. In contrast, 3DGS is a discrete point-based rendering method, making direct adoption of SDF infeasible. This constitutes the fundamental distinction between our method and Neus.\n\nIn summary, Our REArtGS has essential differences from these methods at the theoretical level and has achieved substantial improvements rather than simple reuse or combination.\n\n**5. Flawed Qualitative Results**\n\nThank you for your insightful comments on our paper. In fact, the reconstruction of self-luminous screens and flat surfaces lacking texture features is a non-trivial task for current surface reconstruction technique. These two cases impose strict requirements on the geometric flatness of the reconstruction results and pose significant challenge for existing methods. In future work, we will introduce illumination decomposition to address self-luminous materials and enhance the planar constraints of 3DGS through RANSAC to enhance the reconstruction of flat surfaces lacking features\n\nHowever, our method still achieves the best CD(rs) and EMD scores on washer and laptop,  and accurately recovers the global structure as shown in Fig. 4. We also observe that key parts such as the keyboard and the washing machine lid are all reconstructed with high quality. Therefore, these local imperfections in the reconstructions do not affect the actual manipulation of articulated objects. \n\n**6. Missing Qualitative Comparison**\n\nWe sincerely appreciate your invaluable feedback. Following your suggestions, we have already finished the qualitative comparisons with other methods on AKB-48 datasets, the qualitative comparison with Ditto, as well as the qualitative ablation results of geometric constraints.\n\nUnfortunately, given the limitation that images and external links cannot be uploaded during this rebuttal, we sincerely apologize for not being able to share these qualitative results with you at the first time, and we formally promise to add these results in this paper after accepted.\n\nMoreover, the content already presented in this paper is sufficient to illustrate the aforementioned issues. Firstly, we conduct extensive comparisons on synthetic datasets, comprehensive demonstrating the superiority of our method. For real-world experiments, our qualitative results aim to fully showcase the generalization ability of the method on real-world data, and the quantitative results in Table. 5 further confirm our performance advantages. Even though the qualitative results of Ditto are not presented, we present the qualitative comparisons with A-SDF, which also uses 3D supervision. And we have conductd a quantitative comparison with Ditto in Table. 1, which already indicates our superiority.  Finally, we have presented the qualitative ablation results of unbiased SDF regularization at distribution level in Fig. 3, and the quantitative ablation results of geometric constraints in Table. 3, validating the effectiveness of proposed geometric constraints.\n\n**7. Comparison with 3DGSR**\n\nWe appreciate the time you devoted to the related works. Although 3DGSR also uses SDF and a similar bell-shaped function as ours, we are sorry that we cannot provide a comparison with it because its codes are not available and its official experimental results on articulated objects are not provided. Based on your valuable suggestions, to further demonstrate the effectiveness of our unbiased SDF regularization, we have conducted a quantitative comparison with GSDF (Yu, 2024), which also introduces SDF in 3DGS, shown as following:\n| Metrics   | Method          | Stapler  | USB     | Scissor  | Fridge   | Foldchair | Washer   | Blade    | Laptop   | Oven     | Storage  | Mean     |\n|-----------|-----------------|----------|---------|----------|----------|-----------|----------|----------|----------|----------|----------|----------|\n| CD(ws)↓   | GSDF            | **2.96** | 10.23   | 0.64     | 2.99     | 0.81      | 19.54    | 0.85     | 0.90     | 22.17    | 9.38     | 7.05     |\n|           | REArtGS(Ours) | 3.47 | **0.75** | **0.29** | **1.50** | **0.40**  | **12.20** | **0.72** | **0.53** | **8.89** | **8.27** | **3.79** |\n| CD(rs)↓   | GSDF            | 2.732    | 3.810   | 2.856    | 2.506    | 1.146     | 2.142    | 3.571    | 0.708    | 3.053    | 2.704    | 2.523    |\n|           | REArtGS(Ours) | **2.186** | **1.433** | **2.291** | **0.475** | **0.180**  | **1.204** | **2.596** | **0.038** | **0.784** | **1.330** | **1.236** |\n| F1↑       | GSDF            | 0.232    | 0.146   | 0.435    | 0.075    | 0.305     | 0.042    | 0.358    | 0.367    | 0.024    | 0.046    | 0.203    |\n|           | REArtGS(Ours) | **0.256** | **0.307** | **0.598** | **0.165** | **0.502**  | **0.069** | **0.488** | **0.419** | **0.065** | **0.066** | **0.294** |\n| EMD↓      | GSDF            | 1.715    | 1.760   | 1.105    | 1.067    | 0.530     | 1.334    | 1.630    | 0.210    | 0.642    | **0.719**  | 1.071    |\n|           | REArtGS(Ours) | **1.060** | **0.847** | **1.078** | **0.485** | **0.097**  | **0.777** | **1.112** | **0.111** | **0.627** | 0.755 | **0.695** |"}, {"review_id": "PANZevtDbd", "reviewer": "Reviewer_BVdL", "summary": "This paper tackles an interesting task: generation articulatable objects from multiview observations collected in two distinct states of the object articulation. \nIt improves upon prior work PARIS and ArtGS. The former uses a NeRF representation, and the latter uses Gsplats but requires RGB-D images whereas the proposed methos REArtGS needs only RGB images.\nThe method differs from prior work by providing a much more accurate mesh reconstruction in the initial state by adopting ray-traced GS formulation (Gaussian Opacity Field) and connecting the that opacity with a jointly learned SDF. \nSecondly, during the articulation learning step, it also incorporated heuristic, but effective, rules to correctly determine the moving parts and their articulation type. \nThe paper showed impressive improvements compared to prior work in both synthetic Part-Net data and real-world captured data.", "questions": "I'm curious what is the fundamental difference between a NeRF-based approach like PARIS and 3DGS-based approach, such as REArtGS? \nThe paper focused on introducing geometry regularization specifically for 3DGS. But what benefit do we get by using 3DGS? If I used NeuS instead of NeRF in PARIS (thus no need these additional techniques introduced in this paper) and if I applied similar deformation optimization, would I get similar result? \nIs there any gains in terms of training speed, texture quality etc?\n\nSecondly, I couldn't find how many images are required for optimizations in the two stages.\n\nLastly, how does the method compare with other work in terms of training time?", "limitations": "I think a key limitation, not restricted to this paper alone, is potential failure when the observations of the initial state is incomplete. \nIn this case, one may think of combining the second observed state and jointly optimize the reconstruction and deformation.\nIt might be worthy mentioning this in the paper.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strength\n- The paper is clearly written. Moreover, the authors ensure the reproducibility of their implementation by stating that core modules and generation inference codes are provided in the supplementary materials.\n- The paper presents convincing visual and quantitative improvements upon prior art. Qualitatively, REArtGS demonstrates \"significantly smoother and clearer surfaces\" for reconstruction\n\n# Weaknesses\n- I find the reporting of the tables and figures curiously unmatched. Why do the figures report D-3DGS while the tables don't even include this method? The close contender ArtGS is not shown only one figure in the Appendix.\n- Since the paper mentioned multi-part and outlined a solution in the appendix, I would like to see a couple of examples. Otherwise, the paper feels rather incomplete.\n- Motivation of using 3DGS (see my questions below). \n- The training time seems rather long - 95 minutes in total. There is no reference to the training time of prior work.\n\n# Minor weaknesses\n- For texture extraction, I'm curious if the texture considers only SH0 and discard the rest of the SH degrees? If so, it might be better to mention if the reconstruction is done with only sh0.", "was_revised": true, "final_justification": "The rebuttal sufficiently addressed my question. I remain positive about the paper.", "rebuttal": "We sincerely appreciate your recognition of our method. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time. We sincerely look forward to the subsequent discussion with you.\n\n**1. Motivation of Using 3DGS**\n\nThanks for the insightful opinions. NeRF and NeuS represent 3D scenes through neural implicit radiance fields, posing four major limitations. (1) The implicit representation tends to yield entangled neural representations, leading to the shape-radiance ambiguity.