SAP: Exact Sorting in Splatting via Screen-Aligned Primitives
Authors: Zhanke Wang
Zhiyan Wang
Kaiqiang Xiong
Jiahao Wu
Yang Deng
Ronggang Wang
Venue: NeurIPS 2025 poster ()
Keywords: 3DGS; NeRF;Novel View Synthesis
Primary area: applications

Abstract: Recently, 3D Gaussian Splatting (3DGS) has achieved state-of-the-art rendering results. However, its efficiency relies on simplifications that disregard the thickness of Gaussian primitives and their overlapping interactions. These simplifications can lead to popping artifacts due to inaccurate sorting, thereby affecting the rendering quality. In this paper, we propose Screen-Aligned Primitives (SAP), an anisotropic kernel that generates primitives parallel to the image plane for each view. Our rasterization pipeline enables full per-pixel ordering in real time. Since the primitives are parallel for a given viewpoint, a single global sorting operation suffices for correct per-pixel depth ordering. We formulate 3D reconstruction as a combination of a 3D-consistent decoder and 2D view-specific primitives, and further propose a highly efficient decoder to ensure 3D consistency.  Moreover, within our framework, the primitive function values remain consistent between view space and screen space, allowing arbitrary radial basis functions (RBFs) to represent the scene without introducing projection errors. Experiments on diverse datasets demonstrate that our method achieves state-of-the-art rendering quality while maintaining real-time performance.

SAP: Exact Sorting in Splatting via Screen-Aligned Primitives
Zhanke Wang', Zhiyan Wang', Kaiqiang Xiong" Jiahao Wu!?, Yang Deng', Ronggang Wang 12+
"Gunngdong Provincial Key Laboratory of Ultra High Definition Immersive Media Technology,
Shenzhen Graduate School, Peking University. ?Pegg Cheng Laboratory wang, zywang23, xiongkaiqiang, wjh0616, dengyang) pku edu. cn rgvang@pkusz. edu. cn
Abstract
Recently, 3D Gaussian Splatting (3DGS) has achieved state-of-th thte-of-theerrttt rendering results. However, its efficiency relies simplifications that disregard the thickness of Gaussian primitives and their overlapping interactions. These simplifications lead to popping artifacts due to inaccurate sorting, therehy affecting the dering quality. In this paper, we propose Screen-Aligne Primitives (SAP), an anisotropic kernel that generates primitives parallel to the image plane for each view. Our rasterization pipeline enables full per-pixel ordering in real time. Since the primitives are parallel for a given viewpoint, single global sorting operation suffices for correct per- per-pixel depth ordering. We formulate 3D reconstruction as a combination of 3D-consistent decoder and 2D view-specific primitives, and further propose a highly efficient decoder to ensure 3D consistency. Moreover, within our framework, the primitive function values remain consistent between view space and screen space, allowing arbitrary radial basis functions (RBFs) to represent the scene without introducing projection errors. Experiments on diverse datasets demonstrate that our method achieves state-of-the-art rendering quality while maintaining real-time performance.
Introduction
Neural Radiance Fields (NeRF) (2344 5)
have demonstrated exceptional performance in 3D
scene representation and novel view synthesis, but come with high computational costs. Recently, 3D Gaussian Splatting (3DGS) (6) has garnered widespread attention by introducing the rasterization of primitive points, achieving real-time rendering while maintaining rendering quality. Building this foundation, researchers have explored various representations, including 2D planar Gaussians ( generalized Gaussian kernels (8), and neural Gaussians (9) (O). However, these methods rely on the coarse sorting mechanism inherent to 3D Gaussian Splatting, which fundamentally limits their depth ordering precision.
critical limitation of 3DGS (6) is popping artifact, which arises from its depth sorting mechanism. Specifically, 3DGS performs depth sorting based solely Gaussian centers before alpha blending, assuming that Gaussians do not overlap. For anisotropic ellipsoids, sorting based solely on centers is inherently inaccurate in practice. As illustrated in Fig. [c). while Gaul appears before Gau2 in view-space depth ordering, certain pixels require Gau2 to be rendered first due to overlapping regions. Several methods have been proposed to address this issue. StopThePop (II) employs the maximum of a ID Gaussian along the view ray as a more precise depth estimation. However, it also neglects Gaussian overlap and lacks the capability perform full per-pixel sorting, shown in Fig. dd). EVER 12) employs ray tracing for the per-pixel rendering accuracy, but at the cost of doubling the *Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

(a) Exact Sort
(b)
(c) Depth Sort
(d) Ray Sort
SAP
3DGS
View Space
Image Planc
Ground Truth
PSNRa55 0331 ( (Ouns)
FSNR:32 d6d0 (DDGS)
PSINR 24/8 (Stp ThePop)
Figure Comparative analysis of sorting strategies: (a) Precise per-pixel sorting ensures correct rendering order for every individual pixel. (b) Our Screen-Aligned Primitives guarantee accurate per-pixel ordering through a single sorting pass, inherently eliminating overlap artifacts. (c) View-space depth ordering (6) prioritizes Gaul over Gau2 across all overlapping pixels when
Gaussians intersect. (d) Sorting by maximum pulse intensity of 1D Gaussians (11) places Gau2 first, yet fails to distinguish per-pixel coverage.
rendering overhead. In this work, we improve the original representation of 3DGS by constraining the primitives be parallel to the image plane. To fundamentally eliminate overlaps between different primitives, our primitives are parallel thin slices, ensuring that they do not intersect. Under this condition, depth sorting along the z-axis becomes equivalent to exact per-pixel sorting, enabling accurate ordering without introducing additional computational overhead. Another drawback of 3DGS that it uses an affine projection approximated by the Jacobian matrix (I3) to construct the 2D Gaussian plane in the screen space, which introduces projection errors. Our parallel primitives eliminate this projection error because there no variation in depth within the same primitive. We perform exact projection through simple geometric scaling, while enabling exploration of more flexible and varied kernel representations.
If we directly define explicit representation, it is impossible determine primitive that remains parallel to the image plane across all viewing directions. By leveraging anchor-based Gaussians 9 [4), we introduce neural networks generate primitives aligned parallel each specific plane. This design ensures that our Screen- Aligned Primitives maintain strict parallelism with the image plane across all perspectives. We design 3D-consisten decoder based on the FiLM architecture (15), which is widely used in controllable image generation (16). Unlike conventional usage, we condition the decoder the viewing direction to learn direction-aware 3D representation. In summary, our framework employs a 31D-consistent decoder to model view-dependent representations while utilizing 2D primitives for each viewpoint. Since representation anisotropic, the conventional densification strategy may fail under large viewpoint variations. To address this, we introduce a maximum positional gradient-based densification method improve reconstruction quality.
summary, the main contributions our paper are as follows:
We introduce 3D-consistent decoder which enables framework be constructed 3D feature network combined with 2D reconstruction primitives.
We propose Screen-Aligned Primitives (SAP) representation that ensures more accurate sorting.
We demonstrate that our framework supports accurate and unbiased projection, allowing for the use of more flexible and expressive kernel representations.
We present a densification strategy based on the maximum positional gradient, which in- creases point density in regions with significant view-dependent variation, thereby enhancing reconstruction quality.
2
Related Work
Novel View Synthesis. NVS has emerged as pivotal task the fields of computer vision and graphics, with significant implications for applications such as media generation (17), virtual reality

---

(88), and autonomous driving. Over the past few years. NeRF ① has demonstrated remarkable performance in this field, attracting widespread attention. NeRF employs multilayer perceptron (MI.P) to model scenes and utilizes ray marching for image rendering. However, NeRF requires multiple queries to the neural network for each pixel, leading to considerable computational overhead. Although various approaches (19) 20 21 22 (3) have been proposed to accelerate the speed of NeRF, they continue to face notable limitations.
Gaussian Splatting. 3D Gaussian Splatting (3DGS) (6) represents scenes as collections of anisotropic Gaussian ellipsoids achieving photorealistic rendering quality and real-time perfor- mance through an efficient tile-based rasterizer. It relies on the splatting method (13) to construct
2D Gaussians from 3D Gaussians. Subsequent research rapidly expanded the capabilities of 3DGS across various tasks, such as anti-aliasing 24 25). 3D generative modeling (26 27 28), dynamic modeling (29: 30
31 32), surface reconstruction (33 7 34 35), and densification improvement
(36 37 38 (9). These methods optimize 3DGS from various perspectives, allowing it to adapt to different applications.
At the same time, some works are dedicated exploring better scene representation methods. Among them, several 7 40 41) focus on modifying the kernel expressions of the functions to address more complex scenes and tasks. Although these methods offer more flexible representations, they all adopt the original sorting approach of 3DGS. We propose a new framework in which arbitrary kernels can be used without considering projection errors. Additionally, we extend the Gaussian kernel (8) in our framework to achieve a more compact representation.
Popping Artifact and Sorting. The original work on splatting was presented by (42). Popping
artifacts persist
intrinsic limitation of such projective rendering paradigms. 3D Gaussian Splatting (6) employs EWA splatting
(33 to project anisotropic 3D Gaussians onto the imaging
plane. 43 introduced aligning sheet buffers parallel the image plane, and (44) 45) introduced
slice-based volume rendering methods that do not suffer from popping artifacts. Although 2DGS ( uses Gaussian planes to represent the scene, it still does not address the intersection issues between different primitives. Unlike traditional methods based on explicit graphical primitives, we leverage deep learning to fit rendering primitive that is parallel any viewpoint.
Recently, several methods based on 3DGS (6) have been dedicated to mitigate popping artifact. Stop (II uses the maximum value of ID Gaussian as depth, improving popping artifacts during view rotation. 3DGRT (46)and EVER (2) accurately determine the intersection points between primitives and rays by ray tracing. Sort-Free (47) calculates alpha blending using order- independent transparency and (48) approximates the integration of values along the ray to calculate transmittance more accurately. However, these methods still involve many approximations in their computations, and mny-tracing-bet based approaches incur significantly higher computational cost. In contrast, our method achieves outstanding results while retaining the original fast rasterization pipeline.
3 Preliminaries
3.1 3D Gaussian Splatting
3D Gaussian splatting represents scenes as a of differentiable semi-transe transsransp particles defined by their kernel function and renders images by rasterizing the projected 2D counterparts. Each 3D) Gaussian g3D centered a point μ E R with covariance matrix Σ E R3x3 is given by:
g3D ( -e--ww"' (x-
RSST RT.
(I)
where x E 123 is arbitrary position within the scene, R E 3 3 is rotation and S 33x3 a scaling matrix.
The dieeddependent appearance of each 3D Gaussian is modeled by third-order spherical harmonics (SH) coefficients F E R combined with opacity a E TR. To render an image, we need to project our 3D Gaussian G&D to 2D 2D Gaussian G2D for rendering. The 2D covariance matrix >' is given as follows:
E' = JWEWT."
(2)
3

---

where W is a viewing transformation and J is the Jacobian of the affine approximation of the projective transformation. The tile-based rasterizer employs depth I sorting in viewspace to render 3D Gaussian primitives and employs a-blending to compute the color of pixel x'.
3.2 Anchor-Based Gaussian Splatting
To obtain primitives parallel to the plane from different viewpoints, we employ anchor-based Gaussian splatting @ (0) to characterize Gaussian attributes. Each &o anchor carries a position coordinate I, E R3, a local feature f, E R and la E R is scaling factor controlling the predicted offsets O E TR kx3 The positions yr of neural Gaussians are calculated
{co: .... 1 = Ze {Ou.... Lu-
Additionally, a corresponding tiny MLP decodes the opacities, scales, rotations, and colors from the anchor features, as well as the distance between the anchor and the camera dee and the viewing direction de..
From anchor-based Gaussian Splatting, we derive a key observation: if entirely distinct primitives are generated for each view, and each viewpoint only observes single face of the 3D Gaussians, then the necessity of maintaining full 3D representation becomes questionable. This insight motivates our exploration of 2D primitives as an alternative.
4 Methodology
To achieve exact sorting during primitive render- ing, we first introduce 3D-consistent decoder that generates planar primitives for each view- ing direction (Sec. 4.1.. Based on this decoder, we further propose a Screen-Aligned Primitives (SAP) framework to address Gaussian sorting and overlap issues without incurring additional time overhead (Sec. 4.2) Leveraging the SAP
Do open
anchor
D. rg
theta
F
Decoder
D2 scule
Y.P
FiLM
framework, we enable unbiased projection, en- abling the use of fiexible kernel functions to represent the scene more accurately (Sec. (4.3). Finally, detail the training procedure and densification strategy (Sec.
Encoding
d2
d
View Space
Figure 2: Schematic illustration of SAP. For each input viewpoint, we generate gcreen-aligned prim- itives directly in view space using machor-based decoding. A lightweight decoder takes the anchor features and directional encoding of the view- ing direction input, and outputs 2D primitives aligned with the corresponding view plane. Un- like prior methods that typically operate in world space, our approach generates primitives that are consistently aligned with the viewing direction.
4.1 3D-Consistent Decoder
We decompose the 3D reconstruction process into a 3D-consistent decoder and 2D primitive- based renderer. In this section, we present the design and formulation of our 3D-consistent de- coder. In NeRF (I), researchers typically em- ploy positional encoding combined with view- ing directions as input to an MI.P for color and density prediction. Subsequent works such as Instant-NGP (19) improve upon this by introducing hash-based encoding, while PlenOctree 233 incorporates spherical harmonics to assist directional learning. Similarly, in Gaussian representations based anchors 2 (0). local anchor features concatenated with viewing directions are fed into lightweight MLP for decoding.
Directional encoding, In this paper, we employ direction decoding framework based on the FiLM network (15), where the direction serves as a control signal, as shown in Fig. 2 Additionally, we explore the impact of different directional encodings on the results. Our experiments reveal that using spherical harmonic direction encoding significantly improves the decoding and rendering quality. We employ real-valued spherical harmonics (SH) to encode the input unit direction vector d' d== (z, y, 2). The spherical harmonics encoding up to degree are defined as:
SH(J) = Yo (d)) Y (d

