Reframing Gaussian Splatting Densification with Complexity-Density Consistency of Primitives
Authors: Zhemeng Dong
Junjun Jiang
Youyu Chen
Jiaxin Zhang
Kui Jiang
Xianming Liu
Venue: NeurIPS 2025 poster ()
Keywords: 3D Gaussian Splatting
Novel View Synthesis
3D Reconstruction
Computer Vision
Primary area: applications
TL;DR: We propose CDC-GS, a 3DGS densification strategy based on visual prior which is perpendicular to existing gradient-based ones. Our method improves the novel view synthesis quality by a large margin without increasing the number of Gaussians.

Abstract: The essence of 3D Gaussian Splatting (3DGS) training is to smartly allocate Gaussian primitives, expressing complex regions with more primitives and vice versa. 
Prior researches typically mark out under-reconstructed regions in a rendering-loss-driven manner. 
However, such a loss-driven strategy is often dominated by low-frequency regions, which leads to insufficient modeling of high-frequency details in texture-rich regions. As a result, it yields a suboptimal spatial allocation of Gaussian primitives.
This inspires us to excavate the loss-agnostic visual prior in training views to identify complex regions that need more primitives to model. 
Based on this insight, we propose Complexity-Density Consistent Gaussian Splatting (CDC-GS), which allocates primitives based on the consistency between visual complexity of training views and the density of primitives. 
Specifically, primitives involved in rendering high visual complexity areas are categorized as modeling high complexity regions, where we leverage the high frequency wavelet components of training views to measure the visual complexity. 
And the density of a primitive is computed with the inverse of geometric mean of its distance to the neighboring primitives. 
Guided by the positive correlation between primitive complexity and density, we determine primitives to be densified as well as pruned. 
Extensive experiments demonstrate that our CDC-GS surpasses the baseline methods in rendering quality by a large margin using the same amount of Gaussians. 
And we provide insightful analysis to reveal that our method serves perpendicularly to rendering loss in guiding Gaussian primitive allocation.

Reframing Gaussian Splatting Densification with Complexity-Densing Consistency of Primitives
Zhemeng Dong, Junjun Jiang, Youyu Chen, Jiaxin Zhang, Kui Jiang, Xianming Liu
Faculty of Computing, Harbin Institute of Technology
23.24
IG8: 106/2.75M
3DCS
PSNBL- 23.76
Rendered Image
Zoomed-in Comparison
Gauscian
Ground Truth
Glgis/ow complesity sagion)
Figure 1: Comparison between vanilla 3DGS and our CDC-GS on the rendering quality and distri- bution of Gaussian primitives. CDC-GS allocates Gaussian primitives in more efficient fashion, using more primitives modeling complex region and less model plain area, and thus significantly improves the rendering quality with a similar level of primitive number.
Abstract
The essence of 3D Gaussian Splatting (3DGS) training to smartly allocate Gaus- sian primitives, expressing complex regions with more primitives and vice versa. Prior researches typically mark out under-reconstructed regions in a rendering- loss-driven manner. However, such a loss-driven strategy is often dominated by low-frequency regions, which leads to insufficient modeling high-frequency details in texture-rich regions. As result, it yields suboptimal spatial alloca- tion of Gaussian primitives. This inspires us to excavate the loss-agnostic visual prior in training views to identify complex regions that need more primitives model. Based on this insight, we propose Complexity-Demi -Dnssiy Consistent Gaussian Splatting (CDC-GS), which allocates primitives based the consistency between visual complexity of training views and the density of primitives. Specifically, primitives involved in rendering high visual complexity areas categorized modeling high complexity regions, where we leverage the high frequency wavelet components of training views to measure the visual complexity. And the density primitive is computed with the inverse of geometric mean of its distance to the neighboring primitives. Guided by the positive correlation between primitive complexity and density, we determine primitives to be densified as well as pruned. Extensive experiments demonstrate that our CDC-GS surpasses the baseline meth- ods in rendering quality by large margin using the same amount of Gaussians. And we provide insightful analysis reveal that our method serves perpendicularly to rendering loss in guiding Gaussian primitive allocation. Our implementations are available on our project page: githuu.........
"Corresponding author. E-mail: jiangjunjun @ hit.edu.cn.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
3D reconstruction, as a long investigated task of both computer vision and compute graphics com- munities, aims to build 3D representation of the scene from a batch of posed input views, which can be utilized for novel view synthesis, geometry reconstruction, semantic understanding and other downstream tasks. 3D Gaussian Splatting (3DGS) [1] has emerged as the leading paradigm for this task, offering compelling combination of photorealistic and real-time rendering performance. Benefiting from explicitly modeling the scene with a set of Gaussian primitives, 3DGS is friendly to graphical rasterization pipeline, and thus being far more efficient than Neural Radiance Fields (NeRF) [2] in novel view synthesis. Recent researches have revealed that the allocation of Gaussian primitives is the key to high quality 3DGS representation [3, 4, 5, 6]. referring to the densification and pruning of Gaussian primitives in 3DGS training process.
The training of 3DGS starts with set of sparse Gaussian primitives, which are then iteratively optimized, densified, and pruned to form a well-distributed and compact representation. Vanilla 3DGS [1] assigns the positional gradient of each Gaussian primitive to themselves as the densification score, and mark out the coarse primitives with densífication score above the densification threshold to be densified. While recent works have explored alternative densification scores beyond positional gradient [7, 4, 5, 8), they are basically driven by rendering loss. Such loss-driven densification schemes typically struggle with expressing high-complexity visual details, where the rendering loss is smoothed out and fails to mark out the coarse Gaussian primitives for densification (Figure 1). Though one can solve this problem by decreasing the densification threshold for more primitives, this will lead to explosive growth of primitives in plain regions. These redundant primitives can barely improve the rendering quality but hinder the rendering efficiency.
Inspired by the fact that the failure of loss-driven densification happens in high visual complexity regions, we argue that we can specify these regions with visual prior measuring the visual complexity. Sparse Gaussian primitives in complex regions should be densified to allocate more primitives the regions, while the redundant dense primitives in plain regions should be pruned for simplification and efficiency. With this insight, we propose Gaussian primitive allocation method to existing loss-
Ceaplexity-Densiie Consistent Gaussian Splatting
(CDC-GS), which serves perpendicularly driven ones. Our method measures the visual complexity of training views with the high frequency component of Discrete Wavelet Transform (DWT) [9], and categorizes the primitives involved most with rendering the high frequency areas of training views as modeling complex regions. To measure the density of the neighboring space around primitive, we utilize the inverse of geometric mean of its distance to the neighboring primitives. Combining the above two measurements, we define loss-agnostic prior-based densification score, partitioning all primitives into four quadrants, where the two axes are complexity and density of primitives, as shown in Figure 2. Our CDC-GS suppresses the primitives in the left-up and right-down corner (see Figure 4a), which corresponds to the under-reecosstructed and over-reconstruucte regions, respectively.
To further improve the performance of CDC-GS, we introduce a complexity adaptive den- sification threshold scheme, which adjusts the densification threshold in a primitive-wise manner. Primitives modeling complex regions are assigned with a lower densification threshold, which helps to allocate more Gaussians to complex regions, and vice versa.
Extensive experiments are performed on standard 3DGS benchmarks, which demonstrate that our method substantially improves the rendering quality with the same level of primitive number compared to baselines. We also provide insightful analysis on why the proposed prior-based primitive allocation strategy are perpendicular to existing loss-based ones, which further advocates the soundness of our method. To summarize our contributions,
We propose a novel Gaussian primitive allocation scheme based on loss-agnostic visual prior, which guides 3DGS to allocate Gaussian primitives smartly by modeling complex regions with dense primitives and plain regions with sparse ones.
We develop Haaplexxty-Denniie Consistent Gaussian Splatting, which utilizes the wavelet frequency prior and primitive density to detect primitives under-recoossrructed and over- reconstructed regions for densification and pruning.
Insightful analysis provided to demonstrate why the proposed complexity-densin consistent prior serves perpendicular primitive allocation strategy against existing loss-driven methods.