\n(2) Their ray marching sampling may skip over thin structures, resulting in unsatisfactory reconstruction of details. (3) When extracting surface meshes from NeRF-based methods, post-processing algorithms like Marching Cubes are typically required. However, using Marching Cubes from the neural representations often introduces unconsidered errors, producing noisy surface mesh results. (4) The texture is strongly coupled with the implicit representation, and high-frequency textures rely on positional encoding, which is prone to causing over smoothing.\n\nIn contrast, our motivation for adopting 3DGS is based on the following benefits. (1) 3DGS is an explicit point-based representation, which is inherently more consistent to surface mesh reconstruction. Through the anisotropic Gaussian primitives, 3DGS can precisely recover detailed structures. (2) The Spherical Harmonics (SH) of 3D Gaussian primitives support direct texture baking for texture extraction. For a detailed discussion on SH, please refer to Point 5. (3) In terms of training time, 3DGS uses the rasterization instead of volume rendering, significantly improving the training speed. For example, NeuS, which also introduces SDF, requires more than 12 hours. Please refer to Point 3 for details. (4) Leveraging the explicit nature of 3DGS, we can explicitly obtain the deformed Gaussian primitives through deformable fields. In contrast, Nerf-based methods like PAIRS require composite neural radiance fields for the two-stage inputs. Since spatial overlap exists between the composite density fields of the start and end states, the volume rendering with neural implicit representation produces noisy surface reconstruction results. As shown in Fig. 5, PARIS yields unsmooth surface mesh results while our method achieves high-quality detailed reconstruction. Therefore, **the degraded mesh results stems from the limitations of the neural implicit radiance field and cannot be resolved merely by using NeuS.**\n\n**2. Input View Setting**\n\nWe follow the same input settings as PARIS and ArtGS, using 64 multi-view images and 50 test images per stage. We have also supplemented an ablation study on the number of input images from each stage below. We report the average surface mesh generation results on PartNet-Mobility dataset.\n| Views | CD (ws)$\\downarrow$ | CD (rs)$\\downarrow$  | F1$\\uparrow$ | EMD$\\downarrow$ |\n|--------|-------|-------|-------|-------|\n| 64 | **4.10** | **1.063** | **0.298** |**0.670** |\n| 32 | 4.35 |1.284  | 0.280  |  0.743 |\n| 16 | 6.73 | 1.510 | 0.201 |  0.857 |\n| 8 | 48.21 | 4.652 | 0.074 |  1.552 |\n\nThe experimental results demonstrate that even if the number of input images per stage is decreased to 16, our method still exhibits robust surface generation results.\n\n**3. Comparison of Training Time**\n\nWe sincerely appreciate your invaluable comments. In the early experiments, the training process takes 65 minutes for reconstruction and 30 minutes for generation. Nevertheless, we have now implemented engineering optimizations in our approach, which significantly reduce the training time to approximately 30 minutes for reconstruction and approximately 10 minutes for generation. Moreover, Our approach still maintains SOTA results with the acceleration. Specifically, our main engineering optimizations can be summarized as following. (1) We calculate $f(x\\_{i+1})$ through Taylor's first-order expansion, i,e, $f(x\\_{i+1}) =f(x\\_{i})+{f}'(x\\_{i}) \\Delta x$. In previous experiments, we define $\\Delta x = RS\\cdot r$, where $R\\in \\mathbb{R}^{3\\times3}$ is the rotation matrix derived from Gaussian’s quaternion, and $S\\in \\mathbb{R}^{3}$ represents Gaussian's scaling. $r$ is the normalized ray direction. However, we observe that this calculation consumes a lot of time and it is difficult to obtain $\\Delta x$ when the object size is extremely small. Therefore, we have refined the calculation to $\\Delta x = \\frac{z\\_{\\text{far}}-z\\_{\\text{near}}}{l} $, where  $z\\_{\\text{far}}$ and $z\\_{\\text{near}}$ are the distances from the near and far cutting surfaces along the Z-negative axis to the viewpoint respectively. $l$ is set to 64. This approach not only remarkably enhances the computational efficiency, but also demonstrates better robustness against extremely small objects. For PartNet-Mobility data in the paper, the average cd(ws) $\\downarrow$ reduces -0.008 compared with previous results. (2) Inspired by PARIS, we also employ the Tiny-cuda-nn to accelerate our SDF network, achieving a significant time reduction. Besides, this acceleration have almost no impact on the mesh results. (3) We observe that our method can stop early at 20,000 iterations during the generation stage, and the mesh quality only suffers a slight degradation (approximately +0.1 at average cd(ws) $\\downarrow$).