---

where Y denotes the basis function of the real spherical harmonics of degree I and order m, evaluated in direction d.
perection-modulae MLP. We use a Direction-modultie MLP as the 3D decoder D. Given an input feature f, and viewing direction d, our network first transforms the input via linear layer:
h Wifa b
then applies feature-wise linear modulation using scale and shift parameters derived from the direction encoding SH(d):
r. (SH(a)) h2 = o h + B),
where (()) is a non non-linear activation, and @ denotes element-win multiplication. Finally, the output is predicted via second linear layer:
0, = W22h b2).
(6)
where 0 and denote the rotation and anisotropic scale parameters, respectively, and sigmoid(.) is the element-wise sigmoid activation function. For the learning of other parameters, we follow the settings of Scaffold-GS (9)
4.2 Screen-Aligned Primitives
3DGS (6) performs global sort of Gaussians based on the view-space z-coordinate t, = of their mean. However, since each 3D Gaussian is defined by covariance matrix E,, which defines an anisotropic ellipsoid in a 3D space. When Gaussians overlap, their per-pixel depth orders may contradict the global sorting, resulting in rendering artifacts such as incorrect transparency blending.
We construct a plane parallel the screen through the center of the viewpoint space, thereby constraining all primitives to be parallel. As shown in Fig. [ for each specific viewpoint, our rendering primitives all parallel. This planar alignment enables single-pass global sorting to guarantee pixcl-accurate depth ordering, as all primitives share identical orientation relative to the view direction. Within this parallel plane, each primitive is parameterized by 2D rotation 0 E [0. 2x) and scaling = (sz. sy). We do not perform 3D rotations; instead, we construct 2D transformations within the local plane. We explicitly construct the view-space covariance matrix Σ, through composition of 2D scaling matrix S, E 2xx and rotation matrix R. E R222 as detailed below:
Σn R.S.SSS R.T
For given viewpoint, we effectively use 2D primitives to reconstruct the 2D image. this case, our rendering method is similar to (49). where 2D Gaussian function is used to reconstruct the 2D image.
In summary, our framework employs a 3D-cconisstent decoder to generate view-specific 2D shape parameters for Screen-Aligned Primitives, which are then sorted by depth t.
4.3 Unbiased Projection
Sereen-Aligned Primitives Splatting. Gaussian Splatting (6) projects 3D ellipsoids onto the imaging plane as 2D Gaussians. To preserve the differentiability, it employs an affine approximation (I3) constructed via the Jacobian matrix, Eq. 2 However, this approximation introduces geometric distortions, particularly under perspective projection with significant depth variations strong parallax effects.The affine projection considers only the depth at the center, making accurate only near the center point, with increasing error the distance from the center grows. Some have analyzed this projection error and introduced more accurate projection works (50) 51 52 53) computations.
Since our parallel primitives exhibit no depth variation, their projection onto the imaging plane simplifies to a geometric scaling centered at the original depth t:
(8)
fg
where fesfy are the horizontal and vertical focal lengths of the camera, respectively.Therffors screen-space covariance matrix Eg is constructed as E. PT.
5

---

In fact, the space Mahalanobis distance and screen-space Mahalanobis distance in our framework are equivalent, as proven Appendix B.5. Specifically:
(x, ( Σ (x. po)) = (x. - 11,) "²)""=111 ( -Ma).
where (+), and (+)s represent variables in the view coordinate system and the screen coordinate system, respectively. Therefore, the distributions in view space G, and screen space Ge are equivalent under our parameterization, i.c.,
GolMo, = Go (Ms, E.).
(10)
Versatile Kernel Representation. The edge distribution a 3D Gaussian is still Gaussian, which simplifies the computation of splatting. Ges (8) utilizes generalized Gaussian kernel, but due to projection errors, approximates the kernel by introducing a scaling parameter in place of the exact generalized Gaussian kernel function. However, in our framework, the distribution in the view space and the screen space are equivalent, allowing us to define any kemnl.. Formally, let KC(-) be an arbitrary differentiable kernel function; our projective isomorphism guarantees:
(Zri Mv: En) (., Ps, Eg).
(11)
Building upon this equivalence, we generalize the Gaussian kernels. Let the Mahalanobis distance be defined as M (r;; μ1 Σ) = (x u)² Σー --1(xx (1) and (0, ) generalized kernel function is expressed as:
K GG (1; u. 2 ee (M)p))) M(:; 14, 2) E (0),
(12)
The Generalized Gaussian kernel K.es defines more flexible primitives, allowing us to achieve similar rendering quality with fewer primitives. At the same time, we restrict the value range of the generalized Gaussian kernel KG to within 3//P long axis range, with a detailed proof available in
Appendix B.5
4.4 Optimization
Improved Densification. Similar to prior methods (6 9), we utilize positional gradients as a criterion for dynamic anchor growth. However, previous approaches used averaging positional gradients across all training views. This uniform averaging fails to prioritize underoptimized viewpoints with high gradient variance, leading to insufficient anchor growth in regions that are poorly reconstructed from specific perspectives. To address this, we introduce max- -ex-dindient V that prioritizes the most significant positional gradients across viewpoints V:
OLk
| max
max
(13)
0u2n
When using average position gradient densification, some regions are prone to gradient vanishing, resulting in holes blurriness. To balance the robustness of the average gradients and the sensitivity of the maximum gradients, our densification condition combines both metrics. Growth occurs when either the average gradient magnitude exceeds Ti the maximum gradient magnitude exceeds T2. Ti and T2 are the predefined thresholds.
Loss. We retain the original loss function of 3DGS (6) As our primitives do not overlap, scaling regularization ( not necessary. The loss function integrates an Li metric combined with loss of structural similarity (SSIM) Lassm:
C A1 + Assim Essim
(14)
5 Experiments
5.1 Experimental Setup
Dataset and Metrics. We evaluated Screen-Aligned Primitives (SAP) diverse set of real-world datasets to demonstrate superior visual quality. Specifically, we tested our approach on various public datasets, including 9 scenes from MipNeRF360 (3), 2 scenes from & Temples (54),

---

Table 1: Quantitative evaluation the Mip-NeRF360 (3), & Temples (54) and Deep Blending (55) datasets. Our method achieves the best rendering quality on most datasets. We follow the experimental settings and dataset partitioning of Scaffold-Ga GS (9).
Dataset
Temples
Mip-NeRF 360
Deep Blending
Method
PSNR
SSIM
LPIPS
PSNR1
SSIM1
LPIPS.
PSNR1
SSIM
LPIPS.
Mip-NeRF 360
B
22.22
0.758
0.257
27.56
0.793
0.234
29.40
0.900
0.245
3D-GS 66
23.71
0.845
0.178
27.43
0,813
0.217
29.46
0.900
0.247
2DGS 7
22.96
0.825
0.217
27.03
0,804
0.239
29.49
0.899
0.259
Scaffold-GS
24.19
0.854
0.174
27.55
0.810
0.232
30.28
0.909
0.239
StopThePop [1]
23.21
0.843
0.173
27.28
0.810
0.213
29.86
0.904
0.234
DisC-GS (58)
24.96
0.866
0.120
28.01
0.833
0.189
30.42
0.907
0.199
3DGS-MCMC (39
24.29
0.860
0,190
28.00
0.831
0.178
29.67
0.890
0.320
SAP (Ours)
25.04
0.870
0.145
28.05
0.835
0.208
30.02
0.910
0.236
Table 2: Ablation on the T Dataset
(54)
We evaluate the performance of two
different rendering primitives: 3D Gaussian Primitives 6 9 and Screen-Aligned Primitives, Sec. 4.2)
FiLM: FiLM-modulated MLP, Sec. 4. SH encoding: real-valued spherical harmonies(SH) encoding,
Sec. max: maximum view-direction gradient threshold, Sec. 4.4 The numerical difference from
the best cest-performing result is shown in the bottom-right corner.
Components
3DGaussian Primitives
Screen-Aligned Primitives
FiLM SH encoding
V max
PSNR
SSIM
LPIPS 4
PSNR
SSIM
LPIPS
24.15.a.0
0,858.p012
24.59.a45
0.846.am34
0..8s
24.25
0.858.
0.165.u.c0
24.67.a.7
0.847.am23
0.179.ous4
24.45.a.50
0.859.aom
0.1 0.163.por
24.79.aa5
0.853.a.11
0.175 0..
24.30.a.74
0.862.n.08
0.154.0.00
24.68.a36
0.859
0.16 0.161_ame
24.52.a.52
0.860.u.0
0. 66 10.00
24.74.u30
0.852.o.ms
0.176.
24.42.a.62
L..00
24.80.a34
0.860.am10
0.161
24.51
0.863.
0.1 0.155
24. 24.89...1
0.858
0.164.a.m
24.56.
0.864.n.ov n.006
0.155,0.000
25.04
0.870
0.145
scenes from DeepBlending (55). These datasets cover a range of environments, from bounded indoor spaces to unbounded outdoor settings, providing comprehensive evaluation of the performance of our method. We adopt the experimental settings and dataset partitioning as established in Scaffold-Gr (9). In particular, for the MipNeRF 360 dataset (3), scenes with resolutions exceeding 1600 are downsampled to 1600. Consistent with previous studies, we assess reconstruction quality using three metrics: PSNR 1. SSIM 1 (56, and LPIPS (57). We color each cell as best. second best and third best. We refer our Screen-Aligned Gaussian kernel SAP.
Implementation Details. Our PyTorch implementation is built upon the Scaffold-GS (9) framework, in which we re-implement the 3D-consistent decoder. We modified the CUDA kernel to replace spatial primitives with screen-aligned primitives. These modifications do not affect the original rendering efficiency; in fact, by reducing matrix computations (from 3D matrices to 2D matrices), approach achieves slight -peed-up parameter settings from Scaffold-GS to ensure a fair comparison. The difference is that our parallel kernel leverages the prior along the z-axis. Therefore, instead of using the anchor view direction, we modify the input of the Decoder for covariance to be the camera's z-axis direction. Detailed hyperparameter settings and model architecture are provided in Appendix an2 Appendix B.3 We conducted all experiments on a single NVIDIA L40S GPU.
the baseline in constant time. We retained most of the
5.2 Results and Comparisons
Quantitative results. We evaluated SAP against various state-of-the-are techniques both novel
view synthesis tasks. The quantitative results three datasets (55 3 54 are presented in Table I
with additional details per scene available Appendix B.9 We sequentially compare 6ipNeRF360
(3), 3DGS (6), 2DGS (7), Stop-the-Pop (.. Scaffold-GS (). DisC-GS (58) and 3DGS-MCM
7

---

19.70
19,80
20.12
20.58
S
28 1
27.21
27.28
27.78
22.39
23.25
24.84
26.50
Ground Truth
3DGS
StopThePop
Scaffold-GS
Ours
Figure 3: Qualitative comparisons across diverse datasets (55 3 54). We compare 3DGS (6).
Stop-the-Pop (ID. and Scaffold-GS ( sequentially. Regions where method outperforms others are highlighted red. Additionally, the PSNR of each image is annotated in the top-left corner. Our approach achieves high-quality reconstruction methods commonly exhibit blurriness, floating artifacts, and other inconsistencies in these regions. This can be attributed the accuracy of parallel primitive ordering and our effective densification strategy.
in several challenging areas, whereas other
Table 3: Comparison of different encodings. We conduct comparative evaluation of various encoding methods, namely: no positional encoding, MLP encoding (MLP), Fourier encoding (FE), and spherical harmonics encoding (SH), the Tanks&Temple Dataset (54).
no encoding PSNRt /SSIM/ /IPIPS.
MLP
FE PSNK" 1SIMT / LPPISL
SH PSNRT /SIMO /LPIPS.
PSNRT SSIM / L.PIS..
24.74/ / 0.852 / 0.6 24.80 / 0.856 0.169
24.88 / 0.863 0.161 25.04/ 0.870 / 0.145
As shown in Table I our SAP achieves the best results on Tanks & Temples as well as Ne3660, ranking first or second in nearly all metries. The table indicates that although 2DGS (7) improve geometric accuracy, they compromise rendering quality. Our 2D screen screen-aligned primitive representation, however, not only preserves also significantly boosts rendering quality, outperforming even the state-of-the-art 3DGS baseline.
33)
Qualitative results. In Fig. t we showcase the comparisons between our method and other approaches. We can observe that our method significantly reduces artifacts and aliasing compared to previous approaches. For example, the fifth row, other methods produce artifacts, whereas ours avoids them. This improvement is due to the accurate ordering of our primitives, which prevents interference between different primitives during rendering, ensuring that primitives intended for one region are not mistakenly rendered in another. Additionally, our method reduces blurriness, as