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2 Related Work
3D Reconstruction. The target of 3D reconstruction is to obtain high quality 3D representation of the scene. Each time when the representation paradigm evolves always brings a new trend to the research community. Early works use point clouds to reconstruct the scene [10, 11, 12. 13], which remain popular these days in certain domains but struggle to recover textures, failing in novel view synthesis. Alternatively, Neural Radiance Fields (NeRF) [2] represents the scene as an implicit radiance field encoded in multi-layer perceptron (MLP). While showing significant advantage in novel view synthesis against prior methods, NeRF based reconstruction methods have bottleneck the efficiency of training and rendering [14, 15, 16, 17J. More recently, 3D Gaussian Splatting (3DGS) [1] emerges as a new leading paradigm for 3D reconstruction, highlighted with fast training and real-time rendering. Over time, numerous extensions have further enhanced its efficiency [8. 18, 19, 20], compactness [21, 22, 23, 24), and robustness under challenging conditions [25, 26, 27, 28, 29]. Using set of 3D Gaussian primitives expressing the scene, 3DGS can be adopted to extensive tasks, such as novel view synthesis [30, 31, 32, 33], geometric reconstruction [34, 35, 36, 37, 38], 3D segmentation [39, 40, 41], and semantic understanding [42, 43, 44, 45).
Primitive Allocation for 3DGS. To obtain high quality 3DGS representation of the scene, it is vital to correctly allocate Gaussian primitives over the space. The allocation is expected to use more primitives model the complex regions and less primitives to model the plain regions. For primitive densification, prior works propose different densification scores to measure if a primitive modeling an under-reconstruuced region. Vanilla 3DGS [1] adopts high positional gradient of primitives centers derived from the rendering loss as the densification score. Absgs [4] takes step forward by calculating the sum of pixel-wise absolute gradient, addressing the conflicts in gradient direction of vanilla 3DGS [1]. Revising-3DGS [7] utilizes the primitive-involved high rendering error instead, which differs from positional gradient but is still driven by the rendering loss. Taming- mixing primitive attributes and positional gradient. All of
3DGS [8] proposes densification these methods specifies mecersreconstrutte primitives in a loss- manner, thus they are either struggled with mnderrreconstruction in complex regions (vanilla 3DGS, Revising 3DGS, Taming- 3DGS) or werrreconstruution in plain regions (Absgs). On the other hand, redundant primitives pruned slim the primitives. The most widely adopted metric is prune primitives with low opacity [46, 47, 48). There are also methods pruning the primitives with over-dense neighbors [3, 21].
Frequencc-basee based 3DGS Densification. Since our work use frequency information of training views to guide the allocation of Gaussian primitives, we specifically introduce the works investigating the use of frequency theory for primitive allocation. FreGS [49] improves 3DGS optimization with loss frequency domain, but at the cost of explosive primitive growth, resulting in two times of primitives compared to 3DGS. Although FDS- GS [50] proposes frequency- aware density control method, they mainly focus on the connection between density and scale of primitives and do not really investigate method explicitly utilize the frequency
how visual frequency impacts 3DGS. Compared to them, information in training views as a prior to guide the densification, addressing the reoostrrcontttutctoon and ver-reconstruution in simple and efficient scheme. Furthermore, provide experimental evidence to prove that our method perpendicularly discovers under-reconstruuted Gaussian primitives ignored by prior loss-driven method, which further emphasizes the superiority of our method.
3 Method
In this section, we introduce our CDC-GS detail. In Section 3.1, 1, we first review preliminaries about 3D Gaussian Splatting and Discrete Wavelet Transform. In Section 3.2, we introduce how CDC-GS computes the complexity and density of Gaussian primitives. In Section 3.3, we explain how CDC-GS utilizes complexity-densice consistency to specify coarse and redundant primitives in under-reconttruucted and over-recenttruuttd regions, which is the key of our method to allocate Gaussian primitives based loss-agnostic visual prior.
3.1 Preliminary
3.1.1 3D Gaussian Splatting
3D Gaussian Splatting (3DGS) represents a 3D scene using a set of Gaussian primitives {G.).N) where N is the number of primitives. Each primitive G, is a 3D Gaussian distribution, parameterized
3

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AAA
A
DWT
Filter
IDWT
Training Images
Complexity Maps
Gaussians
Scatter of Gaussians
Densify
Complexity
Multi-View Projection
KNN
Prune
Density
Complexity
Density
CDC Primitive Allocation
Figure 2: Overview of our Complexity-Densiiee Consistent Primitive Allocation. We extract complexity maps for training images using DWT and back-projected the complexity maps onto Gaussian primitives to parameterize their complexity, while the density each primitive estimated with geometrical statistics about its neighbors. By densifying the primitives with low density vs. high complexity and pruning the primitives with high density vs. low complexity, CDC-GS adaptively allocates Gaussian primitives across the scene based complexity of the space.
by its center μs E RR' opacity o, E IR_, a full 3D covariance matrix 2, E 1g8x3, and Spherical Harmonic (SH) coefficients oi e 13x16 encoding anisotropic appearance. The probability density function of the primitive is defined as,
G.(z) = exp (- us) - mi)
where x E R is an arbitrary point 3D space, For rendering, primitives are projected to the image plane 2D Gaussians G?D and the color C(x') E R3 of pixel x' IR22 is rasterized as,
j-1
C(x') = Co a, = oz
T₁ = -=II
II (1-aa) ax).
(2)
j=1
1=1
where the number of primitives covering pixel x', and ej is the response of cith to the current camera view. The optimization of primitives supervised with color rendering loss [1].
Besides the numerical optimization for primitives, the vanilla 3DGS adopts adaptive primitive allocation to express the scene better. Primitives receiving a positional gradient beyond threshold Tpos from the rendering loss are recognized as underfitting, and are densified to allocate more primitive to the region. Meanwhile, primitives possessing low opacity contribute little to modeling the scene according to Equation 2, which are pruned reduce the primitive redundancy.
3.1.2 Discrete Wavelet Transform
2D Discrete Wavelet Transform (DWT) [9] is a potent tool to analyze frequency information of images. DWT decomposes image into multiple sub-bands using pair of orthogonal low-pass and high-pass filters, denoted by FL and Fn, respectively. Given a one-channel image / E H where H and W denote height and width of the image, one-level 2D Haar wavelet decomposition is formulated as,
ILL HHL
LLH
DWT(/)
[ AT..
HH
FH
Here, fll, I 1 7HH are four sub components of decomposed by DWT, where ILI denotes the low-frequency structure (e.g., plain areas) and the rest three components correspond to high- frequency structure of the image (e.g., complex areas and edges). Moreover, DWT is an in- vertible transformation. which means one can obtain image with its four sub-components, as I = IDWT(1LL ,LH H HH).

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3.2 Complexity and Density of Gaussian Primitives
Before introducing how our CDC-GS allocates Gaussian primitives with complexity eensstxty-deensty consis- tency prior, we first define the complexity and density of each Gaussian primitive in this section.
The complexity of a primitive is to measure whether it's modeling complex region, and we excavate this information from the frequency information of training views. We apply DWT to each training view 7 and break it down into four sub-components, defined in Equation 3. By removing the low frequency component 7LL and retain the other three components, we extract the high frequency part of image 1. And we define the complexity map of image / as,
E IDWT(0, l! y /""!),
(4)
which back projected to Gaussian primitives to compute the complexity of each primitive. Specifically, given a primitive G, involved to rendering pixel x' with weight wo (x(xx) a,T, the complexity of G; with respect to x' is defined as r'),,²) = Er (z') wi (x')/ max (wy (w)()')), where P takes the same meaning as in Equation 2 and the max operator enumerates all the primitives covering x' as normalization. Considering all 7(G,, -), which is to enumerate all pixels covered by G, in all training views { we take the maximum complexity to represent the complexity of Gs, which is formulated as,
I(G.)
= max max (1(G),z)) I,E(7) ZZ
(5)
The definition of y ensures that the complex areas in training views mainly affect the complexity of the primitives involved most in their rendering, and suppress their influence the invisible primitives from the view.
Complexity alone cannot affirm if a primitive is in under-reconstrruted region or an over- reconstructed region. For example, high complexity region filled with dense Gaussian primitives is probably well reconstrueted, while sparse primitives in such region typically indicate under- reconstruction, which can be ignored by loss-driven indicators such as gradient when the rendering loss is smoothed out with the figh-frequency details. It's of necessity to cooperatively take both complexity and density of primitives to specify under-reconstruucton and over-reconstruutton. To estimate the density of the neighboring space of primitive G;, compute the inverse of geometric mean of the center distance between G; and its neighbors, formulated as,
(G.) =
114 II JEM
15l1
where M, the set of nearest neighbors of G,. Both formulations are empirically validated to yield more stable and efficient primitive allocation (see Appendix B-1...
3.3 Complexity-Densig Consistent Primitive Allocation
With the complexity and density of Gaussian primitive defined in Section 3.2, we can now introduce how the proposed CDC-GS allocates primitives based on them. As already discussed, the complexity and density of primitive are expected to share consistency in well-reconstructeed region, otherwise could indicate possibility of umder-reconstruction or over-reconstruction To formulate the consistency between the complexity and density of primitive G3, we use the production of their normalized value,
I(G.) 8
I Imean T I'sad
(G:).
V
mean
(7)
V
std
where meann V mean are the mean of complexity and density of all primitive respectively, and I'std, sed denote the corresponding standard derivation. Positive value of s; indicates the consistency of complexity and density, while low complexity vs. high density and high complexity vs. low density results in negative s, indicating oversseconttruutionn and underrreconstrruction respectively.
Our complexity-densioe consistency serves as a perpendicular complementary to existing primitive allocation method. Denoting primitives selected densified in a certain optimization step M, CDC-GS decomposes M into Misss and Make where M Misss U U Miss refers to the primitives selected by existing loss-driven densification method positional gradient), and Mede
5

