EGGS: Exchangeable 2D/3D Gaussian Splatting for Geometry-Appearance Balanced Novel View Synthesis
Authors: Yancheng Zhang
Guangyu Sun
Chen Chen
Venue: NeurIPS 2025 spotlight ()
Keywords: Gaussian Splatting
Novel View Synthesis
Primary area: applications

Abstract: Novel view synthesis (NVS) is crucial in computer vision and graphics, with wide applications in AR, VR, and autonomous driving. While 3D Gaussian Splatting (3DGS) enables real-time rendering with high appearance fidelity, it suffers from multi-view inconsistencies, limiting geometric accuracy. In contrast, 2D Gaussian Splatting (2DGS) enforces multi-view consistency but compromises texture details. To address these limitations, we propose Exchangeable Gaussian Splatting (EGGS), a hybrid representation that integrates 2D and 3D Gaussians to balance appearance and geometry. To achieve this, we introduce Hybrid Gaussian Rasterization for unified rendering, Adaptive Type Exchange for dynamic adaptation between 2D and 3D Gaussians, and Frequency-Decoupled Optimization that effectively exploits the strengths of each type of Gaussian representation. Our CUDA-accelerated implementation ensures efficient training and inference. Extensive experiments demonstrate that EGGS outperforms existing methods in rendering quality, geometric accuracy, and efficiency, providing a practical solution for high-quality NVS.

EGGS: Exchangeable 2D/3D Gaussian Splatting for Geometry-Appearance Balanced Novel View Synthesis
Yancheng Zhang, Guangyu Sun and Chen Chen
Institute of Artificial Intelligence, University of Central Florida lyczhang, guangyu.sun, chen. chennquck edu
PSNR
SSIM
Caraiin
36
6-914
<T8K 76.11
D-454
250 63.63
5-474
477K
Truth
3DGS
EGGS
Figure 1: Comparison of 3DGS, 2DGS, and our EGGS. While 3DGS achieves high-fidelity ap- pearance, often produces inaccurate geometry, with imprecise surfaces and blurred edges. 2DGS improves geometric consistency across views but suffers from reduced appearance quality due to over-smoothed surfaces and loss of detail. In contrast, EGGS employs an exchangeable hybrid Gaussian representation that achieves both accurate geometry and high-quality appearance.
Abstract
Novel view synthesis (NVS) is crucial in computer vision and graphics, with wide applications in AR, VR, and autonomous driving. While 3D Gaussian Splatting (3DGS) enables real-time rendering with high appearance fidelity, it suffers from multi-view inconsistencies, limiting geometric accuracy. contrast, 2D Gaussian Splatting (2DGS) enforces multi-view consistency but compromises texture details. address these limitations, we propose Exchangeable Gaussian Splatting (EGGS), hybrid representation that integrates 2D and 3D Gaussians to balance appearance and geometry. To achieve this, we introduce Hybrid Gaussian Rasterization for uni- fied rendering, Adaptive Type Exchange for dynamic adaptation between 2D and Optimization that effectively exploits
3D Gaussians, and the strengths of each type of Gaussian representation. Our "UDA-accelerater implementation ensures efficient training and inference. Extensive experiments demonstrate that EGGS outperforms existing methods in rendering quality, geomet- ric accuracy, and efficiency, providing practical solution for high-quality NVS. Code and demo available at/http:://gthubbbo wow./oooo///GGSS
1 Introduction
Novel view synthesis (NVS) is a fundamental task in computer graphics and computer vision, with broad applications in augmented reality (AR), virtual reality (VR), and autonomous driving [I] B. Neural Radiance Fields (NeRF) 4 reconstruct implicit radiance fields via differentiable volume rendering. Despite achieving photorealistic appearance and accurate geometry, NeRF-based methods 5
9 10) typically suffer from long training times and slow rendering speeds. 3D Gaussian Splatting (3DGS) has emerged efficient alternative, leveraging anisotropic
6 7
g
39th Conference on Neural Information Processing Systems (NeurIPS 2025).

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PSNR
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Gaussian
Raster- izer
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Regular-
2005
Method
Type
ization
Setting
SSIM
LPIPS
3DGS S:00RAm'22
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General
Figure 2: Left: Comparison of 3DGS and 2DGS in appearance and geometry metrics. Right:
Comparison between EGGS and related works. Prior works either use only single representation or do not explore complementary advantages of 3D and 2D Gaussians. Gaussian Surfel [15] directly sets the z-selle of 3D Gaussian to zero and uses the rasterizer from 3DGS. HybridGS [1 uses
image-frame single-view 2D Gaussians [9 20 instead of 2D Gaussians in the 3D space 112
3D Gaussians for real-time, high-quality rendering. While 3DGS excels in appearance fidelity, its anisotropic nature often leads to multi-view inconsistencies, limiting geometric accuracy 12 As shown in Figure ! this can lead inaccurate edges and surfaces.
Following 3DGS, a line of work has focused on improving its geometric accuracy and reconstruction quality through additional regularization and novel representations, as shown in Figure 2 (right).
SUGAR [4] and GaussianPro 13] introduce normal-bare based regularization, such as planar loss, to
align Gaussian normals and encourage flatter shapes, thereby improving surface consistency. Gaussian Surfles [13] and GOF [2 incorporate additional geometry-aware constraints to enhance spatial coherence. 2D Gaussian Splatting (2DGS) [2] replaces 3D ellipsoids with 2D surfels, significantly improving multi-view consistency and geometric accuracy, as shown in Figure (left). However, this comes the cost of degraded appearance quality, as surfel-based representations struggle to preserve high-frequency details. TextureGS [16] attempts to decouple appearance and geometry within the 2DGS framework, but the single representation still limits overall rendering performance. Recently, HybridGS (17) combines 3DGS with image-space 2D Gaussians to address transient objects, but its radiance field remains fully represented by 3D Gaussians. HorizonGS [88, designed for surying-altitude scenes, decodes 2D Gaussians for surface reconstruction and 3D Gaussians for view synthesis separately via an MLP in ScaffoldGS (22] While effective in their target domains, these methods do not explore unified hybrid radiance representation. As result, the complementary strengths of 2DGS and 3DGS in geometry and appearance remain underutilized.
Effectively combining 3D and 2D Gaussians to jointly improve appearance and geometry is non-trivial, as simply mixing the two representations does not necessarily improve reconstruction quality (18). To start, the geometric accuracy of 2D Gaussians relies on a ci--splatiintesscctoo--eee designed enforce multi-view consistency. Using the projection-based 3DGS rasterizer to render 2D Gaussians can lead to suboptimal geometry [5). Moreover, Gaussian parameters change significantly during training. For instance, 3D Gaussians may flatten to approximate surfaces, while 2D Gaussians may expand volumetrically to capture thin structures or translucent effects. Fixing the Gaussian type throughout optimization can limit the model's expressiveness. Finally, relying solely on photometric loss is insufficient to balance geometry and appearance. Additional regularization is required to guide the optimization of hybrid representations. Most importantly, the regularization strategy should account for the distinct characteristics of 3D and 2D Gaussians.
rasterizer
In response to these challenges, we introduce Exchangeable Gaussian Splatting (EGGS), an adaptive hybrid representation that unifies 2D and 3D Gaussian splatting in a single framework. EGGS provides a practical and efficient solution for high-quality novel view synthesis and 3D reconstruction. Our main contributions are as follows:
To preserve the complementary strengths of 3D and 2D Gaussians, we develop Hybrid Gaus- sian Rasterization, unified rendering framework that supports both projection-basee and mgy-splat-interssetinn- based rasterization. We implement this framework with CUDA for efficient optimization, and ensure compatibility with existing 3DGS and 2DGS pipelines.
We propose Adaptive Type Exchange, which enables an exchangeable hybrid of 2D and 3D Gaussians. We use effective rank auxiliary criterion to determine whether each Gaussian should dynamically switch its type during training, resulting in a more flexible and content- adaptive representation.
2

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To better balance geometry and appearance, we introduce Frequency- -eecouledd Optimization, regularization strategy in the frequency domain. Using the Discrete Wavelet Transform (DWT), we extract low-frequency components to guide scene geometry and high-frequency components refine appearance. We supervise 3D and 2D Gaussians asymmetrically to exploit their distinct characteristics, where high-frequency signals guide 3D Gaussians toward detailed appearance, while low-frequency signals supervise 2D Gaussians for geometric consistency.
We conduct extensive experiments demonstrating that EGGS significantly improves the trade-off between appearance fidelity and geometric accuracy. It outperforms both 3DGS and 2DGS in appearance quality, while achieving geometric accuracy and multi-view consistency comparable 2DGS. Moreover, EGGS serves as a versatile representation that performs well in challenging scenarios such as few-shot and out-of-distribution view synthesis.
2
Related Works
Radiance Fields for Novel View Synthesis. Neural Radiance Fields (NeRF) 4 have emerged as fundamental approach for novel view synthesis (33), representing scenes as continuous volumetric functions optimized via differentiable rendering. While NeRF achieves high-fidelity reconstruction, it requires dense sampling and significant computational resources. Subsequent works have improved or efficiency [5]
but the excessive training and rendering time remains major bottleneck. To address this, recent efforts have explored more efficient alternatives, such as 3D Gaussian Splatting (3DGS) [.] which represents scenes using a set of 3D Gaussians that can be efficiently rasterized and optimized for real-time rendering. To further improve the performance and efficiency of 3DGS, several extensions have been proposed. ScaffoldGS (2 introduces a voxel-based representation where an MIP is used to decode 3D Gaussians within each voxel. 3DGS-MCMM [27] formulates Gaussian densification as Markov Chain Monte Carlo sampling process, enabling a more efficient and adaptive distribution of Gaussians across the scene.
either quality 24 [25
26 61
Crometry-Appearaneee Ballnced Gaussian Splatting. While 3DGS achieves high appearance fidelity and is efficient in both training and rendering, the anisotropic nature of 3D Gaussians often exhibits multi-view inconsistency, resulting in limited geometric accuracy. To address this, several works propose geometry regularization techniques. SUGAR [14] and GaussianPro [13] introduce normal-based regularization to encourage flatter Gaussians that better align with scene surfaces. Gaussian Surfels [15] and GOF (28) further enforce depth accuracy and normal consistency to enhance geometric reconstruction. Instead of relying solely on regularization, 2DGS [2] adopts 2D surfel representation with specialized may-sppaatinterssctton rasterizer, ensuring multi-view consistency and significantly improving geometric accuracy compared to 3DGS. It also incorporates additional depth and normal regularization. However, this comes the cost of reduced appearance quality, as 2D surfels struggle to preserve high-frequency detail. TextureGS [16) attempts to decouple geometry and appearance modeling within the 2DGS framework, but its appearance fidelity remains limited due to the inherent drawbacks of the 2D representation.
As demonstrated in Figure (left). 3D Gaussians achieve better appearance quality in PSNR, SSIM, and LPIPS. In contrast, 2D Gaussians offer superior view consistency and geometric fidelity, resulting in more robust PSNR under out-of-distribune
(OOD) conditions, improved point cloud accuracy in Chamfer Distance (CD), and higher depth accuracy in score. As shown Figure (right), most rely on single Gaussian representation to reconstruct radiance fields, which limits their flexibility and adaptability. Although HybridGS (17] incorporates both 3D Gaussians and image-space 2D Gaussians to better handle transient content, its radiance field remains solely represented by 3D Gaussians. A radiance field that jointly leverages both 2D and 3D Gaussians remains largely unexplored. It is still unclear how 2D and 3D Gaussians can be made exchangeable during training and how to fully exploit their complementary strengths in appearance and geometry. We provide more detailed discussion in Appendix B
existing methods 12 11 14, 13 29
30
22
31
32
33
K4
3 Method
We provide an overview of the EGGS framework in Figure 3
enable the joint training of 2D and 3D Gaussians within unified framework, we first introduce Hybrid Gaussian Rasterization in Section 3.1 which supports both -ay-sppaatinteersecton----o projection-based rendering for 3D Gaussians. Next, Aresent Adaptive Type Exchange in Section 3.2
rendering for 2D Gaussians and
3

