DC4GS: Directional Consistency-Driven Adaptive Density Control for 3D Gaussian Splatting
Authors: Moonsoo Jeong
Dongbeen Kim
Minseong Kim
Sungkil Lee
Venue: NeurIPS 2025 poster ()
Keywords: Computer Vision
Novel-View Synthesis
3D Gaussian Splatting
Density Control
Directional Consistency
Primary area: applications
TL;DR: We introduce a directional consistency-driven adaptive density control for 3D Gaussian Splatting to guide split decisions and placements based on structural complexity, improving reconstruction fidelity with fewer primitives.

Abstract: We present a Directional Consistency (DC)-driven Adaptive Density Control (ADC) for 3D Gaussian Splatting (DC4GS). Whereas the conventional ADC bases its primitive splitting on the magnitudes of positional gradients, we further incorporate the DC of the gradients into ADC, and realize it through the angular coherence of the gradients. Our DC better captures local structural complexities in ADC, avoiding redundant splitting. When splitting is required, we again utilize the DC to define optimal split positions so that sub-primitives best align with the local structures than the conventional random placement. As a consequence, our DC4GS greatly reduces the number of primitives (up to 30\% in our experiments) than the existing ADC, and also enhances reconstruction fidelity greatly.

DC4GS: Directional Consistency-Driven Adaptive Density Control for 3D Gaussian Splatting
Moonsoo Jeong'
Dongbeen Kim?
Minseong Kim
Sungkil 12,,,,
1 Department of Electrical and Computer Engineering, Sungkyunkwan University, South Korea 2 Department of Computer Science and Engineering, Sungkyunkwan University, South Korea Department Immersive Media Engineering. Sungkyunkwan University, South Korea {moonsoo101, 101, rlaehdqls021, leon0106, sungkil)@skku. edu
Abstract
We present a Directional Consistency (DC)-driven Adaptive Density Control (ADC) for 3D Gaussian Splatting (DC4GS). Whereas the conventional ADC bases its primitive splitting on the magnitudes of positional gradients, we further incorporate the DC of the gradients into ADC, and realize it through the angular coherence of the gradients. Our DC better captures local structural complexities in ADC, avoiding redundant splitting. When splitting required, we again utilize the DC to define optimal split positions that sub-primitives best align with the local structures than the conventional random placement. As a consequence, our DC4GS greatly reduces the number of primitives (up 30% in our experiments) than the existing ADC, and also enhances reconstruction fidelity greatly.
1 Introduction
Prinriive
1008
AbsGs DCAGS
D-SSMM:
1004
Ixeation
(Dun)
0.163
Ground Truth (GT)
(a) Evolution of primttive counts during training
(b) Rendering quality improvement in high-frequency details
Figure 1: Comparison of AbsGS (38] and our Directional Consistency-drris -rrive density control (DC4GS)
in terms of (a) primitive counts during training and (b) reconstruction quality. DC4GS saturates much earlier (here, 6k iterations) than the AbsGS does. Upon convergence, it achieves significant reduction in primitive counts (here, 30%) and high-quality splits as well, resulting in much higher reconstruction quality (b) for high-freyuency details (here, the red inset).
3D Gaussian Splatting (3DGS) can synthesize high-quality renderings well, even from sparse point clouds [14. Its efficiency stems from its adaptive density control (ADC) that leverages 2D positional gradients, derived from reconstruction loss, indicating how effectively the observations of the input signals represented. When the primitives in fact likely require finer details (i.e., over- reconstruction), the ADC spawns new primitives by splitting coarse ones where they matter most.
"Corresponding author.
Code available at htttps://githin http:///thuuu.boom//gg//////////
39th Conference on Neural Information Processing Systems (NeurIPS 2025).

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Updale
Upditw
Ground muth [bomogenenue)
Durput (gaussiin interssity
fruth (hoerggeeeouu))
(gruzosenn interslly)
Grtune brdh
High var variancc
SITE DUIN
Need split
High DC
Gracient Billd (low variance)
aigreed with QT
Gradient Teedd (high variance)
silll not algred with OT
Per pizl DC
Low DI
(n) High Directional Consistency (DC)
(b) Low DC
(c) Visualization of per-pixel DC
Figure 2: Visualization of how DC reflects structural complexities. In (a), Gaussian can be aligned with a single-peak ground truth (GT) using simple shift, which is indicated by a low angular variance (i.e., high DC). In contrast, (b) requires splitting due the mismatch from the two-peak GT. This can be reflected in its divergent gradients (i.e., low DC), but not the gradient magnitudes. (c) visualizes the per-pixel DC values in real-world image, distinguishing directionally coherent (e.g., the sky) and incoherent (the train) regions well.
The positional gradients include valuable information of reconstruction, but the majority of existing 3DGS-basel methods still take only their magnitude (1.2 norm) into account [14] 38 40
The amount of information available from the magnitude is limited representing distributions of individual primitives, and often leads redundant splits where they actually not required (c.g., low-frequency or already well-refined areas). Furthermore, split positions are randomly chosen and thereby disregard local structural cues, which often result in misaligned or overlapping sobp-rimitives.
In order for ADC to better reflect the homogeneity of the local structures, we exploit the directional distributions of the positional gradients as well as their magnitudes. When the directions of the gradients are coherent, the regions encompassing them are likely to be simpler, not requiring splitting. In contrast, regions with incoherent gradients require improving details. This approach can take advantages both of primitive counts and reconstruction quality (see F for example). To this end, we introduce Directional Consistency (DC) that captures the spatial coherence of the directional patterns of positional gradients within Gaussians. For its simple yet effective realization, implementation uses the angular variance gradient directions across pixels. Fig. 2 exemplifies the two Gaussian patterns whose gradient magnitudes identical, but their DCs are different.
Building on this insight, we use DC as versatile criterion in determining whether split primitive and where to place its cob--rrmitives. To guide the splitting, we incorporate DC into the existing ADC criteria, which better detects primitives structurally complex regions. For split placement, we present DC-guided split, splitting primitive where the DCs of its sub-primitive candidates are maximized and the structural complexity each sub-primitive represents is minimized. By leveraging the DC in both decision and placement of splitting, achieve higher reconstruction fidelity with much fewer primitives than the previous simpler approaches.
To summarize, the contributions of this paper can be listed in what follows:
introduction of Directional Consistency (DC) as a criterion better capture the structural complexity of local positional gradients in 3DGS;
a DC-guided split decision so that structurally complex regions are better selected;
DC-guided split scheme so that the DCs of resulting sub-primitives are maximized and thereby their structures are best distinguished.

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2 Related work
2.1 3D Gaussian splatting
The 3DGS [14) has emerged as real-time alternative to Neural Radiance Fields (NeRFs)
24 that
remains computationally intensive despite extensive advances acceleration 6 9 25
28 33
39
anti-aliasing [H3), and robustness [17] 34). Unlike NeRFs, 3DGS enables efficient rendering by directly rasterizing explicit 3D Gaussian primitives without requiring dense regular grids/fields
However, 3DGS suffers from aliasing, blurring, and high-frequency detail loss in reconstruction 77]
To address aliasing from mismatched scale and insufficient filtering, several 3DGS-based methods [19
21 32 40) introduce multiscale filtering and analytic rasterization to reduce artifacts and improve
sharpness.
To better preserve
details and mitigate blurring caused by over-reconstruction, FreGS 442 applies progressive Fourier-space regularization emphasize texture-rich structures, and
BAGS 26 learns spatial blur kernels to recover over-smoothed details.
Geometric inconsistencies in 3DGS have also been addressed. Optimal-GS [3 reduces projection errors through local affine approximations, and Scaffold-CC GS (22) adopts unchor-based hierarchical representations, where neural anchors spawn offset primitives to model local structures, preserving global structural coherence.
2.2 Adaptive density control for 3D Gaussian splatting
The conventional ADC scheme in the 3DGS refines Gaussian primitives by iteratively splitting or cloning them based on positional gradient magnitudes. However, the ADC is sensitive to hyperparam- eters and often causes redundant splits and spatial misalignment.
To improve the selectivity of the ADC, several methods refine the processing of view-space positional gradients. AbsGS [38] and GOF [41] mitigate gradient cancellation by using the magnitude of homodirectional (absolute) gradients and the norm of positional gradients. Pixel-GS [44 introduces
pixel-aware gradients by weighting contributions hased on pixel coverage and view-space depth, densifying under-sampled regions.
The ADC was reformulated from alternative optimization perspectives. Revising Densification [29 guides growth via pixel-level error propagation, while Markov Chain Monte Carlo-based method 15 interprets the ADC as stochastic sampling using Stochastic Gradient Langevin Dy-
namics 4 to reallocate inactive Gaussians without explicit densification.
Memory-efficient ADC is explored in Compact-3DGS [18. which prunes primitives using volume masks, and GES 10. which applies frequency-based pruning via generalized exponents. Recently, Localized Points Management (L.MM) (37] improves ADC by identifying error-contributing zones under multi-view constraints and applying localized densification with opacity reset.
While the existing 3DGS-based methods often over-refine homogeneous regions and misalign sub- primitives, our work incorporates the DC to evaluate the homogeneity of Gaussians, enabling more selective splitting and better alignment with scene structure. This results in significant improvements in both the quality and storage efficiency.
3 Preliminary: adaptive density control in 3D Gaussian splatting
In this section, we briefly review ADC in the standard 3DGS 14 The 3DGS is typically initialized with sparse points derived from
(SfM) R0 311, and densifies
Gaussians via the ADC. This process entails evaluating view-space positional gradients 0L/ap's where L is reconstruction loss and μı' is the center of projected 2D Gaussian. The gradients used to identify regions requiring higher details. The ADC criterion V L is computed every hundred optimization iterations, and is defined as the average magnitude of the positional gradients:
a v
L
11
(1)
Opl
3

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Tynad
DCC (Sec. 4.2)
Pi Tyraf
magnituda (I1@l))
Random sampling split
Appropaiinl gricatt
DCS (Sec. 4.3)
DC (K) Gradient megnitude (I181))
Sampling
Polynomial regrossion
Split
(a) Conventional ADC
(b) DC4GS
Figure 3: Comparison the conventional ADC scheme (e.g., 3DGS [1], AbsGS [88, and Pixel- GS 444) and our DC4GS. (a) Gaussian primitives selected using the positional gradient magnitude- based criterion, and the new Gaussians are randomly spawned within the pre-split Gaussian. (b) Our DC-based split Criterion (DCC) further integrates the DC (the circular mean of the positional gradients) into the previous ADC criterion. Also, our DC-guided Split (DCS) better places the new sub-primitives that their DCs are best distinguished.
where y denotes the number of views in which Gaussian i is observed, and T.p is the loss for the view v. When uu of Gaussian exceeds a threshold Tp and its maximum scale ||S:]] surpasses TS. the Gaussian i is split, and produces N sub-primitives (N=2 by default) by randomly sampling new centers within its coverage. the gradient exceeds Ty. but ||S is below Ts, the Gaussian is cloned in place. Gaussians with opacity below a given threshold are pruned out for efficiency.
We can extend only the ADC criterion of the 3DGS Eq. I.. but also the recent criteria still based on the gradient magnitude [38 44), by incorporating DC into them. These extended criteria guide both the split decisions and sub-primitive placements. The details of how to define and apply our DC into the ADC are presented in Sec.
4 DC4GS: Directional consistency-driven adaptive density control for 3DGS
The key idea of DC4GS is to quantify the directional coherence of positional gradients within Gaussian primitive, which thereby enhances the gradient magnitude-basel ADC schemes. The DC serves as an effective cue for assessing how homogeneous the region represented by a primitive is. We incorporate the DC into ADC to facilitate two key operations: 1) deciding whether primitive should be split; 2) determining where to place sub-primitiver when splitting is required.
To this end, we extend the existing densification criterion (Eq. (T) by weighting it with the DC, which we refer to as the De-wgithted split Criterion (DCC). When DCC value is high, a single Gaussian primitive is likely to cover heterogeneous region, which cannot adequately capture the region; this suggests refinement through splitting. Once a primitive determined to be split, we also improve the placement of the newly spawned primitives; the conventional scheme places them randomly. We evaluate multiple candidate split locations within it and select the one that minimizes a DC-ba cost. This divides heterogeneous region into distinct sub sub-regions that are internally homogencous. We referred this scheme as the DC- OCgguided Split (DCS).
Fig. 3 illlustrates the differences between the conventional ADC and our DC4GS. Our DC4GS is readily compatible with the existing 3DGS-based pipelines, and thereby, can be easily plugged into their pipelines.
4.1 Directional consistency
The DC is computed from the positional gradients within a Gaussian, derived from reconstruction loss. Since the positional gradient magnitude also reflects how sensitive the loss is to positional changes, combining them together allows the 3DGS to better understand whether each primitive represents the regions well or not.
To quantify the DC within Gaussian, first assess the directional coherence of its positional gradients using a circular mean (or negative circular variance) (3 that a statistical measure of angular dispersion of set of unit vectors. Given set of N unit vectors Wj, its circular mean is defined as = n Σ/ Uj. and its L2 norm |C|| reflects directional alignment. ||C|| zs 1 implies

