Reframing Gaussian Splatting Densification with Complexity-Density Consistency of Primitives

[Weaknesses, Questions]

​We sincerely thank you for this thoughtful comment. We agree that using complexity-density correlation (CDC) as an evaluation metric requires careful justification, especially given that our method is explicitly designed based on these two factors. Below, we provide a more thorough explanation, and include additional experiments to demonstrate how uneven CDC distributions affect rendering outcomes.

To answer the reviewer's concern - "3DGS should perform better than other baseline methods. However, the quantitative results do not consistently reflect this":

• CDC is not the only factor that affects rendering performance. In our method, CDC primarily serves as a guiding prior in the densification stage, aiming to better allocate Gaussian primitives in accordance with the scene’s structural complexity. The correlation metric reflects how well the primitive distribution matches the structural needs of the scene, but the final rendering quality also depends on subsequent stages such as opacity-guided optimization and rasterization, as demonstrated in prior 3DGS works. Thus, high CDC alone does not deterministically lead to better rendering, but rather provides a principled foundation for better primitive allocation, especially under a constrained primitive budget. It is not a deterministic predictor of final rendering score. We will revise the manuscript to clarify this distinction.

• Minor CDC gains may not yield visible improvements. While vanilla 3DGS does show a slight CDC improvement at later stages (as noted in Fig. 4b), the Pearson coefficients remain low (typically 0.1–0.3), which we consider insufficient to meaningfully affect rendering. In contrast, our method achieves a much higher CDC (~0.7), which we believe leads to more accurate primitive allocation and ultimately contributes to improved rendering under similar budgets. Thus, the reviewer’s concern highlights an important nuance: CDC matters, but only when enforced strongly and consistently.

• Other methods optimize rendering performance from different perspectives. For example, baselines like Mini-Splatting and AbsGS enhance densification through techniques such as depth-based splitting and absolute gradient accumulation. These strategies do not explicitly aim to align complexity and density, so their rendering improvements may not correlate with CDC scores. This further justifies our choice to evaluate CDC-guided densification in isolation, rather than treating CDC as a universal indicator of rendering quality. Therefore, it is reasonable that quantitative rankings in rendering performance do not always align with CDC scores across all methods.

• We further support this argument with a reverse ablation on MipNeRF 360 dataset. To assess the impact of CDC more directly, we design a control variant called 3DGS + reverse CDC, where we intentionally densify Gaussians in low-complexity & high-density regions, and prune those in high-complexity & low-density ones — essentially flipping the CDC guidance.

  Method	PSNR ↑	SSIM ↑	LPIPS ↓	#GS ↓
  3DGS (baseline)	27.79	0.826	0.201	2.59M
  3DGS + reverse CDC	27.62	0.817	0.224	2.71M

  As shown in above, the reverse CDC variant degrades rendering performance (PSNR −0.17 dB, SSIM −0.009, LPIPS +0.023), and also increasing the number of Gaussians, indicating inefficient allocation. This result empirically confirms that disrupting the complexity-density alignment harms rendering qaulity, while reinforcing it (as our method does) leads to improvement.

• Theoretically, CDC fits the nature of Gaussian splatting. Since Gaussians are ellipsoidal and composited via alpha-blending, a higher number of Gaussians in structurally complex regions enables better approximation of fine geometry and texture. Conversely, smooth areas (e.g., walls) require fewer primitives. Aligning density with visual complexity avoids both under- and over-reconstruction, which we visualize in Figure 1.

​We will incorporate these clarifications in the final version, and we thank the reviewer again for highlighting this important aspect. We hope this additional analysis supports your consideration to raise the score.

[Weaknesses 1]

Thank you for pointing out. The correct description should be: “Γmean, Ψmean are the mean of complexity and density”. We will fix it in the final version.

[Weaknesses 2, 3, 4]

We clarify the key concepts:

1. Identifying Under-/Over-Reconstructed Regions

   As formalized in Equation 7 and Section 3.3 (Line 184), we use the CDC score sᵢ to measure local mismatch:

   • sᵢ < 0 with high complexity and low density → Under-reconstructed region → Apply densification
   • sᵢ < 0 with low complexity and high density → Over-reconstructed region → Apply pruning

2. Pruning Sampling Based on Opacity oᵢ

   The parameter oᵢ refers to the opacity of the Gaussian primitive, as introduced in Section 3.1.1 (Line 127). We use oᵢ as the sampling probability in pruning because opacity is a reliable indicator of a Gaussian’s contribution to the final rendering. Pruning requires more caution than densification, as mistakenly removing an important Gaussian can lead to unrecoverable degradation, while opacity oᵢ helps retain perceptually important Gaussians and avoids overly aggressive pruning.