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See 3.1
color
DWT
DWTT
Hybrid Rasterization
See 3.3
Lrow
Input
See 3.2
30
SIM & Initialization
eranke119 1.9
Lnigh
3D Gaussiams
2D Gaussians
Hybrid Caussian Model
Adaptive Type Exchange
Trequency-Decoupleel Regulation
Figure 3: Overview of the EGGS framework. We initialize 2D and 3D Gaussians from sparse points obtained via structure-from from-motion (SfM) 35 36] Their parameters then jointly optimized using our acceleecceer differentiable hybrid rasterization. To enhance the flexibility of the hybrid representation, Adaptive Type Exchange is introduced allow each Gaussian switch between 2D and 3D types during training. Finally, we apply Discrete Wavelet Transform (DWT) (37] and introduce Frequency- Trequency-Decoupled Decoupled Optimization balance geometric accuracy and appearance fidelity.
which enables dynamic switching between 2D and 3D types during optimization. Finally, optimize the hybrid model for balanced geometric consistency and appearance fidelity, we propose Frequency- Decoupled Optimization in Section 3.3 supervision strategy that leverages the distinct frequency characteristics of 2D and 3D Gaussians.
3.1 Hybrid Gaussian Rasterization
Differentiable rasterization was introduced in 3DGS to enable gradient-basee optimization of Gaus- sian parameters using a projection-based pipeline for real-time rendering. 2DGS later developed a -i-pllatinntesection--eee
rasterizer tailored to 2D surfel representations, improving multi-view consistency and geometric accuracy. However, the architectural distinction between these two ras- terization pipelines makes it non-trivial to render and optimize hybrid model within unified framework. While 2D Gaussians can be viewed as degenerate 3D Gaussians with zero scale along the z-axis, directly rendering them with the 3D rasterizer leads to geometric inaccuracies [12. This due to the affine projection approximation used in 3DGS, which introduces distortion at all points except the Gaussian center. We further analyze this issue in Section 4.2]
To leverage the complementary strengths of 3D and 2D Gaussians, within a unified framework. To this end, we propose Hybrid Gaussian Rasterization, which integrates both projection-bee based and ray-splat- splat-intersection-beee based pipelines. our rasterizer, each Gaussian primitive G is parameterized by center μ E R3, scale E R3, rotation quaternion r E R1, opacity E I. and spherical harmonic (SH) color coefficients f E (3x(1+))² where / is the degree of view-dependent color. The view-dependent RGB color c is decoded from f. The Gaussian shape is defined by the covariance matrix Σ RS R where E R3x3 is the rotation matrix derived from r. and S diag(su: (s 8z) 3 is the scaling matrix. We augment each Gaussian with type specifier t E {0, 1] to indicate whether it is a 2D (t = 0) or 3D (t = 1) Gaussian. 2D Gaussians initialized with 8: 0, while the remaining parameters follow the initialization of 3DGS.
necessary render them
we rasterize Gaus- sians according to their types, where affine projection is used for 3D Gaussians and mny-splat-interssction is used for 2D Gaussians. The contribution of G.dd and G evaluated by computing the distance from the image-space pixel xp to Gpros G?dd in the 2D image plane or tangent frame, respectively:
As shown Figure
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Figure 4: Illustration of Hybrid Gaussian Rasteri- zation. The contribution of 3D Gaussians and 2D Gaussians is computed via affine projection and eny-splat-inteereettne respectively.
(M,,(Z,))) m2(2,)² d, 4- [1sp p'a,)) '(p p otherwise
(I)
where p'a,, and Σ; are the projected center and covariance of the 3D Gaussian computed via affine projection, and wz( and i; (xrp) denote the coordinates of the intersection between the ray through Tp and the Gaussian. The distance d, can be computed simultancously for both 3D and 2D Gaussians. The final contribution of each Gaussian

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is then computed uniformly as â; a;e" 144 where a; is the opacity of the i-th Gaussian. With the above formulation, both 3D and 2D Gaussians can be rendered in a single a-blending pass:
C(xp) EseN C [1 (1,ā)
where the final color at pixel zp is computed from color C, and contribution å; of each Gaussian primitive. To support efficient and parallel rendering, we implement our hybrid rasterizer in CUDA. More details on initialization and densification provided in Appendix A and those projection- based and wassssalllnntesettiinn baase rasterization procedures are deferred to Appendix C
3.2 Adaptive Type Exchange
While the type specifier introduced in Section 3.1 enables unified rendering of 2D and 3D Gaussians, each Gaussian primitive is initialized with a fixed type. Such fixed type assignment can limit the expressiveness of the model, as Gaussians may naturally deviate from their initial type during optimization. For example, 3D Gaussians may become increasingly flat to better model surfaces, while 2D Gaussians may take on more volumetric properties to capture semi-transparent regions. To fully exploit the ficxibility of the hybrid model, the type of each Gaussian should dynamically adapt to its evolving geometric characteristics. To this end, propose Adaptive Type Exchange, which allows each Gaussian to switch between 2D and 3D types during training.
The key to Adaptive Type Exchange is detecting discrepancies between Gaussian's 's assigned type and its effective geometric dimensionality. Therefore, we introduce the effective rank (erank) [38] 39] as indicator of this dimensionality, allowing the model to determine when type switching is needed during training. Given a Gaussian G with scaling 8
(8zz Sy: 82), we define its effective rank as:
erank(g) exp
Ei=
Tall
log q:
where q (6 sy
As illustrated in Figure [] erank provides a principled signal for deciding when to switch types. A perfectly isotropic 3D Gaussian has erank- = 3, while flattened Gaussian approaches erank 2. a Gaussian primitive Gi is assigned as 3D (1, = 1) but its effective rank falls below a threshold l.. we mark it for conversion 2D by setting & O. Similarly,
update 2D Gaussians to 3DD 1) when their effective rank exceeds the threshold. Yet, merely flipping the type specifier can lead to unstable parameter transitions, the sg scale is treated as least significant in 2D Gaussians. To ensure stable conversion, we reparameterize the covariance of 3D Gaussians during switching and adjust gradient flow to 8₂ for 2D Gaussians.
Reparameterization. (3D + 2D) All three scales of a 3D Gaussian are initially opti- mized, whereas 2D Gaussians ignore the s, scale during ray- sppptttiteeseettiinne based rasteri- zation. Accordingly, when converting a 3D Gaussian to 2D, only $2 and sy are retained and s. is discarded. However, directly discarding 8, can lead to instability during training when is not the least significant scale. To prevent this, we reparameterize the 3D Gaussian be- fore conversion is aligning s, with the least significant scale while preserving covariance Σ RSS R We first construct the converted scaling matrix S using a permutation matrix P that moves the least significant scale the z-axis:
that s, corresponds the smallest axis. The key to stable conversion
S' PSP
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P set to Pa or Py if 8r or sy is the least significant scale, respectively, where:
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10
20
0 0
0 0
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Figure 5: Illustration of Adaptive Type Exchange.
Then, ensure the covariance Σ remain un- changed in E' = R S* we set the rotation of 2D Gaussian as R' R We note that R" is converted to quaternions during optimization. To ensure valid conversion, the rotation matrix R" must be orthogonal with a positive determinant. P and P, are designed to preserve these properties. Additional details are provided in Appendix D
Scale Modulation. (2n - 3D) When converting 2D Gaussians to 3D, all parameters are retained with the type specifier flipped. However, as mentioned above, the s, scale of 2D Gaussians is not
5

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optimized during rasterization. However, to allow 2D Gaussians to develop volumetric capacity and transition to 3D when needed, gradient flow must also be introduced along the z-axis. To support this, we incorporate 8, into the computation graph via soft modulation based on opacity o, aligning geometric expressiveness with visual transparency. The intuition behind this design is that 2D-to-3D transitions often occur in regions with cmmi-transparent volumetric effects that flat primitives cannot represent well. This mod- ulation enables 8, be optimized throughout training, while ensuring its updates remain sta- ble and smoothly conditioned on opacity:
Ground Truth
Iter. 1.5K
Ber 7
a = age x
(6)
where s denotes the activated z-axis scale, com- puted via a soft gating function:
High Freq.
Ervor Map
Emoor Map
Figure Illustration of reconstruction error during training. In early iterations, the model focuses on overall scene geometry, while high-frequenc, local details are progressively refined in later stages.
sigmoid
O2 T.
82
The soft scale modulation allows 2D Gaussian to remain effectively two-dimensional when 83 insignificant, in which case s approaches zero. Conversely, as 2D Gaussian evolves toward more volumetric form, an increasing s, leads to reduced opacity, effectively enabling the representation of semi-tran transirannparent or volumetric effects. Additional details on the effective rank threshold, 3D Gaussian reparameterization and permutation, and 2D Gaussian scale modulation are provided in Appendix D
3.3 Trequency-Decouplee Optimization
With our hybrid rasterization and adaptive type exchange mechanism, 2D and 3D Gaussians can be jointly optimized within a unified and flexible framework. However, relying solely photometric loss is insufficient to effectively optimize the hybrid model for balanced geometry and appearance. 2D and 3D Gaussians exhibit distinct characteristics during optimization and specialize in different aspects of the scene. 2D Gaussians are better suited for enforcing geometric consistency, while 3D Gaussians excel at capturing high-freug frequency appearance details. To fully leverage these complementary strengths, we introduce Frequency- -ecoouped Optimization, a supervision strategy that decouples low- and high- figh-frequency components and assigns them asymmetrically to 2D and 3D Gaussians, respectively.
Frequency Decoupling via Discrete Wavelet Transform. As shown in Figure G scene in- formation can be effectively separated in the frequency domain. High-frequency components typically correspond to fine details that are refined later training stages (e.g.. 7K iterations), while low-frequency components capture overall scene geometry and are optimized earlier. This frequency-based separation aligns well with the complementary roles of 3D Gaussians mod- eling appearance and 2D Gaussians in capturing geometry. Motivated by this, we introduce Frequency- -Decoopped Optimization to supervise the hybrid model in the frequency domain. We apply DWT (37) to decompose the ground truth image I into low- and high-frequene, components: I, (I). The same transformation is applied to the rendered image I to obtain I, and In.
The frequency loss is defined as L. ||ž I, for i E {low, high}. We also include the standard appearance loss used in 3DGS: Leoher (1 A)C, + XLD SSIM- With access to frequency-specife losses, a naïve strategy is to combine all terms and apply them uniformly to all Gaussians:
disciio
low g
g high
Project
color
Conflicting frequency gradients
Non-conflicting Grndients
g
L = Leolor + NnowLoww + Atigh Lrghh
(8)
Figure 7: Illustration of frequency gradient projection. We project gradients from high- frequency loss onto the normal vector of gra- dients from www-freqency for 2D Gaussians.
where Liow and Lhigh are applied equally to all 2D and 3D Gaussians. While supervision is decoupled in the frequency domain, this approach overlooks the distinctions of each representation.