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Table Quantitative comparison on novel view synthesis. Results are reproduced with the official implementation of baselines. Bold indicates the best results. Our method consistently achieves superior performance across datasets with a fewer or comparable number of Gaussian primitives.
MipNeRI 360
Tanks & Temples[51]
Deep Blending|
Method
PSNR
SSIM
LPIPS
#GS
PSNR
SSIM
LPIPS 1 #GS
PSNR
SSIM
LPIPS
#GS
3DGSI11
27.79
0.201
2.59M
0.853
0.170
1.57M
29.73
0.238
2.47M
Taming 3DGS(18
27.91
0.821
0.211
2.53M
24.32
0.862
0.157
160M
29.73
0.908
0.234
2.07M
Ours (0.01)
28.02
0.183
0.866
0.149
1.60M
29.84
AbsGS[4]
27.72
0.835
0,169
4.06M
23.22
0.856
0.152
1.90M
29.28
0.903
0.233
3.13M
Mini-Splating-D111
27.78
0.841
0.163
0.855
4.27M
29.93
0.210
4.63M
Pixel-GS[51
27.84
0.835
0.176
5.27M
23.66
0.856
0.150
4.50M
28.95
0.896
0.247
4.65M
Ours (0.02)
28.11
0.164
0.867
0.140
2.56M
30.03
0.912
0.218
denotes the primitives selected by the proposed complexity-density consistency. For the primitives in under-reconstrructed regions, we randomly sample up to Pa -N of them for densification, where the sampling probability determined with |s:]- For the primitives in over-reconstructed regions, we randomly sample to Pp N of them to be pruned, where the sampling probability is determined with og. The original pruning strategy of 3DGS at every 100 steps is removed, which is alternated to pruning all primitives with opacity below 0.1 for every 3000 steps.
To further improve the quality of Misss relieving more primitives from under- propose to adjust the densification threshold of each Gaussian primitive based on its complexity. The complexity-avee densification threshold defined as,
(T) = Tlow + (Tupp Tlw) [1 a r)],
(8)
where Tlew and Tupp the lower and upper bound of the densification threshold, respectively, refers to the Sigmoid function, and À is hyper- typer-parameter.
4 Experiments
4.1 Experimental Settings
Dataset. We evaluate our method the real-world datasets widely adopted in novel view synthesis. Specifically, we follow the standard protocol in vanilla 3DGS [1], using 9 scenes from the MipNeRF- 360 [30] dataset, the playroom and drjohnson scenes from Deep Blending [52] dataset, and the train and truck scenes from Tanks & Temples [51] dataset. The preprocess of training data also strictly follows vanilla 3DGS [1].
Metrics. We report quantitative results with three standard metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Metrics (SSIM) [53] and Learned Perceptual Image Patch Similarity (LPIPS) [54). All metrics are computed on test views using the original evaluation protocol. We report the average score across all scenes for each dataset. Each experiment is repeated three times with different seeds, and we report the average performance across runs to account for randomness.
We compare our method with representative methods investigating Gaussian primitive allocation, including vanilla 3DGS[1], Taming-3DGSII (constrained to the same number of primi- tives to our Pa = 0.01 version), AbsGS[4] (with the densification threshold set to 0.0004, the dense version of [4]). Mini- ] (densification-nnl version without pruning), and Pixel-GS[S], All baseline results reproduced using the official implementations and default configurations to ensure fairness of experiments.
Baselines.
Implementation Details. Our method is implemented on top of the official 3DGS codebase [1]. We extract complexity map of input views using one-level Haar DWT. And the density of Gaussian primitives is computed with 3 nearest neighbors, which is to say [N] = 3 for all primitives. We set Pa = 0.01 and Ap 0.01 by default. We also evaluate an additional setting by increasing the splitting ratio to Pa = 0.02. Our complexity-aware densification threshold is configured with Now 1.5 x 10-1 Tupp = 10-1 and X = Other saprr-parameters are consistent with the vanilla 3DGS [1]. All experiments are performed on single NVIDIA RTX 3090 GPU.

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Train
Truck
Room
Drjbonson
Trechill
3DGS
SAA.SSSE C-
Pixel-GS
Taminng TDGS
Ours
Figure 3: Qualitative comparison on novel view synthesis results. Compared to baseline methods, method yields sharper textures. more faithful structures, and fewer artifacts without increasing primitives, which is attributed to our CDC strategy that improves the allocation primitives.
4.2 Comparison to Baseline Methods
Quantitative Comparison. We report quantitative comparison between our CDC-GS and baseline methods in Table 1, where methods with approximate primitive number grouped together for fair comparison. In the sparse group, CDC-GS (pa 0.01) consistently outperforms baselines, demonstrating superior fidelity and perceptual quality without increasing the number of primitives. In the dense group, we set Pa = 0.02 to match the primitive number of baselines, ensuring a fair and meaningful comparison. While utilizing fewer primitives in general, CDC-GS achieves the best rendering quality across all benchmarks. The results further validate that our proposed complexity- density consistent allocation strategy enables more precise modeling of intricate structures while improving primitive allocation efficiency.
Qualitative Analysis. We show qualitative comparisons corresponding to Table I across various scenes in Figure 3. Our method consistently presents more detailed textures, cleaner structural boundaries, and fewer artifacts. The results advocates that method success to discover the under-reconstruuted regions that the baseline methods tend to overlook.
4.3
CDC as a Perpendicular Densification Indicator to Rendering Loss
In this subsection, we reveal that the proposed complexity consistency serves as perpendic- ular indicator against the loss-driven ones to specify the under-reeoosttmuttd regions.

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3DG3
Ours
ComplexityDDnme Correlation Inrations
1.0
Cur:: 0.333
Cor: 0.684
Complestyy Dorliy Conelation
0.7
Cunsiamny Score
6.6
Complexty
Complexty
6.5
0.4
0.3
6.1
0.0
0.0
0.5
1.0
0.0
0.5 Deniity
0001
3000
9000
12000
15000
Doniiy
Htrniton
(a) Complexity-densigy map of primitives.
(b) Complexity-density correlation along densification.
Figure 4: Analysis for complexity-densiee consistency on the scene "kitchen" of MipNeRF-360
dataset [30]. (a) The scatters depict the primitives at the end of densification (15k iteration) for
3DGS and our CDC-GS, with each primitive localized by its density and complexity. The color of each primitive indicates its consistency score s; (see Equation 7). The overall Pearson correlation [55] of complexity and density of primitives shown top-right. Color in the two scatters are normalized and aligned to ensure the same color corresponds to the same consistency score value. (b) Variation of complexity-densto Pearson correlation over the densification progress (600-15k iteration).
In Figure 4a, we present two scatter diagrams for vanilla 3DGS [1] and CDC-GS, with all Gaussian primitives represented by their complexity and density. The scatters show the degree of the primitives in the optimized 3DGS model of scene "kitchen" matching the rule of complexity-density consistency, While vanilla 3DGS exhibits little consistency in complexity and density, CDC-GS significantly reduces the primitives in the left-up and right-down corner, which indicates the most inconsistent primitives are remove with our proposed primitive allocation strategy. Accompanied with Table and Figure 3, we can draw the conclusion that the reduction of primitives in these regions do contribute to the quality of 3DGS model.
Moreover, in Figure 4b, we also provide the variation of complexity-density consistency along the training process of CDC-GS and all the baselines the scene "kitchen". We use Pearson correlation [55] to evaluate the overall consistency between the complexity and density over all Gaussian primitives, which evaluate the degree of scatters in Figure 4 constrained in the first and the third quadrant. While CDC-GS performs a consistent increase in the consistency, baseline methods fail to largely improve the consistency alone the training process. Notably, slight improvement in the consistency of the baseline methods can be observed along the training process, which demonstrates consistency naturally relates to the optimization of 3DGS, but struggles
that the cmmplxxttyddnsiie to improve without explicit manipulation. This advocates that the complexity-density consistency is perpendicular to loss-driven densification indicators.
To further consolidate this conclusion, we categorize the primitives in of vanilla 3DGS (left of Figure 4a) into two groups with the positional gradient of primitives and the densification threshold, which is presented in Figure 5a. We perform the same operation to AbsGS [4] and show the result in Figure 5b. The color of primitives indicates their positional gradient. Patterns by splitting the primitives with the densification threshold, demonstrating that coarse primitives recognized with positional gradient (Mioss. see Section 3.3) doesn't 't contain the primitives recognized with complexity-densit consistency (Mode), which is to say that Mede shares little cross with Mi We believe the above experiment results are convineing enough to support the perpendicularity of complexity-densit consistency against loss-driven densification indicators.
be barely drawn
4.4 Ablations
We perform ablation studies the Tanks & Temples dataset [51] using the vanilla 3DGS [1] as backbone to assess the individual contributions of the proposed Complexity -Aware Adaptive Threshold (CAAT) and Complexity -Density Consistency (CDC) introduced in Section3.3. Result is summarized in Table 2.
Ablation on CAAT. CAAT improves the reconstruction quality by manipulating densification threshold with complexity of Gaussian primitives. Slight increase in the number of primitives is observed because of aggressive densification in complex areas.
8