3. How $\rho_d$ Is Determined

   $\rho_d$ is a fixed hyperparameter (e.g., 0.01) controlling the proportion of Gaussians selected for densification. It is not derived from the CDC score sᵢ. Instead, we identify Gaussians with sᵢ < 0 (indicating a strong mismatch between complexity and density), and use multinomial sampling with probabilities proportional to |sᵢ| to prioritize the most structurally inconsistent Gaussians. Therefore, a high value of |sᵢ| does not indicate good consistency, but rather a stronger inconsistency — and thus a higher priority for refinement.

[Weaknesses 5, Questions: why the positional gradient is still required]

As noted in Section 4.5 (Line 293), we retain the positional gradient because our CDC prior improves allocation, but not per-view geometry. The gradient, derived from rendering loss, is essential for view-dependent refinement. We will clarify this dual-role design in the final version.

[Weaknesses 6, Questions: the paper misses intuitive explanations, for instance: how formula 8 is designed]

In Equation 8, $τ_{low}$ and $τ_{upp}$ are set very similarly because densification in 3D Gaussian Splatting is highly sensitive — even small threshold changes can cause large shifts in Gaussian count and quality. Our CAAT strategy adaptively modulates it between $τ_{low}$ and $τ_{upp}$ based on complexity and targets only structurally complex regions for more aggressive densification while avoiding redundancy in simple areas.

[Weaknesses 7, Questions: hyperparameters ablation.]

We provide ablations for all major hyperparameters on MipNeRF 360 dataset:

• KNN neighbor count |$N_i$|. As shown in the table below, fewer neighbors (e.g., |$N_i$| = 1, 2) improves quality slightly by enhancing sensitivity to local structures, but also increases noise and instability. Therefore, we select |$N_i$| = 3 as a balanced choice.

  |$N_i$|	PSNR ↑	SSIM ↑	LPIPS ↓	#GS ↓
  1	28.05	0.838	0.179	2.51M
  2	28.03	0.837	0.179	2.54M
  3	28.02	0.836	0.183	2.53M
  4	28.02	0.836	0.182	2.55M
  5	28.01	0.836	0.183	2.55M

• $τ_{low}$, $τ_{upp}$ (CAAT Module). Ablation shows that reducing the fixed threshold from 0.0002 to 0.0001 improves PSNR (+0.53 dB) but nearly triples gaussian count (2.74M→7.89M). This highlights the sensitivity of the threshold and motivates our adaptive design. We set $τ_{upp}$ = 0.0002 and $τ_{low}$ = 0.00015 to improve quality with minimal overhead. Due to characters limitation, we omit the full table here but will include it in the final version.

• λ (CAAT Module). Ablation varying λ from 1 to 10 shows that the method is not sensitive to the value of λ. PSNR varies within 0.07 dB and gaussian count increases slightly and gradually, with no sharp drop in performance. The default setting λ = 6 achieves a balanced trade-off across scenes. Due to rebuttal length limits, we omit full tables but will include them in the final version.

[Weaknesses 8]

This is a typographical error, and the correct symbol should be $\rho_d$ instead of $\rho_s$ in Line 230. We will correct it in the final version.

[Weaknesses 9]

Thank you for pointing this out. The figures reflect real training behaviors on different scenes and are consistent with our method.

• Scene differences: Figure 4b shows kitchen (MipNeRF 360), while Appendix Fig.1 includes garden, train, drjohnson, and averages across 13 scenes. Differences in geometry and frequency naturally lead to trend variation, but the core finding remains: CDC-GS consistently improves complexity-density correlation, unlike baselines.
• Multi-factor influence: While our CDC-GS promotes complexity-density alignment, downstream optimization can cause scene-specific fluctuations. Nevertheless, an overall upward trend is observed across scenes, validating the method’s robustness.
• Periodic pruning: The drops every 3000 iterations are due to pruning low-opacity Gaussians (<0.1), which momentarily alters density. The rapid recovery confirms that our method is adaptive and resilient to structural changes.