---

Figure 4: Comparison of the effeets of two splitting methods. We have magnified the rendered image and the point distribution of the highlighted region. In the left two columns, the original average position gradient is employed, which results in numerous voids leading to blurring; in the right two columns, the combination of average and maximum position gradients effectively fills these voids, yielding improved rendering quality.
Table 4: Comparison of different kernels. We compare Anchor-3DGS 9 Ges 8 and our three different kernels, on the Tanks& Temples Dataset (54)
Anchor-2DGS (T)
Scaffold-GS
Ancher 2DGS
Ges
SAP-Eps
SAP-Ges
SAP Gaussian
(199S)
SSIMY
24.19 0.85//054/// 0.1174 0.174 23.52/0.883 0.835 /0.199 23.35 / 0.836 / 0.1998
20.53 0.667 004409 24.75 / 0.861 0. 25.04/ 0.870 / 0.145
shown in the fourth row of Fig. particularly on the ground This improvement is attributed to our densification strategy, which effectively fills in the gaps. As illustrated in Fig. [4] we zoomed in on the red-boxed area and separately presented the rendering results and the distribution of primitive points. It can be intuitively observed from the figure that our densification strategy can improve scene rendering.
5.3 Ablation Studies
Efficacy Screen-Aligned Primitives. Table. Sable.Zeeeer eevaluates the impact of various configurations and kernel choices on the rendering quality for the Tanks&Temples dataset. We conduct a comprehensive evaluation of the rendering quality variations resulting from different combinations of our SAP and 3D Gaussian primitives with other system components. Each of our components achieves improvements over the baseline, among which directional encoding and the SAP kernel yield the largest enhancements. Our FiLM decoder also achieves better connsssitt decoding performance compared to the MLP decoder. We believe that employing FiLM for directional modulation enables more effective learning of direction-dependent attributes than simply concatenating direction vectors with features as input to an MIP. Furthermore, our maximum densification of the position gradient Vmax effectively improves the quality of the scene reconstruction. The original densification strategy tends to fail when there is a significant viewpoint difference, whereas maximum position gradient densification alleviates this issue effectively.
Results of different directional encoding. We explore how various directional encoding strategies affect the rendering quality in Table In particular, we compare four methods: (1) no directional encoding; (2) a simple MIP that encodes the direction into a 32-dimensional feature vector; (3) Fourier encoding adopted from NeRF @ and (4) hard-coded spherical harmonies encoding. Our results show that the spherical harmonics encoding yields the best performance. This can be attributed to the inherent design of spherical harmonic functions, which are well-suited for capturing directional properties, making them particularly effective control signals for enforcing 3D consistency and learning direction-dependent attributes.
Results of different kernels. We compared the rendering quality for different kernels in Table 4 Scaffold-GS (9), also known as Anchor-3DGS In DSt (I0). Anchor-2DGS was implemented by combining sliced- sliced-plane Gaussian sheets (7) with anchors. Ges (8) provides a generalized Gaussian kernel. In our comparisons, SAP-Epa adopts the generalized Epanechnikov kernel (59). For clarity, SAP-Ge Aep utilizes 2D generalized Gaussian kernel (8), as defined in Eq. 12 whereas the standard SAP-Gaussian employs 2D Gaussian primitives. Specifically, we tested SAP-Ges with p learnable parameter. SAP-Gaussian a special case of SAP-Ges when p 1. Our SAP-Gaussian achieves the best reconstruction quality. Our experimental results show that, although Ges is superset of

---

Gaussian kernels, it performs worse than the standard Gaussian kernel in rendering quality. We believe this be likely because Gaussian Splatting serves as mixture of multiple primitives, and when the number of primitives is sufficient, the specific shape of each kernel has limited impact on rendering quality. Additionally, the higher complexity of the Ges representations complicates the optimization process, making it harder to identify the best learning parameters.
Limitations and conclusions
Limitations. Although our method explores two different kernel behaviors, both are radial basis functions constructed based on Mahalanobis distance. In fact, within our framework, we can experiment with a wider range of kernels, not limited radial basis functions, such as asymmetric kernels (60) 40). Furthermore, since our approach does not take surface normals (7) into account, it may present challenges mesh extraction. This limitation will be addressed in future work.
Conclusions. In this work, we introduce Screen-Aligned Primitives (SAP), novel framework for 3D representation. Our approach employs a neural network decoder to enforce parallel alignment between each primitive and the rendered plane, enabling accurate primitive ordering reduced computational cost. Our framework decomposes the 3D representation into a combination of a 3D) decoder and 2D primitive representations. Additionally, we demonstrate that our primitives are adaptable to various kernel functions. Extensive experiments on several challenging datasets validate that SAP achieves real-time rendering performance.
Acknowledgments. This work financially supported by Guangdong Provincial Key Laboratory of Ultra High Definition Immersive Media Technology (Grant No. (224B121201006) this work is also financially supported for Outstanding Talents Training Fund Shenzhen, Shenzhen Science and Tech- nology Program GGrant No. SYSPG202412111734442 and Grant No. CCJC20200714110 (TCC0200011114435557777 14435057).
References
[1] B. Mildenhall, P. Srinivasan, M. Tancik, J. Barron, R. Ramamoorthi, and R. Ng, "Nerf: Representing scenes neural radiance fields for view synthesis," Communications of the ACM, vol. 65, no. 1, pp. 99-106, 2021.
[2] T. Barron, Mildenhall, M. Tancik, Hedman, R. Martin Martin-Brualla, and P. P. Srinivasan, "Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields." in Proceedings of the IEEE/CVF international conference on computer vision, 2021, pp. 5855-5864.
[3] T. Barron, Mildenhall, Verbin, P. Srinivasan, and Hedman, "Mip-nerf 360: Unbounded anti-aliased neural radiance fields," in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 5470-540 5479.
[4] "Zip-nerf: Anti-aliased grid-based neural radiance fields." in Proceedings of the IEEE/CVF International Conference on Computer Vision, 2023, pp. 19 6969-199709 705.
[5] D. Verbin, P. Hedman, B. Mildenhall, T. Zickler, J. T. Barron, and P. P. Srinivasan, "Ref- nerf: Structured view-dependent appearance for neural radiance fields," in 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2022, pp. 5481-5490.
[6] B. Kerbl, G. Kopanas, T. Leimkühler, and G. Drettakis, "3d gaussian splatting for real-time radiance field rendering." ACM Trans. Graph., vol. 42, 4, pp. 139-1, 2023.
[7] B. Huang, Z. Yu, A. Chen, A. Geiger, and S. Gao, "2d gaussian splatting for geometrically accurate radiance fields." ACM SIGGRAPH 2024 conference papers, 2024, pp. 1-11.
[8] A. Hamdi, L. Melas-Kyriazi, J. Mai, G. Qian, R. Liu, C. Vondrick, B. Ghanem, and A. Vedaldi, "Ges: Generalized exponential splatting for efficient radiance field rendering," in Proceedings of the IEFF/CVE Conference on Computer Vision and Pattern Recognition, 2024, pp. 118
19 822.
10

---

[9] T. Lu, M. Yu, L. Xu, Y. Xiangli, L. Wang, D. Lin, and B. Dai, "Scaffold-gs: Structured 3d gaussians for view-adaptive rendering," in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024, pp. 20 604-200
[10] K. Ren, L. Jiang, T. Lu, M. Yu, L. Xu, Z. Ni, and B. Dai, "Octree-gs gs: Towards consistent real-time rendering with lod-structured 3d gaussians," arXiv preprint arXiv:2403.17898 2024.
[11] L. Rada, M. Steiner, M. Parger, A. Weinrauch, Kerbl, and M. Steinberger, "Stopthepop: Sorted gaussian splatting for view-consistent real-time rendering," ACM Transactions on Graphics (TOG), vol. 43, no. 4, pp. 1-17, 2024.
[12] A. Mai, P. Hedman, G. Kopanas, D. Verbin, D. Futschik, Q. Xu, F. Kuester, J. T. Barron, and Y. Zhang, "Ever: Exact volumetric ellipsoid rendering for real-time view synthesis," arXiv preprint arXiv:2410.01804 2024.
[13] M. Zwicker, H. Pfister, J. Van Baar, and M. Gross, "Ewa splatting." IEEE Transactions Visualization and Computer Graphics, vol. 8, no. 3, pp. 223-238, 2002.
[14] Z. Yang. X. Gao, Y.-T. Sun, Y. Huang, X. Lyu, W. Zhou, S. Jiao, X. Qi, and X. Jin, "Spec- gaussian: Anisotropic deeeddepnndent appearance for 3d gaussian splatting," Advances in Neural Information Processing Systems, vol. 37, pp. 61 192-61 61 216, 2025.
[15] E. Perez, F. Strub, H. De Vries, Dumoulin, and A. Courville, "Film: Visual reasoning with a general conditioning layer," in Proceedings of the AAAI conference on artificial intelligence. vol. 32, no. 1, 2018.
[16] W. Peebles and Xie, "Scalable diffusion models with transformers," in Proceedings of the IEEE/CVF international conference on computer vision, 2023, pp. 4195-4205.
[17] J. Ren, L. Pan, J. Tang, C. C.Zann, A. Cao, G. Zeng. and Z. Liu, "Dreamgaussian4d: Generative 4d gaussian splatting," " arXiv preprint arXiv: 2023.
[18] Z. Li, Z. Zheng. L. Wang, and Y. Liu, "Animatable gaussians: Learning pose-dependent gaussian maps for high-fidelity human avatar modeling," in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2024, pp. 19711-19722.
[19] T. Müller. A. Evans, C. Schied, and A. Keller, "Instant neural graphics primitives with multiresolution hash encoding," ACM transactions on graphics (TOG), vol. 41, no. 4, pp. 1-15, 2022.
[20] Q. Xu, Z. Xu, J. Philip. S. Bi, Z. Shu, K. Sunkavalli, and U. Neumann, "Point-nerf: Point-based neural radiance fields." in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022, pp. 5438 5448.
[21] A. Chen, Z. Xu, A. Geiger, J. Yu, and H. Su, "Tensorf: Tensorial radiance fields," in European conference on computer vision. Springer, 2022, pp. 333-350.
[22] S. Kridovich-Keil, A. Yu, M. Tancik, Q. Chen, B. Recht, and A. Kanazawa, "Plenxxes:: Radiance fields without neural networks," in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 5501-5510.
[23] A. Yu, R. Li, M. Tancik, H. Li, R. Ng, and A. Kanazawa, "Plenoctrees for real-time rendering of neural radiance fields." in Proceedings of the IEEE/CVF international conference computer vision, 2021, pp. 5752-5761.
[24] Z. Yu, A. Chen, B. Huang, T. Sattler, and A. Geiger, "Mip-splatting: Alias-free 3d gaussian splat- ting," in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2024, pp. 19 497-499944 456.
[25] Z. Liang. Q. Zhang. W. Hu, L. Zhu, Y. Feng, and K. Jia, "Analytic-pplating: Anti-aliased 3d gaussian splatting via analytic integration," in European conference computer vision. Springer, 2024, pp. 281-297.
[26] Tang, J. Ren, H. Zhou, Liu, and G. Zeng, "Dreamgaussian: Generative gaussian splatting for efficient 3d content creation." arXiv preprint 2t..Xi223099.65333 2023.
11

---

[27] J. Chung, S. Lee, H. Nam, J. Lee, and K. M. Lee, "Luciddreamer: Domain-frees generation of 3d gaussian splatting scenes," arXiv preprint arXiv:2311.13388 2023.
[28] J. Tang, Z. Chen, X. Chen, T. Wang, G. Zeng, and Z. Liu, "Lgm: Large multi-view gaussian model for high-resolution 3d content creation," in European Conference on Computer Vision. Springer, 2024, pp. 1-18.
[29] Z. Yang, X. Gao, W. Zhou, Jiao, Y. Zhang, and X. Jin, "Deformable 3d gaussians for high- fidelity monocular dynamic scene reconstruction," in Proceedings of the IEEE/CVE conference on computer vision and pattern recognition, 2024, pp. 20 331-203411 341.
[30] J. Yan, R. Peng, L. Tang, and R. Wang, "4d gaussian splatting with scale-aware residual field and adaptive optimization for real-time rendering of temporally complex dynamic scenes," in Proceedings of the 32nd ACM International Conference on Multimedia, 2024, pp. 7871-7880.
[31] J. Wu, R. Peng. Z. Wang, L. Xiao, L. Tang, J. Yan, K. Xiong, and R. Wang. "Swift4d: Adaptive divide-and-conquer gaussian splatting for compact and efficient reconstruction of dynamic scene," in The Thirteenth International Conference
Learning Representations.
[32] G. Wu, T. Yi, J. Fang, I.. Xie, X. Zhang, W. Wei, W. Liu, Q. Tian, and X. Wang. "4d gaussian splatting for real-time dynamic scene rendering," in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2024, pp. 20 20310-2003 320.
[33] A. Guédon and V. Lepetit, "Sugar: Surface- Surface-aligned gaussian splatting for efficient 3d mesh reconstruction and high-quality mesh rendering." in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024, pp. 5354-5363.
[34] M. Yu, T. Lu, L. Xu, L. Jiang, Y. Xiangli, and B. Dai, "Gsdf: 3dgs meets sdf for improved rendering and reconstruction," arXiv preprint arXiv:2403. 16964, 2024.
[35] Z. Yu, T. Sattler, and A. Geiger, "Gaussian opacity fields: Efficient adaptive surface reconstruc- tion in unbounded scenes," ACM Transactions on Graphics (TOG), vol. 43, no. 6, pp. 1-13, 2024.
[36] S. Rota Buld, L. Porzi, and Kontschieder, "Revising densification in gaussian splatting," in European Conference on Computer Vision. Springer, 2024, pp. 347-362.
[37] Z. Zhang, W. Hu, Y. Lao, T. He, and H. Zhao "Pixel-gs: Density control with pixel-aware gradient for 3d gaussian splatting," " in European Conference on Computer Vision. Springer, 2024, pp. 326-342.
[38] Z. Ye, W. Li. S. Liu, P. Qiao, and Y. Dou, "Absgs: Recovering fine details in 3d gaussian splatting," in Proceedings of the 32nd ACM International Conference on Multimedia, 2024, pp. 1061-
[39] S. Kheradmand, D. Rebain, G. Sharma, W. Sun, Y.-.. Tseng, H. Isack, A. Kar, A. Tagliasacchi, and K. M. Yi, "3d gaussian splatting as markov chain monte carlo," Advances in Neural Information Processing Systems, vol. 37, pp. 80 965-880886 2024.
[40] R. Xu, W. Chen, J. Wang. Y. Liu, Wang, L. Gao. S. Xin, T. Komura, X. Li, and W. Wang. "Supergaussians: Enhancing gaussian splatting using primitives with spatially varying colors." arXiv preprint arXiv:241 18966, 2024.
[41] R. Liu, D. Sun, M. Chen, Y. Wang, and A. Feng, "Deformable beta splatting," arXiv preprint 27X1::2501.18630 2025.
[42] L. Westover, "Interactive volume rendering," in Proceedings of the 1989 Chapel Hill workshop on Volume visualization, 1989, pp. 9-16.
[43] K. Mueller and R. Crawfis, "Eliminating popping artifacts in sheet busfer-based splatting," in Proceedings Visualization '98 (Cat. No. 98CH36276). IEEE, 1998, pp. 239-245.
[44] A. Van Gelder and K. Kim, "Direct volume rendering with shading via three-dimensional textures," in Proceedings of 1996 Symposium on Volume Visualization. IEEE, 1996, pp. 23-30.
12