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Selected by AbsGS criterion
Selected by DCC
Difference
Count: 90.073
Count 69, 29,821
Count: 20,252
Figure 4: Comparison of split candidates selected by the criterion of AbsGS and DCC from the identical training states. After 14,900 training steps on the Stump scene using the 3DGS, Gaussians selected for splitting visualized in yellow (AbsGS) and red (DCC). The difference (green) shows (potentially redundant) 20,252 Gaussians are not split by the DCC. Most of these differences are already of tiny sizes, suggesting limited structural gain from further splitting.
the vectors are aligned, and ||C|| ~ 0 implies angularly dispersed vectors. On the other hand, the circular variance is given by V
||C'|| E [o, 1], and represents directional inconsistency.
In our case, given a Gaussian i, we define its directional consistency K; ||Ci]|- In the context of 3DGS, we evaluate the circular mean with respect to its positional gradients. For each pixel influenced by the Gaussian i, let 9t.t = -Lts/ay', , be the positional gradient and uay 9.3/1191.511 be its unit vector. The circular mean C/2 of the positional gradients is computed as:
C
Us.i E
(2)
j=1
4.2 Directional wonsistnncy-weightedd split criterion
Our DC can guide whether a Gaussian should be split. To this end, we introduce DC-guided split Criterion (DCC), which integrates the DC with the positional gradient magnitude. It identifies primitives that have a higher impact on the reconstruction and cover regions that cannot be well modeled by single Gaussian.
To utilize DCC, we first aggregate the positional gradient magnitudes at pixels affected by Gaussian as 9: Σn I following the homodirectional positional gradients accumulation in AbsGS (38). We use this formulation by default, but can be replaced with other alternatives, such as that used in 3DGS (Eq, or Pixel-GS 4 we demonstrate their integrations in Sec.
Then, the DCC for Gaussian can be defined as:
DC
E ki,")
|1 ||=
where v is the number of views in which the Gaussian is visible, and KA, denotes the DC evaluated for view v. follow the vie-view averaging scheme the 3DGS [14), but augment the positional gradient magnitude with the complement of the DC, ki as weighting factor. The Gaussian i is selected for splitting, if its DCC, VDC L, exceeds the gradient threshold Tp. and its maximum scale ||Sa]| smaller than the scale threshold Ts. Gaussians with high DC values, typically corresponding to homogeneous regions, are thus excluded from splitting.
As shown in Fig. DCC well filters out refined primitives that are unlikely to benefit from succeeding subdivision, and thereby, reduces the effective number of primitives selected for splitting compared to the gradient magnitude-bane based criterion.
4.3 Directional consistency-guidee split
Our DCS improves the previous random sub-primitive placement by selecting split locations so that each sub-primitive is assigned to distinct, locally homogeneous region. Since single-peaked Gaussian inherently suited for homogeneous regions, we guide the placement by evaluating the DC-based cost over candidate split locations, leading to sub-primitives being placed in regions with high DC.
5

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Directional consistency-
Uniform
Projecton
Pricepalaads
DCS
Mean:
Ground truth
Gaussian intensity
Divecforal-condsstaryy
Polynomiaa regression
Spli:
Random spiit
Mean: 0.812
Abd Aite
Local nininum
DCS (SSIM: 0.994)
Rendom split (SSIM: 0.849)
SSIM boxplot (10,000 samples)
Ma3
(a) Overview of DCS
(b) Comparison of DCS and random split in 2D
Figure 5: Overview and examples of the DCS. (a) Candidate points are uniformly sampled along the principal axis and projected onto the image plane. The split cost [xx) (x)) J.(xx) is computed using the directional consistency and gradient magnitudes, and the polynomial regression is used to find the optimal split position Zopt from the limited set of discrete samples. (b) 2D experimental example, our DCS well aligns the split along the regions structural change occurs, resulting in faithful reconstruction. The plot demonstrates quality statisties in over 10,000 randomized samples.
We constrain candidate split locations to lie along the principal axis of the Gaussian, defined as an axis having the largest scale in the anisotropic matrix S. This axis, Plocal transformed to world coordinates as p = R Plocal, using the rotation matrix R of the Gaussian. The split is then performed orthogonally to this axis. Since the principal axis often spans multiple structures, a single elongated primitive exhibits large spatial variance, which increases blur and causes fine details to be smoothed out structurally distinct regions. This axis- sois-eligned sub-primitive placement mitigates such issues by reducing spatial spread and avoiding the overlaps commonly introduced by random placement, which could otherwise lead to structural discontinuities and incomplete coverage of the pre-split primitives.
To determine the optimal split location, we evaluate the DC-based cost over N candidate locations, placed symmetrically along p relative the Gaussian center. each candidate position æ, a split line orthogonal to the projected 2D principal axis divides the primitive into left and right sub-regions. For each sub-region, we compute the DC, k(z), and the homodirectional gradient magnitude (x) The sub-region costs are defined (1)) = (z)) [[]r(x)] and (z) = (1 K. (x)) (x)
respectively. The total split cost (zx) is: [zz) J((x) ) + Jz)..
Minimizing the DC-based cost facilitates splitting at point that divides a heterogeneous region into more homogeneous sub-regions, preventing reconstruction sensitivity from being concentrated in single sub-primitive. Continuously evaluating J(x) is costly in terms of computation and storage, and hence, we employ discrete sampling for efficiency. The overall procedure is illustrated in Fig. 5(a). In our implementation, we empirically set the samples of N=5. Finding the best candidates among the discrete samples can straightforward, but may require too many samples for a complex junction. To improve this without dense sampling, polynomially regress the samples (T.. This allows to efficiently estimate the optimal split location Zope with a minimal number per-primitive samples; Appendix A.2 for details.
Notably, the DC-based cost aligns with our DCC in Eq. reinforeing consistent reasoning in the decision to split and the placement of sub primitives. Although the cost is evaluated before the actual split, minimizing it implicitly guides the sub-primitives toward homogeneous regions, which are less likely to require further splitting.
To validate the effectiveness of DCS, compare it against random placement using 2D toy exam- ples (see Fig. ((b)). Here, DCS produces splits that more closely align with the ground truth, and demonstrates more consistent and accurate results over 10,000 randomly generated examples. Its practical effectiveness is demonstrated in Sec.

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Algorithm Optimization and Densification
|||| maximum Gaussian scale, Tp. Ts: thresholds for VDLL and ||S||| N: number of split candidates
M.S. S. C. < InitAttributes()
b Positions, Scales, Rotations, Colors, Opacities b. DCC-weighted split criterion, iteration counter, visibility counter
< 0, <0 while not converged do
VDC L
V, f + SampleTrainiig ViewO +- Rasterize(M.. S, R, C, A, + Los aL Zy f- VL
view-projection camera matrix, ground truth
> backpropagation i: index of a Gaussian
for all Gaussians G, visible do 1/4 1. + M,
K; < ExallDirectioaaloonssseee
AL 8p?
Algo.
9: Σ;
aL. ग..
V DC
14 L+ (1 k.)
-19:ll j: pixel position influenced by
J: J, EvalSplitCostt((4, S₁, R, V. N, AL 8ug
D Algo.
[SRefinemennttcaatin(())) then for all Gaussians G; do
DC f- (V m/z 1)/u,
if
V DC Hr
L Tp and || Ts then Topt PolynomialRegrresionll SplitGaussian Copt, p4, S₁ Ri, C₁, A,)
N) V DC L + 0, J, - 0, 14 +-
> Algo. 5
M,S.R, A A, Adam ( kt
update parameters and increment iteration
Implementation details
Our DC4GS can be integrated seamlessly into the existing 3DGS pipelines. We implemented on top of the 3DGS [14], as well as its recent extensions: Pixel-GS [44] and AbsGS (38). Algorithm summarizes the procedure, where yellow- hiigh-iigghigtteed lines indicate the modifications the previous ADC schemes. Clone and prune operations are identical to the baselines and thus omitted here.
For each visible Gaussian DC-based split cost J, over N candidate split location samples along the principal axis. The primitive selected for splitting its DCC exceeds the gradient threshold and its maximum scale ||] smaller than the scale threshold Ts. Once selected for splitting, the optimal split location Tep is determined via the polynomial regression over J, Additional details are provided in Appendix A.1
evaluate its DC K4, accumulate its DCC Vp. L, and estimate its
Experiments
6.1 Experimental details
Datasets and metrics. We evaluate our DC4GS on the three standard datasets: Mip-NeRF 360 2 (five outdoor and four indoor scenes), and two scenes each from Tanks and Temples [16] and Deep Blending [12), following the 3DGS [4]. Every 8th frame is used for test. Rendering quality is evaluated by PSNR, SSIM [35. and LPIPS
We also report memory requirements for 3DGS parameters and the number of primitives to assess storage efficiency.
Experimental setup. To ensure fair comparison with the baselines 14
adopt their training schedules, loss functions, and all hyperparameters, including the gradient threshold and the scale threshold Tş- As with the baselines, halt the densification after 15K iterations. All the experiments are conducted on single NVIDIA A6000 GPU with 48GB of memory.
38 77
6.2 Comparison with 3DGS-based methods
We compare DC4GS with the aforementioned baselines by integrating it into their ADCs. Our comparisons with the baselines also include non-3DGS novel-view synthesis methods, including