[Weaknesses 10]

We use the geometric mean for density estimation (Eq. 6) as it better captures local crowding — one close neighbor strongly lowers the mean. As shown in Supplementary B.2, this leads to better quality and fewer Gaussians than the arithmetic mean.

[Weaknesses 11, Questions: why the DWT is the best choice]

We chose DWT for the following key reasons:

• Multi-scale decomposition: Unlike single-scale filters, DWT captures both fine and coarse structural details, crucial for modeling spatially varying 3D complexity.
• Directional sensitivity: DWT provides high-frequency responses in multiple orientations (LH, HL, HH), enabling richer structural analysis than edge-only filters.
• Frequency separation: By discarding the LL band and inverting DWT, we isolate high-frequency components, preserving more relevant geometric cues.
• Empirical support: DWT-based approach consistently improves rendering quality and reduces Gaussian count across scenes.

[Weaknesses 12]

We now include the missing pruning ablation results on MipNeRF 360:

This demonstrates that our pruning strategy significantly reduces the number of Gaussians without degrading quality.

The motivation is, overlapping Gaussians in dense regions often have low opacity due to alpha-blending. These are likely redundant and can be safely removed. Periodic pruning thus improves compactness and provides a more accurate density estimate for CDC-based allocation.

[Weaknesses 13]

We conducted an ablation study on the MipNeRF 360 dataset to quantify the additional training cost of our complexity and density components:

KNN over millions of Gaussians is expensive, but we mitigate this via CUDA-based acceleration to fully leverage GPU parallelism, keeping the density overhead modest. Likewise, complexity computation is integrated into the alpha-blending stage of 3DGS rendering to reduce cost.

Notably, rendering speed remains unaffected. Our method maintains the same FPS with vanilla 3DGS while improving reconstruction quality.

[Weaknesses 14]

Figure 3 uses reduced resolution to meet NeurIPS file limits. We will replace it with a higher-quality version in the final paper.

[Weaknesses 15]

We extended the ablation to all 9 MipNeRF 360 scenes. Results match main paper conclusions:

[Weaknesses 16]

We include comparisons with representative compaction methods (Mini-Splatting, LightGaussian, Taming-3DGS) proposed in the paper suggested by the reviewer, and will incorporate related references accordingly in the final version:

​The results show that Our pruning-only variant not only reduces the number of Gaussians by over 1.1 million, but also slightly improves rendering quality compared to vanilla 3DGS.

[Weaknesses 17]

We integrated CDC into 3DGS-MCMC. With the same number of Gaussians, performance improves:

This confirms that CDC is plug-and-play and can enhance existing 3DGS variants.

​We will include these analyses in the final version and sincerely appreciate the reviewer’s constructive feedback.

[Questions 1]

Thank you for raising this important point. To clarify:

• Our default proposed method is "Ours (0.01)", which includes CDC (with both densification and pruning) + CAAT + periodic pruning, as shown in the main paper (Table 1).
• "Ours (0.02)" is a variant with a more aggressive densification budget ($\rho_d$ = 0.02), leading to higher quality but more gaussians for fair comparison with other 3DGS baseline methods that use a similarly high number of gaussians.
• "Ours Prune Only" is an ablation variant that removes CAAT and densification in CDC, keeping periodic pruning and CDC pruning to test its standalone effect.
• When integrating into 3DGS-MCMC, we only use CDC (with both densification and pruning), since 3DGS-MCMC already controls primitive count, making CAAT and pruning less relevant.

We will clearly annotate each configuration and its components in the final version. For practical usage:

[Questions 2]

We clarify that the +CAAT results in the rebuttal did not use periodic pruning, while the +CDC results included it, since we treat periodic pruning as an integral part of the CDC module. To isolate the impact of each component, we conducted an additional ablation on the MipNeRF 360 dataset, removing periodic pruning from the +CDC setting:

These results indicate:

• CAAT slightly increases the number of gaussians (+0.23M) while consistently enhancing quality (+0.07dB PSNR).

• CDC brings a more significant quality boost (+0.13dB PSNR), but increases gaussians substantially (+0.7M).

• Periodic pruning effectively reduces the number of gaussians (−0.89M) without compromising rendering quality, and serves as a good complement to CDC.