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Asymmetrical Gradient Update with Projected Conflicts. We denote the gradients to G from Lcolors Llow and Ligg as go glo and g; high respectively, As illustrated in Figure 7 conflict- ing gradients can arise when losses from different frequency components are directly applied to update Gaussian parameters (i.e., Eq.(8), diminishing the effectiveness of frequency- regularization. Such conflicts stem from the distinct characteristics of 2D and 3D Gaussians. 2D Gaussians are more effective capturing overall geometry and ensuring multi-view consis- tency, where low-frequency signals offer more relevant guidance, while high-frequency gradi- ents may counteract this by encouraging appearance-driven updates. Conversely, 3D Gaussians specialize in modeling fine-scale appear- ance and benefit more from high-freyuency supervision, whereas low-frequency sig- nals contribute less to their performance.
Algorithm 1: Frequency- Frequency-Decouplee Decoupled Optimization
Require Gaussiaas (Gi ]=== appearance loss Leotors
frequency loss Ltow and Liigh-
color low g'" hhgh + VgLcotor, Viglow, V Chight
To address this issue, we propose an asym- metrical update strategy that applies fre- quency supervision based on Gaussian type, shown in Algorithm[1 [T] For each Gaussian, we check for potential gradi- conflicts by computing the inner prod- uet between g!ow and g. hish where neg- ative value indicates divergent update di- rections [40]. When such conflict is de- tected, we retain the frequency component most relevant to the Gaussian type and project the other. Specifically, for 2D Gaus- sians, we preserve supervision from low- frequency and remove the conflicting com-
// Process per Gaussion gradient conflict
for i <- O N do
There are confiict Gradients in different frequencies
if g." g.igh < 0 then
if
then
g. high
+ g high
g Ahih Jow Low,
g
g
(9)
// Type 2D, project g. high onto normal of g!!
else
gow f- goo
hash low high; Ig 1g
(10)
// Type 3D, project g!" do onto normal of g; high
AG. gi goolor + gow high
return Update AG
high ponent of fregufrryeeccy by projecting g; onto the normal vector of g!!"" shown in (9) Similarly, for 3D Gaussians, we retain g; metrical supervision ensures each Gaussian is updated along its most informative direction while minimizing interference from less relevant frequency signals. More details on DWT and the gradient projection strategy are provided in Appendix and Appendix F respectively.
high and project glow as indicated in (10) This asym-
4 Experiments
Datasets and Metrics. We evaluate EGGS on several widely used benchmarks. For appearance evaluation, we use Mip-NeRF360 125. LLFF [41] Tanks&Temples 42), and DTU 43 For geometry evaluation, we use DTU, which provides ground-truth point clouds, and Tanks& Temples which offers ground-truth depth maps. Additional dataset details are provided in Appendix A Following prior work appearance quality of synthesized novel views. For geometry, we follow 12 Distance [46] on DTU to assess reconstruction accuracy.
[2], we report PSNR, SSIM [4], and LPIPS 45] to evaluate the
39 and report Chamfer
Baselines. To demonstrate the effectiveness of EGGS, we compare against several single- representation methods that use either 3D or 2D Gaussians. For 3D Gaussian-based methods, we include vanilla 3DGS [[]]. GaussianPro [13 and GOF (28), which incorporate geometric regu- larization, and FreGS [4)) which introduces frequency- based supervision. For 2D Gaussian based methods, we consider vanilla 2DGS 122 and TextureGS [16), which improves the appearance fidelity of 2D Gaussians. Additional discussion of related methods is provided in Appendix B
Implementation. We implement our hybrid rasterizer based on the CUDA rasterization code of 3DGS [TT]. We used the Haar filter for the DWT (37 48. For Deequency-Dccoupe we set the weight for the frequency components as Atow 0.2 and Atow = 0.4. For Adaptive Type Switch, we set the erank threshold as 2.05. We offer more details about our training pipeline and parameter setting in Appendix A All experiments are conducted on an A5000 GPU.
Optimization,
7

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Ground Truth
3DGS
2DGS
GaussianPro
Ours
1016
Figure 8: Qualitative comparison on LLFF, Temples and Mip-NeRF360 3DGS suffers from inaccurate scene geometry. While 2DGS improves geometric fidelity, overlooks texture and local details. EGGS recovers more accurate geometry while preserving high-frequency details. Additional visual results and videos are available in the supplementary material and project wehsite
Table 1:
Quantitative comparison Mip-NeRHi NeRF6603 LLFF and Tanks& Tanks&Temples datasets. The best, second -eestt
and third-best entries are marked in red
orange and ycllow respectively.
Nip-NeRF360
LLFF
Tanks& Temples
Method
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM f
LPIPS
2DGS 30008AP1'24
12
26.81
0.796
0.297
24.93
0.815
0.147
22.96
0.802
0.195
TeatureGS 202
27.14
0.803
0.285
25.58
0.837
0.117
22.43
0.811
0.189
GOF
28
27.42
0,826
0.234
25.57
0.854
0,121
22.41
0.831
0,172
GaussianPro 121L134
1
27.92
0.825
0.208
26.33
0.867
0.105
23.92
0.855
0.162
FreGS
47
27.85
0.826
0.209
26.11
0.860
0,102
23,96
0.849
0,178
Ours
27.91
0.831
0.192
27.34
0.893
0.083
24.41
0.923
0.133
4.1 Results
Appearance. Figure & and Table Tshow qualitative and quantitative comparisons on Mip-NeRF360, LLFF, and Tanks& Temples. 3D Gaussian-based methods generally achieve better PSNR, SSIM, and LPIPS but often produce blurred geometry due to anisotropic Gaussians. GaussianPro and FreGS improve reconstruction via geometric or frequency regularization but still lack geometrie accuracy. 2DGS produces cleaner edges and better geometry, yet oversmooths details and underperforms in appearance. TextureGS enhances 2D appearance but remains inferior to 3D-based methods. In contrast, EGGS outperforms all baselines by combining the strengths of 2D and 3D Gaussians. It recovers more accurate geometry while preserving high-frequency visual details.
Geometry. We evaluate geometry reconstruction quality on Tanks& T Temples and DTU. As shown in Figure both 2DGS and EGGS produce more accurate depth maps than 3DGS, with sharper surfaces and clearer edges. However, 2DGS sacrifices appearance fidelity due to the lack of high-frequenc, detail. In contrast, EGGS improves geometry over 3DGS while also preserving appearance quality. Table Treootts Chamfer Distance on the DTU dataset, where EGGS outperforms 3DGS and SUGAR. Note that SUGAR, 2DGS, and GOF prioritize surface reconstruction and mesh extraction, often at the cost of appearance. Although 2DGS is slightly more accurate geometrically, EGGS achieves better trade-off, offering stronger appearance quality alongside competitive geometry.
Efficiency. Table 3 compares the model size and training time of EGGS with 3DGS, 2DGS, and GaussianPro on LLFF and Tennk&&emppes. While 2DGS uses the fewest Gaussians, its training time exceeds that of 3DGS. GaussianPro enhances appearance quality over 3DGS but incurs significantly higher training cost. In contrast, EGGS strikes a favorable balance, requiring fewer Gaussians than both 3DGS and GaussianPro, while achieving the shortest training time among all methods.
8

---

RGB
Depth Map
3DGS
2DGS
Figure 9: Qualitative comparison Tanks& Temples. EGGS achieves better overall reconstruction quality,
producing more accurate depth maps than 3DGS and recovering seeeurruyency details better than 2DGS.
Table 3:
Comparison efficiency. # Gaus- sians is the average number Gaussians.
Table Ablation study. Repr. stands for Gaus- sian type, Hyb. for hybrid rasterization, Ex. for type exchange, and Freq. for frequency regularization.
Dalasel
Method
PSNR
#Gaussians
Training
3DGS
26.12
919K
10min
ID
Repr.
Hyb.
Ex.
Freq.
PSNR1
SSI
LPIPS 4
LLFF
2DGS
24.93
343K
Imin
3D
26.12
0.865
0.099
GaussainPro
933K
20min
EGGS
27.34
581K
9rin
3D+20
26.01
0.859
0.105
Bi
3D+2D
26.23
0.867
0.097
3DGS
23.85
1502K
13min
iv
3D+2D
26.58
0.874
0.093
Tanks& Temples
2DGS
22.96
416K
15min
GaussainPro
1381K
35min
W 3D+2D
26.41
0.871
0.096
EGGS
24.41
754K
11min
3D+2D
0.895
4.2
Ablation and Generalization Analysis
Ablation Study. We evaluate the effectiveness of each component in EGGS in Table 4 Row is the vanilla 3DGS baseline. In row ii, we adopt hybrid 2D/3D representation but rasterize all Gaussians using the 3DGS rasterizer, which leads to performance degradation. Row iü incorporates our hybrid rasterizer, which renders Gaussians according their type. However, this setting still lacks flexibility and regularization. Row iv incorporates adaptive type exchange to enhance the flexibility. Rows v-vii study frequency-basee bassed supervision, which provides only limited gains for non-hybrid 3DGS (row v) but is more effective in the hybrid setting. The full model in row vii achieves the best performance, indicating that decoupled frequencies more effectively exploit the strengths of the exchangeable hybrid representation. We provide more ablation and analysis in Appendix F
Generalization Analysis. We evaluate the robustness of EGGS in challenging scenarios, including few-shot and out-of-distribution (OOD) settings. Following prior work,
Traisin
we use L.LFF [1 for few-shot evaluation [49 (50) and OOD-NVS [51] for OOD) evaluation
(52). More details
are provided in Appendix [A] As shown in Table I1 and
Figure I0 EGGS achieves robust performance both set- tings, benefiting from its balanced multi-view consistency and appearance fidelity. This indicates that the hybrid rep- resentation generalizes better than single-type baselines.
Teu
S0GS
JIKS
Figure 10: Comparison in the OOD setting.
Table 5: Generalization performance.
We also emphasize that EGGS serves as general derlying representation and is compatible with various optimization strategies developed for specialized set- 54
Serting
Method
SSIM
LPIPS
3DGS
20GS
55 [11. We discuss these orthogonal techniques in Appendix B and provide further remarks on limitations and broader impacts in Appendix H
tings 449 55 53
E0GS
20.13
0.258
3DGS
20.21
0.763
0,242
COD
20038
23.52
0386
0.188
EOGS
24.17
0.907
0.151
Table Quantitative Geometry Comparison on DTU. Chamfer Distance (CD) is reported per scene, mCD and PSNR denote the mean Chamfer Distance and mean PSNR across all scenes, respectively.
Method
24
37
40
55
65
69
97
105
106
110
114
118
122
mCD
PSNR
3DGS
2.14
2.08
1.68
2.21
1.43
1.75
1.53
1.96
SUGAR
1.47
1.33
1.13
0.61
2.25
1.71
1.15
1.63
1.62
1.07
0.79
2.45
0.98
0.88
0.79
1.33
31.59
2DGS
0.48
0.39
0.76
0.40
GOF
0.50
0.82
0.37
0.37
1.12
0.78
0.73
1.18
1.29
0.71
0.77
0.90
0.44
0.69
0.49
0.74
32.58