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Primitiives above
Primitives below
Primitives above
Primitives below Fpo
1.0
1.0
1.0
10
Gradient
Completty
Complesit
0.6
Compleity
Conalestt
0.5
0.5
0,5
Iveitbon
0.5
405
0.4
0.0
1.0
0.0
0.3 Demily
1.0
0.0
%.0
03 Dessity
1.6
%
0.3 Denuity
90
Deasity
(a) Vanilla-DDGS [1].
(b) AbsGS [4].
Figure 5: Perpendicularity between complexity-density consistency and positional gradient. We breakdown Figure 4a, categorizing the Gaussian primitives into two groups by if their positional gradient are above the densification threshold or not. And we show the same statistical information for AbsGS in Figure 5b. Color of primitives indicates the normalized magnitude of positional gradient. Primitives are categorized in a caaplextt-denssinn consistency agnostic way, advocating that the proposed complexity-deme
consistency perpendicular to the loss-driven positional gradient.
Table 2: Ablation study on Tanks & Temples dataset. We evaluate the contribution of the proposed modules: Complexity-ANee -ware Adaptive Threshold (CAAT) and Complexity-Denee Consistency (CDC). The full method (CDC-GS) combines both.
Method
SSIM
3DGS
23.79
0.853
0.170
1.57M
3DGS CAAT
24.00
0,859
0,163
1.70M
3DGS CDC
24.22
0.862
0.153
1.5IM
CDC-GS (Ours)
Ablation on CDC. CDC achieves substantial gain by simultaneous densification in under- reconstructed region and pruning in over-reconstructed region. Improvement in visual quality demonstrates that the proposed CDC strategy successfully mitigates the under-reconstructed problem vanilla 3DGS[1], while the concurrent reduction of Gaussian primitives confirms its effectiveness in eliminating unnecessary primitives in low-complexity regions.
Full Method. When combining CAAT and CDC, the two modules act synergistically: CAAT intro- duces complexity-aware densification to refine local details, while CDC enforces global complexity- density consistency by adjusting the primitive distribution according the complexity of the scene. As result, CDC-GS sigmificantly improve the reconstruction quality while maintaining a Gaussian primitive count comparable the vanilla 3DGS[1], demonstrating the strength of the proposed Gaussian primitive allocation strategy.
5 Conclusion
In this paper, we propose CDC-GS, a novel Gaussian primitive allocation method, which is perpen- dicular to existing loss-driven ones, such as the ones using positional gradient. Our method explores the reconstreon region with high complexity and low density, and the over-reconstructed region with low complexity and high density. Extensive experiments are performed demonstrate the superiority our method and its perpendicularity to existing primitive allocation methods. It's power is fully played as a complementary to existing loss-driven primitive allocation methods. We believe it is valuable for finding the sub-optimally reconstructed regions ignored by existing methods in prior driven manner.
Limitations. While improving Gaussian primitive allocation from an orthogonal perspective, our method still requires existing loss-driven cues (e.g., positional gradients). as the visual prior itself lacks direct awareness of reconstruction quality. In future work, we plan further investigate how visual priors influence primitive allocation, toward more coherent and adaptive allocation strategies.

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Acknowledgments
The rescarch was supported by the National Natural Science Foundation of China (U23B2009. 62471158).
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Appendix
A Impletation Details
A.1 Algorithmic Implementation of CDC-GS
Algorithm I provides detailed pseudocode of the training pipeline in CDC-GS. Built upon the vanilla 3DGS [1] framework, our procedure starts from a sparse initialization of Gaussian primitives and proceeds with joint optimization and CDC-guided density control across iterations. This pseudocode comprehensively implements the pipeline described in Section 3 of the main paper, integrating both loss-driven and prior-based cues for efficient and high-fidelity Gaussian allocation.
A.2 Haar-based DWT Implementation
In method, the visual complexity of each training view is extracted using single-level 2D Discrete Wavelet Transform (DWT)[9). We adopt the Haar wavelet basis due to its simplicity and efficiency. The filtering process is separable and implemented two 1D convolutions along height and width, as defined in Equation of the main paper, where Fi [1, 1]/v2, Fi [-1, 1] 12 are the ID low-pass and high-pass Haar filters. The resulting four subbands correspond to different frequency directions. Each 2D kernel derived from outer products of filters summarized in Table 3.
Table 3: 2D Haar DWT convolution kernels derived from filter outer products.
Subband
LL
LH
HL
HH
1
Kemnl K
To compute the visual complexity of each image, construct a high-pass filter by discarding the non- directional low-frequency subband 1tt and reconstruct the complexity map as defined Equation of the main paper. This effectively preserves only the high-frequenee directional responses (vertical, horizontal and diagonal), enabling the resulting map to serve as spatially-varying representation of complexity.
B
More Ablations
B.1 Comparison to Classical High-Pass Filters
To validate the effectiveness of our DWT-based design, we replace our DWT-based frequency estimation with three classical high-pass filters: Sobel[56), Scharr[57] and Laplacian[58], defined in Table then integrate each into the CDC-GS framework without any other modifications.
Table 4: High-pass filter kernels used for comparison.
Sabel
Scharr
Laplacian
-3
K.
-1
1
-2
-1
-3
10
-3
Ky
0
As shown in Table 5, all methods achieve similar performance in rendering quality, demonstrating the robustness of our CDC-GS framework the choice complexity estimator. Notably, the DWS--based variant slightly outperforms the others in both rendering quality and Gaussian compactness. We
20

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Algorithm CDC-GS Optimization and Density Control
Input: w, h: width and height of the training images
MM f- SfM Points
Positions > Covariances, Colors, Opacities Iteration Count > Eq.3
2: S, C,
InitAttributes()
3: (-0 0
4: (It1, _ 1 + DWT(I)
5: <- IDWT(O, 7LH 7HL, THH)
b Eq.4
6: while not converged do
7:
< TrampeerainnngVieee Î < Rasterize M, S, C, A)
Camera and Image I b Rendered Image i > Loss
8:
9:
4 1))
10:
M,S, A Adam(V
Backprop & Step
11:
if (TSRefinemmentteratonn)))) then
12:
I Complexity (M, E)
> Eq.5
13:
+ Density(M,, S, AA)
b Eq.6
14:
ConsistencyScore([ V
> Eq.7
15:
Compute sampling probabilities:
16:
pdens [8x] if i;; > pr, V < Pb
pruee
High-complexity, Low-density Low-complexity, High-density
17:
Pi x Oi if < pr,, v; p
18:
Sample Made density ~ Multinomial (pdnns Pd N) Sample Made
19:
Medeeprune prune Multinomial (p prue Pp N) for all Gaussians (j, c. in (M, S. C. A) do
20:
21:
if (j, E, ai) E Maak_prie then RemoveGaussian(yy o)
22:
D CDC Pruning
23:
end if
24:
if (i mod 3000 = 0) and (a < 0.1) then RemoveGaussian(a: E,
Periodic Pruning
26:
end if
TTT) Adrapiie
b Eq.8
28:
Misss + {Ge VpL; > T(T:)} Mdensify -Mioss Mede densify
b Gradient-based
30:
if (p. a, E Matnsity then
31:
if |Σ > T3 then
32:
SplitGaussian(y, C, else
D Over-reconstrructon
33:
34:
end CloneGaussian(j, L,
Under-recconstruction
35:
36:
end if
37:
end for
38:
end if
39: + i+1
40:
end while
41:
return Optimized Gaussian primitives (M,S,C,
attribute this to the multi-scale and multi diltiiddreectonall nature of the DWT, which enables more accurate modeling of visual complexity.
B.2 Geometric Arithmetic Mean
In Table 6, compare two variants of our CDC-GS framework that differ only in how they compute the density of Gaussian primitives. Specifically, the Arithmetic Mean variant uses the inverse of the arithmetic mean of distances to neighboring Gaussians, whereas the Geometric Mean variant (our default, as defined Equation 6 of the main paper) adopts the geometric mean formulation. Both variants are evaluated under identical settings.
Results show that using the geometric mean consistently yields slightly better rendering quality and reduces the number of Gaussians across all benchmarks. This confirms choice, the geometric
21

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Table Comparison classical high-pass filters on MipNeRF 360 [30]. We replace our DWT- based complexity estimation with Sobel, Scharr and Laplacian filters to construct complexity maps for CDC-GS. Our DWT-based formulation achieves the best performance across all metrics.
Filter
PSNR 7
SSIM
LPIPS 4
#GS
Subel
27.96
0.834
0.186
2.60M
Scharr
27.97
0.835
0.186
2.59M
Laplacion
27.96
0.835
0.184
2.54M
DWT
28.02
0.836
0.183
2.53M
mean provides sensitive estimation of local density, especially for short distances. We adopt the geometric mean formulation throughout the main paper.
Table 6: Geometric Arithmetic Mean in density computation. We compare two variants of CDC-GS that differ only in whether the geometric or arithmetic mean used for density estimation. The geometric mean consistently yields better performance with fewer Gaussians.
MipNeRF 360[30]
Temples(51]
Deep Blending[52]
Mothod
PSNR 1 SSIM 1 LPIPS #GS
PSNR
SSIM
LPIPS 1 #GS 1 PSNR 1
SSIM LPIPS
AGS
Arithmetic
27.98
0.834
0.185
2.54M
24.28
0.862
0.159
1.70M
29.82
0.909
0.234
2.14M
Geometric
28.02
0.836
0.183
2.53M
24.42
0.866
0.149
1.00M
29.83
0.909
0.234
2.07M
B.3 Reverse-CDC Ablation
To further examine the role of complexity- denssty alignment, we designed reverse variant in which Gaussians are densified low-complexity & high- high-density regions and pruned in high-complextty & low-density ones, thereby inverting the CDC guidance.
Table 7: Reverse-CDCC ablation on MipNeRF 360 [30]. Comparing vanilla 3DGS with Reverse- CDC shows degraded quality and increased number of Gaussians, highlighting the necessity of complexity-densee alignment.
Method
PSNR 1
SSIM 1
LPIPS 1
#GS
3DGS
27.79
0.826
0.201
2,59M
Reverse-CIXC
27.62
0.817
0.224
2.71M
As shown in Table 7, this reverse allocation leads to degradation in rendering quality and larger number of Gaussians. Although more primitives are introduced. the reconstruction becomes worse, demonstrating that enforcing complexity-densic alignment is essential for efficient modeling.
B.4 Efficiency Analysis of CDC-GS
We summarize the additional training cost introduced by the complexity and density modules. As shown in Table 8, the average overhead is dominated by the wavelet-based complexity computation, whereas both modules benefit from CUDA acceleration, keeping the cost practical. Although the training time increases, the rendering speed remains identical to vanilla 3DGS, and CDC-GS achieves higher reconstruction quality with a moderate additional cost.
C Additional Experiment Results
C.1 Extended Visualization Complexity- Correlation
As supplement to the consistency analysis in Section 4.3 of the main paper, we provide additional visualizations of the complexity-density correlation variation on three scenes from different datasets: the outdoor scene "garden" from MipNeRF 360 [30], "train" from Tanks & Temples [51], and indoor
22