\n\nFollowing your suggestion, we present a quantitative comparison for the average training time and the average CD(ws) results on PartNet-Mobility dataset, shown as following. “acc” denotes the aforementioned acceleration, and “Recon.” and “Gen.” are reconstruction and generation respectively.\n\n| Methods | Time $\\downarrow$ | Recon. CD (ws)$\\downarrow$  | Gen. CD (ws)$\\downarrow$  |\n|--------|-------|:-:|:-:|\n| NeuS | >12h | 4.43 | -|\n| GOF | **28 min** | 6.09 | - |\n| PARIS | 45 min |3.94  | 0.280  |  8.16 |\n| ArtGS | 30 min | 4.75 | 0.201 |  4.92 |\n| Ours w/ acc | 40 min | **3.71** | 4.20 |\n| Ours w/o acc | 95 min | 3.79 | **4.10** |\n\n**4. Two-stage Joint Optimization**\n\nWe sincerely appreciate your professional review comments. Although we adopt a two-stage optimization strategy, the data of each stage is not isolated. In fact, the two-stage image supervision can mutually compensate for each other's unseen regions. Since initialization of the generation stage inherits the Gaussian primitives from the reconstruction stage, the incomplete observation regions in the reconstruction stage can be effectively optimized by the image supervisions of the generation stage. Note that since the deformable field acts solely on movable parts, the rendering loss during the generation stage can be mapped to reasonable pixel coordinates.\n\nMoreover, if the viewpoints in the generation stage do not completely cover the object, the reconstruction stage enables to provide a high-quality initialization for generation. To further validate the analysis, we have conducted ablation experiments with different input views for the two stages, shown as following. “View-1” and “View-2” denote the views of reconstruction and generation stage respectively.\n\n| Views-1 | Views-2 | Recon. CD (ws)$\\downarrow$ | Gen. CD (ws)$\\downarrow$  | \n|--------|-------|-------|-------|\n| 64 | 64 | **3.79** | **4.10** |\n| 64 |16| **3.79** | 5.46 | \n| 16 | 64|6.48|5.10 |\n| 16 |16|  6.48 | 6.73 |\n\nThe experimental results demonstrate that when one stage utilizes incomplete observation data (16 random sampled views) and the other stage offers more supervisions (64 views), the mesh results exhibit improvement compared to the case where both stages employ incomplete observations, demonstrating our analysis.\n\n\n**5. The SH coefficient in texture extraction**\n\nThank you for your professional technical review. This is an interesting question. In fact, we first use all the Spherical Harmonics (SH) to obtain view-dependent rendered images when extracting textured meshes. However, The TSDF fusion only bakes the static RGB renderings, which is equivalent to SH0. This design aligns with two core objectives: (1) Higher-order SH coefficients with view-dependent effects are challenging to bake into fixed textures. (2) The view-dependent effects encoded by higher-order SH terms are spatially variant and non-transferable to novel lighting conditions. Retaining them in the static texture maps would introduce artifacts when relighting the mesh.\n\n**6. Questions on Table and Figure**\n\nSince Deformable-3DGS (D-3DGS) is a dynamic generation method, we only compare the mesh generation results with it. The qualitative results are shown in Fig 5 and 10, corresponding to the quantitative data in Table 2. ArtGS is essentially an RGBD image-based method. In the main draft, we have already compared its surface mesh reconstruction and generation results without depth inputs with our method to demonstrate our superiority on the core topic of this paper. In the supplementary material, we aim to further demonstrate the completeness of our method REArtGS, including part segmentation and joint estimation. Thus we mainly present the visualization results of our method in the supplementary material. Following your suggestions, we have finished additional qualitative comparisons with ArtGS in part segmentation and joint estimation and will supplement them after acceptance, due to the limitations on images and external links in this rebuttal.  