---

[45] B. Cabral, N. Cam, and J. Foran. "Accelerated volume rendering and tomographic recon- struction using texture mapping hardware," in Proceedings of the 1994 symposium on Volume visualization, 1994, pp. 91-98.
[46] N. Moenne-Loccoz, A. Mirzaei, O. Perel, R. de Lutio, J. Martinez Esturo, G. State, S. Fidler, N. Sharp, and Z. Gojcie, "3d gaussian ray tracing: Fast tracing of particle scenes," ACM Transactions Graphics (TOG), vol. 43, no. 6, pp. 1-19, 2024.
[47] Q. Hou, R. Rauwendaal, Z. Li, H. Le, F. Parhadzadeh, F. Porikli, A. Bourd, and A. Said, "Sort-free gaussian splatting via weighted sum rendering," arXiv preprint arXiv:2410. 2024.
[48] C. Talegaonkar, Y. Belhe, R. Ramamoorthi, and N. Antipa, "Volumetrically consistent 3d gaussian rasterization," arXiv preprint arXiv:2412.03378. 2024.
[49] X. Zhang. X. Ge, T. Xu, D. He, Y. Wang, H. Qin, G. Lu, J. Geng, and J. Zhang. "Gaussianim- age: 1000 fps image representation and compression by 2d gaussian splatting," European Conference Computer Vision Springer. 2024, pp. 327-345.
[50] L. Huang. J. Bai, J. Guo, Y. Li, and Y. Guo, "On the error analysis of 3d gaussian splatting and an optimal projection strategy," in European conference on computer vision. Springer, 2024, pp. 247-263.
[51] H. Qi. T. Cai, and X. Han, "Projecting gaussian ellipsoids while avoiding affine projection approximation," arXiv preprint 2XXi:22411007777 2024.
[52] F. Hahlbohm, F. Friederichs, T. Weyrich, L. Franke, M. Kappel, S. Castillo, M. Stamminger, M. Eisemann, and M. Magnor, "Efficient perspective-correet 3d gaussian splatting using hybrid transparency," in Computer Graphics Forum. Wiley Online Library, 2025, p. e70014.
[53] L. Huang, J. Bai, J. Guo, Y. Li, and Y. Guo, "On the error analysis of 3d gaussian splatting and an optimal projection strategy," Computer Vision - ECCV 2024. Cham: Springer Nature Switzerland, 2025, pp. 247-263.
[54] A. Knapitsch, J. Park, Q.-Y. Zhou, and V. Koltun, "Tanks and temples: Benchmarking large- scale scene reconstruction," ACM Transactions on Graphics (ToG), vol. 36, no. 4, pp. 1-13, 2017.
[55] Hedman, J. Philip, T. Price, J.-M. Frahm, G. Drettakis, and G. Brostow, "Deep blending for free-viewpoint image-based rendering," ACM Transactions on Graphics (ToG), vol. 37, no. 6, pp. 1-15, 2018
[56] 7. Wang, A. C. Bovik, Sheikh, and E. P. Simoncelli, "Image quality assessment: from error visibility to structural similarity," IEEE transactions on image processing, vol. 13, no. 4, pp. 600-612, 2004.
[57] R. Zhang, P. Isola, A. A. Efros, E. Shechtman, and O. Wang, "The unreasonable effectiveness of deep features perceptual metric." in Proceedings of the IEEE conference computer vision and pattern recognition, 2018, pp. 586-595.
[58] H. Qu, Z. Li, H. Rahmani, Y. Cai, and J. Liu, "Disc-gs: Discontinuity-awar gaussian splatting," Advances in Neural Information Processing Systems, vol. 37, pp. 122 282-112 309, 2024.
[59] Condor, Speierer, L. Bode, A. Bozic, S. Green, Didyk, and A. Jarabo, "Don't splat your gaussians: Volumetric ray ray-traced primitives for modeling and rendering scattering and emissive media," ACM Transactions on Graphics, 2025.
[60] H. Li, J. Liu, M. Sznaier, and O. Camps, "3d-hgs: 3d half-gaussian splatting," arXiv preprint arXivv:2400 240:202000.2200 2024.
[61] Z. Yu, T. Sattler, and A. Geiger, "Gaussian opacity fields: Efficient adaptive surface reconstruc- tion in unbounded scenes," ACM Transactions on Graphics, 2024.
13

---

NeurIPS Paper Checklist
The checklist is designed to encourage best practices for responsible machine learning research, addressing issues of reproducibility, transparency, research ethics, and societal impact. Do not remove the checklist: The papers not including the checklist will be desk rejected. The checklist should follow the references and follow the (optional) supplemental material. The checklist does NOT count towards the page limit.
Please read the checklist guidelines carefully for information on how to answer these questions. For each question in the checklist:
You should answer [Yes], [No], or [NA].
[NA] means either that the question is Not Applicable for that particular paper or the relevant information is Not Available.
Please provide short (1-2 sentence) justificcton right after your answer (even for NA).
The checklist answers are an integral part of your paper submission. They are visible to the reviewers, area chairs, senior area chairs, and ethics reviewers. You will be asked to also include (after eventual revisions) with the final version of your paper, and its final version will be published with the paper.
The reviewers of your paper will be asked to use the checklist as one of the factors in their evaluation.
While "[Yes] " is generally preferable to "[No]", ", it is perfectly acceptable to answer "[No] provided proper justification is given (e.g., "error bars are not reported because it would be too computationally expensive" or "we were unable to find the license for the dataset we used"). In general, answering "[No] or "[NA] is not grounds for rejection. While the questions are phrased in binary way, we acknowledge that the true answer often more nuanced, so please just use your best judgment and write justification to elaborate. All supporting evidence can appear either in the main paper or the supplemental material, provided in appendix. If you answer [Yes] to a question, in the justification please point to the section(s) where related material for the question can be found.
IMPORTANT, please:
Delete this instruction block, but keep the section heading "NeurIPS Paper Checklist",
Keep the checklist subsection headings, questions/answers and guidelines below.
Do not modify the questions and only use the provided macros for your answers.
1. Claims
Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Question:
Answer: [Yes]
Justification:
The title and abstract clearly articulate the core contributions and structure of the proposed framework; please see Abstract and Introduction.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes]
14

---

Justification:
The paper ends with concise discussion of its current limitations and outlines possible future improvements, Sec. 6
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-ten system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: We provide mathematical derivation on our algorithm in Appendix B.5 and Sec. + and the proposed method is validated through comprehensive experimental results.
Guidelines:
The answer NA means that the paper does not include theoretical results. All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: We clearly differentiates the configurations of each module in detail Ap- pendix B.2 and B.3.
15

---

Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-sonnee open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [No]
Justification: We will provide our CUDA code, which our SAP and the core component of our method. With only minor modifications, it can be integrated into existing frameworks. We also commit to releasing the full code after the paper accepted.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.co cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
/ //nips. www.iiiciguiieeeieeeeeeeeeeeeeee
ssionPolicy for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
16

---

At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (c.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: We provide detailed descriptions the experimental setup in Sec. 5 and the Appendix B.2.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, or as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: The experiments conducted under sufficiently general settings, effectively minimizing randomness, Table 2
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out range (e.g. negative enror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification:
The Appendix B.7 provides detailed runtime conditions.
Guidelines:
17

---

The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer:
[Yes]
Justification:
We confirm that our work complies with the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. if there is special consid- cration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer:
[Yes]
Justification:
We discuss broader impacts in Appendix A.1.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA No, they should explain why their work has no societal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious unintended uses (c.g., disinformation, generating fake profiles, surveillance), fairness considerations deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of ML..
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, scraped datasets)?
Question:
Answer: [NA]
18

---

Justification:
This work does not introduce any known or foreseeable risks, our method is 3D reconstruction method, hence are not releasing any model.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: All code and datasets employed in this work originate from open-source sources or public databases, and have been appropriately cited to ensure compliance, see
Sec. 5.1
Guidelines:
The answer NA means that the paper does not existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset used and, possible, include URL
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com/datases has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information is available online, the authors encouraged to reach out the asset's 's creators.
13. New assets
Question: Are assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification:
We do not introduce new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their
submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
19

---

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification:
This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According to the NeurIPS Code of Ethies, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country or institution) were obtained?
Question:
Answer: [NA]
Justification: This paper does involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA]
Justification: The method proposed in this paper does not involve the use of large language models (LLMs) component.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to our L.LM policy httpgs//merrrps.cc//offfeeereeee for what should or should not be described.
20

---

Appendix
A Broader Impacts and Limitation
A.1 Broader Impacts
Our method focuses on exploring a novel representation for 3D reconstruction and improving the rendering quality of 3D reconstruction. It does not have direct social impact. However, it may trigger a chain reaction in some downstream applications. For example, when using 3DGS to reconstruct digital humans, if the rendering quality is high enough to make it difficult for people to distinguish between real and fake, may raise social and ethical concerns, as well as issues related to the forgery of personal portrait assets. Our method can improve the quality of 3D rendering in certain scenarios, which may exacerbate such risks. This is concern that any technology should take into account, and urge users to carefully consider the potential consequences when applying our method.
A.2 Limitation
Our method is applicable to various kernel representations, not limited to Gaussian kernels. In this paper, we only explore the Gaussian kernel and the generalized Gaussian kemne;; however, approach is, in fact, generalizable to the vast majority of kernels. Many existing works have investigated alternative kernel representations (60) 40). many of which are based on 2DGS 7 to leverage its inherent 2D structure and the convenience of projection-basee computation. Similarly, our method adopts a 2D representation and is compatible with many of these approaches, which could provide significant inspiration for future research this field.
Our method focuses on improving the quality of 3D rendering without incorporating normals to enhance the geometric consistency, such as (1)... This may cause difficulties in applications like surface reconstruction and mesh extraction.
Our method does not address lighting and physical reflection. Prior works (14 have shown that fitting complex lighting conditions can significantly improve rendering quality. We consider this to be a valuable direction for future research.
B
More Technical Details
B.1 Overview
This appendix is organized as follows: (Sec. [.2) Experimental Setup; (Sec. BB3) Network Archi-
tecture; (Sec. B.4b Proof of Unbiased Projection; (Sec. B.5) More Details of SAP-Ges; (Sec. B.6)
Experiments on Computational Resources; (Sec. B.7 View-dependent Gaussian Attribute Decoding;
(Sec. B.8) More Ablation on Kernels; (Sec. B. Additional Results;
B.2 Experimental Setup
Experimental Setup on the Mip-NeRF360 Dataset. is worth noting that in Scaffold-GS ()) images with resolutions larger than 1600 are downsampled to 1600. In contrast, some methods such as 3DGS-MCMC (39) downsample outdoor scenes by factor of 4 and indoor scenes by factor of 2. These differences in preprocessing can lead slight variations in the results, In this paper, we follow the experimental setup of Scaffold-GS.
Hyperparameter Settings. Most of our hyperparameter settings follow those of Scaffold-GS. Specifically, we used 10 neural Gaussians for each anchor; We set the threshold for the average gradient magnitude (7)) to 0.0002, and the threshold for the maximum gradient magnitude (72) to 0.0015: The initial learning rate of our 3D-consistent decoder is set at 0.004 and gradually annealed to 0.00004 during training; the learning rate for the features is set to 0.0025. All other hyperparameter settings follow those of Scaffold-GS to ensure fair comparison.
21

---

FiLM
32
SH Encoding
3
32
L (32, 32x2)
Encoding
32
32
X 32
Y
F
3D-Consistent Decoder
Scale
Sigmoid
x (k) 2
(32, 32)
FiLM
ReLU
F X 32
72 X 32
(k) x 3
Rotation
(32, k=3)
Sigmoid x π
X (k) 1
Figure 5: Illustration of the 3D-Consistent Decoder. The top shows the direction modulator, while the bottom depicts the full decoder architecture. Here, I.(.) denotes linear layer.
B.3 Network Architecture
We condition the network the viewing direction, which is first encoded and passed through a linear layer to generate modulation parameters. These parameters are then used to linearly modulate the features to produce the final output. The rest of our network architecture remains consistent with that of Scaffold-GS (9).
Our 3D-Con AD-Consistent Decoder architecture is illustrated in Fig. 5
B.4 Proof of Unbiased Projection
As shown in Fig. 6 3DGS (6) introduces errors due to the use of an approximate affine projection, whereas our method can effectively avoid this issue.
In our projection framework, the function values of the screen-space kernel and the view-space kernel are equivalent. If we ignore the z-axis depth, assuming the view-space mean point is (pg Pg) and the screen-space mean point is (n my)) For given depth / and horizontal and vertical focal lengths
fz 2etanFovx ffg 2etmnFovy the transformation matrix from space screen, based on our geometric scaling projection, can be expressed as:
height
lx
P
(15)
The relationship between the covariance matrices " and E can be expressed as:
m = PT"
(16)
For the camera model established in 3DGS, the perspective projection matrix M Merspective can be expressed as:
2+Erenr right- left
0
right-leett right left top bottom top- bottom zfar
0
2eSnear top bottom
(17)
0
0
-fjartnncrr Efar Brecar
2for Enear
0
0
With the additional conditions: bottom top; left = - right; Znear tanFovx
0.1; Zfar
100 ; top
2near right tanFovy Fnear. We can simplify it to:
tonF
0
lanFavy
(18)
0
0
00.01
0
0
22