---

Table Training efficiency analysis of CDC-GS components on MipNeRF 360 [30]. "+ Density Only" and "+ Complexity Only" denote adding the KNN- and DWT-based modules individually.
Truining
Overhead
3DGS (baseline)
29:06
Density Only (KNN)
30:40
+1:34
Complexity Only (DWT)
33:19
+4:13
CDC-GS (Full.
35:36
+6:30
Complexity- -Density Correlation Varistion on "Garden"
Complexity Comelation Variation on "Trin""
ConplaittyDDritt Crenchiie
02
0.2
06-
-0.2
402
15000
5000
(a) Scene: Garden (MipNeRF 360).
(b) Scene: Train (Tanks & Temples).
Complexity- Density Correlation Variation on "Drjahonson"
Average Complexity Variation
Complesity Candatioe
Conpleityy Deasit Condatio
04
02
0.0-
610
3000
6000
Decatoon
9000
12000
15000
600
3000
6000
9000
12000
15000
(c) Scene: Drjohnson (Deep Blending).
(d) Average across all 13 scenes.
correlation variation across datasets. We show the Pearson correla- tion between visual complexity and local primitive density over training iterations. Our CDC-GS consistently improves and maintains this correlation, indicating stronger structural consistency com- pared to baseline methods.
Figure 6: Complexity
scene "drjohnson" from Deep Blending [52]. We also report the average correlation variation across all 13 evaluated scenes.
These results in Figure 6 further validate the robustness of our CDC-GS framework in aligning visual complexity with local density across different scenes and datasets. In contrast, baseline methods often show unstable correlation trends or even negative correlation values, which contradict the expected relationship between structural complexity and spatial density, leading persistent under-reeonstrrucion in complex regions and over-reconstruution in simple areas.
C.2 Supplementary Qualitative Results
As presented in Tables 9-12, our CDC-GS method consistently outperforms baselines across diverse benchmarks in terms of PSNR, SSIM, and LPIPS, while maintaining a significantly lower or com- parable number of Gaussians. Specifically, under the same or fewer primitives, CDC-GS achieves better fidelity high-complexity, detail-rich regions, thanks to its frequency-guided complexity modeling. This highlights the effectiveness of our complexity-densee cating primitives to structurally complex areas, offering a complementary and orthogonal benefit to existing loss-driven methods. Our approach proves especially advantagcous under constrained Gaussian budgets, delivering improved rendering quality without sacrificing efficiency.
consistency strategy in allo-
23

---

Table 9: Per-scene PSNR consistently achieves competitive or superior results across diverse scenes.
three datasets. Bold indicates the best results. Our method
MipNeRF 360130]
Tanks & Temples(51]
Deep Bleading)521
Method
Flowers Trechill Garden Bicycle Stump Kitchen Bonsai Counter Room
Train
Truck
Drjohnson Playroom
3DGS[1]
21.92
22.86
27.88
25.68
26.91
31.42
32.47
29.18
31.81
22.07
25.51
29.37
30,09
Hamingg-DGSS
21.81
23.08
27.78
25.47
26.63
32.05
32.84
29.38
32.12
22.62
26.01
29.43
30,03
Ours (0.01)
22.01
22.69
28.14
25.96
27.13
32.18
32.32
29.41
32.37
22.61
26.22
29.61
30.06
AbsGS[4]
21.78
22.19
27.87
25.76
27.04
31.48
32.32
29.18
31.87
21.14
25.30
28.61
29.96
Mini-Splatting-DB3
21.89
22.59
27.80
26.00
27.46
31.48
52.35
28.62
31.83
21.22
25.39
29.40
30.47
Pisel-GSi.51
21.94
22.52
27.88
25.72
27.18
31.92
32.60
29.29
31.46
21.89
25.44
28.08
29.82
Ours (0.02)
22.14
22.74
28.26
25.99
27.39
32.25
32.38
29.51
32.33
22.74
26.19
29.68
30.39
Table 10: Per-scene SSIM scores across three datasets. Bold indicates the best results. Our method consistently achieves competitive or superior results across diverse scenes.
MipNeRI 360[30]
Tanks & Temples(51]
Deep Blending[52]
Method
Hlwwrs Trechill
Bicycle Stump Kitchen
Counter
Truck
Dejohnson Playroom
3DGS(]]
0.622
0.652
0.875
0.779
0.783
0.933
0.948
0.916
0.929
0.820
0.885
0.905
0.907
Taming-3DGS13]
0.613
0.646
0.871
0.775
0.771
0.930
0.946
0.910
0.922
0.831
0.893
0.908
0.908
Ours (0.01)
0.648
0.656
0.883
0.801
0.794
0.936
0.947
0.921
0.936
0.837
0.895
0.908
0.911
AbsGS[4]
0.654
0.645
0,883
0.801
0,795
0.935
0,951
0.920
0,935
0.822
0.890
0.899
0.907
Mini Splatting D(3)
0.659
0.659
0.884
0.811
0.816
0.936
0.953
0.918
0.936
0.819
0.890
0.906
0.908
Pixel
0.653
0.652
0.879
0.792
0.798
0.936
0.952
0.922
0.930
0.825
0,887
0.887
0.905
Ours (0.02)
0,660
0,660
0.887
0.808
0.812
0.938
0.947
0.925
0.940
0.838
0.895
0.912
0.912
Table 11: Per-scene LPIPS scores across three datasets. Bold indicates the best results. Our
method consistently achieves competitive or superior results across diverse scenes.
MipNeRF 360[30]
Tanks & Temples[51]
Deep Blending(52]
Method
Flowers Trechill
Bicycle Stump Kitchen
Counter
Drjohnson Playroom
3DGS(1]
0.328
0.316
0.102
0.203
0.209
0.113
0.173
0.178
0.191
0.197
0.142
0.236
0.240
Faming-3DGGSj8
0.334
0.310
0.200
0.126
0.200
0.123
0.233
0.235
Ours (0.01)
0.274
0.289
0.090
0.175
0.206
0.109
0.165
0.167
0.170
0.181
0.118
0.232
0.235
AbsGS[4]
0.244
0.256
0.089
0.157
0,182
0.106
0,155
0.162
0,168
0,182
0.122
0.236
0.229
Mini-Splatting-DESS
0.246
0.256
0.086
0.151
0.163
0.105
0.142
0.152
0.162
0.181
0.100
0.218
0.203
Pixcl-GS[5]
0.252
0.270
0.093
0.173
0.106
0.162
0.120
0.255
Ours (0.02)
0.240
0.256
0.085
0.154
0.169
0.104
0.155
0.153
0.162
0.171
0.108
0.220
0.216
Table 12: Per-scene number of Gaussian primitives across three datasets. Values are reported in millions; bold indicates the lowest per scene. Our CDC-GS achieves competitive or significantly lower primitive counts, demonstrating its superior efficiency.
MipNeRF 360[30]
Tanks & Temples|51]
Deep Blending|52]
Method
Flowers Treehill Garden Bicycle Stump Kitchen Bonsai Counter Room
Train
Truck
Drjohnson Playroom
3DGS11|
2.75M
3.16
3.65M
4.68M
4.14M
1.54M
104M
1,99
205M
3.11M
1.84M
Taming 3DGS[8]
3.09M
3.90M
3.62M
4.42M
3.92M
0.94M
L00M
0.82M
L07M
1.3M
2.07M
2.53M
L60M
Ours (0.01)
3.09M
3.90
3.62M
4.42M
3.92M
0.94M
1.00M
0.82M
1.07M
1.13M
2.53M
1.60M
AbsGS[4]
5.16M
6.13M
4.68M
7.63M
5.62M
2.34M
1.2MM
1.49M
2.12M
163M
2.16M
4.04M
2.22M
Spalt-ppatting-11311
4.76M
4.83M
5.85M
3.6MM
3.76M
3.3M
4.06M
395M
4.91M
4.35M
Pixel GS[5]
7.10M
7.47M
7.64M
8.59M
6.49M
3.05M
2.06M
2.50M
2.49M
3.80
5.21M
5.55M
3.74M
Ours (0.02)
5.14M
5.39M
7.05M
1.50M
1.65M
1,3M
1.64M
1.78M
3.34M
3,09M
1.89M
24