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Table I: Quantitative comparison of the 3DGS, Pixel-GS, and AbsGS real-world datasets without and with integrating DC4GS. The results denoted by '*" were excerpted from the 3DGS paper. The rest were obtained through our in hous experiments. The top score second-higher score and third-highest score are color-coded in red, orange, and yellow, respectively.
Methed
NeRP56
Tanksd LPIPS
Blending
PSNR T
SSIM T
LIMES
Prins
Men.
PSNR. T
55334
Pris.
Men.
PSNR
55031
LPIPS 1 Prin.
Man.
INGPaig
25.594
0.099
11331
41MB
21.920
0.745
0.335
45518
24.560
1.517
4SMB
3e0
0.792
0.237
22,220
0.759
0.501
30188 [x]
574414
0881
01218
1150K
753MB
21655
0.844
0.179
1591
427
70
01886
0.348
2811K
670MB
ScathMMGG
27:61
0810
24008
0:511
2670K
30.55
1710K
LPM
27.589
0325
11312
$10MB5
23.87
0.847
1634K
451MB
13500
2525K
597MB
Pivet-OS
27,537
23.259
4623K
AboGS
27.504
0.15
3149K
7443B
23,636
0.852
1332K
315MB
20.500
1961K
AbeGS (MI (ue)
27.59
0.87
11
31NKK
24RMI
240019
6USS
0.65
1313
311M8
26.355
0.505
01340
1953X
454MB
27.000
01814
0313
200K
301MB
23-756
0.545
0.170
1ROKK
007MB
35 35565
11
0.345
264K
635MB
0810
0.225
4750K
144MI
24005
0.549
0.137
M00K
63
00907
0.257
40MB
GES- DES-DCAGS
27,09)
0.797
B325K
23:515
0:541
145TK
LPM-DORGS
27.556
0819
0.218
2112K
641MB
23,852
0.846
0.156
15CK
305MB
29.564
0.343
0.344
2350K
555MB
27,000
098
23:370
0.855
4100K
4764K
101351B1
ABGSS-DC4GS
618MB
1499K
Mip-NeRF360 2) iNGP-big (25) and Plenoxels 8 All the baselines are either re-run using their official implementations with default settings, or taken directly from published results for fairness.
6.2.1 Quantitative comparison
Table a quantitative analysis for the three datasets. Overall, when DC4GS is integrated into the baselines [14
10 [7 it consistently improves them to competitive superior quality, For Scaffold-GS 22 which does not involve any explicit primitive splitting logic, we only apply our DC-weighted Split Criterion (DCC) and omit the DC-guided Split (DCS). In addition to the quality improvement, DC4GS significantly reduces the number of primitives and memory usage for 3DGS parameters; the largest reduction (on average 20%) is observed in combining our density control with AbsGS, and consistent savings for the other basclines are observed as well. Notably, the combination of DC4GS with AbsGS also yields the greatest improvement in reconstruction quality. DC4GS also achieves up to 11.5% fewer primitives with 3DGS, 11% with Pixel-GS, and 12-18% with Scaffold GS, GES, and LPM, improving quality metries. In contrast, simply extending AbsGS training to 60K iterations yields only marginal or even negative gains, indicating that the improvements of DC4GS stem from structural complexit-aware splitting rather than brute-force optimization or longer training (see Table
[8
44
22
6.2.2 Training and rendering efficiency comparison
the training and per-frame rendering times between the baselines and their DC4GS- integrated models. Here, the rendering time is measured by averaging the time taken to render all test-set images for each dataset. The integration of the DC4GS introduces moderate training overhead due to the additional computation of the DC and DC-based cost evaluation. However, this additional cost is confined to training only. At inference time, DC4GS improves rendering efficiency by reducing the number of Gaussian primitives. The consistent speedups in rendering align with the reduced primitive counts, demonstrating the practical scalability of our DC4GS.
6.2.3 Qualitative comparison
Fig. 6 visually compares the improvements achieved by DC4GS. Compared to 3DGS and AbsGS, our DC4GS more faithfully preserves fine structures, such as the window frames, railings, and rods in the figure, where both the baselines often exhibit objectionable discontinuities. It also better maintains object boundaries (the third and last rows), which tend to be oversmoothed in the baselines. While AbsGS generally achieves high visual quality, it is likely to over-split already fine textures, such as the leaves in front of the windows or the grass near rocks (the fourth row), which can result in visual occlusions and structural artifacts. These observations indicate that DC4GS better preserves connected structures such as window frames and railings, which often appear fragmented or discontinuous in the baseline results. It also retains fine details in high-frequency textures, like the leaves or grass, without being occluded by background objects, which is frequently observed in the baselines.
8

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Table 2: Comparison of training time and per-frame rendering time (ms) for the baselines and
DC4GS DCCGS--integrated models on the Mip-NeRF360, Tanks& Temples, and Deep Blending datasets.
Mip-NeRF360
Tanks& Temples
Tanks&Temples
Deep Blending
Method
Training
Rendering (ms)
Training
Rendering (ms)
Training
Rendering (ms)
3DGS
34m
10.472
19m
7.87
30m
9.646
3DGS+DCAGS
49m
9.836
27m
7.518
47m
9.023
Scaffold-GS
Ih Im
9.705
29m
7.015
42m
6.298
Scaffod
Ih Im
9.563
31m
6.933
44m
5.748
GES
32m
6.981
18m
5.593
40m
6.835
GES+DC4GS
42m
6.698
22m
5,441
45m
6.571
LPM
38m
10.702
18m
7.143
30m
9.090
LPM+DCAGS
54m
9.462
27m
6.370
49m
8.512
Pixel-GS
49m
17.163
35m
15,212
41m
14.271
DDDG-GGS
1h 6m
16.211
45m
14,450
1h 1m
13.469
AbsGS
37m
9.975
17m
6.175
27m
7.353
AbsGS (60K iter.)
lh 19m
10.247
38m
6.690
57m
7.549
AbsGS+DCAGS
51m
9.191
23m
5.778
40m
6.378
3DGS 3DGS-DD4G5
ADSGS+DCAGS
Figure 6: Qualitative comparison of the baseline methods (3DGS and AbsGS) without and with the integration our DC4GS. The scenes, from top to bottom, are: Garden, Treehill, Room, Stump, and Bonsai from the Mip-NeRF360 dataset, Truck from the Tanks& Temples, and Playroom from Deep blending dataset.

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Table 3: Ablation study evaluating DCC (Sec. 4.2 and DCS (Sec. 4.3 T Tamps&Temples and Deep Blending dataset. The AbsGS 38 is selected as the baseline.
the Mip-NeRF360,
Mip-NoRE500
Tankss/eemples
Bllndingg
Rasdine
DCC
DES
PSNNK
SSIMET
1.11PS
Mrr.
PSNR
33IM
1PIS
PSNR
1.295
Prim
27.507
1961K
676-11
0.164
385MI5
01901
1799K
+2538B
27.587
0.826
0.187
2877K
690MB
24,18
0.837
0.158
1198K
283MB
29.591
0.985
0.335
1609K
3808EB
PART
Catorance Image
DCC only
DCS only
Figure 7: Qualitative visual comparison of our ablation study on the Garden and Treehill scenes from the Mip-NeRF330 dataset.
6.3 Ablation study
To assess the effectiveness of each component, we conduct an ablation study based on the AbsGS baseline (38]. The results are summarized in Table 3
Directional Consistency-weige
split Criterion (DCC). The effect of applying the DCC (Sec (Sec
shown in the second row of Table 3 The main effect of DCC is the reduction of the primitive counts. Here, it achieves up 24% reduction (Room scene). Notably, still maintains improved or comparable quality on datasets compared to the baseline.
Directional Consistency-guide Split (DCS). The effect of the DCS (Sec 4.3 appears in the third row of Table Its main effect the improvement of qualities. Compared to the baseline, the DCS achieves consistently better quality even with fewer primitives.
Combination DCC and DCS. Combining DCC and DCS synergistic, which produces the most pronounced improvements. DCC and DCS individually reduce primitives and improve quality, but their integration achieves the fewest primitives and the highest fidelity. In Fig. [ while each component alleviates artifacts such as occluded or broken cages and railings, their combination better reconstructs fine structures faithfully even with fewer primitives.
Conclusion
We introduced DC4GS, directional consistency- density control for 3DGS, which selectively refines primitives by analyzing the angular coherence of positional gradients. Our density control employs directional consistency effectively densifying primitives to align with local structural complexities. We demonstrated that our method can be integrated into the existing 3DGS pipelines and greatly enhances novel-view synthesis quality in diverse scenes with fewer primitives.
structural cue for both split selection and sub- sub-primitive placement,
Acknowledgement
This work supported in part by the Mid-career Research Program and CRC Program through the NRF Grants (Nos. RS-2024-0033966 and RS-2023-00221 186), and IITP grants (No. RS-2024- 00454666), funded by the Korea govermment (MSIT). Correspondence concerning this article can be addressed to Sungkil Lee.
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A Appendix
A.1 Additional implementation details
This section provides detailed implementation components that support the overall optimization and densification process summarized in Algo. A Sec. [ Specifically, we describe the key modules in DC4GS: the evaluation of the directional consistency (DC), DC-based split costs, and the generation of sub- brimbiriiiiies. Each corresponds to a modified line in Algo. I and is detailed in the following subsections with standalone pseudocode for clarity and reproducibility.
A.1.1 Directional consistency
Algorithm 2 Directional consistency (DC) from positional gradients aL positional gradients w.r.t projected Gaussian center j
By
function EvalDireciinallConsttnnnyy Al
N t-0 0
for all E do 0u
N c N +
+ 19ll
accumulate unit vector of positional gradient
C return |C||
D circular mean
D DC
end function
presents the implementation of the DC defined in Section 4.1 Given a set of 2D positional 0t. where each gradient corresponds to a pixel affected by the Gaussian, we first normalize gradients Op²
Algo.
each gradient to obtain a unit vector indicating its direction. These unit vectors are accumulated and averaged to form the circular mean C. The directional consistency is then computed as the L2 norm ||O|| this mean vector.
A.1.2 DC-based split cost
Algorithm DC-hased split costs for N (odd) candidates along principal axis. S, R: Gaussian center, scale, rotation; V: view-proe view-projection matrix
function EvalSplitCosts(u, S, R, V. N, Dy
+ arg (a..22) S(i)
>> select principal axis D basis vector along axis a axis in world space >> diameter of a gaussian b end point of the principal axis
Phocal + e(a)
p R Plocal
d + 6 5(a)
und μ + 0.5d
and Project2DDr V)
<- d/(N +
b sampling interval
J - 0. K [N/2]
for i = -K to +K do
J i x + Pro)ect2D(x;", V)
J JUCostA((zz? 2D 8L
Alg.
Op
return J end function
Algo. and implement the DC-based cost evaluation process for the directional eecristeney-guiidee split (DCS), as described Sec. 4.3
ssmmplss N candidate split points symmetrically along the principal axis of a Gaussian, defined as the direction of maximal scale the anisotropic matrix S and transformed to world coordinates via the rotation matrix R. Each 3D candidate point 23D is projected into image space using the
20

---

Algorithm 4 DC-based cost for a candidate split Fg: split point, Fend= principal axis endpoint, (z. pixel position and gradient
function CostAt(Zg, Zend.
al Op
Vaxis < Fend F
2D principal axis direction
Pi - []. Pr + |
Åt 00 gr +0
for all (z, E Du
do
Vpi f- x 2k, d t Vaxis Vpx
> dot product to determine side of split > left of split line
if d < 0 then
P: - P: U (g), 91 t 01 + l9l
else
right of split line
P. - P, u (g). fr < fr + [g]
Ki cosaliirectooallCnniseennyy
Hr <- EvalDiiectinaalCnnstteeeyyy
Alg.
Jj - (1 - K() |l J, + (1 - k,) |1
return Ji + J,
end function
view- view-projection matrix V, and the corresponding DC-based cost is computed at each z22D using Algo.
Algo. 4 computes the cost for a single split point I'k (i.e., zn from Algo. B). A split line orthogonal to the projected principal axis divides the affected pixels into left and right subsets. For each subset, the DC x is evaluated using Algo. 2 and the gradients [g] are accumulated, The cost for each side is computed (1 H.) ||ğl|, and the final cost is the sum of both sides.
A.1.3 Sub-primitive generation DCS
Algorithm 5 Splits Gaussian into sub-primitives at Topt u, S, R, c, o, center, scale, rotation, color, and opacity of a Gaussian
function SpliGaaussian(<ap μl R, c, 0)
- arg (a..s) S(i)
> select principal axis >> axis in world space diameter of gaussian
Plocal t -(aa, p t R Pixca
s(a)
di - d. (1 ), d, + d Topt
H1 < μ μ- (d//2) p. 14 + p + (d,/2)
S - S, Si(a) + Si(a) Tapt
S, + 5. + S,(a) (1
01 Tapt Or + 0. (1 Togt)
G t Gaussain(H), (p1, St, R, c, 01), Gr t Gaussain(Hr:: Sp,, R, c,
G (U(G,
add sub- tob-primitives to the Gaussian set
end function
Algo. 50i.555immeentt the sub- -ob--rimiiive generation step after determining the optimal split position Topt- This operation spawns two new Gaussians by dividing the original one along principal axis.
To perform this split, the function computes the left and right extents from the center based on the optimal split position Tapt, using the principal axis direction defined during cost evaluation (see Algo.Bi, p.. The new centers μ4 and Hly are offset from the original center μ., and the corresponding scales along the principal axis are proportionally adjusted to Fopt and Fopt- Opacity values also redistributed in the same ratio to avoid unintentionally increasing or decreasing the overall density of the original Gaussian. Each resulting sub-primitive retains the original rotation and color and is subsequently added to the primitive set.
A.1.4 Training-time overhead analysis
In practice, DC4GS reduces the number of primitives, which accelerates the rendering time. To quantify the computational trade-offs, we provide a breakdown of DC-related overhead in Table
21