Meanwhile, please refer to the response to Reviewer E8MT for more quantitative comparison results with ArtGS, due to character limitations.\n\n\n**7. Qualitative Results of Multi-Part Articulated Objects**\n\nThank you for your feedback. We have already presented the high-quality reconstruction and generation results of an articulated object with three movable parts at the fourth row of Figure 6 in the main draft. More qualitative results of multi-part articulated objects will be presented after acceptance, due to the limitation of uploading images and external links."}, {"review_id": "907MSd7SHu", "reviewer": "Reviewer_Jnu3", "summary": "This paper purposed reartgs with can reconstruct the articulated object with given two states, and generate the internal state between the given training state. The method first extends GOF, a volume rendering based GS method, with the SDF representation to enhance the reconstruction quality. Then a deformable field is applied to the GS to predict the deformed GS for rendering.", "questions": "1. The author should provide more detail mentioned in the weaknesses. How to define the defomable network, and more details about generation mesh with different states.\n2. More results on reconstruction datasets should be provided. Since the proposed method extends GOF with SDF, the author should also clarify why introducing SDF is important for this task, otherwise the comparison with the previous reconstruction methods is needed.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:​​\n\n1. Motivation is compelling. Formulating reconstruction for articulated objects (dynamic reconstruction) remains an open challenge for 3DGS. \n2. The performance surpasses that of the baselines.\n\n​​Weaknesses:​​\n1. The motivation to apply an 8 layer mlp for SDF prediction is unclear. The author can provide more details about it. For example, the sdf can be a property on each GS while there is no need an implicit function to predict it as f(x) = sdf.\n2. The definition of $x_{i+1}$ is missing. It might be the index of the sorted GS for each pixel.\n2. Section 3.2 (\"Mesh Generation with Motion Constraints\") lacks clarity. Despite its title, the section does not discuss mesh generation. It describes using point clouds (based on the center of GS) to compute deformable fields, while the definition of the deformation network is missing, it might be (q,d,s)=g(x).\n3. The initialization of the gs is missing. In line 189, the proposed method uses s=0.5 as the init states, and the images from s=1 used for warning up. To this end, the initialization position of the points will be important. Based on the description in line 111, the reconstruction is  built on s=0. It is confusing.\n3. Since the proposed method extends GOF with SDF representation, reconstruction results on standard datasets like Tanks and Temples, DTU, and DeepDeform should be reported.", "was_revised": true, "final_justification": "Although I found it is wired that the authors introduced SDF into GS ONLY to improve the reconstruction of articulated objects without comparing results with other surface reconstruction methods, the paper demonstrates SOTA performance across multiple datasets: DTU and TNT. After carefully reviewing the feedback from other reviewers and the authors' rebuttal, I am inclined to raise my overall recommendation since integrating SDF enhances reconstruction quality and benefits the community.", "rebuttal": "We sincerely appreciate your valuable suggestions. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time. We earnestly look forward to the subsequent discussions with you.\n\n**1. Motivation of Using MLP for SDF**\n\nThank you for the insightful comments. The main motivation of using an 8-layer MLP is to map **any spatial position** $x\\in \\mathbb{R}^{3} $ to its corresponding SDF value. This mapping is crucial for the unbiased SDF regularization, as shown in Eq. 8. We can obtain $f(o +t^*  r)$ through the MLP and further encourage it approaches zero. Conversely, if the SDF is treated as an property of each Gaussian primitive, it is difficult to achieve point-level mapping because 3D Gaussian primitive is essentially a local probability representation. For example, if the SDF value at the center of a Gaussian primitive is taken as its SDF, the SDF value at $x = o + t^*  r$ cannot be directly obtained.