---

Conclusion
This paper presents EGGS, a hybrid Gaussian Splatting framework that combines the appearance fidelity of 3D Gaussians with the geometric accuracy of 2D Gaussians. The design integrates Hybrid Gaussian Rasterization for unified rendering, Adaptive Type Exchange for flexible representation. and Decoupupe Optimization to balance geometry and appearance. EGGS outperforms both 2D- and 3D-only baselines across multiple benchmarks. Future work includes extending the hybrid representation to more diverse and challenging scenarios.
Acknowledgments: This work was supported by Intelligence Advanced Research Projects Ac- tivity (IARPA) via Department of Interior/Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Gov- emmmental purposes, notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government.
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Appendix
Table of contents:
Appendix A Implementation Details. Additional information on the training pipeline, parameter settings, and evaluation datasets and protocols used in our experiments.
Appendix B Related Works. Extended discussion the distinctions between our method and other re lated approaches, including hybrid and task-specific splatting methods.
Appendix C Differentiable Rasterization for 2D/3D Gaussian Splatting. Technical details of the rasterization procedures used in 3DGS and 2DGS, which serve as the building blocks for our Hybrid Gaussian Rasterization module.
Appendix D Effective Rank and Adaptive Type Exchange. More ablations and analysis on the effective rank threshold. We also detail the design of permutation based reparameteri- zation, and report the evolution and distribution of Gaussian types during training.
Appendix Discrete Wavelet Transform. A detailed explanation of the DWT used in our Frequency- Decouuple Optimization, including mathematical formulation and visualization of decomposed frequency components.
Appendix F Gradient Conflict Analysis in Frequency-Decoupled Optimization. In- depth analysis of gradient conflicts arising from different frequency components, supported by empirical statistics. We also compare different loss application strategies and highlight the benefits of our projection-basee solution.
Appendix H Discussion. Discussion on limitations, broader impacts, and the generalization potential of our hybrid representation in more diverse scenarios.
A Implementation Details
Training Pipeline and Parameter Setting, Our training setup closely follows 3DGS 11 We assume camera poses are provided or can be estimated using structure-fromd from--ooooooooonn (SfM) [35] Initial sparse point clouds are generated via COLMAP 335 36). All methods, including EGGS and baselines, are trained for 30K iterations. Learning rates for Gaussian parameters follow the default configurations from 3DGS and 2DGS. We adopt the densification strategy from 3DGS, which refines Gaussian distributions by pruning or duplicating them in under- over-reconstructed regions. Densification begins at iteration 500, ends iteration 15K, and is performed every 100 iterations.
In EGGS, we employ Hybrid Gaussian Rasterization, where each Gaussian is rendered according its assigned type. Gaussian types are randomly initialized. To enable flexible representation, we introduce Adaptive Type Exchange, which is performed every 500 iterations from step 500 to 30K. During type switching, we set the effective rank threshold 0, 2.05. For scale modulation, which allows 2D Gaussians to evolve into 3D Gaussians as the scale becomes more significant, we use 0₂ = 1.05 and temperature T= 0.001 in Eq. 7 Additionally, we incorporate frequency- supervision using the Discrete Wavelet Transform (DWT). More details on Frequency -eeeceyp--e Optimization are provided Appendix F
Datasets and Evaluation Protocols.
We evaluate the performance of EGGS and baselines on several
widely used datasets, including Mip-NeRF360 (25), LLFF [41], Kanks&Temples [42), DTU
[3
and OOD-NVS [51]. We follow the standard train/test splits used in prior work (25), with additional dataset statistics provided in Table 6 To ensure fair comparison with baselines
2 we
downsample input images using the same factors as in [52]. All datasets provide RGB images for evaluating appearance quality. DTU additionally offers ground-trutt point clouds for computing Chamfer Distance, while Temples provides ground-true truth depth maps for depth accuracy evaluation. Beyond standard dense-view evaluation, we also perform evaluation under few-shot settings using 3 views from LLFF, and out-of (OOD) setting using OOD-NVS.
B Related Works
Following 3DGS [II, a line of work has been proposed to enhance the geometry accuracy and reconstruction quality. As discussed in the related work section, most existing methods are based on
14

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Table 6: Details on the datasets used for evaluation of appearance and geometry.
Dataxet
Ground Truth
Evaluation Metric
Evaluation Protocol
Factor
Mip-NeRF 360 (outdoor) 15
RGB image
Appearance
Standard
Mip-NeRF 360 (indoor) 25
RGB image
Appearance
Standard
LLFF [1]
RGB image
Appearance
Standard and Few-shol
TTmples
RGB image: Depth
Appearance and Geometry (FI)
Standand
DTU FXc
RGB image; Point Cloud
Geometry (chamfer distance)
Standard
OOD-NVS 51
RGB image
Appearance
OOD
single representation
12 15 28 16 47 Here, we further expand several recent efforts
that aim to exploit the advantages of 3D and 2D Gaussians, as summarized in Table 7 method to be general if the training pipeline follows the standard 3DGS.
We consider a
proposes to combine 3D Gaussians and image-space 2D Gaussians to remove transient objects during reconstruction. However, the 2D Gaussians in HybridGS are defined in the image frame, lacking the multi-view consistency provided by 2DGS [1]. Additionally, HybridGS employs three-stage training pipeline specifically designed for transient object removal, making it less general than pipelines based on 3DGS. Moreover, since the training code of HybridGS not publicly available, direct comparison with EGGS is not feasible.
HybridGS 17
HorizonGS [8] on the other hand, built upon ScaffoldGS, where voxel-based MLPs are used to decode Gaussian primitives. HorizonGS generates 3D Gaussians from MLPs for novel view synthesis and 2D Gaussians for surface reconstruction. Thus, it still follows a single-representation scheme. Furthermore, HorizonGS is specifically designed for aerial-groume scenarios and introduces a two-stage training pipeline to address conflicts from varying altitudes. Similar to HybridGS, this design is task-specific and less generalizable.
In contrast to HybridGS and HorizonGS, we note that several recent optimization techniques are more general and adhere to the 3DGS training pipeline, such as ScaffoldGS (22] and DDGS-MCMC [27]. ScaffoldGS improves efficiency by introducing voxel-based MLPs, while 3DGS-MCMC enhances the densification process by reformulating 3D Gaussians as Markov Chain Monte Carlo (MCMC) samples. These methods are orthogonal to EGGS. Since EGGS serves as general underlying representation, we believe such orthogonal optimizations can be incorporated to further enhance our framework. Exploring the potential of integrating these techniques with our exchangeable hybrid representation is a promising direction for future work.
In this work, we assume that camera poses are either available or be estimated using structure- from-motion (SfM) [35], and that initial sparse point clouds can be generated using COLMAP [35] 36). However, in practice, recovering geometric information such as camera poses and point clouds re- mains challenging. Recently, 3D Geometric Foundation Models (GFMs) have emerged as a promising approach improve the generalizability of 3D reconstruction
[56]. Feed-forward models such as DUSt3R [57] MASt3R [58] and VGGT [39] can predict robust geometric attributes in a single forward pass, even when the input multi -iew images exhibit minimal or no overlap. Incorporating GFMs can potentially enhance the reconstruction quality of our method in open- open-world scenarios.
Table 7: Comparison of the setting with related works.
Method
Gaussian Type
Setting
Training Pineline
3DGS
|1|
3D
General
Single-stage
2DGS
12
2D
General
Single-stage
HybridGS
17
3D+2D
Transient
Three-stage
HorizonGS
18
3D/2D
Varying-altituse
Two-stage
ScaffoldGS
22
3D
General
Single-stage
3DGS-MCMC
27
3D
General
Single-stage
EGGS
3D+2D
General
Single-stage
15