---

Table 4: Breakdown of per-iteration training-timi -iiee overhead introduced by DC4GS, measured on the bicycle scene of Mip-NeRF360 dataset.
Module
Time (ms)
Directional Consistency (DC) evaluation
0.010
DC-based split cost computation Sub-primitin generation
31.020
16.913
Total Additional Overhead
47.943
Dense argmin (SSIM:0.965)
Polynomial regression (SSIM: 0.961)
Argmin (SSIM: 0.946)
(a) Inferred split results (1 sample)
Ground
0.983
Avgi: 0.979
Avg:: 0.977
Caussian intensity
Gradient Field
(b) SSIM boxplot (10,000 samples)
(c) Gradient Field
Figure Comparison split location selection strategies our consistency-guided split using synthetic toy examples. (a) On synthetic sample, we compare three strategies: dense argmin (N=60), polynomial regression (N=5), and argmin (N=5). Dense and regression methods yield sub-primitives well-aligned with the ground truth and capture structural boundaries where gradient directions conffict (see gradient field), while argmin slightly overextends the left side. (b) SSIM boxplots over 10,000 samples. Regression achieves near-equal accuracy dense argmin. It outperforms argmin in accuracy and stability (tighter IQR), demonstrating robust performance under limited sampling.
These results are based on the Mip-NeRF360 bicycle scene with 44,206 primitives. This breakdown clarifies that most of the overhead arises from atomic operations in DC-based splitting.
A.2 Effect of sampling resolution and selection method
We evaluate how the accuracy of split estimation is affected by the sampling resolution N and the choice of selection method in our DCS. We compare three settings: 1) dense argmin (N=60), 2) polynomial regression
[1I] over N candidates, and sparse argmin (N-5).
Fig. 8 (a) shows a synthetic example where both the dense argmin and regression identify the structural boundary well, while the sparse argmin misplaces the split, slightly overextending the left. As shown Fig. C)c), this boundary aligns with a region where gradient directions conflict. The regression successfully detects this transition, preserving the underlying structure.
Fig. ()) shows SSIM boxplots over 10,000 samples. Dense argmin achieves the highest average (0.983), followed by the regression (0.979) and sparse argmin (0.977). The regression also exhibits the tightest distribution (median=0.987. IQR (InterQuartile Range)=0.0136), outperforming sparse argmin (median=0.983 IQR=0.0194). These results confirm that the regression provides accurate and stable split estimation, even under limited sampling.
22

---

Table 5: Quantitative comparison for the Mip-NeRF360 scenes. From the top row to the bottom row, the results indicate PSNR, SSIM, LPIPS, and the number of primitives, respectively.
Model
bicycle
bonsai
counter
flowers
garden
kitchen
room
stump
treehill
3DGS (14]
25.1331
32.1688
29.0042
21.4235
27.2435
31.3263
31.3873
26.5487
22.4933
3DGS+DC4GS
25.1866
32.1594
28.9499
21,5535
27.3492
31.4530
31.6532
26.6118
22.4582
Pixel-GS [+4]
25.2318
32,5194
29.1654
21.5205
27.3366
31,6594
31,4681
26,8100
22.1198
PixCI-GSDDC4GSS
25.3140
32.4600
29.1790
21.7308
27.4599
31,6957
31,5255
26,8978
22.3223
AbsGS (38]
25,2407
32.3531
29.1104
21.1861
27.5704
31.8096
31.6676
26.6322
21.9733
AbsGS+DC4GS
25.5344
32.2905
29.0290
21.5621
27.7356
31.7880
31.6649
26.9562
22.0716
Model
bicycle
bonsai
counter
flowers
garden
kitchen
room
stump
treehill
3DGS
0.7602
0,9400
0,9061
0.6019
0,8619
0,9259
0.9178
0.7691
0.6307
3DGS+DC4GS
0.7655
0.9399
0.9060
0.6059
0.8638
0.9261
0.9188
0.7743
0.6331
PixeI-GS
0.7757
0.9445
0.9121
0.6337
0.8661
0,9292
0,9206
0.7836
0.6316
Pxxc-GGS-D4GS
0.7798
0.9442
0.9122
0.6403
0,8680
0.9293
0,9212
0.7876
0.6375
AbsGS
0.7800
0.9453
0.9120
0.6174
0.8713
0.99997
0.9253
0.7753
0.6133
AbsGS+DC4GS
0.7925
0.9445
0.9113
0.6348
0.8741
0.9300
0,9252
0.7924
0.6287
Model
bicycle
bonsai
counter
flowers
garden
kitchen
room
slump
trechill
3DGS
0.2159
0.2050
0.2019
0.3411
0.1092
0.1265
0.2197
0.2186
0.3292
3DGS+DC4GS
0,2104
0.2058
0.2026
0.3366
0.1083
0.1267
0.2189
0.2142
0.3310
Pixel-GS
0.1818
0.1934
0.1844
0.2617
0,1003
0.1195
0.2110
0.1868
0.2787
PXxe--GSDD4GSS
0.1793
0.1938
0.1857
0.2654
0.0996
0.1199
0.2105
0.1858
0.2848
AbsGS
0.1729
0.1894
0.1874
0,2713
0.0992
0.1206
0.1999
0.1979
0,2801
AbsGS+DC4GS
0.1663
0.1907
0.1892
0.2684
0.0977
0,1211
0,2018
0.1884
0.2733
Model
bicycle
bonsai
counter
flowers
garden
kitchen
room
stump
treehill
3DGS
6056K
1285K
1226K
3618K
5694K
1839K
1592K
4895K
3944K
3DGS+DC4GS
5299K
1124K
1112K
3389K
5269K
1677K
1419K
3980K
3438K
Pixel-CIS
9028K
2102K
2603K
7517K
8574K
3180K
2588K
6610K
8396K
Pixel GS-DCAGS
8047K
1860K
2378K
6966K
7914K
2945K
2332K
5730K
6906K
AbsGS
6051K
1045K
970K
3886K
3790K
1243K
1471K
4845K
5037K
ADsGS+DCAGS
5021K
830K
754K
3330K
3300K
930K
1036K
3898K
4432K
Table 6: Quantitative comparison for the Tanks& Temples scenes. From the top row to the bottom row, the results indicate PSNR, SSIM, LPIPS, and the number of primitives (Prim.), respectively.
Train
Truck
Method
PSNR
SSIM t
LPIPS $
Prim.
PSNR t
SSIM f
LPIPS
Prim.
3DGS
21.8415
0.8103
0,2103
1099K
25.4690
0,8777
0.1486
2687K
3DGS+DC4GS
21.9974
0.8116
0,2112
1048K
25.5747
0.8801
0.1469
2358K
Pixel-GS
21.9925
0.8236
0.1804
3857K
25.5262
0.8828
0.1216
5338K
PixeI-GSDDCAGS
22.2010
0.8260
0.1799
3561K
25.6590
0,8856
0.1213
4650K
AbsGS
21.5800
0.8178
0.1927
1008K
25.6926
0.8869
0.1322
1657K
AbsGS+DCAGS
22.3767
0.8291
0.1871
787K
25.8666
0.8894
0.1317
1399K
Table 7: Quantitative comparison for the Deep Blending scenes. From the top row to the bottom row, the results indicate PSNR, SSIM, LPIPS, and the number of primitives (Prim.), respectively.
Dr Johnson
Playroom
Method
PSNR
SSIM t
LPIPS 1
Prim.
PSNR 1
SSIM f
LPIPS
Prim.
3DGS
29,0423
0.8977
0.2471
3321K
29.7464
0.8997
0.2490
2345K
3DGS+DC4GS
29.1892
0.9000
0.2455
3158K
29.9417
0,9021
0.2459
2131K
PixcI-GS
27.9112
0.8843
0.2602
5491K
29.7131
0.8989
0.2446
3754K
Pixel-GSDDCASS
28.5347
0.8914
0.2500
5203K
29,8276
0.9010
0.2429
3365K
AbsGS
29.0475
0.8956
0,2420
2455K
29.9527
0.9049
0.2330
1467K
AbGGS+DCAGS
29.2328
0.9027
0,2370
1905K
30.0759
0,9087
0.2331
1093K
23

---

A.3 Additional experimental results
A.3.1 Per-scene quantitative results
Tables 7 report detailed per-scene metries, including PSNR, SSIM, LPIPS, and the number of primitives, for all datasets. The results show that DC4GS consistently reduces the number of primitives and maintains improves reconstruction quality compared to each baseline method.
In the stump scene, applying DC4GS to 3DGS results in up to 19% reduction in primitives. With Pixel-GS [44), DC4GS achieves up 18% reduction in the treehill scene. The largest reduction is observed with AbsGS [8), where DC4GS reduces the number of primitives by up to 30% in the room scene. In all cases, PSNR, SSIM, and LPIPS metrics remain superior comparable to each baseline, demonstrating that DC4GS enhances both compactness and reconstruction fidelity in 3DGS- based pipelines.
A.3.2 Additional qualitative comparisons
Fig. 3DGS
9 provide additional qualitative comparisons between the baselines (Pixel-GS and AbsGS 38) and their DC4GS- models.
44).
Comparisons with Pixel-GS As shown in Fig. 9 DC4GS more effectively preserves linear bound- aries, such door panel patterns, counter edges, window frames, and lane markings. It also improves contrast in fine details and maintains distinct separation between adjacent regions, mitigating over- shooting and bleeding artifacts.
Comparisons with 3DGS Fig. shows that DC4GS improves the sharpness of architectural lines and geometric boundaries. It more accurately reconstructs fine structures like door pancls, counter surfaces, window outlines, and wall trims. Straight edges and corners appear cleaner and less distorted, with reduced blending between adjacent objects and surfaces.
Comparisons with AbsGS In Fig. I1 DC4GS more reliably recovers structures such as window frames, rods, and wall seams, and reduces floating artifacts and blending at region boundaries (e.g., between sky, trees, and train). It suppresses redundant splits and improves local separation, resulting in clearer reconstructions with sharper object boundaries and fewer visual artifacts.
DC4GS consistently improves the reconstruction of fine structures and local detail, enhancing the separation between distinct objects and surfaces. This leads to reduced structural blending and clearer geometry in various scenes.
24

---

Ground truth
Pixel-GS
Pixel-GS+DC4GS
Figure 9: Qualitative visual comparisons between PixeIGS and PixeIGS integrated with DC4GS. The scenes, from top to bottom, are: Bonsai, Counter, Garden, Kitchen from the Mip-NeRF360 dataset, Truck from the T Temples dataset, and Dr Johnson from the Deep Blending dataset.
25

---

Ground truth
3DGS
3DGS+DC4GS
Figure 10: Qualitative visual comparisons between 3DGS and 3DGS integrated with DC4GS. The scenes, from top to bottom, Bonsai, Counter, Garden, Kitchen, Room from the Mip-NeRF360 dataset, and Dr Johnson from the Deep Blending dataset.
26

---

Ground truth
AbsGS
AbsGS+DC4GS
WESTE
WES
Figure 11: Qualitative visual comparisons between AbsGS and AbsGS integrated with DC4GS. The scenes, from top to bottom, are: Bicycle, Bonsai, Stump from the Mip-NeRF360 dataset, Train, Truck from the & Templesemples dataset, and Dr Johnson from the Deep Blending dataset.
27