---

Z.
3D-Gaussian
SAP
y
X y
X
Affine Projection
Accurate Projection
Figure 6: A simplified diagram of different projection methods. On the left is the projection process of the 3D Gaussian sphere: the blue represents the standard perspective projection, while the red represents the affine projection approximated by the Jacobian matrix. On the right is our 2D slice transformation, where our projection an affine transformation that achieves the same effect as the exact projection.
y", t, 1). the transformation to screen space can be Therefore, for any view-space coordinates (x",8", written as:
2: y
y
Mperspective
(19)
z
where w" = f and (x" y/, 20, wn) are the NDC coordinates.. Therefore, the normalized coordinates V² respectively. That is,
r" and y" in screen space given by 2" and
2 y
FORKHE
(20)
Land FoVKe!
According to the defined NDC transformation:
(x" +1) +1)+wwdtthh-
(v" +1) Db-ihihhh
(21)
y
Therefore, for any given (a", y²), and (11 pg))
x
11
Le (x=" - 146)
}
(22)
y
11
(y" 1.)
The relationship between them is:
x 11 m
x."² - 10t
P
(23)
y"
81" - M
Finally, the distance function value in screen space is:
xx
11 1c 1²
T
Σ
2
14
pil' p
x
11
1²
1
Myy
(24)
x 1
Σ
y
In summary, our framework, we can define any functional kernel using the Mahalanobis distance. At this point, the function values in screen space and view space are equivalent. For 3DGS, an affine projection, approximated by the Jacobian matrix, used approximate the covariance. Since the projection from 3D to 2D is non-invertible, this identity does not hold.
23

---

Figure 7: Generalized kernal Function.
Table 5: Timings. We compare the training and inference time of our method with that of Scaffold-GS 9). evaluating both with and without proposed densification strategy. for the "Train" scene in Tanks& T dataset (54).
Train
Ours
Ours
Scaffold-GS (9)
Scaffold-GS
Metrics
Method
wo V max
W max
wo max
w V max
PSNR t #Anchor(k) +
23.56
23.76
22.77
22.89
393.8
584.4
353.3
520.0
Training Time 4
26 minutes 80
32 minutes
24 minutes 88
29 minutes
Rendering FPS 1
75
79
B.5
More Details of SAP-Ges
In this paper, we extend the generalized Gaussian kernel:
Ges (2; p4, Σ) = e- (²)) M(x) E [0,
(25)
Its illustration is shown in the first row of Fig. For 3DGS, its pixel radius is 3λ, where À is the largest eigenvalue of the covariance matrix, which corresponds to the major axis. To ensure that (3X,
< 9, 3DGS imposes a condition on the covariance matrix ΣS, This condition guarantees that the squared Mahalanobis distance for the point (3\, 0) is less than or equal to 9, ensuring that the distance function does not exceed certain threshold. To ensure that the distance value is less than 9, we take the radius of the generalized Gaussian kernel as 31/PA, The specific formula is:
(3UPAx0)">>> Σ "-1T,)0>>~~3311000 (3VPA.))) P 9.
(26)
When p > 1, the generalized Gaussian kernel is more compact than the Gaussian kernel. When p the radius of the generalized Gaussian kernel becomes larger.
B.6 Experiments on Computational Resources
Our method shares a rendering pipeline that is highly similar to 3DGS (6), so the training and rendering times are approximately equivalent given the same number of primitives. However, because of potential differences in the gradients produced by our method compared to the original one, different numbers of points may generated under the corresponding densification strategies. While the number of points is approximately proportional to the computation time, our method demonstrates superior rendering quality under a comparable point count. We report the training and rendering overhead of our method and the baseline under two different densification strategies, as shown in Table 5
B.7 View-dependent Gaussian Attribute Decoding
We visualized our Gaussian attribute decoder, as shown in Fig. 8 Specifically, we uniformly sampled directions on the sphere and used these as input to the decoder, obtaining the corresponding decoded attributes for each direction. We visualized properties such color, opacity, rotation, and scale. As
24

---

-12
(a) Color
(b) opacity
(c) rotation
(d) scale
Figure 8: View-dependent Gaussian attribute decoding. We uniformly sample directions the
sphere to evaluate the performance our attribute decoder.
Table Comparison of different kernels. We compared different parameter designs SAP-Ges.
SAP-Ges(p 2)
SAP-Ges(p 0.5)
SAP-Ges(Plearnable) MMmm
SAP-Gaussian(p 1) PSNR1 Mem, FFPSt
PSNR1 /Mema
PSNRt/ Mem/ /FST
24.65 124.61 / 90 24.43 86.83 70
24.52 99.89. 76
25.04 / 103.53 / 82
illustrated, our decoder maintains degree of continuity across adjacent viewpoints while exhibiting anisotropic characteristics.
B.8 More Ablation on Kernels
We conducted experiments on SAP-Ges with different parameter settings, the Tenks&Temples Dataset (54), T
2: This produces a more compact kernel than the Gaussian, resulting in more points and higher memory usage, but faster rendering.
0.5: This leads wider kernel range with fewer points and the lowest memory consumption. However, rendering is the slowest because of large Gaussian extents.
Learnable p: The results lie between the above two. We attribute this the challenge of finding an optimal learning rate for p.
Gaussian kerne (p 1): This setting achieves the best rendering performance with good trade-off between memory and speed.
B.9 Additional Results
Here we list the error metrics used in our evaluation across all methods and scenes considered, as shown in Tab. 7
25

---

Table Quantitative evaluation of rendering efficiency per scene Mip-NeRF3603)
PSNR trechill
bicycle
flowers
garden
stump
counter
kitchen
bonsai
Avg.
Mip-NcRF360
24.40
21.64
26.94
26.36
22.81
31.40
29.44
32.02
33.11
27.57
3D-GS (6
25.18
21.48
27.24
26.62
22.45
31.49
28.98
31.35
32.10
27.43
2D-GS 7
24.82
20.99
26.91
26.41
22.52
30.86
28.45
30.62
31.64
27.03
StopThhPPpp |I]
25.20
21.50
27.16
26.69
22.43
30.83
28.59
31.13
31.93
27.28
Scaffold-GS (9]
24.81
21.42
27.17
26.27
23.08
31.93
29.34
31.30
32.70
27.55
DisC-GS (58)
28.01
3DGS-MCMC (39
25.67
22.09
27.65
27.47
23.2
32.32
29.26
31.82
32.54
28.00
SAP(Ours)
25.26
21.48
27.48
26.76
23.02
32.88
29.94
31,90
33.73
28.05
SSIM treehill
bicycle
flowers
garden
stump
room
counter
kitchen
bonsai
Avg.
Mip-NeRF360
0.693
0.583
0.816
0.746
0.632
0.913
0.895
0.920
0.939
0.793
3D-GS
0.763
0.603
0.862
0.772
0.632
0.917
0.906
0.925
0.939
0.814
2D-GS
0.731
0.573
0.845
0.764
0.630
0.918
0.908
0.927
0.940
0.804
StopThePop
0.767
0.604
0.862
0.775
0.635
0.917
0.903
0.925
0.939
0.814
Scaffold-GS
0.725
0.587
0.842
0.784
0.644
0.925
0.914
0.928
0.946
0.810
DisC-GS
0.833
3DGS-MCMC
0.784
0.609
0.866
0.810
0.665
0.934
0.921
0.937
0.950
0.831
SAP(Ours)
0.758
0.631
0.875
0.780
0.707
0.945
0.915
0.939
0.962
0.835
LPIPS
bicycle
flowers
garden
stump
trechill
counter
kitchen
bonsai
Avg.
Mip-NeRF360
0.289
0.345
0.164
0.254
0.338
0.211
0.203
0.126
0.177
0.234
3D-GS
0.213
0.338
0.109
0.216
0.327
0.221
0,202
0.127
0.206
0.217
2D-GS
0.271
0.378
0.138
0.263
0.369
0.214
0.197
0.125
0.194
0.239
StopThePop
0,206
0.335
0.107
0.210
0.319
0.216
0,200
0.126
0.202
0.213
Scaffold-GS
0,256
0.359
0.146
0.284
0.338
0.202
0.191
0.126
0.185
0.233
DisC-GS
0.189
0.202
0.246
0.112
0.194
0.300
0.181
0.174
0.114
0.176
0.188
SAP(Ours)
0.227
0.314
0.123
0.248
0.305
0.173
0.192
0.123
0.169
0.208
26

---

Table 8: Quantitative evaluation of rendering efficiency per scene in Tanks
& Temples Dataset (44 and Deep Blending 55
PSNR
Truck
Train
Avg.
Dr Johnson
Playroom
Avg.
Mip-NeRF360
24.91
19.52
22.22
29.14
29.66
29.40
3D-GS
25.39
22.04
23.71
29.06
29.86
29,46
2D-GS
22.96
29.49
StopThePPp
24.93
21.48
23.21
29.42
30.31
29.86
Scaffold-GS
25.89
22.48
24.19
29.73
30.83
30.28
DisC-GS
24.96
30.42
26.11
22.47
24.29
29.00
30.33
29.67
SAP(Ours)
26.31
23.76
25.04
29.62
30.41
30.02
SSIM
Truck
Train
Avg.
Dr Johnson
Playroom
Avg.
Mip-NeRF360
0.857
0.660
0.758
0.901
0.900
0.900
3D-GS
0.878
0.813
0.845
0.898
0.901
0.900
2D-GS
0.825
0.899
StopThePop
0,878
0,808
0.843
0.903
0.905
0.904
Scaffold-GS
0.885
0.822
0.854
0.910
0.907
0.909
DisC-GS
0,866
0.907
3DGS-MCME
0.890
0.830
0.860
0.890
0.900
0.895
SAP(Ours)
0.905
0.835
0.870
0.908
0.911
0.910
LPIPS|
Truck
Train
Avg.
Dr Johnson
Playroom
Avg.
Mip-NeRF360
0.159
0.354
0.257
0.237
0.252
0.245
3D-GS
0.148
0.208
0.189
0.247
0.246
0.247
2D-GS
0.217
0.259
StopThePop
0.142
0.204
0.173
0.234
0.235
0.234
Scaffold-GS
0.143
0.204
0.174
0.235
0.242
0.239
DisC-GS
0.120
0.199
ADGSSMCME
0.140
0.240
0.190
0.330
0.310
0.320
SAP(Ours)
0.114
0.175
0.145
0.228
0.244
0.236
27