We will include these results in the final version to clearly illustrate their effect on the number of Gaussian primitives. Thank you again for raising this important question.

[Questions 3]

You are absolutely right that a negative sᵢ indicates inconsistency, while positive sᵢ indicates consistency. We clarify that:

• We only perform CDC densify/prune on Gaussians where sᵢ < 0, i.e., when the complexity and density are mismatched (e.g., high complexity but low density, or vice versa).
• For these inconsistent Gaussians, we use |sᵢ| to measure the degree of inconsistency — the higher the absolute value, the more severe the mismatch.
• Gaussians with sᵢ > 0 are will not be refined regardless of their |sᵢ| value, since they already align in structure.

This ensures that our method focuses exclusively on inconsistency correction, not on suppressing highly consistent gaussians.

We will clarify this in the final version to avoid misunderstanding. Thank you for this important clarification request.

[Questions 1]

We sincerely appreciate your insightful questions.

As shown in Equation 5 from the main paper, we compute the complexity of each Gaussian by applying maximum aggregation both within a single view and across views. This design is intentional to preserve the most structurally informative responses, and we elaborate on the rationale below:

• Single-view maximum: Each Gaussian projects to multiple pixels within a single image view. These pixels may exhibit different frequency responses due to varying local image content. Averaging across these pixel responses would dilute the impact of strong signals, making it harder to identify structurally complex regions. Therefore, we take the maximum pixel-wise frequency response within the view to retain the most prominent signal associated with the Gaussian.
• Across-view maximum: A Gaussian may appear highly complex in one view but be occluded or lie in a flat region in other views. Averaging across all views would suppress the significance of such important but view-specific complexity cues. Thus, we adopt a maximum across views, ensuring that if a Gaussian is deemed structurally important from any perspective, this information is preserved in its final complexity score.

To further support this design choice, we conducted an ablation study comparing four different aggregation strategies. The results on the MipNeRF 360 dataset are summarized below:

The Max-Max configuration consistently outperforms other combinations in both rendering quality and compactness, supporting our claim that preserving the strongest structural signal leads to better modeling decisions.

[Questions 2]

Thank you for the insightful suggestion. We conducted an additional experiment with a more aggressive pruning setup, in which only the CDC pruning strategy is applied, without any CDC-based densification. We then compared this variant — Ours (Prune Only) — with Mini-Splatting, LightGaussian, and Taming-3DGS.

The results show that Mini-Splatting and LightGaussian achieve more aggressive compression ratios, but at the cost of noticeable quality degradation (PSNR drops by −0.44 dB and −0.52 dB, respectively). In contrast, our pruning-only variant not only reduces the number of Gaussians by over 1.1 million, but also slightly improves rendering quality compared to vanilla 3DGS.

This confirms that our CDC pruning strategy remains effective in a compact setting by selectively removing redundant Gaussians in over-reconstructed regions, supporting its utility beyond full-scale densification.

[Questions 3, Weaknesses 2, Limitations 1]

Thank you for the suggestion. We have conducted an ablation study to measure the additional computational costs of our complexity and density components on the MipNeRF 360 dataset, using the same experimental setting as in the main paper. Specifically, we add each module (DWT-based complexity estimation and KNN-based density estimation) independently to vanilla 3DGS, and record the corresponding training time increase. The total overhead of our method is approximately +6:30 per scene. Individually, we measured +4:13 for complexity and +1:34 for density, each evaluated in isolation on top of vanilla 3DGS:

We acknowledge that performing KNN over millions of Gaussians can be computationally expensive. To address this, we implement CUDA-based KNN acceleration to fully leverage GPU parallelism. This makes the density overhead relatively modest and practical in training scenarios.

Likewise, complexity computation is integrated into the alpha-blending stage of 3DGS rendering to reduce cost. However, since it requires aggregation across all training views and is recomputed every 100 iterations from step 600 to 15000, it contributes the majority of the overall cost.

Notably, the additional training overhead does not impact rendering performance. Our method maintains the same FPS with vanilla 3DGS while improving reconstruction quality:

As requested, we report the training time comparison across representative methods on the MipNeRF 360 dataset, covering all methods discussed in both the main paper and the rebuttal across all reviewers:

[Questions 4]

Thank you for the helpful suggestion. We have conducted additional experiments to compare our method with 3DGS-MCMC on the MipNeRF 360 dataset, under the same experimental setting as in the main paper. The total number of Gaussians is controlled to match our method (Ours 0.01), to ensure a fair comparison.