---

C Differentiable Rasterization for 2D/3D Gaussians Splatting
In this section, we detail the differentiablee rasterization procedures used in 3DGS |T and 2DGS 12] focusing on how the intermediate coordinates in Eq. T are computed. In both methods, images are rendered by computing the color at each screen-space pixel Vp from a set of N Gaussians { --11 The final pixel color is obtained by rasterizing the Gaussians onto the image plane, but the rasterization procedures differ significantly between 3DGS and 2DGS.
3DGS employs affine approximation to the projective transformation for rasterization. For a 3D Gaussian G.dd with type i, = 1, it is first projected onto the image plane via affine projection [[]] The resulting projected Gaussian is denoted as G, with 2D center U'd,, and covariance Σ in the image plane. The projected covariance is computed as:
Σ -WWEEW
(11)
where is the Jacobian matrix of the affine projection, and W accounts for the world-to-cament transformation [1I]. Once Σ is obtained, the projected center plsd, can be computed accordingly.
On the other hand, 2DGS applies ray-splat- interttintersectionn to rasterize 2D Gaussians. For a 2D Gaussian G2dd with t; = is not directly projected onto the image plane. Instead, to preserve the geometric accuracy of G7dd the pixel 2p is unprojected into the local tangent frame defined by the Gaussian [12]. This is done by computing the intersection between the ray passing through Tp and the tangent plane of g.dd, resulting in the local coordinates:
h M h hih!
h h hLA! h1hh 1a4
u(zp))
e(z,)
(12)
where hy and h. are derived from the homogeneous plane equations associated with the pixel Fp (x., y) as:
h. (WH)"), h. (WH))
(13)
More details about the homogeneous transformation matrices H and W can be found in 2DGS 12 By solving Eq. (12), obtain the 2D position of rp in the tangent frame, denoted u, (z
(zp)), (zp)) Note that the center M2d, of G is defined as the origin of this tangent frame.
With the projected center يlg and covariance E; for 3D Gaussians, and the intersection coordinates (xpp)) and v; (x(x)) for 2D Gaussians, we can perform hybrid rasterization as described in Section 3.1
D Effective Rank and Type Switch
In this section, we provide additional details about Adaptive Type Exchange. We focus on the effective
rank threshold and the design choices behind 3D Gaussian reparameterization and 2D Gaussian scale modulation. We also present statistics the distribution of Gaussian types over training iterations.
Table 8: Ablation on different crank thresholds.
We evaluate the appearance of EGGS on the LLFF dataset with different erank thresholds.
erank threshold
PSNR
SSIM
LPIPS
Effective Rank Threshold. As described in Section 3.2 we use the effective rank (erank) to assess the mismatch between a Gaussian's assigned type and its actual geometric dimen- sionality. We set the crank threshold to 2.05 in experiments and study its effect in Table 8
1.9
26.15
0.871
0.103
1.95
26.23
0.868
0.101
26.49
0.874
0.097
2.05
27.24
0.885
0.086
2.1
26.37
0.844
0.113
2.15
25.78
0.831
0.126
When a 3D Gaussian becomes increasingly flat and its crank drops below the threshold, it is converted to 2D Gaussian. Conversely, if a 2D Gaussian's 's erank exceeds the threshold, it is switched to 3D. A higher threshold causes more 3D Gaussians to be converted to 2D, as more will fall below the threshold. This can degrade performance when the threshold is set too high. In contrast, lower threshold (e.g.. 1.9) results in fewer 3D Gaussians being converted to 2D, causing the model to behave more like the 3DGS baseline and limiting the benefits of hybrid representation.
While the erank metric has been previously introduced 38 39], our contribution lies in integration into a dynamic type exchange mechanism for hybrid Gaussian representation. We acknowledge that
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erank is heuristic measure of effective dimensionality and may not behave monotonically in all scenarios. When Gaussian has scales (1, 1,,,,,,, sz) with the first two scales fixed. the erank increases with initially but may drop as becomes dominant (e.g., erank returns to 2 when R 2.6). In such cases, volumetric Gaussian could technically fall below the threshold 0. and be converted to 2D. However, note that such configurations are rare in practice. All three scales are updated jointly during training, and our method includes reparameterization and soft modulation to ensure that type transitions remain stable and consistent with the evolving shape. Although the erank threshold does not come with theoretical guarantees for edge cases, demonstrates empirical effectiveness across diverse datasets.
Number Gausssians
320K
2D Gaussiars
240K
3D Gaussians
160K
0
3000
6000
9000
12000
15000
18000
21000
24000
27000
30000
Iteration
Figure 11: The number 3D and Gaussians different iterations during training.
Permutation-Bast Reparameterization The key to reparameterizationis is preserving the covariance during type switching. We achieve this using permutation matrices Pa and py, designed to be orthogonal with positive determinant. Specifically, we define:
0
D
0
P.
0
Ps
0
(14)
0]
where PP" I and the identity matrix, and (Pt(P) 1. During conversion, the new S
scaling and rotation R2 computed using these permutation matrices ensure that the transformed covariance Σ R.SRR' remains unchanged:
S = PSP" and R RP
(15)
is easy to see the converted covariance unchanged:
E" RR 5" S R.T
RP" PSP PST PT PR
= R. (R.(P"P) S. (P P). s" (P"'))
-RSST RT
=
(16)
In addition to preserving the covariance, the permutation must ensure that the converted rotation matrix R" has positive determinant. This is important because R" is converted into a quaternion during optimization, and most 3D graphics frameworks assume right-handed coordinate systems [46). negative determinant implies reflection, which cannot be represented by unit quaternion. Given that the original rotation matrix R satisfies det R) > O, and the permutation matrices Pz and P, the determinant of the converted rotation Rt RRP is given by: det(R*) det R) det det(P")) det det((e det (R) 0. Therefore, P. and P, preserve both the covariance and the positive determinant of the rotation matrix, ensuring compatibility with quaternion-based optimization.
orthogonal with del(
Taussian-Type Distribution. Figure shows the distribution of 2D and 3D Gaussians throughout training. As described in Appendix A we randomly initialize Gaussian types, resulting in roughly equal numbers of 2D and 3D Gaussians at the start. During optimization, both types increase due to densification, with a more significant rise in 3D Gaussians. This trend can be attributed to the SfM-initialized points already containing geometric structure, allowing 2D Gaussians capture coarse geometry in early iterations. Notably, the number of 2D Gaussians gradually decreases in
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the later stages of training, especially after densification ends at 15K iterations. This suggests that many 2D Gaussians are being converted to 3D Gaussians, likely to better recover mnder-reconstruuted regions and capture finer scene details.
Gaussian-Type Initialization. key feature of EGGS is its exchangeable representation, which allows each Gaussian primitive to change its type as needed, regardless of its initial type. To verify this capability, conduct a simple experiment by investigating three initialization scenarios: initialize all Gaussians as 2D, all as 3D, or with random type assignments, and observe the distribution of Gaussian types throughout training. Below, we show the percentage 3D Gaussians different iterations. As shown in Table 99] even when the model is initialized entirely with 2D Gaussians, part of the Gaussians are converted to 3D Gaussians during training, leading to hybrid model in the final stage. This demonstrates that 2D Gaussians can indeed transition to 3D types during training, despite potentially incorrect initialization, and vice versa.
E Discrete Wavalet Transformation
frequency 1
High frequency JL. (lanisn))
DWT
RGB image I
ligh frequency j4ft
ligh frequency JMN (duparaa)
(vemical)
Figure 12: Illustration of the level-1 Discrete Wavalet Transformation.
In this section, we provide additional details on the Discrete Wavelet Transform (DWT) used in our Frequency-Decouppe analysis. Given an image I. DWT decomposes into four sub-bands: one low-frequency component and three high-freque frequeeyyy components corresponding to horizontal, vertical, and diagonal directions. Formally, we define the low-pass filter matrix L as:
Optimization. DWT is widely adopted technique for frequency-domain
E
Eo
L
(17)
to
81
where L is the ID low-pass wavelet filter. Similarly, the high-pass matrix is derived from the 1D high-pass wavelet filter h. We orthogonal 1D wavelet filters such that &. and h are the same 37 48 The four sub-bands are computed as:
I LILT:
I HITT"
T LIHT.
THE HIH..
(18)
We provide illustrative example in Figure 12
We extract the low-frequency feature as I, I and the high-frequency component I, the composition of directional details: ILH (horizontal), THE (vertical), and HHH (diagonal). In our implementation, we use level-1 1 Haar filter for the DWT. Table Effect of Gaussian percentage on reconstruction quality. PSNR denotes the peak signal-to-noise ratio at each iteration step under different initialization strategies.
Iter.
3000
6000
9000
12000
15000
18000
21000
24000
27000
30000
PSNR
anitialization
29.1%
41.4%
43.2%
All 3D intialization
100.0%
86.2%
75.3%
69.0%
63.9%
59.7%
58.7%
58.0%
57.4%
$7.0%
57.0%
27.51
Random intiaaizaatinn
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Total Gaussians
Conflicted Gaussiars
Confict Ratio
Gaussian Number
500K
50
Ratio (%
400K
40
200K
35
30
100K
-25
3000
6000
9000
12000
15000
18000
21000
24000
27000
30000
Iteration
Figure 13: The number of Gaussians with conflicted gradients in different iterations during training.
F
Gradient Conflict Analysis in Frequency-Decoupler Optimization.
We provide additional details on Frequency -eccoulee Optimization and Algorithm|] [ After applying DWT, both 3D and 2D Gaussians receive gradients from the high-frequency and low freeennyyy losses. As discussed in Section 3.3 the distinct roles of 3D and 2D Gaussians-when 3D Gaussians prioritize fine detail and 2D Gaussians emphasize geometric structure- can lead to conflicting gradient directions.
We empirically analyze this in Figure 13 where "conflicted Gaussians" are defined those with negative inner product between low- and high-frequency gradients, i.e., glow g
high 0 in Algo- rithm I In early training (e.g., before 15K iterations), about 45% of Gaussians exhibit such conflict..
Although the conflict ratio gradually decreases as training progresses, around 20% of Gaussians still experience conflicts convergence. This supports motivation that naively combining Ciow and Lhigh as Eq. (8) for all Gaussians pro- vides suboptimal supervision, and underscores the need for the proposed asymmetrical update strategy. In Table I0, we compare different strategies for applying frequency- baaued super- vision. As baselines, and EGGS without Sesquencc--eccopphe mization (EGGS w/o FDO), which includes hybrid rasterization and type exchange but frequency regularization. EGGS w/ DWT applies frequency losses directly as in Eq.(8), yielding only marginal gains due unresolved gradient conflicts (Figure[3). A simple alternative frequency gradients-for example, ignoring high-frequency gradients for 2D Gaussians. We denote this variant as EGGS w/ DWT mask. While masking helps reduce conflicts, may discard useful gradient signals. In contrast, our full method achieves the best performance by leveraging gradient projection to suppress only the conflicting components while retaining informative gradients. For theoretical background gradient projection and conflict resolution, we refer readers to [40].
Table 10: Ablation on different use of the frequency loss. FDO stands for Frequency-Decouple Optimiza- tion.
Method
PSNR
SSIM
LPIPS
3DGS
26.12
0.865
0.099
EGGS w/o FDO
26.58
0.874
0.093
EGGS DWT
26.82
0.877
0.092
EGGS w/ DWT + mask
27.07
0.881
0.089
include vanilla 3DGS
EGGS
27.34
0.895
0.083
Opti-
mask out conflicting
Table 11: Comparison of inference efficiency. We report the average FPS in each dataset.
Method
Tanks&Teeplle
Mip-NeRF360.
3DGS
323
158
2DGS
187
59
76
GaussianPro
308
121
EGGS
268
125
104
G Inference Efficiency
As shown in Table I1 we compare the rendering efficiency of different methods in terms of frames per second (FPS). During training. the number of parameters significantly impacts performance, backpropagation and parameter updates computationally expensive. In contrast, inference