---

AbeGS rendered RGB
AbsGS-DC4GS rendered RGB
AbsGS rendered depth
AbsGS-DC4GG rendered depth
Ground truth
Figure 12: Qualitative depth visualization comparison between AbsGS and AbsGS integrated with DC4GS. The scenes, from top to bottom, are: Bicycle from the Mip-NeRF360 dataset, and Truck from the Tanks&Templer dataset.
Ground truth
AbsGS
AbsGS+DC4GS
Figure 13: Qualitative comparisons on challenging cases between AbsGS and AbsGS integrated with DC4GS. The scenes, from top to bottom, are: Truck from the Tanks& Temples dataset (transparent objects), and Dr Johnson from the Deep Blending dataset (strong textures).
Table 8: Quantitative comparison between AbsGS and AbsGS integrated with DC4GS challenging cases: transparency (Truck Tanks& Temples) and strong textures (Dr. Johnson in Deep Blending).
Scene
Region
Method
PSNR
SSIM
LPIPS
Truck
Transparent object
AbsGS
20.875
0.621
0.333
AbsGS + DC4GS
21.098
0.642
0.301
Dr. Johnson
Strong texture
AbsGS
25.741
0.717
0.334
AbsGS + DC4GS
26.462
0.761
0.294
A.3.3 Depth visualization comparison
We qualitatively assess geometric fidelity through depth map visualizations. To obtain depth maps, we adapt the original 3DGS rendering equation by replacing the RGB color contribution with per- aer-Gaussian depth values d;:
D T. az d, T, = ---))
j=1
where ag is the alpha and T; is the transmittance value of the i-th Gaussian primitive.
As shown Fig. [2] The baseline produces noisy depth maps. This noise mainly stems from the presence of numerous false-positive primitives that persist without proper density control. Such
28

---

Table 9: Quantitative comparison of 4DGS and 4DGS with DC4GS on D-NeRF and DyNeRF datasets, reporting quality metrics (PSNR, SSIM, LPIPS) and efficiency metrics (number of primitives, memory. membr... training time, and rendering time in ms).
Dataset
Method
PSNR f
SSIM
LPIPS
Prim.
Mem. L
Training
Rendering
D-NeRF
27
4DGS (36
34.063
0,978
0.026
45K
10MB
9m
15,233ms
4DGS + DC4GS
34.124
0.978
0.026
40K
9MB
11m
14.531ms
DyNeRF 20
4DGS
30.736
0,933
0.059
123K
59MB 56MB
50m
32.537ms
4DGS DC4GS
31,092
0.936
0.056
119K
Ih 13m
32.259ms
primitives contribute spurious depth values, leading to fragmented and unstable geometry. In contrast, DC4GS effectively suppresses false-positive primitives, yielding cleaner and more coherent depth reconstructions. This suggests that the benefits of DC4GS extend beyond RGB fidelity to improved structural consistency.
A.3.4 Applicability to challenging scenarios
To evaluate DC4GS under challenging conditions, we perform region-specific comparisons on transparency and strong textures. Quantitative results, measured on the masked inset regions in Fig. 13 are reported in Table B and the corresponding qualitative comparisons are also shown in
Fig.
13
For the transparent objects (4th test image of the Truck scene in Tanks Temples), the baseline fails reconstruct the internal features behind the glass (e.g., steering wheel), whereas DC4GS successfully preserves these structures. For strong high-frequency textures (9th test image of the Dr. Johnson scene in Deep Blending), such as carpet patterns and wood scratches, DC4GS achieves superior metrics over the baseline, showing its ability to capture fine details. These results suggest that DC4GS can better handle transparent and high-frequency regions that are challenging for the baseline.
A.3.5 Applicability to dynamic scenes
We further evaluate DC4GS dynamic scenes by integrating it into 4DGS 36 and testing D-NeRF (27) and DyNeRF [20). As shown in Table DC4GS yields consistent improvements in reconstruction quality, while reducing the number of primitives and memory usage, which also leads to faster rendering. Qualitative comparisons in Fig. 14 show that DC4GS produces sharper geometry and more temporally stable appearance, whereas 4DGS often exhibits blurred details and temporal artifacts. Despite the increased training time, these results suggest that DC4GS remains effective and robust dynamic scenarios.
A.4 Limitations and future work
DC4GS enables high-quality reconstruction with substantially fewer primitives, resulting in faster rendering and reduced memory consumption for 3DGS models. Although the method introduces addi- tional training overhead due to directional consistency evaluation and candidate split cost estimation, this overhead is confined the training phase and be entirely removed once the densification stage is complete (typically after 15,000 iterations). Future work will focus on optimizing the DC computation and split estimation pipeline, particularly the cost evaluation and polynomial regression, to further reduce training time without compromising reconstruction quality.
A.5 Broader impact
DC4GS improves the efficiency of 3DGS by reducing primitive count without compromising quality. This leads to lower memory usage for 3DGS parameters and faster rendering, making high-quality 3D reconstruction more accessible for real-time and resource-constrained applications such as AR/VR and mobile platforms.
As with other 3D reconstruction techniques, there is potential for misuse (e.g., unauthorized du- plication of real-world scenes). Responsible use and ethical considerations remain important in downstream applications.
29

---

Ground truth
4DGS
4DGS+DC4GS
Figure 14: Qualitative comparisons on dynamic scenes between 4DGS and 4DGS with DC4GS. The scenes, from top bottom, Bouncing balls and Hell warrior from the D-NeRF dataset, and Coffee martini and Flame steak from the DyNeRF dataset.
30

---

A.6 Dataset licenses
We use the following datasets our experiments:
Mip-NeRF360 htpps//jonbarron.nfoommmio
2 no explicit
license
terms
provided.
Available at
Tanks and Temples [6]] released under the Creative Commons Attribution 4.0 International (CC BY 4.0). Available at http://wwwwwaaaannnness...og////
Deep Blending
12: no explicit
license
terms
provided.
Available at
http://visual.cs... cs. www..ullc....kkkps//cppeennnnnn.
31