Reviews:
[{"review_id": "nXME5Csnhz", "reviewer": "Reviewer_zbg4", "summary": "This paper addresses the problem of depth-sorting inaccuracies in 3D Gaussian Splatting. Depth-sorting inaccuracies cause popping artifacts and rendering inconsistencies due to overlapping anisotropic Gaussians. The paper proposes Screen-Aligned Primitives (SAP) as a solution. SAP generates per-view, plane-parallel primitives to eliminate per-pixel overlap errors and enables exact sorting without additional computational cost. The design is supported by a 3D-consistent decoder and flexible kernel choices. It is validated through comprehensive experiments, which show improved rendering quality and real-time performance.", "questions": "1. How does the proposed screen-aligned primitive design handle highly complex geometry or scenes with strong non-Lambertian appearance, where local shape details or view-dependent reflections may challenge the planarity and directional consistency assumptions? More experiments and discussion are needed to clarify how the method performs for materials with transparent or semi-transparent properties, which may not be well approximated by a single opaque plane.\n2. Could the authors discuss how the method performs in scenes with large depth ranges or multiple layers of fine occlusion, where a single global sorting order may not fully resolve local ordering conflicts?\n3. Clarify how the maximum-gradient densification strategy deals with noisy regions or high-frequency texture boundaries, and whether it risks adding unnecessary primitives that increases computation without clear quality benefits.\n4. Please provide more information on training and inference memory usage, runtime cost, and possible trade-offs between sorting precision.", "limitations": "The paper discusses the main limitations and outlines possible directions for future improvement.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n-- The proposed approach is intuitive and easy to understand. Introducing screen-aligned primitives allows per-pixel ordering with low computational cost, which well addresses the depth-sorting issue in 3D Gaussian Splatting. \n\n-- The method is compatible with existing frameworks and supports flexible kernel designs without projection bias. \n\n-- Experimental results on several benchmarks show that the method improves rendering quality and consistency compared to related baselines.\n\n\nWeaknesses:\n\n-- The method assumes that all primitives can be well approximated as screen-parallel slices. This may not be always true, limiting its adaptability to highly complex or non-Lambertian scenes. \n\n-- The current design focuses mainly on radial basis kernels and does not yet explore asymmetric or more diverse kernel shapes. Some implementation details, such as potential trade-offs between sorting precision and densification cost, could be elaborated further.", "was_revised": true, "final_justification": "After reading the authors' rebuttal and the comments from other reviewers, I am basically positive about the paper.  Thus my assessment maintains the original rating: BA.", "rebuttal": "We thank the reviewer for the valuable comments. Below is our supplementary response to the reviewer’s concerns.\n\n# Q1. How does SAP handle highly complex geometries or scenes with strong non-Lambertian appearances, where local shape details or view-dependent reflections may challenge the assumptions of planarity and directional consistency?\n\nThis is indeed a representative and potentially misleading concern for readers. We address your concern regarding the “screen-aligned slicing” assumption from both experimental and theoretical perspectives:\n\n**1. Theoretical Analysis:**\n\nAt the microscopic level, the primitives we construct are all aligned with the screen. However, in practice, our method is an unstructured **primitive-based representation that conceptually resembles a hybrid between neural rendering and explicit anchor-based primitives**, rather than relying solely on explicit geometry to fit object surfaces. Instead of modeling object surfaces with complex geometric primitives, **our approach represents appearance through the collective blending of a large number of simple, planar primitives during rendering.** For example, a complex curved surface is not modeled by a single curved primitive, but rather emerges from the layered and aggregated contributions of thousands of flat primitives. As a result, the overall representational capacity of the model far exceeds the limitations of any single primitive's shape.\n\nThis is analogous to how 2D images are composed: although each pixel is a simple square, a high-resolution image can express complex structures and details through dense sampling. Similarly, our primitives serve as the minimal representational units in 3D space. In regions with intricate geometry, our SAP and adaptive density control module automatically allocate a large number of primitives to ensure sufficient coverage and accurate appearance modeling. As illustrated in **the point distribution visualization in Appendix Table 4**, dense clusters of small primitives are concentrated in geometrically complex regions.\n\n**2. Experimental Validation:**\n\nThe datasets we selected are **among the most commonly used and challenging benchmarks in this field.** The qualitative results we present already cover the two types of scenarios mentioned by the reviewer. For instance, **the first row of Figure 3 in the main paper showcases a flowerbed and grassy area, which represent scenes with high-frequency textures and complex geometries. Additionally, the sixth row illustrates the truck's window glass — not only are we able to reconstruct the transparent glass surface, but we also faithfully reproduce the reflections on it.** Our method accurately fits these regions and consistently demonstrates superior visual quality compared to the baseline. To further address the reviewer’s concern, we additionally include experiments on the NeRF-Synthetic dataset, which **contains several scenes with strong non-Lambertian effects**. In particular, the Mic, Materials, and Drums scenes exhibit complex view-dependent reflections and specularities. The supplementary experimental results are presented below.\n\n| Scene     | PSNR  | SSIM  | LPIPS  |\n|-----------|-------|-------|--------|\n| mic       | 36.75 | 0.991 | 0.009  |\n| materials | 30.37 | 0.954 | 0.051  |\n| drums     | 26.31 | 0.945 | 0.049  |\n\n\n# Q2. How does the proposed method perform in scenes with large depth ranges or complex multi-layer occlusions, where a single global sorting order may not fully resolve local visibility conflicts?\n\nOur method performs robustly even in scenes with large depth ranges and intricate multi-layer occlusions. It is important to clarify that the \"single global sorting\" we refer to is a one-time global sorting performed during rendering. Our approach does not maintain a static point cloud; rather, **it dynamically generates neural primitives based on the rendering viewpoint, neural network outputs, and explicit anchors.** In other words, the primitives representing the same scene vary across different viewpoints.\n\nMoreover, our primitives are zero-thickness planar slices aligned with the screen, so **sorting them requires no complex handling of volumetric overlaps.** The occlusion relationships are dynamically determined by the rendering viewpoint and depth sorting during rendering, rather than by fixed geometric topology. This dynamic mechanism enables our method to handle local visibility conflicts effectively, even in challenging scenarios with fine occlusions and large depth variations.\n\nFor example, **the fifth row in Figure 3 (the train scene) provides a clear illustration. It contains both distant background elements (the sky) and nearby complex structures (the train)**. If we focus solely on the anchors without considering our rendered primitives, due to the adaptive density control, the anchors in **the sky region are relatively sparse, whereas the foreground train and the gravel road exhibit densely distributed anchors**. These explicit anchors collectively form a coarse geometric structure of the scene.\n\nEach anchor maintains a local neural rendering field. When rendering from a specific viewpoint, these anchors generate corresponding view-dependent planar primitives, which are then globally sorted once to produce correct geometry, appearance, and consistent occlusion relationships. In contrast, prior methods—as illustrated in our Figure 1—**handle overlapping primitives by relying solely on the depth of their centers for ordering.** This approach leads to ambiguous and inconsistent depth relationships across different pixels when primitives overlap.\n\n# Q3. Clarification on the Maximum Gradient Densification Strategy Regarding Noise and High-Frequency Boundaries\n\nThis is an excellent question and lies at the core of much ongoing research on 3DGS densification. We attribute the issue to the gradient-based densification methods currently used, which **tend to suffer from gradient vanishing problems in complex scenes**, as noted in works like Pixel-GS and ABS-GS. \nIn our method, we observe that in certain challenging scenarios (e.g., noisy regions), **the shapes of rendered primitives vary significantly across different directions.** As demonstrated in Appendix Figure 6(d) and supported by the Pixel-GS paper, the sizes of Gaussians can differ depending on the viewpoint, leading to large discrepancies in gradient magnitudes from different directions. Averaging these gradients often suppresses the high-gradient signals from certain viewpoints, causing densification to fail in those critical regions. **By considering the maximum gradient instead of the average**, our approach effectively mitigates this problem, **enabling more reliable densification in areas with strong directional variation in gradient signals**. \n\n**Balancing Densification and Computational Cost:**\nWe present additional experimental results in **Appendix Figure 5** to illustrate this trade-off. As shown, when the number of primitives is relatively low, increasing the number of points correlates almost linearly with improved rendering quality. However, **beyond a certain threshold, further increasing the number of primitives no longer yields noticeable gains in quality.** We further supplement **our analysis with additional comparisons of densification levels in terms of computational cost, memory usage, and training and inference overhead.** We conducted experiments on the train scene of the Tank & Temple dataset, with all tests performed on a single NVIDIA L40S GPU. Here, SAP num denotes the average number of SAP primitives involved in rendering per viewpoint, while anchor refers to the total number of scene anchors.\n\n| PSNR  | SSIM  | LPIPS | SAP num (k) | FPS     | Training Time (min) | Anchor (k) | Memory (MB) |\n|-------|-------|-------|-------------|---------|---------------------|------------|-------------|\n| 23.54 | 0.841 | 0.168 | 1693        | 53.89   | 1530                | 957        | 284.84      |\n| 23.56 | 0.840 | 0.162 | 1020        | 88.20   | 18.95               | 555        | 165.22      |\n| 23.52 | 0.838 | 0.178 | 789         | 98.95   | 16.60               | 392        | 116.74      |\n| 23.31 | 0.828 | 0.188 | 679         | 109.66  | 15.85               | 313        | 93.14       |\n| 23.12 | 0.823 | 0.207 | 588         | 117.00  | 15.95               | 270        | 80.28       |\n\nFrom the table, it can be observed that increasing the number of primitives significantly improves reconstruction performance when the count is low. However, **beyond a certain threshold, further increases yield diminishing returns.** Regarding **training and inference time costs, these scale roughly proportionally with the average number of SAP primitives per viewpoint**, since the primary computational expense lies in the forward and backward passes during rendering, which are performed per primitive. As for **storage costs, they scale proportionally with the number of anchors**, which also influence the number of SAP primitives generated. \n\nRegarding the trade-off between computational cost and performance, this is often closely tied to hyperparameter choices in 3DGS-based methods. As shown in Appendix Figure 5, **improving the densification strategy can lead to better reconstruction quality under the same computational budget.**\n\n\n>  Zhang, Z.; Hu, W.; Lao, Y.; He, T.; Zhao, H. Pixel GS: Density control with pixel-aware gradient for 3D Gaussian splatting. \\\n> Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. 2021. Nerf: Representing scenes as neural radiance fields for view synthesis."}, {"review_id": "xROIfcW4e0", "reviewer": "Reviewer_F3jw", "summary": "The paper introduces Screen-Aligned Primitives (SAP) to improve 3D Gaussian Splatting rendering. The primary issue with 3DGS is \"popping artifacts\" caused by an inaccurate sorting of primitives that doesn't account for their thickness and overlapping regions. To solve this, the authors propose a method that generates primitives constrained to be parallel to the image plane for any given viewpoint. Because all primitives are parallel, a single global depth sort becomes sufficient to achieve a correct per-pixel rendering order, fundamentally eliminating the sorting problem without extra computational cost. The framework uses a neural decoder to generate these view-specific 2D primitives conditioned on anchor features and viewing direction, which allows for an error-free projection and the use of more flexible rendering kernels.", "questions": "- The ablation study in Table 2 shows a curious inconsistency where Screen-Aligned Primitives improve PSNR over the baseline, yet score worse on SSIM and LPIPS in most intermediate configurations, which warrants a deeper analysis of the qualitative trade-offs between the two representations. \n\n- To better understand the method's generalization capabilities, a robustness study would be valuable, such as evaluating performance with sparser input views, especially given the framework's similarity to multi-plane image rendering which can be sensitive to training data density.", "limitations": "See questions and weakness.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n+ The paper is well-motivated and clearly written, making its contributions easy to understand. \n+ The core idea of using Screen-Aligned Primitives is straightforward and intuitive. \n+ This approach is conceptually similar to multi-plane image (MPI) based rendering, providing a strong rationale for why it effectively eliminates overlap artifacts and allows for a simple, global sorting pass.\n\nWeakness:\nThe method's strong similarity to multi-plane image (MPI) based rendering suggests a potential limitation, common to such approaches, which is its dependency on the training data's density and distribution. The framework's performance is likely to be strongest when rendering novel views that are interpolated between the dense viewpoints seen during training. However, in the qualitative results, authors did not illustrate the distribution of training and testing views, the video demos in supp are also rendered from simply trajectories. Similarly, the approach may struggle if the training data itself is sparse, as the multiplane-based representation might not generalize well across large, unseen gaps between viewpoints. The paper does not fully investigate these challenging scenarios.", "was_revised": true, "final_justification": "Authors rebuttal addressed most of my concerns. Given the experiment results I do think this is an insightful improvement of 3DGS/2DGS. I'm raising my score to BA.", "rebuttal": "We thank the reviewer for the valuable comments.\n\n# Q1. Comparison with Multi-Plane Image (MPI)-based Rendering Models and Robustness under Sparse Viewpoints.\nRegarding the reviewer's concern about the quality of view synthesis under sparse viewpoints, we clarify this issue from both theoretical and experimental perspectives as follows:\n1. **Theoretical Analysis:**\n\nThe MPI method is less capable of supporting observations from the side or back relative to the reference views. In contrast, SAP does not rely on selected reference views but instead **models the entire 3D space in an equitable manner, thereby enabling observations from test viewpoints far from the training viewpoints. Meanwhile, SAP uses explicit anchors to represent the scene, which endows it with relatively clear geometric properties. The planes here serve more as appearance textures.** \n\nFurthermore, although both MPI and SAP represent 3D space with primitives parallel to the camera image plane during modeling, they differ in key aspects. **MPI is a dense volumetric representation, incurring high memory overhead, whereas SAP is an adaptively optimized sparse representation with lower memory usage.** Additionally, **the number of depth layers in MPI is a manually set hyperparameter**, lacking sufficient flexibility to fit the true continuous 3D space. In contrast, the **adaptive splitting and pruning mechanism** of SAP allows it to learn an appropriate complexity and continuously varying attributes, thereby fully representing the target scene.\n\n2. **Experimental Validation:**\n\nAddressing the reviewer's concern regarding robustness under sparse viewpoints, we recognize this as a highly valuable research area, with numerous 3DGS-based works already making improvements in this regard. For 3DGS-based methods, we believe that dense viewpoints significantly benefit the reconstruction process. Additionally, we supplement here with experiments to demonstrate that **our primitive framework does not compromise performance in reconstructing sparse viewpoints (compared to previous methods), even without specific optimization for sparse viewpoints**.