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efficiency is primarily determined by the rasterization strategy. 3DGS-based methods, including GaussianPro, employ affine projection-base based rasterization, which is efficient but less accurate, resulting in higher FPS at inference. Since both 3DGS and GaussianPro use the same projection-based rasterization pipeline, the difference their inference speed mainly arises from model size- that is, the number of Gaussians used. While the number of primitives affects performance, its influence remains moderate given the similar scale of models.
In contrast, 2DGS adopts a may-slla-innerrsetion rasterization pipeline, which provides improved geometric accuracy but more computationally intensive, resulting in slower rendering. EGGS integrates both 2DGS and 3DGS rasterization strategies in hybrid manner, achieving favorable balance between accuracy and efficiency. While EGGS FPS slightly lower than that of 3DGS, remains significantly faster than 2DGS. Additionally, EGGS benefits from a shorter training time than 3DGS, owing its reduced model size and more effective optimization dynamics.
H
Discussion
Broader Impact. This work introduces exchangeable hybrid Gaussian splatting framework that improves the trade-off between geometry accuracy and appearance fidelity in neural rendering. By enabling flexible type adaptation and frequency-awar supervision, our method can enhance 3D reconstruction quality in both synthetic and real-world scenarios. Potential applications include au- tonomous driving, augmented reality, and robotics, where accurate scene geometry and photorealism are both essential. While our approach primarily targets academic benchmarks, it may inform future developments in real-time perception systems.
Limitations. The current initialization of Gaussian types random and does not incorporate semantic or structural cues from the sparse point cloud, which may limit early-stage optimization. Incorporating semantic priors could improve convergence and final quality. Additionally, as general-purpont representation, method has not been explicitly tested under extreme conditions such low-light environments, highly reflective surfaces, or scenes with significant transient content. Evaluating and adapting the framework such challenging scenarios may further demonstrate the robustness and versatility of the hybrid representation.
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Reviews:
[{"review_id": "EJtbfrw9MM", "reviewer": "Reviewer_5biL", "summary": "This paper proposes EGGS, Exchangeable 2D/3D Gaussian Splatting for Geometry-Appearance Balanced Novel View Synthesis. 3D Gaussian Splatting enables real-time rendering with high appearance fidelity, but suffers from multi-view inconsistency. On the other hand, 2D Gaussian Splatting enforces multi-view consistency but compromises texture details. EGGS aims to meet a middle ground to get the best of both worlds: appearance fidelity  as well as multi view consistency.\n\nTo enable this, a few technical novelties are needed: Hybrid Gaussian Rasterization, a unified rendering framework that supports both 2DGS and 3DGS rendering, Adaptive Type Exchange, which enables an exchangeable hybrid of 2D and 3D Gaussians, and Frequency-Decoupled Optimization, a regularization strategy in the frequency domain that allows for asymmetric optimization of 3DGS and 2DGS based on their individual traits. First, each Gaussian is augmented by a ‘type’ variable, that codifies if it is a 2DGS or 3DGS representation. Basically, a 2DGS has a z scale equal to 0. Then, the contributions of each Gaussian is calculated based on its projected distance from the pixel and are together rendered. Additionally,  Gaussians can move from one type to another, based on their effective rank (number of dimensions). However, since 2DGS itself does not backpropagate gradients to the z scale, to enable Gaussians to learn from z scale, opacity is defined to be an inverse function of z scale. Finally, wavelet based decomposition allows for each type of Gaussian to be supervised on parts that they are stronger on, enabling better representation.\n\nAcross several datasets, and when compared with a range of baseline methods, EGGS shows improved qualitative and quantitative performance. The hybrid representation also allows for efficient use of Gaussians, and fast training and rendering. Finally, ablation analyses indicate the benefit of each component.", "questions": "Questions:\n1. Is there any empirical or mathematical evidence that can further emphasize the relationship between opacity and z scale assumed in this work?\n2. If a Gaussian is incorrectly initialized as 2D in a region that needs 3D (or vice versa) do we have any analysis to show that the Gaussians are highly likely to recover to the correct Gaussian type?\n3. Would it be possible to have a primer section on the Math of 2DGS and 3DGS and how they relate more explicitly at the beginning of Sec 3, to make readability better?", "limitations": "Yes, in the appendix. It would be good if this can be in the main paper.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper is well written, easy to follow,\n2. The method is well motivated, explained well, and takes into account various factors that are necessary.\n3. Results show superior qualitative and quantitative performance across a range of baselines, and motivate the various method components well through ablation analyses.\n\nWeaknesses:\n1. I am a bit unsure about the inverse relationship between opacity and z scale. Complex non-planar yet solid structures may benefit from being 3D but opaque, so not sure if this is a mathematically grounded assumption.\n2. In terms of the initialization of the Gaussians, it seems the initialization is random for a Gaussian to be either 2D or 3DGS. But this seems quite non-optimal: why can we not use the wavelet-based decomposition and some coarse metric of scene texture to better blend Gaussian initializations?", "was_revised": true, "final_justification": "I thank the authors for their responses to the questions. I am happy to maintain the Accept rating for this paper, and hope the authors incorporate the feedback from all reviewers in the revision.", "rebuttal": "We thank Reviewer 5biL for their constructive feedback and for recognizing the contributions of our work, including the soundness of our methods and superior qualitative and quantitative performance. Below, we address the main concerns raised in the review.\n\n**Q1: The relationship between opacity and z-scale**\n\n**Representing non-planar yet solid structures.** We appreciate the reviewer’s insight regarding the potential importance of 3D but opaque Gaussian primitives for representing non-planar yet solid structures. This observation actually aligns with our design: the scale modulation between opacity and z-scale applies **only** to 2D Gaussians. Non-planar yet solid structures can still be effectively captured by 3D Gaussians, which remain unaffected by this modulation. During training, the model can either densify 3D Gaussians or convert suitable 2D Gaussians into 3D ones to better represent such regions.\n\n**Empirical analysis on the relationship of opacity and z-scale.** The primary motivation for modulating the z-scale of 2D Gaussians is to enable their transition into 3D Gaussians when necessary. Our intuition is that such a transformation typically occurs when the model needs to acquire volumetric capacity or represent semi-transparent regions. To facilitate this, we introduce an inverse relationship between opacity and z-scale only during training.\n\nTo verify the rationale behind scale modulation, we conducted training *without* explicit z-scale modulation. In this setup, we employed affine approximation-based rasterization for 2D Gaussians to enable gradient flow to the z-scale. While this rasterization is not geometrically accurate, it suffices to observe the dynamics between opacity and z-scale during optimization. We analyze the cosine similarity between the gradient of opacity ($\\nabla_{\\alpha}$) and z-scale ($\\nabla_{s_z}$) for 2D Gaussians.\n\n| Iteration | 3000   | 6000   | 9000   | 12000  | 15000  | 18000  | 21000  | 24000  | 27000  | 30000  |\n|-----------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n| cos($\\nabla_{\\alpha}$, $\\nabla_{s_z}$)     | -0.221 | -0.216 | -0.244 | -0.241 | -0.253 | -0.245 | -0.201 | -0.214 | -0.248 | -0.196 |\n\n\nAs shown in the table, $\\nabla_{\\alpha}$ and $\\nabla_{s_z}$ have negative cosine similarity across different training iterations. This suggests 2D Gaussians with increasing z-scale tend to exhibit decreasing opacity. Such behavior supports our design of soft modulation and validates the effectiveness of our design.\n\n\n**Q2: Alternative initialization of Gaussian type**\n\nWhile more advanced initialization strategies may improve reconstruction quality, designing such initialization is non-trivial. For instance, wavelet-based decomposition can effectively decouple frequency information in the 2D image space. However, during initialization, 2D pixels do not directly correspond to 3D points, which makes it challenging to apply Discrete Wavelet Transform for initializing Gaussian type.\n\nIn our response to Q3 below, we show that different initializations often converge to Gaussian models with similar type distributions and comparable appearance performance. This empirical observation suggests that random initialization serves as a reasonable and effective starting point. As mentioned in our limitations section, 3D point segmentation could potentially enhance initialization. For example, we can segment the initial 3D points into distinct regions and assign different Gaussian types to different semantic segments. This might lead to improved initialization and more efficient training. However, determining an optimal mapping between semantic labels and Gaussian types remains challenging. We thus leave the development of more advanced initialization techniques to future work.\n\n**Q3: Can 2D Gaussians change to 3D if initialization is incorrect?**\n\nA key feature of EGGS is its exchangeable representation, which allows each Gaussian primitive to change its type as needed, regardless of its initial type. To verify this capability, we conduct a simple experiment by investigating three initialization scenarios: we initialize all Gaussians as 2D, all as 3D, or with random type assignments, and observe the distribution of Gaussian types throughout training. Below, we show the percentage of 3D Gaussians at different iterations.\n\n| Percentage of 3D Gaussians  | 0      | 3000   | 6000   | 9000   | 12000  | 15000  | 18000  | 21000  | 24000  | 27000  | 30000  | PSNR  |\n|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n| All 2D initialization | 0.0%   | 19.0%  | 29.1%  | 33.7%  | 35.0%  | 38.9%  | 39.8%  | 41.4%  | 43.2%  | 45.7%  | 47.8%  | 27.25 |\n| All 3D initialization | 100.0% | 86.2%  | 75.3%  | 69.0%  | 63.9%  | 59.7%  | 58.7%  | 58.0%  | 57.4%  | 57.0%  | 57.0%  | 27.51 |\n| Random initialization | 49.9%  | 58.1%  | 59.9%  | 57.3%  | 55.1%  | 52.3%  | 52.5%  | 52.9%  | 52.9%  | 53.1%  | 54.2%  | 27.86 |\n\nAs shown in the above table, even when the model is initialized entirely with 2D Gaussians, part of the Gaussians are converted to 3D Gaussians during training, leading to a hybrid model in the final stage. This demonstrates that 2D Gaussians can indeed transition to 3D types during training, despite potentially incorrect initialization, and vice versa. \n\n**Q4: Improve readability**\n\nDue to space constraints, we included an introduction to the mathematical formulation of 2DGS and 3DGS rasterization in Appendix B. In the revised version, we will add a brief preliminary section at the beginning of Section 3 to further improve readability.\n\nWe sincerely appreciate the reviewer’s constructive suggestions. We will include detailed discussions on the scale modulation and initialization in our revised version to offer more insights into our method."}, {"review_id": "HhkvbeQcXy", "reviewer": "Reviewer_2p4H", "summary": "The paper propose a new Gaussian Splatting framework with the aim of combining the 3D reconstruction capabilities of 2D gaussians with the rendering quality of a 3D gaussian representation. For this the paper introduces a hybrid representation which let's gaussians adaptively switch between 3D and 2D, depending on which capabilities are needed at this point of the scene. Supervision is done in the frequency domain, which allows to split the scene content into general geometry (low frequency) and finer details relevant for rendering (high-frequency).", "questions": "1. What is the purpose of $\\lambda_z$ in Eq. 6? If it is just a scaling factor, couldn't the same role not also be fulfilled by the parameters of the gating function in Eq. 7?