Reviews:
[{"review_id": "J46dRsx76P", "reviewer": "Reviewer_yCGb", "summary": "This paper presents DC4GS, a directional consistency-driven adaptive density control method for 3D Gaussian Splatting (3DGS). By integrating directional consistency into both split decisions and sub-primitive placement, DC4GS effectively captures scene geometry while reducing redundant computation. Experimental results demonstrate that DC4GS reduces the number of primitives while simultaneously improving novel view synthesis quality across diverse scenes.", "questions": "Numerous storage-efficient Gaussian Splatting methods have been proposed in recent years (especially 2024 and 2025). Although some are briefly mentioned in the related work section, they are not included in the experimental comparisons. The current experiments only include two baselines from 2024 along with older methods. It would be more appropriate to compare against more recent approaches, such as Scaffold-GS, to provide a more comprehensive evaluation.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe paper is well-written, and the core idea is clear and reasonable. The experimental results support the contributions claimed by the authors.\n\nWeaknesses:\n- Since the proposed method requires additional computation during training as a trade-off, it is recommended to move the discussion on training costs from the supplementary material to the main paper.\n- Numerous storage-efficient Gaussian Splatting methods have been proposed in recent years (especially 2024 and 2025). Although some are briefly mentioned in the related work section, they are not included in the experimental comparisons. The current experiments only include two baselines from 2024 along with older methods. It would be more appropriate to compare against more recent approaches, such as Scaffold-GS, to provide a more comprehensive evaluation.", "was_revised": true, "final_justification": "The core idea of the paper is clear and reasonable. The authors addressed my concerns during the rebuttal period, demonstrating a better trade-off between quality and storage requirements compared to some state-of-the-art methods. Therefore, I update my final rating to positive.", "rebuttal": "## Regarding Training Cost Analysis\n\n>**Weaknesses 1**\n> Since the proposed method requires additional computation during training as a trade-off, it is recommended to move the discussion on training costs from the supplementary material to the main paper.\n\nWe thank the reviewer for pointing out the importance of discussing the training cost of our method in the main paper. In response, we will move the training time analysis from the supplementary to the main manuscript and expand it with more detailed breakdowns.  \n\nSpecifically, we provide timing results for each major component in our pipeline, corresponding to the stages outlined in Algorithm 1: (1) Directional Consistency (DC) evaluation, (2) DC-based split cost computation, and (3) sub-primitive generation. The table below summarizes the per-iteration overhead measured on the bicycle scene from the Mip-NeRF360 dataset with 44,206 primitives:\n\n> ### Training Time Analysis \n\n|Module|Time (ms)|\n|-|-|\n|Directional Consistency (DC) Evaluation|0.01|\n|DC-based Split Cost Computation|31.02|\n|Sub-primitive Generation|16.913|\n|**Total Additional Overhead**|**47.943**|\n\n## On Comparison with Recent Methods\n\n> **Weaknesses 2 and Questions 1**  \n> It would be more appropriate to compare against more recent approaches, such as Scaffold-GS, to provide a more comprehensive evaluation.\n\nWe appreciate the reviewer’s suggestion and agree that additional storage-efficient Gaussian Splatting methods should be included to strengthen the evaluation.\n\nTo address this, we have extended our experiments to include Scaffold-GS [1] and Generalized Exponential Splatting (GES) [2].\nWe integrated DC4GS into these pipelines as follows:\n\n- For Scaffold-GS + DC4GS, since Scaffold-GS does not include split operation, we apply only the Directional Consistency-weighted split Criterion (DCC) to modulate anchor growth. Even without the Directional Consistency-guided Split (DCS) step, this modification results in notable reductions in memory and primitive count, with rendering quality preserved at a comparable level.\n- For GES + DC4GS, we adopt both the DCC and DCS schemes. Consistent with other setups, the integration led to reductions in primitive count and memory usage, achieving comparable and superior rendering fidelity.\n  \n> ### Mip-NeRF360 dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**27.578**|0.809|0.225|569K|171MB|**49m**|9.244ms|\n|Scaffold-GS + DC4GS|27.577|**0.81**|0.225|**425K**|**128MB**|50m|**8.537ms**|\n|GES [2]|27.04|0.796|0.248|1543K|365MB|**32m**|6.981ms|\n|GES + DC4GS|**27.09**|**0.797**|0.248|**1323K**|**313MB**|42m|**6.698ms**|\n\n> ### Tanks&Temples dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**24.018**|**0.851**|**0.174**|247K|74MB|**29m**|7.015ms|\n|Scaffold-GS + DC4GS|24.016|0.849|0.177|**208K**|**62MB**|31m|**6.933ms**|\n|GES [2]| **23.64** |**0.842**|**0.191**|930K|220MB|**18m**|5.593ms|\n|GES + DC4GS|23.515|0.841|0.194|**816K**|**193MB**|22m|**5.441ms**|\n\n> ### Deep Blending dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**30.252**|**0.904**|**0.255**|171K|51MB|**42m**|6.298ms|\n|Scaffold-GS + DC4GS|30.063|0.903|0.257|**135K**|**40MB**|44m|**5.748ms**|\n|GES [2]|29.562|0.903|0.249|1606K|380MB|**40m**|6.835ms|\n|GES + DC4GS|**29.632**|**0.904**|**0.248**|**1487K**|**352MB**|45m|**6.571ms**|\n\nFurthermore, to validate the scenario generality of our method beyond static reconstructions, we integrated DC4GS into 4DGS [3] designed for dynamic scene reconstruction. Despite the additional temporal complexity, our method yielded improvements in both **PSNR (+1.2dB)** and **efficiency**, demonstrating its robustness and applicability for a diverse settings.\n\n> ### D-NeRF and DyNeRF dataset\n| Dataset | Method | PSNR ↑ | SSIM ↑ | LPIPS ↓ | Prim ↓ | Mem ↓ | Training Time ↓ | Rendering Time ↓ |\n|---|---|---|---|---|---|---|---|---|\n| D-NeRF [4] | 4DGS | 34.063 | **0.978** | **0.026** | 45K | 10MB | 9m | 15.233ms |\n|        | 4DGS + DC4GS | **34.124** | **0.978** | **0.026** | **40K** | **9MB** | 11m | **14.531ms** |\n| DyNeRF [5] | 4DGS | 29.718 | 0.930 | 0.153 | 123K | 29MB | 49m | **32.137ms** |\n|        | 4DGS + DC4GS | **30.983** | **0.937** | **0.148** | **118K** | **28MB** | 1h 23m | 32.275ms |\n\nThese results highlight that DC4GS not only complements existing methods aimed at storage efficiency, but also generalizes effectively to broader scenarios including dynamic scenes, validating its applicability, and performance gains.\n\n## References\n\n[1] Lu, Tao, et al. \"Scaffold-GS: Structured 3d gaussians for view-adaptive rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[2] Hamdi, Abdullah, et al. \"GES: Generalized exponential splatting for efficient radiance field rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[3] Wu, Guanjun, et al. \"4D gaussian splatting for real-time dynamic scene rendering.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024.  \n[4] Pumarola, Albert, et al. \"D-NeRF: Neural radiance fields for dynamic scenes.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.  \n[5] Li, Tianye, et al. \"Neural 3d video synthesis from multi-view video.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022."}, {"review_id": "58V8uyadir", "reviewer": "Reviewer_Gqr6", "summary": "The adaptive density control (ADC) in 3D Gaussian Splatting (3DGS) struggles to accurately represent the distribution of individual primitives, often resulting in redundant splits and misaligned or overlapping sub-primitives due to randomly chosen split positions. To address these limitations, this paper introduces a Directional Consistency (DC)-driven ADC. The proposed DC approach better captures local structural complexity and determines optimal split positions, ensuring that sub-primitives are well-aligned with the underlying geometry.", "questions": "See the Weaknesses.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**:\n\n(1) This paper offers a clear and logical explanation of the limitations arising from 3DGS's adaptive density control.\n\n(2) The proposed method is compatible with various existing approaches and demonstrates strong effectiveness in practice.\n\n**Weaknesses**:\n\n(1) The improvements in rendering quality are marginal—less than 0.5 dB in PSNR, 0.02 in SSIM, and 0.03 in LPIPS—raising concerns about the practical effectiveness of the proposed method.\n\n(2) Since the method introduces additional operations during the ADC stage, it is important to clarify whether this incurs extra training costs. The authors should provide a detailed analysis of both effectiveness and computational overhead.\n\n(3) More qualitative comparisons are needed to clearly demonstrate the advantages of the Directional Consistency (DC)-driven ADC, particularly in terms of geometry visualization such as depth maps.\n\n(4)Missing reference: \n[1] Improving Gaussian Splatting with Localized Points Management (CVPR2025)", "was_revised": true, "final_justification": "The rebuttal experiments resolved some concerns. My rating remains the same.", "rebuttal": "## On Marginal Improvements in Rendering Quality\n\n>**Weaknesses 1**\n> The improvements in rendering quality are marginal—less than 0.5 dB in PSNR, 0.02 in SSIM, and 0.03 in LPIPS—raising concerns about the practical effectiveness of the proposed method.\n\nWe thank the reviewer for the helpful comment. While the absolute gains in PSNR, SSIM, and LPIPS may seem numerically modest, the main contribution behind DC4GS lies in its ability to enhance efficiency by significantly reducing the number of primitives and memory usage without sacrificing rendering quality. In practice, DC4GS achieves consistent 10–30% reductions in both memory and primitive count, all while maintaining or slightly improving visual fidelity.\n\nTo further demonstrate its robustness and generality, we additionally have integrated DC4GS into multiple recent 3DGS pipelines, including Scaffold-GS [1], GES [2], and 4DGS [3], each employing different reconstruction and rendering strategies. In most cases, DC4GS either preserved or improved performance while achieving noticeable savings in memory and primitives. Notably, because **Scaffold-GS** does not involve any explicit primitive splitting logic, we only apply our DC-weighted Split Cost (DCC) module in this case, and omit the DC-guided Split (DCS). Even under this partial integration, the method demonstrates tangible efficiency gains.\n\nMost significantly, when applied to 4DGS, a method specifically developed for dynamic scene reconstruction, our approach not only reduced memory but also produced a substantial **+1.2 dB gain in PSNR** on the DyNeRF [5] dataset. This result is particularly significant as it suggests that DC4GS is not confined to static scenes, but also effective in temporally varying or dynamic settings, demonstrating its broad applicability and practical utility.\n\nThe following results illustrate the consistency of DC4GS across various datasets and methods:\n\n> ### Mip-NeRF360 dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**27.578**|0.809|0.225|569K|171MB|**49m**|9.244ms|\n|Scaffold-GS + DC4GS|27.577|**0.81**|0.225|**425K**|**128MB**|50m|**8.537ms**|\n|GES [2]|27.04|0.796|0.248|1543K|365MB|**32m**|6.981ms|\n|GES + DC4GS|**27.09**|**0.797**|0.248|**1323K**|**313MB**|42m|**6.698ms**|\n\n> ### Tanks&Temples dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**24.018**|**0.851**|**0.174**|247K|74MB|**29m**|7.015ms|\n|Scaffold-GS + DC4GS|24.016|0.849|0.177|**208K**|**62MB**|31m|**6.933ms**|\n|GES [2]| **23.64** |**0.842**|**0.191**|930K|220MB|**18m**|5.593ms|\n|GES + DC4GS|23.515|0.841|0.194|**816K**|**193MB**|22m|**5.441ms**|\n\n> ### Deep Blending dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**30.252**|**0.904**|**0.255**|171K|51MB|**42m**|6.298ms|\n|Scaffold-GS + DC4GS|30.063|0.903|0.257|**135K**|**40MB**|44m|**5.748ms**|\n|GES [2]|29.562|0.903|0.249|1606K|380MB|**40m**|6.835ms|\n|GES + DC4GS|**29.632**|**0.904**|**0.248**|**1487K**|**352MB**|45m|**6.571ms**|\n\n> ### D-NeRF and DyNeRF dataset\n|Dataset|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|-|\n|D-NeRF [4]|4DGS|34.063|**0.978**|**0.026**|45K|10MB|9m|15.233ms|\n||4DGS + DC4GS |**34.124**|**0.978**|**0.026**|**40K**|**9MB**|11m|**14.531ms**|\n|DyNeRF [5]|4DGS|29.718|0.930|0.153|123K|29MB|50m|**32.137ms**|\n||4DGS + DC4GS|**30.983**|**0.937**|**0.148**|**118K**|**28MB**|1h 13m|32.275ms|\n\nThese results confirm that DC4GS can be seamlessly integrated into various 3DGS architectures across both static and dynamic scenarios, achieving meaningful efficiency improvements with superior or comparable quality.\n\n## Computational Overhead\n\n> **Weakness 2**  \n> Since the method introduces additional operations during the ADC stage, it is important to clarify whether this incurs extra training costs. The authors should provide a detailed analysis of both effectiveness and computational overhead.\n\nWe appreciate this important concern. While DC4GS introduces additional computation during training, particularly for Directional Consistency (DC) evaluation and DC-based split cost computation, these operations are limited to the training phase only, and do not affect rendering time. In practice, DC4GS reduces the number of primitives, which accelerates the rendering time.\nWe will move the training-time analysis (previously in supplementary) to the main paper and  include a breakdown of DC-related overhead:\n\n|Module|Time (ms)|\n|-|-|\n|Directional Consistency (DC) Evaluation|0.01|\n|DC-based Split Cost Computation|31.02|\n|Sub-primitive Generation|16.913|\n|**Total Additional Overhead**|**47.943**|\n\nThese results are based on the MipNeRF360 \"bicycle\" scene with 44,206 primitives. Most overhead arises from atomic operations in DC-based splitting. We will include these findings in the revised version to clarify computational trade-offs.\n\n## On the Lack of Qualitative Geometry Comparisons\n>**Weaknesses 3**\n> More qualitative comparisons are needed to clearly demonstrate the advantages of the Directional Consistency (DC)-driven ADC, particularly in terms of geometry visualization such as depth maps.\n\nWe thank the reviewer for highlighting the need for stronger qualitative evidence of geometric improvements.  \nTo address this concern, we computed depth maps from both AbsGS and our method using a modified splatting pipeline, and compared them to evaluate the structural fidelity of the reconstructions.\n\nTo extract depth maps from Gaussian Splatting, we adapt the original color rendering equation by replacing the RGB color contribution with per-Gaussian depth values. Specifically, instead of computing the rendered color as:\n\n$$ C = \\sum_i T_i \\cdot \\alpha_i \\cdot c_i,\\quad \\text{where} \\quad T_i = \\prod_{j=1}^{i-1}(1 - \\alpha_j) $$\nwhere $c_i$ is the RGB color and $T_i$ is the accumulated transmittance, we compute the expected depth as:\n$$ D = \\sum_i T_i \\cdot \\alpha_i \\cdot d_i $$\n\nwhere $d_i$ is the depth of the $i$-th Gaussian in view or camera space.\n\nTo obtain GT depth maps for evaluation, we used the Depth Anything v2 model to perform monocular depth estimation on the GT RGB images. We then used the depth map predicted from the GT RGB as a reference and compared the others against it using standard evaluation metrics:  \n**RMSE**, **SSIM** and **threshold accuracy** (δ < 1.25, 1.25², 1.25³).\n\nThe results, presented below, show that our **DC4GS** yields more geometrically consistent renderings, producing depth more aligned with the reference than the **AbsGS** on the Mip-NeRF360 dataset. We also observed qualitatively better results through depth map visualizations. Although we are unable to include these visualizations due to rebuttal guidelines, we plan to provide them in a revised version.\n\n> ### Depth Consistency Evaluation (MipNeRF360 dataset)\n\n||RMSE ↓|SSIM ↑|δ < 1.25 ↑|δ < 1.25² ↑|δ < 1.25³ ↑|\n|-|-|-|-|-|-|\n|AbsGS|0.277|0.703|0.126|0.272|0.479|\n|AbsGS + DC4GS (ours)|**0.274**|**0.707**|**0.129**|**0.283**|**0.491**|\n|GT RGB (reference)|0.000|1.000|1.000|1.000|1.000|\n\n## Missing Reference\n> **Weaknesses 4**\n> Missing reference: Improving Gaussian Splatting with Localized Points Management (CVPR2025)\n\nThank you for pointing out the omission of the CVPR 2025 paper *\"Improving Gaussian Splatting with Localized Points Management (LPM)\"* [6]. We will add this reference to the revised Related Work section.\n\nTo further assess the generality of our approach, we also applied DC4GS to the Localized Points Management method. The results of this experiment are presented in the table below and demonstrate that our method continues to yield benefits in quality and efficiency when combined with recent 3DGS variants.\n\n> ### Mip-NeRF360 dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim. ↓|Mem. ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|LPM [6]|**27.589**|**0.820**|**0.212**|3426K|810MB|**38m**|10.702ms|\n|LPM + DC4GS|27.556|0.819|0.218|**2712K**|**641MB**|54m|**9.462ms**|\n\n> ### Tanks&Temples dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim. ↓|Mem. ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|LPM [6]|23.878|**0.847**|**0.183**|1824K|431MB|**18m**|7.143ms|\n|LPM + DC4GS|**23.892**|0.846|0.186|**1502K**|**355MB**|27m|**6.37ms**|\n\n> ### Deep Blending dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim. ↓|Mem. ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|LPM [6]|29.483|0.901|0.245|2525K|597MB|**30m**|9.09ms|\n|LPM + DC4GS|**29.584**|**0.903**|**0.244**|**2350K**|**555MB**|49m|**8.512ms**|\n\n## References\n\n[1] Lu, Tao, et al. \"Scaffold-GS: Structured 3d gaussians for view-adaptive rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[2] Hamdi, Abdullah, et al. \"GES: Generalized exponential splatting for efficient radiance field rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[3] Wu, Guanjun, et al. \"4D gaussian splatting for real-time dynamic scene rendering.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024.  \n[4] Pumarola, Albert, et al. \"D-NeRF: Neural radiance fields for dynamic scenes.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.  \n[5] Li, Tianye, et al. \"Neural 3d video synthesis from multi-view video.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022.  \n[6] Yang, Haosen, et al. \"Improving Gaussian Splatting with Localized Points Management.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025."}, {"review_id": "nH345ngfkj", "reviewer": "Reviewer_7zgh", "summary": "This work focuses on the limitations in 3D Gaussian Splatting (3DGS) scene reconstruction via Adaptive Density Control (ADC), specifically the redundant segmentation and random segmentation positions arising from ADC's reliance on positional gradient magnitude for primitive splitting. To address this issue, this paper proposes Directional Consistency-driven Adaptive Density Control (DC4GS), introducing Directional Consistency (DC) as a structural-aware metric to evaluate gradient angular coherence, and further designs a DC-weighted Split Criterion (DCC) for adaptive splitting decisions and a DC-guided Split (DCS) scheme for optimal sub-primitive placement.", "questions": "1) ​​Does the method work on different scenarios (e.g., strong textures, transparent objects)?​​\n​​2) Is the current method applicable to dynamic scenes (e.g., object motion, camera movement)? Could DC during dynamic changes lead to wrong splitting?", "limitations": "yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1) Enhanced Reconstruction Fidelity​. In addtion to reducing the number of primitives, DC4GS can also significantly enhance reconstruction fidelity. It better preserves high-frequency details such as fine structures like window frames and railings, avoiding the common issues of over-smoothing or structural discontinuities in traditional methods.