The results show that 3DGS-MCMC achieves slightly better rendering quality than our method under the same Gaussian count. However, we introduces a novel and orthogonal densification mechanism. Instead of relying on opacity-based redistribution, our CDC strategy explicitly identifies regions exhibiting inconsistency between structural complexity and density, and addresses them through targeted pruning (for over-reconstructed regions) and splitting (for under-reconstructed regions). This complementary perspective enhances structural coverage from a complexity-aware standpoint,and can be combined with existing reallocation-based methods to achieve further improvements.

Moreover, we tested integrating CDC into 3DGS-MCMC, and observed further improvement in rendering quality without increasing the number of Gaussians. This confirms that our approach is plug-and-play and can effectively enhance existing methods by providing a complementary, complexity-aware allocation strategy.

[Weaknesses 1]

Thank you for highlighting this concern. While CAAT introduces a hyperparameter λ, our ablation study on MipNeRF 360 dataset shows that the method is not sensitive to the value of λ. Rendering quality remains stable across a wide range of λ (1 to 10), with no sharp drop in performance.The default setting λ = 6 (used in the main paper) provides a strong balance between quality and Gaussian count across all cases. Due to characters limitation, we omit the full table here but will include it in the final version.

[Limitations 2]

​Thanks for this comment. While we acknowledge that our method does not introduce a fundamentally new architecture, we would like to emphasize that it offers a novel, practical, and generalizable primitive allocation strategy that complements existing 3DGS systems. Specifically:

• The rendering quality of ours is improved consistently across multiple benchmarks without increasing the number of Gaussian primitives. It also introduces a new, orthogonal perspective on primitive allocation based on complexity-density consistency, which brings additional interpretability and controllability beyond standard loss-driven heuristics.
• As discussed in Question 2, our CDC pruning strategy remains effective in a compact setting by selectively removing redundant Gaussians in over-reconstructed regions, supporting its utility beyond full-scale densification.
• As discussed in Question 4, our approach is plug-and-play and can effectively enhance existing methods by providing a complementary, complexity-aware allocation strategy.

[Limitations 1, Weaknesses 1]

We acknowledge that our definitions of complexity and density are heuristic, but they are carefully motivated by the intrinsic requirements of 3DGS rendering: regions with more visual structure require more primitives to accurately represent fine details, while flat or textureless regions can be modeled with fewer Gaussians. To reflect this observation, we introduce these two indicators to guide the allocation of Gaussian primitives:

• Complexity is defined as the image-space high-frequency response, obtained using Discrete Wavelet Transform (DWT). We argue this is appropriate because 3DGS primitives are optimized to render multi-view images, and the high-frequency content (edges, textures, contours) of these images reflects the structural detail that requires more expressive modeling. Our ablation in Supplementary Material Section B.1 shows that DWT-based complexity maps outperform classical high-pass filters like Sobel、Scharr and Laplacian, supporting the suitability of our definition.
• Density is defined as the inverse of the geometric mean distance to neighboring Gaussians. We choose this formulation to reflect the local compactness of Gaussians in 3D space, which directly impacts the alpha-blending outcome in 3DGS. Compared to arithmetic mean, the geometric mean is more sensitive to short distances, aligning better with the splatting kernel’s locality. Supplementary Material Section B.2 further demonstrates that using the geometric mean leads to better reconstruction quality with fewer primitives across multiple scenes.

Building on these two metrics, we propose the Complexity-Density Consistency (CDC) score to measure the alignment between a region’s structural complexity need and its current modeling density. Gaussians with high complexity but low density are interpreted as under-reconstructed and are thus prioritized for densification. Conversely, low-complexity but high-density Gaussians are considered over-reconstructed and are pruned. This is illustrated in Figure 1, where CDC-GS achieves more compact yet structure-aware primitive distributions. Table 1 further validates the effectiveness of our design, showing that CDC-GS improves rendering quality while maintaining (or even reducing) the total number of Gaussians — demonstrating that our definitions, while heuristic, are indeed effective and appropriate in practice.

​We appreciate the reviewer’s concern and will expand this justification more thoroughly in the final version of the paper.