\n\nAll the following experiments were conducted using a single L40S GPU. We performed experiments on the Tanks & Temples dataset. Specifically, we followed **the original training and test set splits, then used 12.5%, 25%, 50%, and 100% of the training viewpoints for reconstruction, respectively, and tested using all test viewpoints**. The experimental results are shown in the table below. Our experiments indicate that our method outperforms our baseline even when the number of viewpoints is significantly reduced.\n\n| Training view ratio   | Method           | psnr   | ssim   | lpips  |\n|--------------|---------------|--------|--------|--------|\n| 12.50%       | 3dgs          | 13.57  | **0.479**  | **0.485**  |\n|              | scaffold-gs   | 13.62  | 0.418  | 0.486  |\n|              | **SAP(ours)**   | **13.84**  | 0.448  | 0.508  |\n| 25%          | 3dgs          | 16.05  | **0.574**  | **0.397**  |\n|              | scaffold-gs   | 16.22  | 0.553  | 0.422  |\n|              | **SAP(ours)**   | **16.44**  | 0.568  | 0.419  |\n| 50%          | 3dgs          | 22.04  | 0.803  | 0.199  |\n|              | scaffold-gs   | 22.46  | 0.808  | **0.193**  |\n|              | **SAP(ours)**   | **22.61**  | **0.809**  | 0.203  |\n| 100%         | 3dgs          | 23.82  | 0.853  | 0.169  |\n|              | scaffold-gs   | 24.14  | 0.859  | 0.163  |\n|              | **SAP(ours)**   | **24.97**  | **0.867**  | **0.151**  |\n\nAdditionally, regarding the reviewer's comment on the similarity between our method and MPI—specifically, that favorable results are often obtained only when testing viewpoints lie between training viewpoints—we acknowledge this as a critical research issue and a well-known pain point in current reconstruction methods. To address this, we conducted supplementary experiments.\n\nAs the reviewer anticipated, **the performance is significantly better when test viewpoints fall within the interpolation range of training viewpoints compared to the extrapolation range. We further found that this limitation is common to all 3DGS-based methods. Even so, our method still outperforms previous approaches under such conditions.**\n\nThe experimental results are presented below. We conducted experiments on the train scenes of the Tanks & Temples dataset, where the numbers in parentheses following the percentages indicate the number of training viewpoints. **\"Interpolation\"** refers to test viewpoints lying within the interpolation range of training viewpoints, and **\"Extrapolation\"** refers to those in the extrapolation range. Our division criterion is: a test viewpoint is categorized as \"Interpolation\" if it lies within the convex hull formed by any two training viewpoints.\n\n| Training view ratio   | Method        | Interpolation |        | Extrapolation |        | ALL |        |\n|:----------------------:|:-------------:|:--------------:|:------:|:--------------:|:------:|:-----:|:------:|\n|                |             | views                 | psnr   | views                 | psnr   | views       | psnr   |\n| 12.5%（32）    | **SAP(ours)**      | 12                    | **19.15**  | 25                    | 9.71   | 37          | **12.77**  |\n|                | Scaffold-GS | 12                    | 18.92  | 25                    | 9.16   | 37          | 12.33  |\n|                | 3DGS | 12                    | 17.93  | 25                    | **9.81**   | 37          | 12.44  |\n| 25%（65）      | **SAP(ours)**       | 16                    | **22.51**  | 21                    | **10.01**  | 37          | **15.42**  |\n|                | Scaffold-GS | 16                    | 22.18  | 21                    | 9.99   | 37          | 15.26  |\n|                | 3DGS | 16                    | 21.51  | 21                    | 9.95   | 37          | 14.95 |\n| 50%（131）     |**SAP(ours)**      | 37                    | **20.58**  | 0                     | 0      | 37          | **20.58**  |\n|                | Scaffold-GS | 37                    | 20.50  | 0                     | 0      | 37          | 20.50  |\n|                | 3DGS | 37                    | 20.01  | 0                     | 0      | 37          | 20.01  |\n| 100%（263）    | **SAP(ours)**       | 37                    | **23.66**  | 0                     | 0      | 37          | **23.66**  |\n|                | Scaffold-GS | 37                    | 22.48  | 0                     | 0      | 37          | 22.48  |\n|                | 3DGS | 37                    | 22.02  | 0                     | 0      | 37          | 22.02  |\n\n\n# Q2.Clarification on SAP's performance in terms of PSNR, SSIM, and LPIPS metrics.\n\nTheoretically, our method is a **pixel-level hybrid approach**, meaning that rendering is achieved by stacking and blending numerous small local planes. This inherently makes it well-suited for pixel-wise comparison metrics like PSNR, and our method is also optimized based on **MSE loss**. Our research has found that in most cases, PSNR and SSIM are positively correlated. However, since our method is a pixel-blending approach, it does not maintain a static point cloud. Instead, it dynamically generates planar primitives according to the rendering viewpoint and then performs pixel-level alpha-blending, which is naturally suitable for the PSNR metric.\n\nAt the same time, because our method uses **dynamic view-dependent primitives**, **edge and other structural information in the scene may be damaged under some special viewpoints, resulting in lower SSIM.** In conclusion, for our primitive-blending model, which is not a specific 3D structure, a small three-dimensional object in space may be formed by the blending of a large number of primitives. **This method, when the primitive density is high enough and the distribution is reasonable — that is, our final scheme (with maximum densification) — will achieve the best performance.** When the density is insufficient, they cannot blend to form sufficiently detailed structural information.\n\nWe have also observed that for metrics such as LPIPS, improvements in densification often lead to better performance. This finding is consistent with the conclusions drawn in Pixel-GS. We speculate that more primitives can enhance the overall visual perception; however, they may simultaneously introduce subtle pixel-wise differences. A close look at **the last image in the first row of Figure 3** reveals that when zoomed in, there are indeed some pixel-level errors, but it remains the best in terms of overall human visual perception. Our ablation study in Table 2 also shows that **the maximum densification method can effectively improve the LPIPS metric across all approaches**. We have supplemented additional experiments on the train scenes of the Tanks & Temples dataset here.\n\n| psnr   | ssim   | lpips  | SAP num(k) | \n|--------|--------|--------|------------|\n| **23.54**  | **0.841**  | **0.168**  | **1693**       | \n| **23.56**  | **0.840**   | **0.162**  | **1020**       | \n| 23.52  | 0.838  | 0.178  | 789        |\n| 23.31  | 0.828  | 0.188  | 679        |\n| 23.12  | 0.823  | 0.207  | 588        |\n\nThe experiments here demonstrate that when the densification process is improved—most simply by **increasing the number of primitives—the LPIPS metric shows a more significant improvement.** This is consistent with the results of our ablation study in Table 2.\n\n>  [1] Z.Zhang, W.Hu, Y.Lao, T.He, and H.Zhao, “Pixel-gs: Density control with pixel-aware gradient for 3d gaussian splatting,” in European Conferenceon Computer Vision.  \\\n>  [2] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics 42(4) (2023) \\\n> [3] Tao Lu, Mulin Yu, Linning Xu, Yuanbo Xiangli, Limin Wang, Dahua Lin, and Bo Dai. Scaffold-gs: Structured 3d gaussians for view-adaptive rendering."}, {"review_id": "2oDcey4xUh", "reviewer": "Reviewer_WHxg", "summary": "Overall, this submission focuses on addressing the popping artifects in 3D-GS. It proposes to deal with this via following Scaffold-GS's anchor-based pipeline and further guiding the generation of screen-aligned primitives.", "questions": "Overall, the reviewer currently votes for borderline accept while he still has the following concerns.\n\n1. The authors propose to use parallel thin slice instead of 3D Gaussians as their primitives and show some appealing properties of this choice. Despite this, intuitively, parallel thin slices can still be regarded as primitives that has less representation freedom than 3D Gaussians. The reviewer is interested to see more discussion from this perspective.\n\n2. For example, one potential disadvantage of parallel thin slices can be that their multi-view inconsistency. While the authors claim here and there that they use a \"3D-consistent\" decoder. The reviewer is still a bit confused about how 3D (multi-view) consistency can be guaranteed for parallel thing slices. The authors are appreciated to theoretically (or at least emphrically) explain this part.\n\n3. In the related works, the authors mention that those methods in the early stage ([44, 45]) do not suffer from popping artifacts. Considering this, the authors are appreciated to better discuss, why such ideas cannot be directly incorporated into the recent 3DGS framework to handle popping artifacts?\n\n4. In line 129, the \"this\" in \"to overcome this limitation\" seems to point to nowhere.\n\n5. in Section 4.1, the authors mention that they decide to use SH for encoding. Yet, one typical problem in SH can be there parameter demanding property (e.g., when used to represent color for Gaussian kernels in 3D-GS). In this case, the reviewer is wondering if the usage of SH in this method's context also suffer it from high memory overhead?\n\n6. In line 167, the authors mention that the activation is \"such as ReLU\". Such ambiguity is not good for reproduction and thus authors are thus suggested to make this part more clear.\n\nIn summary, the reviewer currently votes for borderline accept for this submission while still holding the above concerns.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n\nThis submission is easy to follow. Meanwhile, the reviewer also feels that the methods proposed hold their merits.\n\nWeaknesses:\n\n(See the questions section for more details).", "was_revised": true, "final_justification": "After reading the rebuttal, I believe that my concerns are largely solved. I thus keep my positive rating. Especially, I believe that the authors explain their intuition more clearly in their response to Q1 and I highly suggest the camera-ready to be edited based on this answer to better show the merit of the paper.", "rebuttal": "We thank the reviewer for the valuable comments. Below is our supplementary response to the reviewer’s concerns.\n\n# Q1. Discussion on the Representational Capacity of SAP Compared to 3D Gaussians\n\nThis is an excellent question and, in fact, one of the core insights that directly motivated our initial idea. Our baseline, Scaffold-GS, is a neural network-driven approach that generates a set of 3D Gaussians for each individual viewpoint. In other words, the 3D primitives are generated dynamically per view, and are different for each camera pose.\n\nThis led us to a key observation: **if we are generating entirely different primitives for every view, and each viewpoint only observes one face of the 3D Gaussian, then why do we need a full 3D representation in the first place?** This insight inspired us to explore using 2D primitives instead.\n\nCompared to surface-aligned 2D Gaussians, which still possess 3D degrees of freedom and can **suffer from overlapping and blending artifacts**, our view-aligned planar primitives offer a more constrained yet more targeted representation. Since **the rendering viewpoint is fixed per frame, this effectively fixes one axis of rotation.** Therefore, using planar primitives aligned with the view direction **not only simplifies depth sorting but also makes more efficient use of the viewpoint direction as an input to the neural network.**\n\n# Q2. Clarification on How 3D (Multi-View) Consistency Is Ensured with SAP\n\nFrom an architectural perspective, our method is composed of a 3D decoder and a SAP (Screen-Aligned Primitive) renderer. The **3D (multi-view) consistency is primarily ensured by the 3D decoder,** which encodes scene content in a consistent volumetric space.\nAs illustrated in Appendix Figure 6, **we visualize the decoded attributes of SAPs across multiple views.** It can be seen that, thanks to the 3D decoder, the attributes of the generated primitives exhibit strong continuity across different viewpoints. In fact, **for a given SAP ID, its projections in different views demonstrate high consistency in both spatial location and appearance, even though their orientations vary with the view.**\n\nThis can also be interpreted from another perspective: **the underlying neural field implicitly defines a complex, view-agnostic primitive function in 3D space. Each viewpoint observes only a “slice” of this function, which we approximate as a 2D Gaussian. We do not need to explicitly reconstruct the full 3D geometry of this function — instead, we extract only the per-view 2D shape necessary for rendering.**\n\nIn this design, **the SAP primitives primarily serve as carriers of texture and appearance**, effectively bridging the gap between implicit neural rendering and explicit, structured primitive-based rendering. \n\nAt the microscopic level, the primitives we construct are all aligned with the screen. However, in practice, our method is an unstructured **primitive-based representation that conceptually resembles a hybrid between neural rendering and explicit anchor-based primitives**, rather than relying solely on explicit geometry to fit object surfaces. Instead of modeling object surfaces with complex geometric primitives, **our approach represents appearance through the collective blending of a large number of simple, planar primitives during rendering.** For example, a complex curved surface is not modeled by a single curved primitive, but rather emerges from the layered and aggregated contributions of thousands of flat primitives. As a result, the overall representational capacity of the model far exceeds the limitations of any single primitive's shape.\n\nIn addition, Figure 3 in our main paper demonstrates reconstructions on a variety of challenging scenes, and **our supplementary material further provides 3D visualizations along continuous camera trajectories.** These results effectively validate the 3D consistency of our approach in practice. We additionally include experiments on the NeRF-Synthetic dataset, which **contains several scenes with strong non-Lambertian effects**. In particular, the Mic, Materials, and Drums scenes exhibit complex view-dependent reflections and specularities. The supplementary experimental results are presented below.\n\n| Scene     | PSNR  | SSIM  | LPIPS  |\n|-----------|-------|-------|--------|\n| mic       | 36.75 | 0.991 | 0.009  |\n| materials | 30.37 | 0.954 | 0.051  |\n| drums     | 26.31 | 0.945 | 0.049  |\n\n\n# Q3. Why can't traditional methods be applied to mitigate popping artifacts in 3D Gaussian Splatting (3DGS)?\n\nThere exists a **fundamental difference between Voltx[44] and 3DGS** in terms of their mechanisms and suitability for handling popping artifacts, which stems from the essential differences in their **data representations and rendering logic**:\n\n**Voltx** is designed for continuous, regularly structured volumetric data. It partitions space using **uniform thin slices** and leverages **3D texture hardware interpolation** to enable smooth sampling. Colors and opacities are composited layer by layer in a **back-to-front** manner. The key to mitigating popping artifacts in Voltx lies in its **“uniform discretization of continuous fields”** — with **fixed inter-slice distances** and **interpolable information**, the sampled results across neighboring frames **transition smoothly**. This approach is well-suited for rendering **structured volumetric data** such as **CT and MRI scans**.\n\nIn contrast, **3DGS** represents the scene as a large set of **independent 3D Gaussian primitives**, and the final rendering is a **2D accumulation of their projections**. Popping artifacts in 3DGS are primarily caused by **visibility discontinuities** (i.e., sudden appearance/disappearance of Gaussians) or **attribute discontinuities** (i.e., abrupt changes in projected size or shape). Since Gaussians are **discrete primitives**, they cannot benefit from **“partial inclusion in a slice”** to achieve smooth transitions, as voxels do.\n\nTherefore, **Voltx’s continuous layer-based strategy cannot be directly applied to the discrete nature of 3DGS**. While Voltx addresses **discontinuities arising from coarse sampling** in continuous fields, 3DGS requires solutions tailored to **discontinuities in discrete dynamic elements**. These are **fundamentally different problems** requiring **distinct approaches**.\n\n# Q4. What specific limitation does \"this\" refer to in line 129? The antecedent is unclear.\n\nWe agree that starting the section with “To overcome this limitation” without a clear prior mention may confuse readers. We will revise this sentence to explicitly state that **the limitation refers to the popping artifacts of Gaussian primitives and inaccuracies in their sorting order, thereby improving clarity.