\n2) Primitive Reduction. By introducing Directional Consistency (DC) to drive adaptive density control, DC4GS can effectively avoid redundant segmentation in structurally simple regions, which significantly decrease memory usage.\n3) Extensive experiments conducted on three datasets (Mip-NeRF360, Tanks&Temples, Deep Blending), covering indoor/outdoor and high/low frequency scenes. Three 3DGS methods (original 3DGS, AbsGS, Pixel-GS) were integrated as baselines to ensure the universality of the conclusions.\n\nWeaknesses:\n1) DC calculation per primitive increases per-iteration cost.\n2) There is no significant improvement in quantitative indicators.", "was_revised": true, "final_justification": "The rebuttal resolves most of my concerns, so I maintain my original rating (Accept).", "rebuttal": "## Generalizability to Diverse Scene Characteristics\n\n>**Questions 1**\n> 1\\) Does the method work on different scenarios (e.g., strong textures, transparent objects)?​​​​\n> 2\\) Is the current method applicable to dynamic scenes (e.g., object motion, camera movement)? Could DC during dynamic changes lead to wrong splitting?\n\nWe thank the reviewer for this important question. \n\nTo assess the robustness of DC4GS across diverse scenarios, we performed additional region-level analyses on challenging visual cases from our existing datasets (Mip-NeRF360, Tanks & Temples, Deep Blending), and further evaluated its behavior on dynamic scenes (D-NeRF [4], DyNeRF [5]) datasets using 4DGS [3].\n\n### 1) Applicability to Challenging Scenarios (e.g., Strong Textures, Transparent Objects)\n\nTo evaluate DC4GS under challenging scene conditions, we perform a region-specific analysis on two representative cases involving transparency and strong textures.\n\nFor the Truck scene in Tanks & Temples (4th image), we focused on the transparent window area. AbsGS fails to reconstruct the internal features behind the glass (e.g., steering wheel), while DC4GS successfully preserves these structures.\n\nFor the Dr. Johnson scene in Deep Blending (9th image), which includes strong (high-frequency) textures (carpet, wood scratches), DC4GS achieves superior metrics over AbsGS, confirming its strength in capturing fine details.\n\n|Scene (Dataset)|Region Type|Method|PSNR ↑|SSIM ↑|LPIPS ↓|\n|-|-|-|-|-|-|\n|Truck (Tanks&Temples)|Transparent Window|AbsGS|20.875|0.621|0.333|\n|||AbsGS + DC4GS|**21.098**|**0.642**|**0.301**|\n|Dr Johnson (Deep Blending)|Strong Texture (Carpet)|AbsGS|25.741|0.717|0.334|\n|||AbsGS + DC4GS|**26.462**|**0.761**|**0.294**|\n\nThese results demonstrate that DC4GS performs robustly under high-frequency and transparent conditions.\n\n### 2) Applicability to Dynamic Scenes\n\nTo further evaluate the applicability to dynamic scene, we applied DC4GS to 4DGS [3] on D-NeRF [4] and DyNeRF [5]. Notably, it yields not only reduced memory usage but also consistent PSNR improvements — up to **1.2 dB** in DyNeRF. These improvements confirm that DC4GS operates effectively even under dynamic and temporally varying settings.\n\n> ### D-NeRF and DyNeRF dataset\n| Dataset | Method | PSNR ↑ | SSIM ↑ | LPIPS ↓ | Prim. ↓ | Mem. ↓ | Training Time ↓ | Rendering Time ↓ |\n|---|---|---|---|---|---|---|---|---|\n| D-NeRF [4] | 4DGS | 34.063 | **0.978** | **0.026** | 45K | 10MB | **9m** | 15.233ms |\n|        | 4DGS + DC4GS | **34.124** | **0.978** | **0.026** | **40K** | **9MB** | 11m | **14.531ms** |\n| DyNeRF [5] | 4DGS | 29.718 | 0.930 | 0.153 | 123K | 29MB | **50m** | **32.137ms** |\n|        | 4DGS + DC4GS | **30.983** | **0.937** | **0.148** | **118K** | **28MB** | 1h 13m | 32.275ms |\n\n\n\n## Runtime Overhead of DC Calculation\n>**Weakness 1**\n> DC calculation per primitive increases per-iteration cost.\n\nWe thank the reviewer for raising the concern about the additional operations introduced by the Directional Consistency (DC)-driven Adaptive Density Control (ADC). While it is true that DC computation introduces overhead during training, we emphasize that this overhead is confined to the optimization phase and does not affect the rendering stage. In fact, DC4GS's reduction in primitive count yields faster rendering timing. We will move timing details from the supplementary to the main paper. Additionally, we will include a detailed per-iteration breakdown of the training time for each component, including DC calculation, DC-based split cost computation, and sub-primitive generation.\nBelow is a breakdown of the overhead (measured on the Mip-NeRF360 bicycle scene with 44,206 primitives):\n\n|Module|Time (ms)|\n|-|-|\n|Directional Consistency (DC) Evaluation|0.01|\n|DC-based Split Cost Computation|31.02|\n|Sub-primitive Generation|16.913|\n|**Total Additional Overhead**|**47.943**|\n\nAmong these, the DC-based split cost computation accounts for the largest portion of overhead, primarily due to atomic operations required during parallel processing. We will clarify these findings in the revised manuscript to ensure transparency regarding runtime performance.\n\n## Quantitative Improvements\n>**Weakness 2**\n> There is no significant improvement in quantitative indicators.\n\nWe thank the reviewer for pointing out the modest quantitative gains. DC4GS is designed to achieve a strong balance between rendering quality and resource efficiency, rather than solely maximizing metric scores. Across all benchmarks, DC4GS consistently achieves a substantial **10–30% reduction in both the number of primitives and memory usage**, while **maintaining or even slightly improving** visual fidelity.\n\nImportantly, the effectiveness of DC4GS extends beyond the baselines originally reported in the paper. We have successfully integrated DC4GS into several diverse 3DGS methods, Scaffold-GS [1], GES [2], and 4DGS [3]. For Scaffold-GS + DC4GS, since Scaffold-GS does not include split operation, we apply only the Directional Consistency-weighted split Criterion (DCC). In most cases, DC4GS demonstrated benefits in performance and memory efficiency.\n\nFurthermore, these improvements are not confined to static scenes. On dynamic datasets such as D-NeRF and DyNeRF, where 4DGS serves as the baseline, DC4GS delivers even greater gains in rendering quality (up to **+1.2 dB PSNR**), continuing to reduce memory footprint.\n\nThese findings collectively reinforce the generality and robustness of DC4GS, showing that its contribution goes beyond marginal metric gains and proves valuable in a **broad range of scenarios and 3DGS architectures**.\n\n> ### Mip-NeRF360 dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**27.578**|0.809|0.225|569K|171MB|**49m**|9.244ms|\n|Scaffold-GS + DC4GS|27.577|**0.81**|0.225|**425K**|**128MB**|50m|**8.537ms**|\n|GES [2]|27.04|0.796|0.248|1543K|365MB|**32m**|6.981ms|\n|GES + DC4GS|**27.09**|**0.797**|0.248|**1323K**|**313MB**|42m|**6.698ms**|\n\n> ### Tanks&Temples dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**24.018**|**0.851**|**0.174**|247K|74MB|**29m**|7.015ms|\n|Scaffold-GS + DC4GS|24.016|0.849|0.177|**208K**|**62MB**|31m|**6.933ms**|\n|GES [2]| **23.64** |**0.842**|**0.191**|930K|220MB|**18m**|5.593ms|\n|GES + DC4GS|23.515|0.841|0.194|**816K**|**193MB**|22m|**5.441ms**|\n\n> ### Deep Blending dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**30.252**|**0.904**|**0.255**|171K|51MB|**42m**|6.298ms|\n|Scaffold-GS + DC4GS|30.063|0.903|0.257|**135K**|**40MB**|44m|**5.748ms**|\n|GES [2]|29.562|0.903|0.249|1606K|380MB|**40m**|6.835ms|\n|GES + DC4GS|**29.632**|**0.904**|**0.248**|**1487K**|**352MB**|45m|**6.571ms**|\n\n\n## References\n\n[1] Lu, Tao, et al. \"Scaffold-GS: Structured 3d gaussians for view-adaptive rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[2] Hamdi, Abdullah, et al. \"GES: Generalized exponential splatting for efficient radiance field rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[3] Wu, Guanjun, et al. \"4D gaussian splatting for real-time dynamic scene rendering.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024.  \n[4] Pumarola, Albert, et al. \"D-NeRF: Neural radiance fields for dynamic scenes.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.  \n[5] Li, Tianye, et al. \"Neural 3d video synthesis from multi-view video.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022."}, {"review_id": "wTWy68vkqJ", "reviewer": "Reviewer_1vr6", "summary": "This paper handles the problem of the gradient direction being ignored in original ADC of 3DGS. The authors use directional consistency to assess the directional coherence of its positional gradients. The directional consistency are used to choose the gradient indicating that a Gaussian needs to be split. To make the sub-primitives better fit the regions, the polynomial regression is used to find the optimal split position under min DC-based cost. The experiments show the proposed methods obtain a better rendering quality with less Gaussians.", "questions": "+ I am not very sure that Line 145 and 195 should be \"larger than the scale threshold\".\n+ I would like to know the value of thresholds $\\tau_p$ and $\\tau_S$ in Algorithm 1.\n+ Could the sub-primitives from the splitting operation in the original ADC of 3DGS adjust their positions in the subsequent training process to finally fit the target regions? I think that might be the reason why the improvements caused by the proposed splitting strategy and other methods are not obvious.", "limitations": "Yes, the limitation has been mentioned in the supplementary.", "rating": 3, "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 direction of gradient is useful in distinguishing Gaussians required to be split. The proposed methods are well designed with sufficient theoretical support.\n+ The proposed methods seem novel, and the experiments show a certain improvement effect.\n\n**Weakness**\n\n+ The improvements shown in the experiments are not obvious, which probably cannot demonstrate the effectiveness of the proposed methods.\n+ It seems that there is the same problem in the ablation study.", "was_revised": true, "final_justification": "My main concerns about the performance of the proposed methods have not been addressed. Although this paper has a clear motivation, the experiments on most datasets have unsatisfactory improvements. Only performing well on the ``Dr Johnson'' scene cannot demonstrate the effectiveness of the proposed methods. Also, the geometry evaluation based on Depth Anything cannot convince me because the pseudo GTs generated by DPT are not accurate. In general, I decide to maintain my rating as boardline reject.", "rebuttal": "## Clarification on the Effectiveness of DC4GS\n\n>**Weakness 1**\n> \"The improvements shown in the experiments are not obvious, which probably cannot demonstrate the effectiveness of the proposed methods.\"\n\nWe appreciate the reviewer’s comment regarding the seemingly modest improvements in numerical metrics. While the absolute gains in PSNR, SSIM, and LPIPS may appear limited, the main contribution of DC4GS lies in its ability to achieve a superior trade-off between memory efficiency and rendering quality.\nSpecifically, DC4GS consistently reduces the number of primitives and memory usage by 10–30%, achieving comparable or superior rendering quality. This is further supported by its compatibility with a variety of 3DGS architectures.\n\nTo substantiate DC4GS effectiveness, we additionally integrated it into several recent 3DGS pipelines, including Scaffold-GS [1], GES [2], and 4DGS [3]. For Scaffold-GS + DC4GS, since Scaffold-GS does not include split operation, we apply only the Directional Consistency-weighted split Criterion (DCC) to modulate anchor growth.\nThe observed improvements in each case demonstrate the practicality and generality of our method. Notably, on the DyNeRF [5] dataset using 4DGS, a method tailored for dynamic scene reconstruction, DC4GS not only reduces memory usage but also yields a **1.2 dB** gain in PSNR.  \nThis result is particularly meaningful, as it shows our method is not confined to static scenarios but also effective in dynamic and temporally varying settings, thereby reinforcing its general applicability and practical utility beyond mere metric gains.\n\n> ### D-NeRF and DyNeRF dataset\n|Dataset|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|-|\n|D-NeRF [4]|4DGS|34.063|**0.978**|**0.026**|45K|10MB|**9m**|15.233ms|\n||4DGS + DC4GS |**34.124**|**0.978**|**0.026**|**40K**|**9MB**|11m|**14.531ms**|\n|DyNeRF [5]|4DGS|29.718|0.930|0.153|123K|29MB|**50m**|**32.137ms**|\n||4DGS + DC4GS|**30.983**|**0.937**|**0.148**|**118K**|**28MB**|1h 13m|32.275ms|\n\n> ### Mip-NeRF360 dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**27.578**|0.809|0.225|569K|171MB|**49m**|9.244ms|\n|Scaffold-GS + DC4GS|27.577|**0.81**|0.225|**425K**|**128MB**|50m|**8.537ms**|\n|GES [2]|27.04|0.796|0.248|1543K|365MB|**32m**|6.981ms|\n|GES + DC4GS|**27.09**|**0.797**|0.248|**1323K**|**313MB**|42m|**6.698ms**|\n\n> ### Tanks&Temples dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**24.018**|**0.851**|**0.174**|247K|74MB|**29m**|7.015ms|\n|Scaffold-GS + DC4GS|24.016|0.849|0.177|**208K**|**62MB**|31m|**6.933ms**|\n|GES [2]| **23.64** |**0.842**|**0.191**|930K|220MB|**18m**|5.593ms|\n|GES + DC4GS|23.515|0.841|0.194|**816K**|**193MB**|22m|**5.441ms**|\n\n> ### Deep Blending dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|Scaffold-GS [1]|**30.252**|**0.904**|**0.255**|171K|51MB|**42m**|6.298ms|\n|Scaffold-GS + DC4GS|30.063|0.903|0.257|**135K**|**40MB**|44m|**5.748ms**|\n|GES [2]|29.562|0.903|0.249|1606K|380MB|**40m**|6.835ms|\n|GES + DC4GS|**29.632**|**0.904**|**0.248**|**1487K**|**352MB**|45m|**6.571ms**|\n\n## On the Effectiveness of the DC-driven ADC vs. Original ADC\n\n> **Questions 3**  \n> \"Could the sub-primitives from the splitting operation in the original ADC of 3DGS adjust their positions in the subsequent training process to finally fit the target regions? I think that might be the reason why the improvements caused by the proposed splitting strategy and other methods are not obvious.\"\n\nWe appreciate the reviewer’s insightful question. To evaluate whether the sub-primitives generated by the original ADC in 3DGS can eventually adapt to their target regions through prolonged optimization, we conducted additional experiments using AbsGS as the baseline. Specifically, we doubled the training iterations from the default 30,000 to 60,000, allowing ample time for the sub-primitives to adjust their positions if possible.\n\n> ### Mip-NeRF360 dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|AbsGS|27.504|0.818|0.191|3149K|745MB|**37m**|9.975ms|\n|AbsGS (60K iter.)|27.539|0.817|0.189|3162K|748MB|1h 19m|10.247ms|\n|AbsGS + DC4GS|**27.625**|**0.826**|**0.188**|**2615K**|**618MB**|1h 4m|**9.225ms**|\n\n> ### Tanks&Temples dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|AbsGS|23.636|0.852|0.162|1332K|315MB|**17m**|6.175ms|\n|AbsGS (60K iter.)|24.039|0.855|**0.156**|1313K|311MB|38m|6.69ms|\n|AbsGS + DC4GS|**24.121**|**0.859**|0.159|**1093K**|**259MB**|28m|**5.887ms**|\n\n> ### Deep Blending dataset\n|Method|PSNR ↑|SSIM ↑|LPIPS ↓|Prim ↓|Mem ↓|Training Time ↓|Rendering Time ↓|\n|-|-|-|-|-|-|-|-|\n|AbsGS|29.500|0.900|0.237|1961K|464MB|**27m**|7.353ms|\n|AbsGS (60K iter.)|29.275|0.895|0.240|1962K|464MB|57m|7.549ms|\n|AbsGS + DC4GS|**29.654**|**0.905**|**0.235**|**1499K**|**354MB**|50m|**6.627ms**|\n\nDespite this extended training, DC4GS still outperforms the baseline using the original ADC of 3DGS, both in rendering quality and structural fidelity. To further investigate whether prolonged optimization could compensate for suboptimal primitive splits, we trained the AbsGS baseline with original ADC for 60K iterations—twice the default schedule.\nWhile this extension yielded marginal improvements on the Mip-NeRF360 and Tanks&Temples datasets, it resulted in a performance drop on the Deep Blending dataset. This outcome suggests that simply increasing the number of training iterations is insufficient to correct suboptimal initial splits, as downstream optimization alone cannot fully recover from poor primitive placement.\n\nIn contrast, our Directional Consistency (DC)-guided ADC ensures that sub-primitives are initialized in geometrically meaningful and directionally coherent locations at the moment of splitting. This guided placement accelerates convergence and leads to superior reconstruction performance.\nThese results demonstrate that directionally guided initialization is crucial for effective convergence, emphasizing the importance of incorporating DC in the ADC design.\n\n## Ablation Study Effectiveness\n\n> **Weakness 2**  \n> \"It seems that there is the same problem in the ablation study.\"\n\nWe appreciate the reviewer’s observation regarding the relatively modest impact of each component in the ablation study. While each module may contribute only limited improvement, they are designed to address distinct aspects of the task. When combined, they yield a greater overall improvement, both qualitatively and quantitatively, demonstrating their complementary roles in addressing different aspects of the task. Notably, as reported in the paper, the full model achieves enhanced rendering quality, reducing the number of primitives by approximately 20% on average.\n\n## Clarification on Lines 145/195 and Threshold Values in Algorithm 1\n\n> **Questions 1 and 2**  \n> \"I am not very sure that Line 145 and 195 should be 'larger than the scale threshold'.\"  \n> \"I would like to know the value of thresholds $ \\tau_p $ and $ \\tau_S $ in Algorithm 1.\"\n\nWe thank the reviewer for raising these helpful questions that help improve the clarity of our paper.\n\nRegarding the first question: the phrasing  \"larger than the scale threshold\" in Lines 145 and 195 follows the standard densification scheme used in 3D Gaussian Splatting (3DGS).\nAs described in the Preliminary section, a Gaussian $i$ is split when both of the following conditions are satisfied:\n\n(1) the magnitude of the positional gradient $ \\|\\nabla_{\\mu_i'} \\mathcal{L}\\| > \\tau_p $  \n(2) the maximum scale $ \\|S_i\\| < \\tau_S $\n\nIn our method, we preserve second condition (scale threshold) and only modify the standard gradient-based criterion $ \\nabla_{\\mu_i'} \\mathcal{L} $ by introducing the DCC, denoted as $ \\nabla_{{\\mu'}_i}^{DC} \\mathcal{L} $  in the paper.\n \nThat is, we replace the original positional gradient magnitude $ \\|\\nabla_{\\mu_i'} \\mathcal{L}\\| $ with our DCC, while keeping the same scale-based condition $ \\|S_i\\| < \\tau_S $.\n\nFor the second question: we adopt the default threshold values $\\tau_p$ and $\\tau_S$ as defined in each baseline method without modification. For clarity, we list the values used in our experiments:\n\n**3DGS**: $ \\tau_p = 0.0002, \\tau_S = 0.01 \\times $ scene_extent  \n**AbsGS**: $ \\tau_p = 0.0004, \\tau_S = 0.001 \\times $ scene_extent  \n**PixelGS**: $ \\tau_p = 0.0002, \\tau_S = 0.01 \\times $ scene_extent  \n\nHere, scene_extent is not a new parameter, but rather a dataset-specific normalization scalar already defined and used in the original 3DGS. It reflects the geometric extent of the scene as observed from the distribution of training camera poses.\n\nWe will clarify these details explicitly in the revised manuscript to avoid confusion.\n\n\n## References\n\n[1] Lu, Tao, et al. \"Scaffold-GS: Structured 3d gaussians for view-adaptive rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[2] Hamdi, Abdullah, et al. \"GES: Generalized exponential splatting for efficient radiance field rendering.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.  \n[3] Wu, Guanjun, et al. \"4D gaussian splatting for real-time dynamic scene rendering.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024.  \n[4] Pumarola, Albert, et al. \"D-NeRF: Neural radiance fields for dynamic scenes.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.  \n[5] Li, Tianye, et al. \"Neural 3d video synthesis from multi-view video.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022."}]