[Limitations 2, Questions: The computational overhead may be discussed.]

We have conducted an ablation study to measure the additional computational overhead of our complexity and density components on the MipNeRF 360 dataset, using the same experimental setting as in the main paper. Specifically, we add each module (KNN-based density estimation and wavelet-based complexity estimation) independently to vanilla 3DGS, and record the corresponding training time overhead. The total overhead of our method is approximately +6:30 per scene. Individually, we measured +4:13 for complexity and +1:34 for density, each evaluated in isolation on top of vanilla 3DGS:

​We emphasize that our method prioritizes rendering quality and is designed with efficiency in mind. To reduce overhead:

• We integrate complexity computation into the alpha-blending process of 3DGS rendering to minimize cost. However, as complexity must be aggregated across all training views, and is recomputed every 100 iterations from epoch 600 to 15000, it contributes the bulk of the additional cost.
• Density estimation leverages CUDA-based KNN acceleration on the GPU, which keeps the overhead low and computationally practical.

​Notably, our additional training overhead does not impact rendering speed. As shown below, our method maintains the same FPS with vanilla 3DGS while improving reconstruction quality:

​We will include this analysis in the final version to clarify the cost-benefit tradeoff of our method.

[Limitations 3, Weaknesses 2, Questions: Comparison with the SOTA methods.]

We have conducted additional comparisons with two recent state-of-the-art 3DGS-based methods (Spec-Gaussian and Scaffold-GS) on the MipNeRF 360 dataset. For Spec-Gaussian and our method, we adopted the same training settings as in our main paper, i.e., 4× downsampling for outdoor scenes and 2× downsampling for indoor scenes, following established practice. However, for Scaffold-GS, we followed the original settings reported in its paper, without image downsampling, since it is a voxel-based method and highly sensitive to input resolution. We opted to preserve its original configuration to ensure a fair and representative comparison. Additionally, we do not report the number of Gaussians (#GS) for Scaffold-GS, since it is an anchor-based method that does not rely on explicit Gaussian primitives.

​The results demonstrate that our method achieves superior overall performance. Specifically:

• Our PSNR and SSIM exceed both baselines, reflecting higher reconstruction quality.
• While our LPIPS is slightly higher than Spec-Gaussian, it remains very close (0.183 vs. 0.176) despite using ~700K fewer Gaussians.
• In terms of training efficiency, our method is significantly faster than Spec-Gaussian (35.36 vs. 61.31 hours), and only moderately slower than Scaffold-GS, while achieving much higher quality.

​These results indicate that our complexity-aware allocation strategy enables competitive or superior rendering quality with fewer primitives and lower training cost, compared to strong SOTA baselines. We will include these comparisons in the final version.

[Limitations 4, Weaknesses 3]

Although the quantitative improvements may appear moderate at first glance, it is important to emphasize that CDC-GS operates under constant resource constraints, i.e., using the same number of Gaussians. Achieving consistent quality gains under such conditions is non-trivial and practically valuable. More importantly, the proposed complexity-density guided allocation mechanism also introduces a new, interpretable, and orthogonal perspective on primitive allocation based on complexity-density consistency, which brings additional interpretability and controllability beyond standard loss-driven heuristics.

​To further demonstrate the plug-and-play nature of CDC, we integrate it into 3DGS-MCMC [NeurIPS’24], a recent state-of-the-art 3DGS variant. As shown below, even with the same number of Gaussians, CDC leads to consistent rendering improvements:

​We also evaluated the effectiveness of our method under a compact configuration, where only the CDC pruning component is applied — i.e., no CDC-based densification. We compare this Ours (Prune Only) variant against recent compaction-focused baselines suggested by the reviewer, including Mini-Splatting, LightGaussian, and Taming-3DGS. For easier comparison, We highlighted the best metrics excluding vanilla 3DGS.

​This confirms that even in a heavily pruned setting, our CDC-based strategy can maintain or slightly improve quality while significantly reducing model size, effectively identifying and removing redundant Gaussians in over-reconstructed regions.

Taken together, these results demonstrate that while our improvements may appear modest numerically, they are broadly applicable, structurally motivated, and practically beneficial, especially considering they come without any additional Gaussian budget.

​We will include these analyses in the final version and sincerely appreciate the reviewer’s constructive feedback.