**\n\n# Q5. Does the use of spherical harmonics (SH) in our method introduce high memory overhead?\n\nIt is important to clarify that we employ **hard-coded spherical harmonics (SH)**, meaning that the directional information is lifted via **mathematical formulas**, introducing only **a few dozen additional variables**, which is **negligible in terms of memory overhead**. Meanwhile, when using SH encoding, we **adjust the input dimensionality** of the neural network, which results in a **slight change in memory usage**. However, in practice, the **majority of memory consumption** comes from storing the **anchor point cloud**. Below, we provide a **comparison of the memory usage** between the MLP and the point cloud components across different methods.\n\n| Method | Anchor Num (k) | Anchor Mem (MB) | Network (MB) |\n|--------|----------------|------------------|---------------|\n| No SH  | 114.65         | 385.3            | 0.05          |\n| SH     | 114.33         | 384.2            | 0.05          |\n\nFrom the table, it can be seen that the **storage mainly depends on the number of anchors**, and is **almost unaffected by whether spherical harmonics encoding is used**.\n\n# Q6. Clarification on Activation Function (Line 167)\n\nThank you for pointing this out. We acknowledge that the phrase \"such as\" here may cause misunderstanding. In fact, we use **ReLU** as the activation function for all intermediate layers in the network. More detailed network architecture is provided in **Appendix B.3** for readers to reproduce our work. We commit to revising this in the final version of the paper and releasing the source code to facilitate further reproducibility.\n\n> Tao Lu, Mulin Yu, Linning Xu, Yuanbo Xiangli, Limin Wang, Dahua Lin, and Bo Dai. Scaffold-gs: Structured 3d gaussians for view-adaptive rendering. \\\n> A. Van Gelder and K. Kim,  “Direct volume rendering with shading via three-dimensional textures. \\\n> Binbin Huang, Zehao Yu, Anpei Chen, Andreas Geiger, and Shenghua Gao. 2d gaussian splatting for geometrically accurate radiance fields."}, {"review_id": "vL8KJQ30jn", "reviewer": "Reviewer_1Ft5", "summary": "This paper introduces Screen-Aligned Primitives (SAP), a new rendering framework that solves the depth-sorting problem in 3D Gaussian Splatting. Instead of using 3D Gaussians that often overlap and require approximate sorting, SAP predicts view-dependent 2D Gaussians that are always aligned with the image plane. This allows exact per-pixel depth sorting.\nThe primitives are predicted from a set of 3D anchor Gaussians using a lightweight decoder network, which is conditioned on the viewing direction and some input features. \nExperiments show that SAP achieves state-of-the-art rendering quality with real-time performance, eliminating artifacts like popping, while maintaining a consistent and compact 3D representation.", "questions": "1. The method does not model surface normals or enforce geometric priors, making it difficult to extract meshes. Do the authors have an idea on how to integrate smooth surface constraints to enable mesh extraction with SAP?\n\n2. The tables include publication year and venue, which are not particularly informative for evaluating method performance. I recommend replacing them with the memory consumption, training time, and inference time, as done in the original 3DGS paper.\nIncluding such metrics would better support the real-time rendering claims and improve the empirical comparison.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "+) SAP addresses a well-known issue in Gaussian Splatting: the incorrect ordering of overlapping Gaussians, which leads to popping artifacts due to sorting based on the center position rather than per-pixel depth. In contrast to concurrent methods like EVER, which perform per-pixel sorting at the cost of speed, SAP proposes a neural network that predicts view-dependent 2D Gaussians aligned with the camera's image plane. As a result, a simple global sort by the primitive centers yields correct per-pixel ordering. This approach is effective, and it leads to improved visual quality over prior work. \nThe figures are clear and well-designed, making the core ideas and architecture easy to understand.\nOverall, this is a good submission that improves upon existing methods while maintaining conceptual clarity.\n\n-) SAP introduces view-dependent primitives, meaning the set of rendered splats (and their properties) change with the camera angle. This is handled by the learned 3D-consistent decoder, but it also adds complexity and potential points of failure. If the decoder does not perfectly maintain consistency, there could be flickering or popping of primitives when the viewpoint changes.\n\n-) By relying on a neural network to predict Gaussians conditioned on the camera direction, the method moves away from an explicit 3D representation populated with fixed Gaussians. Instead of maintaining a globally defined set of 3D primitives, the scene is now implicitly represented through a view-conditioned function, making it harder to reason about or extract a concrete 3D structure. In addition, the improvements over other baselines remain relatively marginal in terms of standard quantitative metrics such as PSNR, SSIM, and LPIPS. \n\n-) The approach does not incorporate surface normals or an explicit surface prior, focusing only on rendering quality rather than geometric fidelity. The authors acknowledge that, in the absence of normal constraints, extracting a mesh from the representation is difficult. While mesh extraction is beyond the scope of novel view synthesis, this limitation reduces the applicability of SAP in scenarios that require explicit 3D geometry (though this is a minor concern given the paper’s emphasis on image-based rendering). It would be interesting for future work to explore ways of integrating smooth surface constraints, such as learned normals,... , to enable consistent and accurate mesh extraction from the representation. Are there any ideas on how future work could incorporate smooth surface constraints to enable mesh extraction?\n\n-) In my opinion, the year and conference are not important or necessary to include in the table. I would recommend removing them and instead adding metrics such as memory usage, training time, and inference time (as presented in the 3DGS paper), as these offer significantly more meaningful insights into the performance of the methods.\n\n-) I would also add Zip-NeRF as one of the baselines, as it is currently considered the state of the art on the Mip-NeRF360 dataset.\n\n-) Some minor comments:\n\nL248: Typo — \"Implenmentation Details\" should be corrected to \"Implementation Details.\"\n\nL129: I would avoid starting the section with “To overcome this limitation,” as the specific limitation being referred to is not clearly introduced in this section, and the reader may not understand what it refers to.\n\nThis is just a personal preference, but I would suggest placing the qualitative results of SAP next to the ground truth. This would make visual comparisons easier for the reader.", "was_revised": true, "final_justification": "After reviewing the rebuttal, I find that the authors have fully addressed all of my original concerns. They provided a clear plan for integrating smooth surface constraints to enable mesh extraction, demonstrating awareness of potential geometric limitations and outlining concrete future directions. They also agreed to revise the tables to replace publication year/venue with more relevant performance metrics (e.g., memory usage, FPS, storage size).\n\nThe proposed Screen-Aligned Primitives framework remains technically solid, addresses a well-known limitation of 3D Gaussian Splatting, and achieves high visual quality with real-time performance. The authors’ clarifications further strengthen the significance and reproducibility of the work. I maintain my original positive assessment and accept recommendation.", "rebuttal": "We thank the reviewer for the valuable comments. Below is our supplementary response to the reviewer’s concerns.\n\n# Q1. How to integrate smooth surface constraints to enable mesh extraction with SAP?\nWe fully recognize the value of integrating smooth surface constraints to support mesh extraction, which stands as a key direction for our future work. We are also more than willing to discuss ideas and prospects in this regard with the reviewers. Leveraging the characteristics of the SAP method, potential specific approaches are as follows:\n\n**1. Introducing Learnable Geometric Metrics into the Planar Primitive Framework**\n\nGiven that SAP’s core lies in its \"explicit anchors + neural network-driven primitive representation,\" we can introduce an **additional module for learning geometric attributes for each planar primitive.** For instance, drawing inspiration from the approach in normal-gs and spec-gs—where neural networks directly learn surface normals—we can specifically predict geometrically meaningful metrics such as **normals, signed distance functions (SDF), or depth.** These metrics inherently encode spatial continuity constraints (e.g., normal consistency between adjacent primitives), which can indirectly enforce \"smooth surface constraints.\"\n\n**2. Ensuring primitive correlation and geometric consistency**\n\nUnlike purely implicit representations, the planar primitives in SAP exhibit local spatial correlation, as defined by the positional relationships of anchors. When learning geometric metrics, we will **strengthen constraints between adjacent primitives (e.g., normal gradient penalties, SDF continuity losses)** to ensure that the overall geometry formed by combining primitives is smooth and consistent. This provides a critical foundation for subsequent mesh extraction (e.g., via the Marching Cubes algorithm applied to the SDF field).\n\n**3. Compatibility with the advantages of neural rendering**\n\nNotably, such an extension will not compromise SAP’s strengths in rendering quality: **planar primitives will still serve as carriers of appearance textures, while the newly added geometric metrics will only be used to constrain structural smoothness.** This resembles the division of labor in NeRF, where \"radiance fields encode appearance and density fields implicitly represent geometry.\" **However, the explicit anchor in SAP enable more direct control over geometric accuracy, facilitating targeted optimization for the consistency required for mesh extraction.**\n\n**4. Future Directions: Bridging SAP and Feed-forward 3D Models**\n\nWhile this may be slightly beyond the scope of the current work, we appreciate the opportunity to share some of our future research directions in 3D representations. Recent advances in feed-forward models, such as VGGT and LSVM, have inspired us to reflect on the nature of our SAP framework. In essence, SAP can be viewed as a per-scene optimization variant of LSVM, where multi-view observations are directly used to represent 3D without relying on strong geometric priors.\n\nHowever, due to the lack of data priors in per-scene optimization, geometric anchors (e.g., those introduced in our work) remain necessary to stabilize and guide the learning process. Looking forward, we envision two promising directions:\n(1) Incorporating large-scale pretrained models (e.g., depth or normal predictors) to provide strong priors that improve the reconstruction fidelity and geometric consistency;\n(2) Towards feed-forward Gaussian reconstruction, where existing methods typically generate per-pixel 3D Gaussians. We believe that combining the principles of LSVM and SAP could enable a novel 3D representation paradigm that transcends purely pixel-wise modeling and incorporates more structured geometric reasoning.\n\n# Q2. Optimization of table content\n\nYes, we acknowledge this as a minor oversight on our part. The publication year and venue do not contribute significantly to the core information conveyed in the table, and therefore have limited impact on its clarity or usefulness. In the final published version, we plan to replace these entries with more informative metrics such as **inference FPS** (to highlight our advantage over NeRF-based methods) and **storage size or point count** (to emphasize our inheritance from Scaffold-GS and demonstrate our storage efficiency compared to 3DGS). We have already reported some of these performance results in Table 1 of the appendix, and we will include additional metrics to provide a more comprehensive evaluation.We provide a comparison of computational resources between our method and the main baselines. All experiments were conducted on a single NVIDIA L40S GPU.\n\n| Tanks&Temples | PSNR   | SSIM   | LPIPS  | Mem(M)  | fps    |\n|---------------|--------|--------|--------|---------|--------|\n| 3DGS          | 23.89  | 0.851  | 0.17   | 407.1M  | **103.5**  |\n| Scaffold-GS   | 24.45  | 0.864  | 0.155  | 169.5M  | 90.1   |\n| SAP(ours)     | **24.98**  | **0.868**  | **0.151**  | **165.2M**  | 88.2   |\n\nWe agree with the reviewer’s suggestion to include Zip-NeRF as a baseline. Zip-NeRF is indeed the current state-of-the-art on the Mip-NeRF 360 dataset and should be considered for fair comparison. At the same time, we would like to highlight that **one of the main advantages of the 3DGS-based methods over Zip-NeRF is the significantly faster rendering speed**. Here, we provide a brief comparison between our method and Zip-NeRF, and **we commit to including Zip-NeRF as a baseline in the final version of the paper**.\n\n| Methods          | PSNR   | SSIM   | LPIPS  | Mem     | fps |\n|---------------|--------|--------|--------|---------|----------|\n| zip-nerf      | **28.54**  | 0.829  | 0.218  | 26.82G  | <3 |\n| 3DGS-MCMC     | 28.00     | 0.831  | **0.188**  | 28.86G  | ---|\n| SAP(ours)     | 28.05  | **0.835**  | 0.208  | **11.25G**   | **83.48** |\n\nIt is important to note that due to differences in downsampling strategies, **the data reported in the Zip-NeRF paper are not directly comparable to those commonly used in 3DGS methods.** Specifically, if the downsampling factor employed by Zip-NeRF—namely, 4× downsampling for outdoor scenes—is applied, the performance metrics of the 3DGS-base method would actually exceed the numbers reported in our paper.\n\n|              | indoor(PSNR) | outdoor(PSNR) |\n|--------------|--------------|---------------|\n| zip-nerf     | 32.25        | **25.56**         |\n| SAP(ours)    | **32.28**        | 24.63         |\n\nWe also acknowledge that our method, along with many existing 3DGS-based approaches, does not perform as well as Zip-NeRF on outdoor scenes in the Mip-NeRF 360 dataset.\n\n# Q3. Minor comments:\n1. Thank you for pointing out the typo at L248. We will correct \"Implenmentation Details\" to \"Implementation Details\" in the revised manuscript. \\\n2. Regarding the wording at L129, we agree that starting the section with “To overcome this limitation” without a clear prior mention may confuse readers. We will revise this sentence to explicitly state that **the limitation refers to the popping artifacts of Gaussian primitives and inaccuracies in their sorting order, thereby improving clarity.** \\\n3. We appreciate the suggestion to place the qualitative SAP results alongside the ground truth for easier visual comparison. We will reorganize the figure layouts accordingly in the final version to improve readability.\n\n>  [1] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields. ICCV, 2023. \\\n>  [2] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics 42(4) (2023) \\\n> [3] Tao Lu, Mulin Yu, Linning Xu, Yuanbo Xiangli, Limin Wang, Dahua Lin, and Bo Dai. Scaffold-gs: Structured 3d gaussians for view-adaptive rendering. \\\n> [4] Haian Jin, Hanwen Jiang, Hao Tan, Kai Zhang, Sai Bi, Tianyuan Zhang, Fujun Luan, Noah Snavely, and Zexiang Xu. Lvsm: A large view synthesis model with minimal 3d inductive bias. arXiv preprint arXiv:2410.17242, 2024. \\\n> [5] S. Kheradmand, D. Rebain, G. Sharma, W. Sun, Y.-C. Tseng, H. Isack, A. Kar, A. Tagliasacchi, and K.M.Yi, “3d gaussian splatting as markov chain monte carlo,”Advances in Neural  Information Processing Systems, vol."}]

Author rebuttal:

Meta-review: This paper tackles the depth-sorting problem in 3D Gaussian Splatting, by introducing Screen-Aligned Primitives (SAP), where view-dependent 2D Gaussians aligned with the image plane enable exact and efficient per-pixel sorting. A lightweight decoder generates these primitives from 3D anchors using viewing direction and feature cues. Experiments demonstrate that the proposed method eliminates artifacts while achieving real-time, high-quality rendering.

All reviewers found the paper well-motivated, clearly written, and easy to follow. They acknowledged that the proposed method is simple, effective, and compatible with existing frameworks, while showing consistent improvements over the baseline. However, some concerns were initially raised regarding 3D consistency, robustness under sparse viewpoints, and performance in complex scenes, as well as the completeness of computational evaluations. The authors provided convincing supp. experiments and clarifications in the rebuttal, including viewpoint reduction studies, results on challenging datasets, and additional analyses of computational resources. After the rebuttal, all reviewers agreed that their concerns were sufficiently addressed. 

Overall, given the paper’s clarity, clear motivation and demonstrated effectiveness, the AC recommends acceptance.
Decision: Accept (poster)