\n2. Can you give a bit more intuition into the scale modulation (L196)? From my understanding it just seems like an engineering trick to overcome visual artifact's on transparent areas.\n\nI am more than open to increase the score should the authors address the lacking baselines and provide information on the rendering speed.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "**Strengths** \n\n- **1. Performance:** The method has SoTA rendering performance both in qualitative and quantitative evaluations on common datasets (Mip-NeRF360, LLFF, Tanks&Temples). Additionally, the authors demonstrate competitive geometry reconstruction capabilities fulfilling the claim of balancing appearance and geometry.\n- **2. Idea and novelty:** The idea of combining the best of both worlds, rendering quality of 3D Gaussians and geometric reconstruction capabilities of 2D Gaussians is novel and well-motivated by the authors. Separating the scene into high and low-frequency content is a good idea, and  adaptive approach of separating the scene into high and low frequency components is a good idea which seems to work well in practice.\n\n**Weaknesses**\n \n- **1. Lacking SoTA baselines**: The evaluation lacks a comparison with the SoTA method 3DGS-MCMC (Kheradmand et al. NeurIPS 2024), although shortly mentioning it in the appendix (L580). Additionally the  evaluation should also include NeRF-based methods for completeness, for which I would think an inclusion of MipNeRF360 (Barron et al. CVPR 2022) would be sufficient.\n- **2. Information about rendering speed:** The evaluation does not contain any information about the actual rendering speed of the method and how it compares to the baselines. I would expect this as additional column in Tab. 1 or Tab. 3.\n- **3. Ablation study lacks geometric metrics:** The main claim of the paper is to balance rendering and reconstruction quality, therefore the ablation study (Tab. 4) should also contain information on how the model components influence the geometric reconstruction.\n- **4. Related work too focused on rendering:** The related work focuses purely on rendering-based methods but should at least acknowledge recent methods purely reconstruction such as DUSt3R (Wang et al. CVPR 2024).", "was_revised": true, "final_justification": "The rebuttal submitted by the authors managed to address of my concerns (W1-W4) and answered my questions regarding the scale modulation (Q1, Q2). Therefore I decided to raise the score from \"Borderline Accept\" to \"Accept\".", "rebuttal": "We thank Reviewer 2p4H for their thorough reading of our manuscript, constructive feedbacks and recognizing several positive aspects of our submission, including the novelty of our idea and the improved performance of EGGS in both appearance and geometry. Below, we address the main concerns raised in the review.\n\n**Q1: Comparison with SoTA baselines**\n\nWe thank the reviewer for acknowledging that EGGS improves reconstruction quality and achieves a better balance between appearance and geometry. We provide quantitative comparisons with two additional strong baselines: the SoTA 3DGS-based method 3DGS-MCMC and the NeRF-based method Mip-NeRF360. We evaluated the performance on the Mip-NeRF 360 and LLFF dataset. We also incorporate 3DGS-MCMC into our framework by replacing the vanilla 3DGS component.\n\n| Mip-NeRF 360 Dataset                 | PSNR(↑) | SSIM(↑) | LPIPS(↓) |\n|------------------------|------|------|-------|\n| Mip-NeRF 360           | 27.88 | 0.835  |   0.201    |\n| 3DGS                   | 27.43 | 0.814  |   0.257    |\n| 3DGS-MCMC              | 28.11 | 0.867  |  0.188    |\n| Ours                   | 27.96 | 0.851  |  0.192     |\n| Ours + 3DGS-MCMC       | 28.58    |  0.892    |  0.184  |\n\n| LLFF Dataset               | PSNR(↑) | SSIM(↑) | LPIPS(↓) |\n|------------------------|------|------|-------|\n| Mip-NeRF 360           | 26.79 | 0.871 |  0.092     |\n| 3DGS                   | 26.12 | 0.865 |  0.099   |\n| 3DGS-MCMC              | 27.81    |  0.905 |  0.077 |\n| Ours                   | 27.34 | 0.895 |  0.083   |\n| Ours + 3DGS-MCMC       | 28.03 | 0.931 |  0.069   |\n\nAs shown above, our method achieves comparable performance with both 3DGS-based and NeRF-based SoTA baselines. More importantly, by replacing vanilla 3DGS with 3DGS-MCMC (i.e., Ours + 3DGS-MCMC), our method can outperform the SoTA baselines. This suggests that while current EGGS is built on the vanilla 2DGS and 3DGS, more advanced variants can be incorporated to further improve the performance.\n\n**Q2: Rendering Speed**\n\nWe provided an analysis of the inference speed in terms of frames per second (FPS) in Table 10 of the supplementary materials (included in the .zip file). For convenience, we provide the results below.\n\n| FPS(↑)       | LLFF | Tanks&Temples | Mip-NeRF 360 |\n|--------------|------|----------------|--------------|\n| 3DGS         |  323    |   158            |    145           |\n| 2DGS         |  187    |   59             |    76            |\n| GaussianPro  |  308    |   166             |   121           |\n| Ours         |  268    |   125             |   104           |\n\nThe rendering speed is mostly determined by the rasterization technique. While 2DGS typically has the smallest model size, as shown in Table 3 in our manuscript, its inference speed is slower than 3DGS-based methods. This is because the ray-splat intersection used in 2DGS incurs more intensive computation than affine approximation-based rasterization in 3DGS. Our method combines the two rasterization techniques and has a higher FPS than 2DGS. We note that while EGGS has a lower FPS than pure 3DGS-based method, our method achieves a better balance between model size, training and inference efficiency and reconstruction quality. We will add an additional column to Table 3 to clearly indicate the inference efficiency of each method in our revised version.\n\n**Q3: Ablation on Geometry**\n\nIn Table 4, we perform the ablation study on LLFF dataset. Since LLFF dataset does not provide ground-truth point clouds or depth maps, we did not report geometry metrics in that table. We provide additional ablation results on the DTU and Tanks&Temples dataset, which include ground-truth point cloud. Following the common practice in geometry accuracy evaluation, we report Chamfer Distance (CD) on DTU and F1 score on Tanks&Temples.\n\n| ID | Repr. | Hyb. | Ex. | Freq. | CD(↓)  | F1(↑)  |\n|----|-------|------|-----|-------|-----|-----|\n| i  |   3D         |  ✖    |  ✖   |   ✖    |  1.96    | 0.09    |\n| ii  |   3D+2D     |  ✖    |  ✖   |   ✖    |  2.01    | 0.08    |\n| iii  |   3D+2D    |  ✔    |  ✖   |   ✖    |  1.31   |  0.16   |\n| iv  |  3D+2D      |  ✔    |  ✔   |   ✖    |  1.07   |  0.21   |\n| v  |   3D         |  ✖    |  ✖   |   ✔    |  1.95   |  0.09   |\n| vi  |  3D+2D      |  ✔    |  ✖   |   ✔    |  1.18   |  0.18   |\n| vii  | 3D+2D      |  ✔    |  ✔   |   ✔    |  0.91    | 0.28 |\n\nAs shown in the above table, merely mixing 2D and 3D Gaussians (row ii) or directly adding frequency regulation (row v) can hardly improve the geometry accuracy. Our hybrid rasterizer (row iii) improves both CD and F1 score by a significant margin. This indicates the importance of the ray-splat intersection based rasterization. Incorporating adaptive type exchange (row iv) and frequency decoupled optimization (row vii) allows a more flexible representation, more effectively exploiting the geometric accurateness of 2D Gaussians.\n\n**Q4: Scope of related works**\n\nWe appreciate the reviewer’s suggestion to broaden the related work section. Purely reconstruction-focused methods such as DUSt3R are indeed valuable, particularly in settings where camera poses are not available. In this work, we adopt a commonly used setting for rendering-based methods, where camera poses are assumed to be known. In practice, such poses are often obtained through tools like COLMAP or more recent methods like DUSt3R[1] and VGGT[2].\n\nIn the revised version, we will expand the related work section to acknowledge and discuss recent purely reconstruction methods in more detail.\n\n**Q5: The functionality of $\\lambda_z$.**\n\nOur scale modulation consists of two components: Eq.(7), which applies a soft gating to the raw $z$-scale $s_z$, and Eq.(6), which modulates the opacity using the activated $z$-scale $s_{z*}$. Each plays a distinct role.\n\n- Eq.(7) controls *when* the $z$-scale becomes active by smoothly mapping $s_{z}$ to $s_{z*}$ using a sigmoid gate. When $s_z$ is negligibly small, the gating suppresses the activation and $s_z*$ approaches zero. In this case, the Gaussian behaves like a 2D primitive. As $s_z$ increases beyond the threshold, $s_z*$ effectively approaches the original scale $s_z$.\n- Eq.(6), on the other hand, defines *how much* the activated $z$-scale influences opacity. The parameter $\\lambda_z$ controls the strength of this correlation: as $s_{z*}$ increases, the opacity decreases smoothly, regulated by $\\lambda_z$. This formulation enables opacity to act as a proxy signal to optimize $s_z$ for 2D Gaussians, which otherwise do not receive gradient updates to their $z$-scale.\n\nIn summary, Eq.(7) controls the activation of the $z$-scale, while Eq.(6) introduces a soft correlation between scale and opacity to facilitate learnable type transitions. Although it is possible to combine them into a single equation, we separate them for clarity in both concept and implementation.\n\n**Q6: Clarification on scale modulation**\n\nIn vanilla 2DGS, the $z$-scale is not involved during optimization. The primary purpose of our scale modulation is to enable 2D Gaussians to transition into 3D Gaussians when necessary. Our intuition is that this transition typically occurs when a Gaussian needs to develop volumetric capacity or represent semi-transparent regions. To support this, we introduce a correlation between $z$-scale and opacity for 2D Gaussians, which allows the $z$-scale to receive meaningful gradient updates. We believe that scale modulation is essential for enabling dynamic type exchange between 2D and 3D Gaussians, and for supporting a more flexible representation, instead of merely an engineering trick.\n\n**Q7: Figure margin**\n\nWe appreciate the reviewer’s suggestion. We will increase the margins around Figure 5 and Figure 6 to improve readability.\n\nWe sincerely appreciate the reviewer’s constructive suggestions. In the revised version, we will incorporate additional evaluations with SoTA methods, include efficiency and geometry metrics, expand the discussion on purely reconstruction-based methods, and clarify the scale modulation design. We hope these additions and clarifications address the reviewer’s concerns and would be grateful for a positive reconsideration of the score.\n\n[1] Wang, Shuzhe, et al. \"DUSt3R: Geometric 3D Vision Made Easy.\"\n\n[2] Wang, Jianyuan, et al. \"VGGT: Visual Geometry Grounded Transformer.\""}, {"review_id": "fTKGw4qmrb", "reviewer": "Reviewer_bqq2", "summary": "This paper proposes EGGS, to combine the benefits of 3D- and 2D- Gaussians. The authors developed and implemented the rasterizer, the Gaussian type change mechanism, and the optimization method for the hybrid representation. The proposed representation achieves a better trade-off between the appearance and the geometry.", "questions": "- What is the dataset used in Tab. 4?\n- Is there more visual results regarding the reconstructed geometry (e.g. the rendered mesh, normal map video, or the depth map video)?\n\nMy main concern is about the limited evaluation of the proposed method. I would be willing to raise the rating to 5 if it is addressed.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The motivation is clear and the techniques are sound.\n- The paper is well-written and easy to follow.\n- The proposed representation achieves state-of-the-art performance in NVS across different datasets.\n\nWeakness:\n- Insufficient and Inconsistent baselines: \n    - Given HybridGS [1] is an important related work, it should serve as a baseline.\n    - Why the baselines for evaluating the appearance (Tab. 1) and Geometry (Tab.2) are different, what is the standard for choosing the baselines?\n- Insufficient evaluation of the reconstructed geometry: \n    - The geometry (depth map) of the proposed method in Fig. 9 seems not outperform the baselines (even the 3DGS), especially in the roof region, where significant artifacts can be observed.