Reviews:
[{"review_id": "mIXAxhttAS", "reviewer": "Reviewer_eEWa", "summary": "This paper proposes Complexity-Density Consistent Gaussian Splatting (CDC-GS), an approach to improve 3D Gaussian Splatting by aligning the allocation of Gaussian primitives with visual complexity rather than relying solely on rendering loss. Traditional loss-driven methods tend to favor low-frequency regions, neglecting high-frequency details. CDC-GS addresses this by leveraging wavelet-based visual complexity from training views and computing primitive density based on spatial proximity. By correlating complexity with density, the method effectively identifies regions for densification and pruning. Experiments show that CDC-GS significantly outperforms baseline methods in rendering quality using the same number of primitives.", "questions": "I would like to see the performance comparison with the SOTA methods, such as Spec-Gaussian etc.\nThe computational overhead may be discussed.", "limitations": "The definitions of visual complexity and primitive density are heuristic and lack strong justification. The computational overhead of complexity and density calculations is not analysed.\nThe method is not compared against recent state-of-the-art approaches like Spec-Gaussian or Scaffold-GS. Reported performance gains are modest.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe paper is well-motivated and offers an appropriate analysis of the weaknesses in current practices, which strengthens the rationale behind the proposed solution.\nThe paper introduces a loss-agnostic approach to primitive allocation, shifting away from the conventional rendering-loss-driven strategies. This potentially helps addressing the limitation in existing methods that often overlook high-frequency regions. The proposed complexity-density consistency criterion provides a coherent mechanism for determining where to densify or prune primitives, potentially leading to efficient and accurate scene representations. By leveraging high-frequency components from wavelet transforms to measure visual complexity, the method somehow brings an intuitive and effective signal for guiding primitive allocation, especially in texture-rich areas. The approach complements rendering-loss-based methods by providing an orthogonal signal for guiding Gaussian allocation, making it potentially integrable with existing pipelines.\n\nWeaknesses:\n1. The justification for whether the definitions of complexity and density of Gaussian primitives are appropriate needs to be strengthened.\n2. The paper lacks comparisons with recent state-of-the-art Gaussian Splatting methods, such as Spec-Gaussian, Scaffold-GS, etc.\n3. The improvements appear to be modest rather than significant.", "was_revised": true, "final_justification": "I’m pleased to see that additional experiments have been included to compare with the state-of-the-art methods. Although the improvement is not significant in some cases, the training time has been reduced. I have raised my rating to borderline accept.", "rebuttal": "**[Limitations 1, Weaknesses 1]**\n\nWe 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:\n- **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.\n- **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.\n\nBuilding 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.**\n\n​We appreciate the reviewer’s concern and will expand this justification more thoroughly in the final version of the paper.\n\n**[Limitations 2, Questions: The computational overhead may be discussed.]**\n\nWe 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:\n\n| **Method Variant**      | Training Time (overhead) |\n| ----------------------- | ------------------------ |\n| 3DGS (baseline)         | 29:06                    |\n| + Density Only (KNN)    | 30.40 (+1:34)            |\n| + Complexity Only (DWT) | 33.19 (+4:13)            |\n| Full (Ours 0.01)        | 35.36 (+6:30)            |\n\n​We emphasize that **our method prioritizes rendering quality and is designed with efficiency in mind.** To reduce overhead:\n\n- 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.\n- Density estimation leverages **CUDA-based KNN acceleration** on the GPU, which keeps the overhead low and computationally practical.\n\n​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:\n\n|  Method | PSNR ↑ | SSIM ↑ | LPIPS ↓ | #GS ↓   | Training Time↓ | FPS↑ |\n| ----------- | ------ | ------ | ------- | ------- | -------------- | ---- |\n| 3DGS        | 27.79  | 0.826  | 0.201   | 2585032 | **29.06**          | **112**  |\n| Ours (0.01) | **28.02**  | **0.836**  | **0.183**   | **2531532** | 35.36          | **112**  |\n\n​We will include this analysis in the final version to clarify the cost-benefit tradeoff of our method.\n\n**[Limitations 3, Weaknesses 2, Questions: Comparison with the SOTA methods.]**\n\nWe 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.\n\n| **Method**      | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS ↓**     | **Training Time ↓** |\n| --------------- | ---------- | ---------- | ----------- | ------------- | ------------------- |\n| Scaffold-GS*    | 27.49      | 0.805      | 0.253       | -             | **28:35**           |\n| Spec-Gaussian   | 27.98      | 0.834      | **0.176**   | 3.24M     | 61:31               |\n| Ours (0.01) | **28.02**  | **0.836**  | 0.183       | **2.53M** | 35:36               |\n\n​The results demonstrate that **our method achieves superior overall performance**. Specifically:\n\n- **Our PSNR and SSIM exceed both baselines**, reflecting higher reconstruction quality.\n- While our LPIPS is slightly higher than Spec-Gaussian, it remains very close (0.183 vs. 0.176) **despite using ~700K fewer Gaussians**.\n- 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.\n\n​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.\n\n**[Limitations 4, Weaknesses 3]**\n\nAlthough 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.\n\n​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:\n\n| **Method**      | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS** ↓ |\n| --------------- | ---------- | ---------- | ----------- | ---------------- |\n| 3DGS-MCMC       | 28.13      | 0.842      | 0.179       | 2.53M            |\n| 3DGS-MCMC + CDC | **28.24**  | **0.845**  | **0.175**   | 2.53M            |\n\n​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**.\n\n| **Method**        | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS** ↓ | **Training Time** ↓ |\n| ----------------- | ---------- | ---------- | ----------- | ---------------- | ------------------- |\n| 3DGS              | 27.79      | 0.826      | 0.201       | 2.59M            | 29:06               |\n| Mini-Splatting    | 27.35      | 0.822      | 0.218       | **0.49M**        | 23:42               |\n| LightGaussian     | 27.27      | 0.804      | 0.241       | 0.81M            | 29:05               |\n| Taming-3DGS       | 27.80      | 0.815      | 0.225       | 1.47M            | **12:17**           |\n| Ours (Prune Only) | **27.82**  | **0.825**  | **0.214**   | 1.47M            | 29:04               |\n\n​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.\n\nTaken 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**.\n\n​We will include these analyses in the final version and sincerely appreciate the reviewer’s constructive feedback."}, {"review_id": "Esn4rL3fT0", "reviewer": "Reviewer_MnE1", "summary": "This paper proposes a novel densification strategy that accounts for both the complexity and density of Gaussian primitives. To achieve this, the authors define the complexity of Gaussians using the discrete wavelet transform (DWT) and the density of Gaussians based on the distance between neighboring Gaussians. Leveraging these two concepts, they introduce a Complexity-Density Consistency (CDC) score to determine which Gaussians deserve densified and a Complexity-Aware Adaptive Threshold (CAAT) to adaptively prune Gaussians based on both gradient and complexity. Experimental results show that the proposed method outperforms the rendering quality of existing Gaussian densification approaches.", "questions": "- In the definition of complexity, why do the authors consider the maximum complexity value for all pixels in training views, instead of an average of them?\n\n- It would be valuable to investigate whether the proposed densification strategy remains effective when targeting a smaller number of Gaussians. To this end, I recommend conducting additional experiments with a more aggressive pruning configuration aimed at reducing the number of Gaussians. These results are recommended to be compared with existing compact 3DGS baselines, such as LightGaussian [NeurIPS'24], Mini-Splatting (not Mini-Splatting-D) [ECCV'24], and Taiming-3DGS [SIGGRAPH Asia'24].\n\n- As I mentioned above, additional costs for computing complexity and density might be required. Please report the comparison for the training time of each method.\n\n- It would be better to add 3DGS-MCMC [NeurIPS'24] in comparison.", "limitations": "- Additional computational costs are required for computing the densification standard.\n- Also, limited technical contribution might be seen as a lack of novelty.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "### Strengths\n- The authors address the limitation of the prior loss-based densification criterion and introduce two important factors for densification, complexity and density of Gaussians.\n- It achieves superior rendering quality compared to existing Gaussian densification approaches, such as Mini-Splatting, Taiming-3DGS, and AbsGS.\n- Detailed analysis of the experimental results demonstrates the significance of complexity and density for effective densification.\n\n---\n\n### Weaknesses\n- CAAT depends on a hyper-parameter \\lambda which requires manual setting for various scene types.\n- Additional computation costs are required for computing the complexity (DWT) and density (kNN) of Gaussian primitives. In particular, kNN search for millions of Gaussians requires a lot of computation overhead.\n- Despite the effectiveness of the proposed method, contributing only a densification criterion without additional technical contributions may be seen as lacking sufficient advancement to be accepted in this conference.", "was_revised": true, "final_justification": "The authors have addressed all of my concerns during the rebuttal period. The additional evaluations strengthen the clarity of the proposed method. Notably, it is interesting that it achieves better performance when combined with 3DGS-MCMC, as well as under the aggressive pruning setup. Therefore, I will maintain my positive rating.", "rebuttal": "**[Questions 1]**\n\nWe sincerely appreciate your insightful questions.\n\nAs 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:\n\n- **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.\n- **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.\n\nTo 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:\n\n| Aggregation Strategy | PSNR ↑    | SSIM ↑    | LPIPS ↓   | #GS ↓       |\n| -------------------- | --------- | --------- | --------- | ----------- |\n| Mean-Mean            | 27.93 | 0.834 | 0.187 | 2.62M |\n| Mean-Max             | 27.96 | 0.835 | 0.186 | 2.58M |\n| Max-Mean             | 27.97 | **0.836** | 0.185 | 2.57M |\n| **Max-Max (ours)**   | **28.02** | **0.836** | **0.183** | **2.53M** |\n\n**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.\n\n**[Questions 2]**\n\nThank 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**.\n\n| **Method**        | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS ↓** | **Training Time ↓** |\n| ----------------- | ---------- | ---------- | ----------- | --------- | ------------------- |\n| 3DGS              | 27.79 | 0.826 | **0.201** | 2.59M     | 29:06 |\n| Mini-Splatting    | 27.35 | 0.822 | 0.218 | **0.49M** | 23:42 |\n| LightGaussian     | 27.27 | 0.804 | 0.241 | 0.81M  | 29:05 |\n| Taming-3DGS       | 27.80 | 0.815 | 0.225 | 1.47M  | **12:17**  |\n| Ours (Prune Only) | **27.82** | **0.825**  | 0.214 | 1.47M | 29:04 |\n\nThe 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.\n\nThis 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.\n\n**[Questions 3, Weaknesses 2, Limitations 1]**\n\nThank 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:\n\n| **Method Variant**      | Training Time (overhead) |\n| ----------------------- | ------------------------ |\n| 3DGS (baseline) | 29:06  |\n| + Density Only (KNN) | 30.40 (+1:34)  |\n| + Complexity Only (DWT) | 33.19 (+4:13) |\n| Full (Ours 0.01) | 35.36 (+6:30) |\n\nWe 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.\n\nLikewise, 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.\n\nNotably, **the additional training overhead does not impact rendering performance**. Our method maintains **the same FPS** with vanilla 3DGS while improving reconstruction quality:\n\n| Method | PSNR ↑ | SSIM ↑ | LPIPS ↓ | #GS ↓   | Training Time↓ | FPS↑ |\n| ----------- | ------ | ------ | ------- | ------- | -------------- | ---- |\n| 3DGS | 27.79 | 0.826  | 0.201 | 2.59M | **29.06** | **112** |\n| Ours (0.01) | **28.02** | **0.836**  | **0.183** | **2.53M** | 35.36 | **112** |\n\nAs 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:\n\n| **Method**       | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS ↓** | **Training Time ↓** |\n| ---------------- | ---------- | ---------- | ----------- | --------- | ------------------- |\n| 3DGS             | 27.79 | 0.826  | 0.201 | 2.59M | 29.06 |\n| Taming-3DGS      | 27.91 | 0.821 | 0.211 | 2.53M | 17.31 |\n| **Ours (0.01)**  | 28.02 | 0.836 | 0.183 | 2.53M | 35.36 |\n| AbsGS            | 27.72 | 0.835 | 0.169 | 4.06M | 33.02 |\n| Mini-Splatting-D | 27.78 | 0.841 | 0.163 | 4.61M | 35.02 |\n| Pixel-GS         | 27.83 | 0.835 | 0.176 | 5.27M | 41.22  |\n| **Ours (0.02)**  | 28.11 | 0.842 | 0.164 | 3.95M | 39.22  |\n| 3DGS-MCMC        | 28.13 | 0.840  | 0.180 | 2.53M | 40.42  |\n| Spec-Gaussian    | 27.98 | 0.834 | 0.176 | 3.24M | 61.31 |\n| Mini-Splatting   | 27.35 | 0.822 | 0.218 | 0.49M | 23.42 |\n| LightGaussian    | 27.27 | 0.804 | 0.241 | 0.81M | 29.05  |\n| Scaffold-GS      | 27.49      | 0.805 | 0.253   | -         | 28.35 |\n\n**[Questions 4]**\n\nThank 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.