\n\n**2. Explanation of $x\\_{i+1}$**\n\nThank you for your valuable comments. In fact, $x\\_{i+1}$ in this paper refers to the next sampled point along the ray. We calculate  $f(x\\_{i+1})$ through Taylor's first-order expansion, i,e, $f(x\\_{i+1}) =f(x\\_{i})+{f}'(x\\_{i}) \\Delta x$, where $\\Delta x = \\frac{z\\_{\\text{far}}-z\\_{\\text{near}}}{l} $. $f(x\\_{i})$ is the SDF value of the center of the $i$-th Gaussian primitive. $z\\_{\\text{far}}$ and $z\\_{\\text{near}}$ are  the distances from the near and far cutting surfaces along the Z-negative axis to the viewpoint respectively. $l$ is set to 64. Note that we use the annealing $(1-\\frac{n}{N})(\\Theta (\\frac{1-r\\cdot f' (x\\_{i})}{2} ) )-\\frac{n}{N} (\\Theta (-r\\cdot {f}' (x\\_{i}) )$ to replace ${f}'(x\\_{i})$ in actual computation for adaptive transformation of view-normal angle, where $n$ and $N$ denote the current iteration and total iterations respectively. $r$ is the normalized ray direction.  $\\Theta$ is the ReLU activation Function.\n\n**3. More Details of Mesh Generation and Deformable Field**\n\nThank you for the helpful insights. We have already described the details of the deformable field in Section 3.2. Following your suggestion, we provide a more detailed elaboration on deformable field and mesh generation below. Once we finish the estimation of the joint type, we design different learnable parameters based on the joint type. For rotation joints, we define the pivot point $\\mathbf{o}_{r}\\in \\mathbb{R}^{3}$ of the rotation axis and the normalized quaternion $\\mathbf{q} \\in \\mathbb{R}^{4}$ as learnable parameters. For translation joints, the unit vector $\\mathbf{d}\\in \\mathbb{R}^{3}$ of translation direction and translation distance $m$ are used as learnable parameters. Note that the deformable network in Fig. 2 is composed of these learnable parameters. We sincerely apologize for any misunderstanding we may have caused. Through Eq.10 and Eq.11, we can derive the center position $x\\_{s}$ of the Gaussian primitives at any state $s$ through these learnable parameters. Therefore, the deformable field $\\mathcal{g}$ can be represented as $\\mathcal{g}(x)=x\\_{s}$. Given any state $s$, we first obtain the deformed Gaussian primitives through the deformable field, and then render them into depth, opacity and RGB renderings. Finally we integrate these renderings into a voxel block grid and use TSDF Fusion to extract the surface mesh at state $s$. The mesh extration pipeline is described in Section 3.3.\n\n**4. Clarification on the Section 3.2**\n\nThank you for your feedback. Although the process of mesh extraction is not directly described in Section 3.2, we elaborate on the key of mesh generation, i.e., generating accurate 3D Gaussian primitives. The dynamic texture mesh can be easily obtained by TSDF Fusion when the 3D Gaussian primitives learn the accurate motion, and the TSDF Fusion is illustrated in Section 3.3.\n\n**5. Clarification on Initialization**\n\nThank you for your feedback. In fact, we have elaborated in detail on the initialization of Gaussian primitives of the generation state in Section 3.2. The initialization inherits the Gaussian primitives from the reconstruction stage. We define the canonical state $s^{*}=0.5$ to constrain the rotation $\\theta$ within the interval $\\left [ -\\frac{\\pi}{2}, \\frac{\\pi}{2} \\right ] $, **preventing the singularity in exponential coordinates when $\\theta > \\pi$**. \n\nIn the warm-up stage, we use the image supervisions from stage $s=1$ mainly for the initial part segmentation. Note that this does not affect the learning of Gaussian primitives, since the rendering loss is calculated through the deformed Gaussian primitives, which are obtained from the deformable field. Taking the rotation joint as an example, although the initialization of 3D Gaussians is used from stage $s=0$ and we define the canonical state $s^{*}=0.5$, we employ Eq. 9 and Eq. 10 to derive the deformed Gaussians and then back-propagate the rendering loss. As the rendering loss converges, the Gaussian primitives adjust to the spatial positions at state $s = 0.5$. Besides, the ablation experiments in Table. 9 also demonstrate the superiority of setting the canonical state of rotation joints to 0.5.