Author rebuttal:

Meta-review: They use the directional consistency of gradients using *circular mean* rather than simply summing up, arguing it avoids redundant splitting and is better for defining optimal split position.  

Reviewer yCGb suggested including more storage-efficient methods to compare with state-of-the-art 3DGS methods to see if this work poses a new frontier in the respective field. The authors chose Scaffold-GS (Lu et al., CVPR 2024) and GES (Hamdi et al., CVPR 2024), showing an ablation study of how much their work DC4GS improves performance. On comparison with recent methods, although it is not explicitly mentioned during the rebuttal period, the authors also missed Octree-GS (Ren et al., 2024) and FLoD (Seo et al., 2024). For instance, Scaffold-GS+OctreeGS achieved 28.05 of PSNR and 140MB of Memory, while Scaffold-GS+DC4GS achieved 27.58 and 128MB, respectively, underperforming PSNR while having a similar memory footprint in Mip-NeRF360.

As Reviewers Gpr6 and 1vr6 repeatedly argued for the marginal improvement. 1) Fidelity is not significantly better or even worse in some cases, 2) # of primitives and memory footprints are reduced to some degree, but not significantly compared to other alternatives for memory reduction. 3) Training time is usually prolonged even though the number of primitives is reduced, 4) rendering time is slightly faster, but we do not know the confidence interval since the authors do not assess rigorously.

However, after author-reviewer discussions, Reviewer yCGb raises their score, while Reviewer 7zgh and Gqr6 hold positive opinions. AC agrees on that Reviewer 7zgh’s comment “the directional-consistency signal is simple and model-agnostic.” That’s why the proposed method could be orthogonal to the other storage-efficient methods. AC values its careful and insightful discussion on directional consistency of gradients and its applications to adaptive density control, although it has an inevitable trade-off among fidelity, parsimony, and time complexity.

Therefore, AC recommends this work for poster acceptance, but leaves room for adjustment depending on the overall slot allocation and SAC’s discretion. Good luck.

A minor comment for polishing the manuscript: According to the official NeurIPS style guideline, “all headings should be lower case (except for first word and proper nouns)” in Line 55 (style guide pdf). Please see Section 5 "Implementation *D*etails".
Decision: Accept (poster)