\n\n| **Method**      | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS ↓** |\n| --------------- | ---------- | ---------- | ----------- | --------- |\n| Ours (0.01)  | 28.02 | 0.836 | 0.183 | 2.53M |\n| 3DGS-MCMC | 28.13 | 0.842 | 0.179 | 2.53M  |\n| 3DGS-MCMC + CDC | **28.24**  | **0.845**  | **0.175**   | 2.53M   |\n\nThe results show that **3DGS-MCMC achieves slightly better rendering quality** than our method under the same Gaussian count.\n**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.\n\nMoreover, **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.\n\n**[Weaknesses 1]**\n\nThank 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. \n\n**[Limitations 2]**\n\n​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:\n\n- 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.\n- 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.\n- 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."}, {"review_id": "wkfYdB74kZ", "reviewer": "Reviewer_qsuh", "summary": "This paper proposes a novel method for allocating primitives in 3D Gaussian Splatting. The authors introduce measures of complexity and density for Gaussian primitives to identify under-reconstructed and over-reconstructed regions, and develop an allocation strategy based on these metrics. Experimental results show that the proposed method outperforms baseline approaches overall.", "questions": "My main concern is that the paper does not fully discuss how uneven complexity-density distributions affect rendering performance. I do not doubt the relevance of these two metrics to the 3DGS model, but I believe a deeper discussion is necessary. If the authors could provide a more thorough justification or analysis of this point, I would consider raising my score.", "limitations": "Yes, the author answered the questions in checklist well and the limitations are fully addressed.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "### Strengths:\n- S1. The writing is clear and effectively presents main idea. The methodology is straightforward, and the experimental details are well-presented.\n\n- S2. Most of the quantitative results outperform baselines.\n\n### Weaknesses:\n- W1: Figure 4 shows that the proposed method achieves a higher correlation between complexity and density compared to baseline methods. However, since the allocation strategy is explicitly designed based on these two metrics, it is expected that it would outperform baselines on this specific correlation measure. This raises concerns about the fairness of using this metric to claim the method in the paper is better. Moreover, in Figure 4b, the authors illustrate how the correlation score evolves during training. If a higher correlation is considered indicative of better scene modeling or rendering quality, then 3DGS should perform better than other baseline methods. However, the quantitative results do not consistently reflect this. This discrepancy suggests that the correlation metric may not directly align with final rendering performance, and the paper does not sufficiently discuss or justify this gap.", "was_revised": true, "final_justification": "The authors have answered my question well, and I have no further concerns. I have raised my score to 4. However, I still believe the work does not provide additional insights for related research, so I do not consider it deserving of a score of 5.", "rebuttal": "**[Weaknesses, Questions]**\n\n​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.\n\nTo answer the reviewer's concern - \"**3DGS should perform better than other baseline methods. However, the quantitative results do not consistently reflect this**\":\n\n- **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.\n- **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.**\n- **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.**\n- **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.\n\n  | **Method**         | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS ↓** |\n  | ------------------ | ---------- | ---------- | ----------- | --------- |\n  | 3DGS (baseline)    | **27.79**  | **0.826**  | **0.201**   | **2.59M** |\n  | 3DGS + reverse CDC | 27.62      | 0.817      | 0.224       | 2.71M     |\n\n  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.**\n\n- **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.\n\n​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."}, {"review_id": "ZgNdiBngzb", "reviewer": "Reviewer_Jyxw", "summary": "The authors propose a novel method for densifying and pruning Gaussian primitives with respect to the complexity of the training views and the density of the scene. The complexity is modeled with a high pass filter (2D DWT) and assigned to each Gaussian primitive via alpha compositing and the density is modeled with the average distance of each Gaussian to its three closest neighbors. Using both criteria for determining the densification strategy shows to improve the rendering quality without creating too many Gaussian primitives. The authors provide limited ablations and compare their results quantitatively to some of the current 3DGS methods.", "questions": "While the results show that the proposed method improves the rendering quality, the paper lacks in clarity and evaluation. Although the densification process is the main component of this work, it is not clear how primitives in under-/over-reconstructed regions are selected and how pd is determined. Further, the paper misses intuitive explanations, for instance: how formula 8 is designed, why the positional gradient is still required, or why the DWT is the best choice (other than it works best). Lastly, the paper introduces a lot of parameters while also changing some other components (such as the pruning interval), without proper evaluation / ablation. This makes it difficult to understand what component and which parameters have a big influence on the result. \n\nWithout further evaluation, comparisons and more clear explanations, I cannot confidently accept this paper as a significant contribution to the 3DGS research field.", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n\n- The topic is relevant\n- The idea is interesting\n- The results are promising\n- The evaluation with different high pass filters underlines the choice for the Discrete Wavelet Transform (should be moved to the main paper)\n- Figure 4a demonstrates well the effect of the methods\n\nWarknesses:\n\nIn general, some parts are not clearly explained or confusing:\n- Line 183: “Γmean, Ψmean are the mean of consistency and density” (should be complexity?)\n- Line 195: “the sampling probability is determined with oi” what is oi and what is the intuition?\n- Line 192: how is pd determined from |si| and what is the intuition? High values for |si| indicate good consistency. Why should those regions be further modified?\n- Line 192: It is not clear how under-reconstructed regions and over-reconstructed regions are determined.\n- Why is it required to still use the positional gradient?\n- τlow and τup are set very similarly. It would be interesting if the quality already improves using a fixed threshold of τlow or τup.\n- Where are all hyperparameters coming from? An ablation study would help.\n- Line 230: What is ps?\n- Why is Figure 4b looking completely different to the same graph shown in the appendix Figure 1? \n- Formula 6: Why is the distance to the neighbors calculated with a product and not a sum?\n- The advantages / reasons why the Discrete Wavelet Transform works best, are not discussed\n- The pruning operation is changed without evaluation\n- The runtime is likely increased due to the KNN calculations, but not mentioned in the paper\n- The resolution of the rendered images in Figure 3 is too low\n- The ablation study on T&T is not very expressive as it only includes two scenes\n- More comparisons to related compaction methods from  https://arxiv.org/abs/2407.09510 should be included\n- It would be interesting how well the method integrates into current SOTA methods", "was_revised": true, "final_justification": "I have raised my rating from reject to borderline reject. Although the authors have addressed all of my raised questions and the results outperform current 3DGS variants, I still believe that the paper lacks in originality, clarity and presentation. The contributions are rather small changes and it is not entirely clear which of the proposed components should be applied for future work (some promote compaction and some improve the visual quality). Nevertheless, I believe that with more fine grained evaluation and sensitivity measures, the paper has real potential.", "rebuttal": "**[Weaknesses 1]**\n\nThank 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.\n\n\n\n**[Weaknesses 2, 3, 4]**\n\nWe clarify the key concepts:\n\n1. **Identifying Under-/Over-Reconstructed Regions**\n\n   As formalized in Equation 7 and Section 3.3 (Line 184), we use the **CDC score** *sᵢ* to measure local mismatch:\n\n   - *sᵢ* < 0 with **high complexity and low density** → **Under-reconstructed region** → Apply **densification**\n   - *sᵢ* < 0 with **low complexity and high density** → **Over-reconstructed region** → Apply **pruning**\n\n\n2. **Pruning Sampling Based on Opacity *oᵢ***\n\n   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.\n\n3. **How $\\rho_d$ Is Determined**\n\n   $\\rho_d$ 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. \n\n\n\n**[Weaknesses 5, Questions: why the positional gradient is still required]**\n\nAs 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.\n\n\n**[Weaknesses 6, Questions: the paper misses intuitive explanations, for instance: how formula 8 is designed]**\n\nIn 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**.\n\n**[Weaknesses 7, Questions: hyperparameters ablation.]**\n\nWe provide ablations for all major hyperparameters on MipNeRF 360 dataset:\n\n- **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\n  | \\|$N_i$\\| | PSNR ↑ | SSIM ↑ | LPIPS ↓ | #GS ↓ |\n  | --------- | ------ | ------ | ------- | ----- |\n  | 1 | 28.05| 0.838| 0.179 | 2.51M |\n  | 2 | 28.03| 0.837 | 0.179 | 2.54M |\n  | 3 | 28.02| 0.836 | 0.183 | 2.53M |\n  | 4 | 28.02| 0.836 | 0.182 | 2.55M |\n  | 5 | 28.01| 0.836 | 0.183 | 2.55M |\n\n- **$τ_{low}$, $τ_{upp}$ (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.\n\n- **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.\n\n\n\n**[Weaknesses 8]**\n\nThis 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.\n\n\n\n**[Weaknesses 9]**\n\nThank you for pointing this out. The figures reflect real training behaviors on different scenes and are consistent with our method.\n\n- **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.\n- **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.\n- **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**.\n\n\n\n**[Weaknesses 10]**\n\nWe 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.\n\n\n\n**[Weaknesses 11, Questions: why the DWT is the best choice]**\n\nWe chose DWT for the following key reasons:\n\n- **Multi-scale decomposition**: Unlike single-scale filters, DWT captures both fine and coarse structural details, crucial for modeling spatially varying 3D complexity.\n- **Directional sensitivity**: DWT provides high-frequency responses in multiple orientations (LH, HL, HH), enabling richer structural analysis than edge-only filters.\n- **Frequency separation**: By discarding the LL band and inverting DWT, we isolate high-frequency components, preserving more relevant geometric cues.\n- **Empirical support**: DWT-based approach consistently improves rendering quality and reduces Gaussian count across scenes.\n\n\n\n**[Weaknesses 12]**\n\nWe now include the missing pruning ablation results on MipNeRF 360:\n\n|**Method**|**PSNR ↑**|**SSIM ↑**|**LPIPS ↓**|**#GS ↓**|\n| --------------------- | ---------- | ---------- | ----------- | --------- |\n|3DGS|27.79|0.826|**0.201**| 2.59M|\n|3DGS + periodic prune|**27.81**|**0.828**|0.205|**1.79M**|\n\nThis demonstrates that our pruning strategy significantly reduces the number of Gaussians without degrading quality.\n\nThe 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.\n\n\n\n**[Weaknesses 13]**\n\nWe conducted an ablation study on the **MipNeRF 360** dataset to quantify the additional training cost of our complexity and density components:\n\n| **Method Variant**| Training Time (overhead) |\n| :---------------------- | :----------------------- |\n| 3DGS (baseline) | 29:06 |\n| + Density Only (KNN)| 30.40 (+1:34) |\n| + Complexity Only (DWT) | 33.19 (+4:13) |\n| Full (Ours 0.01) | 35.36 (+6:30) |\n\n**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.** \n\nNotably, **rendering speed remains unaffected**. Our method maintains the same FPS with vanilla 3DGS while improving reconstruction quality.\n\n\n\n**[Weaknesses 14]**\n\nFigure 3 uses reduced resolution to meet NeurIPS file limits. We will replace it with a higher-quality version in the final paper.\n\n\n\n**[Weaknesses 15]**\n\nWe extended the ablation to all 9 MipNeRF 360 scenes. Results match main paper conclusions:\n\n|Method|PSNR ↑|SSIM ↑| LPIPS ↓ | # Gaussians |\n| ------------- | --------- | --------- | --------- | ----------- |\n| 3DGS| 27.79| 0.826| 0.201| 2.59M |\n| + CAAT| 27.86| 0.829| 0.197| 2.82M |\n| + CDC | 27.92| 0.832| 0.189| 2.40M |\n| Full (CDC-GS) | **27.98** | **0.834** | **0.185** | **2.53M**|\n\n\n\n**[Weaknesses 16]**\n\nWe 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:\n\n| **Method** | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS ↓** |\n| --------------- | ---------- | ---------- | ----------- | --------- |\n| 3DGS | 27.79 | 0.826 | **0.201**| 2.59M|\n| Mini-Splatting| 27.35 | 0.822 | 0.218 | **0.49M** |\n| LightGaussian| 27.27| 0.804 | 0.241| 0.81M|\n| Taming-3DGS| 27.80 | 0.815 | 0.225| 1.47M|\n| Ours Prune Only | **27.82** | **0.825** | 0.214 |1.47M|\n\n​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.\n\n\n\n**[Weaknesses 17]**\n\nWe integrated CDC into 3DGS-MCMC. With the same number of Gaussians, performance improves:\n\n| **Method** | **PSNR ↑** | **SSIM ↑** | **LPIPS ↓** | **#GS ↓** |\n| --------------- | ---------- | ---------- | ----------- | --------- |\n| Ours (0.01)|28.02|0.836| 0.183| 2.53M|\n| 3DGS-MCMC| 28.13 |0.842| 0.179 | 2.53M|\n| 3DGS-MCMC + CDC |**28.24**|**0.845**| **0.175** | 2.53M|\n\nThis confirms that CDC is **plug-and-play** and can enhance existing 3DGS variants.\n\n\n​We will include these analyses in the final version and sincerely appreciate the reviewer’s constructive feedback."}]