\n\n**6. Results of More Reconstruction Datasets**\n\nThank you for the valuable suggestions. Although our method is designed for articulated object reconstruction, it can also be generalized to common reconstruction datasets. According to your suggestion, we compared the performance on the general reconstruction datasets Tanks and Temples, DTU with the existing SOTA reconstruction methods 2DGS (Huang, 2024) and GOF. We present the following quantitative results below.\n\n**F1-score $\\uparrow$ results on Tanks and Temples dataset:**\n| Scene | _Barn_ | _Caterpillar_ | _Courthouse_ | _Ignatius_ | _Meetingroom_ | _Truck_ |Mean |\n|----------------|:--------:|:---------------:|:--------------:|:------------:|:---------------:|:---------:|:---------:|\n| 2DGS       | 0.41  | 0.23         | 0.16         | 0.51       | 0.17          | 0.45    |   0.32    |\n| GOF       | 0.51   | 0.41          | 0.28         | **0.68**       | 0.28          | 0.58    |   0.46    |\n| REArtGS (Ours) | **0.63**   | **0.52**      | **0.32**     | 0.65       | **0.39**      | **0.66** |**0.53** |\n\n**CD $\\downarrow$ results on DTU dataset:**\n| Scan ID | 2DGS  | GOF   | REArtGS (Ours) |\n|---------|:-------:|:-------:|:----------------:|\n| 24      | 0.48  | 0.50  | **0.37**       |\n| 37      | 0.91  | 0.82  | **0.48**       |\n| 40      | 0.39  | **0.37** | 0.45           |\n| 55      | 0.39  | 0.39  | **0.22**       |\n| 63      | 1.01  | 1.12  | **0.57**       |\n| 65      | 0.83  | 0.74  | **0.44**       |\n| 69      | 0.81  | 0.73  | **0.59**       |\n| 83      | 1.36  | 1.48  | **0.78**       |\n| 97      | 1.27  | 1.29  | **0.82**       |\n| 105     | 0.76  | 0.68  | **0.41**       |\n| 106     | 0.70  | 0.77  | **0.37**       |\n| 110     | 1.40  | 0.90  | **0.61**       |\n| 114     | 0.40  | 0.42  | **0.33**       |\n| 118     | 0.76  | 0.66  | **0.31**       |\n| 122     | 0.52  | 0.49  | **0.38**       |\n| Mean    | 0.80  | 0.74  | **0.48**       |\n\n**7. The Significance of Introducing SDF**\n\nOpacity constitutes a fundamental attribute for the $\\alpha$-blending in 3DGS. However, since the opacity cannot explicitly define the scene surface, opacity-based 3DGS methods typically yield surface mesh results with artifacts. For example, GOF extracts surface mesh through an opacity level set, but the Gaussian opacity field poses non-strict linearity, leading to mesh extraction with holes. In contrast, SDF has strong linearity and explicitly defines the scene surface. We hence aim to introduce the SDF to regularize the Gaussian opacity field. Concretely, we propose the unbiased regularization, which encourages Gaussians near the surface to exhibit a high opacity value, eliminating artifacts distant from the surface.\n\nOn the other hand, due to the irregular nature of 3D Gaussians, it is difficult to estimate their normal directions. Existing methods, such as 2DGS and PGSR, attempt to facilitate the normal estimation by compressing 3D Gaussian primitives to 2D shapes. This geometric constraint is not reasonable as the restriction on the shape of Gaussian primitives leads to degraded performance in capturing detailed structures. In contrast, our method introduces SDF in 3D Gaussian primitives and leverages the gradients of SDF to accurately define the normals, instead of restricting the shapes of Gaussian primitives."}]

Author rebuttal:

Meta-review: This paper proposes a method for reconstructing articulated objects using 3D Gaussian Splatting from multi-view RGB images of two arbitrary articulation states. 

On the positive side, all reviewers appreciated the overall engineering contribution of the work and the usefulness of the unbiased Signed Distance Field (SDF) guidance to regularize Gaussian opacity fields.

In terms of potential weaknesses, some concerns were raised, particularly regarding novelty and technical differences with GOF, 3DGSR, and NeuS. Reviewers also requested clarifications on the input view setting, training times, reconstruction of multi-part articulated objects, and results on general reconstruction datasets (e.g., Tanks and Temple, DTU). The authors provided the additional results and clarifications, which addressed these concerns.

In the end, all five reviewers leaned positive (three borderline accepts, two accepts). The AC concurs with this assessment and recommends acceptance. The authors are strongly encouraged to incorporate the additional results and clarifications from the rebuttal and discussion into the final version of the paper.
Decision: Accept (poster)