Author rebuttal:

Meta-review: This paper presents a well-motivated and effective enhancement to the 3D Gaussian Splatting (3DGS) framework. The core contribution, Complexity-Density Consistent Gaussian Splatting (CDC-GS), addresses a fundamental and well-identified shortcoming of loss-driven densification strategies: their tendency to under-represent high-frequency, texture-rich regions due to the dominance of low-frequency gradients.

The proposed method is conceptually sound and novel. Its primary strength lies in being loss-agnostic, providing an orthogonal signal for primitive allocation that directly targets visual complexity. The use of a wavelet transform to extract a high-frequency complexity map is an intuitive and appropriate choice for this task. The mechanism of enforcing a correlation between this complexity measure and primitive density offers a coherent and principled criterion for guiding both densification and pruning.

The experimental results demonstrate a clear and significant improvement in rendering quality over baseline methods while using an identical number of primitives. This indicates a more efficient and intelligent distribution of representational capacity, which is a valuable advancement for 3D reconstruction. Furthermore, the authors' analysis of the baseline's weakness strengthens the rationale for their solution.

A minor weakness, common in novel method papers, is that the experimental validation could be expanded to a wider range of scenes and compared against a broader set of recent 3DGS enhancements. However, the demonstrated superiority over the core baseline is convincing. The method's design as a complementary strategy also suggests strong potential for integration with other existing and future improvements to the 3DGS pipeline, increasing its impact and usefulness.

Overall, this work offers a novel perspective on a key problem in 3DGS. It is technically sound, well-presented, and delivers tangible performance gains. The approach is likely to influence future work, making it a valuable contribution worthy of acceptance.
Decision: Accept (poster)