\n    - No quantitative results for geometry evaluation on the Temple and Tanks dataset.", "was_revised": true, "final_justification": "Thanks to the authors' explanation. It addressed my concerns about the evaluation and the baselines. It will be appreciated if the authors could update the final revision with the comparison to the new baseline, evaluation of geometry, and the visual results, as it is stated in the rebuttal.", "rebuttal": "We thank Reviewer bqq2 for careful reading of our manuscript, insightful suggestions and recognizing positive aspects of our submission, including combining the benefits of 3D and 2D Gaussians and improving the performance across datasets. Below, we address the reviewer's concerns.\n\n**Q1: Insufficient Evaluation**\n\n**Comparison with HybridGS.** As noted in Appendix B, HybridGS did not release its training code at the time of our submission, making it difficult for a direct comparison. More importantly, the two approaches target different problem settings and propose orthogonal optimizations. \n\n- HybridGS specifically focuses on dynamic scenes with transient objects. HybridGS represents the 3D scene entirely with 3D Gaussians and leverages single-view image-space 2D Gaussians to fit transient objects. The 3D Gaussians and image-space 2D Gaussians are treated separately and are not exchangeable.\n- In contrast, EGGS focuses on general reconstruction settings and represents the 3D scene using an exchangeable hybrid of 2D and 3D Gaussians. Our hybrid representation can be integrated into the HybridGS framework by replacing its 3D Gaussians with our exchangeable hybrid representation.\n\nFor completeness, we provide quantitative comparisons on two dynamic scenes of different occlusion levels from the NeRF On-the-go dataset. \"3DGS\" and \"EGGS\" denote direct reconstruction of the dynamic scene without decoupling transient objects and \"+ HybridGS\" means HybridGS is used to decouple the static scene and transient objects. We note that at the time of rebuttal, the authors of HybridGS had released only their trained models, not the training code. Therefore, we directly leverage the single-view image-space Gaussians from their checkpoints to remove the transients in \"EGGS+HybridGS\".\n\n| Medium Occlusion (Corner)  | PSNR(↑) | SSIM(↑) | LPIPS(↓) |\n|------------------|----------------|-------|--------|\n| 3DGS             | 20.90          | 0.713 | 0.241  |\n| 3DGS + HybridGS  | 25.03          | 0.847 | 0.151  |\n| EGGS             | 21.21          | 0.745 | 0.228  |\n| EGGS + HybridGS  | 25.74          | 0.896 | 0.122  |\n\n| High Occlusion (Patio-High)  | PSNR(↑) | SSIM(↑) | LPIPS(↓) |\n|------------------|--------------|-------|--------|\n| 3DGS             | 17.29        | 0.604 | 0.363  |\n| 3DGD + HybridGS  | 21.77        | 0.741 | 0.211  |\n| EGGS             | 17.56        | 0.638 | 0.352  |\n| EGGS + HybridGS  | 22.23        | 0.784 | 0.208  |\n\nAs shown in the above table, directly reconstructing dynamic scenes with 3DGS leads to inferior appearance performance. This is because transient objects lead to significant inconsistency across different viewpoints. HybridGS mitigates the viewpoint discrepancy by decoupling transient objects from the 3D scene, improving the appearance by a significant margin. EGGS alone still suffers from transient objects. However, EGGS outperforms the 3DGS counterpart when transients are removed by HybridGS.\n\n\n**Standard for choosing baselines.**\nGaussian Splatting-based methods are developed with a varying focus, some emphasizing appearance fidelity while others prioritize geometric accuracy. To provide a comprehensive evaluation, we consider both aspects. For appearance and geometry, we select state-of-the-art methods that excel in the respective aspect as baselines, allowing us to highlight the strengths of our proposed method.\n\nWe note that while most Gaussian Splatting-based methods report appearance metrics such as PSNR, only a subset with an explicit focus on geometry report metrics like Chamfer Distance. In previous works, geometry-focused methods such as SuGaR, 2DGS, and GOF are commonly used as baselines for benchmarking geometry accuracy (e.g., Table 2 in [1], Table 1 in [2]). In line with this practice, we adopt these methods as baselines in Table 2 to assess the geometry performance of our approach.\n\n**Q2: Geometry Evaluation**\n\n**Qualitative comparison on Tanks&Temples.** In Figure 9, we present rendered RGB images and depth maps on the Tanks&Temples dataset. The main artifacts in our depth maps appear near the sky regions. However, depth in these areas is typically unreliable in Gaussian Splatting-based methods, and is often explicitly masked out during evaluation (e.g., Figure 7 in [3]). In our current visualization, we did not apply such masking, which likely exaggerates the perceived artifacts. We believe the inaccuracies near the sky do not meaningfully reflect overall depth quality. While not as clean as 2DGS, our method produces more accurate depth maps than 3DGS for foreground objects and buildings.\n\nWe provide a quantitative comparison below to further verify the geometry accuracy. We will also update the visualizations and include additional depth map videos in the revised version to improve clarity.\n\n**Quantitative comparison on Tanks&Temples.**  \nWe provide a quantitative geometric comparison on the Tanks&Temples dataset. Following prior works, we report the F1 score based on alignment between the predicted and ground-truth point clouds.\n\n| F1 score(↑) | Barn | Caterpillar | Courthouse | Ignatius | Meetingroom | Truck | Avg. |\n|--------|------|-------------|------------|----------|--------------|--------|------|\n| 3DGS   | 0.13 | 0.08        | 0.09       | 0.04     | 0.01         | 0.19   | 0.09 |\n| SuGaR  | 0.14 | 0.16        | 0.08       | 0.33     | 0.15         | 0.26   | 0.19 |\n| 2DGS   | 0.41 | 0.23        | 0.16       | 0.52     | 0.17         | 0.45   | 0.32 |\n| GOF    | 0.51 | 0.41        | 0.28       | 0.68     | 0.28        | 0.58   | 0.46 |\n| Ours   | 0.35 | 0.18        | 0.12       | 0.45     | 0.15         | 0.41   | 0.28 |\n\nAs shown in the above table, our method consistently outperforms 3DGS in F1 score across all scenes. While 2DGS has a slightly higher F1 score, 2DGS has inferior appearance performance, as shown in Table 1 in our manuscript. While geometry-focused methods like 2DGS and GOF prioritize geometry accuracy for surface reconstruction tasks, they often lead to decreased appearance fidelity even compared to the 3DGS baseline. This aligns with our analysis on the DTU dataset in Table 2. In contrast, our method achieves a better balance, improving the appearance while maintaining high geometry accuracy. \n\n**Q3: Dataset used in Table 4**  \n\nThe ablation study in Table 4 is conducted on the LLFF dataset. We will clarify this in the revised version.\n\n**Q4: More Visualization**  \n\nDue to the rebuttal policy, we are not permitted to submit additional figures or videos at this stage. However, in addition to the quantitative comparisons already provided in our manuscript and in the response to Q2, we will make sure to include more qualitative visualizations in the revised version and on the demo website. These will include depth map videos, normal map videos, and rendered meshes.\n\nWe sincerely appreciate the reviewer’s constructive feedback. In the revised version, we will include the comparison with HybridGS and additional geometry evaluation on Tanks&Temples. We will also provide more visual results to highlight the reconstructed geometry. We hope our response addresses the reviewer’s concerns, and we would be grateful for a positive reconsideration of the score.\n\n[1] Huang, Binbin, et al. \"2D Gaussian Splatting for Geometrically Accurate Radiance Fields.\"\n\n[2] Hyung, Junha, et al. \"Effective Rank Analysis and Regularization for Enhanced 3D Gaussian Splatting.\" \n\n[3] Cheng, Kai, et al. \"GaussianPro: 3D Gaussian Splatting with Progressive Propagation.\""}, {"review_id": "4bDTuv75YL", "reviewer": "Reviewer_wtGw", "summary": "The EGGS proposes a novel hybrid Gaussian Splatting representation, which leverages 2D Gaussian primitives to warrant geometric accuracy while utilizing 3D Gaussian primitives to preserve details. To achieve this, the authors first develop the Hybrid Gaussian Rasterization which allows projection-based (3DGS) and ray–splat–intersection-based rasterization (2DGS) simultaneously. Then, an Adaptive Type Exchange mechanism is proposed to exchange 2DGS and 3DGS according to a predefined effective rank criterion. Finally, a Frequency-Decoupled strategy is proposed to encourage the low-frequency components to guide scene geometry and the high-frequency components to refine appearance.", "questions": "In Figure 11, the authors report the distribution of two Gaussian types during training. However, it will be more interesting to visualize the distribution of two Gaussian types corresponding to a specific rendering result. The rendered distribution can further verify the hypothesis that 2D Gaussians capture geometry structures while 3D Gaussians contribute to finer scene details.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "The proposed EGGS is innovative and insightful. The main contribution, a Hybrid representation, may inspire many subfields in the community, such as few-shot and OOD NVS. The experiments and ablations are comprehensive. Also, the paper is well organized and easy to follow. However, I suggest the authors make more efforts to improve the supplementary video. Compared to a webpage composed of discrete results, a complete video containing all comparisons and ablations can make the results more intuitive and outstanding, since I find the results on the provided anonymous link are compressed to some extent.", "was_revised": true, "final_justification": "The provided rebuttal addressed all my concerns. I believe incorporating the feedback from all reviewers can further polish the quality of this paper. I am glad to keep my original rating of 'Accept (5)'.", "rebuttal": "We thank Reviewer wtGw for their thorough reading of our manuscript, valuable feedback, and for recognizing the contributions of EGGS. The reviewer highlighted several positive aspects of our work: they considered our method novel and insightful, effectively combining the advantages of 3D and 2D Gaussians; found the evaluation to be comprehensive, sufficiently validating the effectiveness of our approach; and acknowledged its potential impact across multiple subfields in 3D reconstruction. Below, we address the reviewer’s concerns.\n\n**Q1: Improving the Videos and Demo** \n\nWe appreciate the reviewer’s suggestion regarding improving the visualization videos and demo website. At the time of submission, we were constrained by the use of an anonymous GitHub repository, which has limited storage and does not support HTML or embedded MP4 files. As a result, we had to convert videos to lower resolution GIFs and rely on markdown for presenting results, which impacted both quality and flexibility.\n\nIn the revised version, we will make efforts to enhance the demo website by including high-resolution videos across different scenes, making comparisons more accessible and intuitive.\n\n**Q2: Visualization of Gaussian type distribution in rendered images**  \n\nWe thank the reviewer for the careful reading of our manuscript and for recognizing our analysis of Gaussian type distribution during training. We will include additional visual examples showing the spatial distribution of 2D and 3D Gaussians in rendered images to better support our hypothesis.\n\nWe sincerely appreciate the reviewer’s suggestions. Due to the rebuttal policy, we are not permitted to submit additional figures or videos or update the anonymous links at this stage. However, we will incorporate these visualizations in the revised version to better illustrate the key ideas and performance of our method."}]

Author rebuttal:

Meta-review: This paper proposes a 2D-3D hybrid representation for Gaussian splatting. The hybrid representation incorporates the best of both worlds (i.e., appearance and geometry). All reviewers spoke very highly of the paper (i.e., all 5 ratings after the discussion). All reviewers have agreed that the proposed method is novel and well-designed, with many potential applications in the field, and the results are excellent. The frequency-decoupled optimization was also deemed effective. The weakness questions were mostly focused on some detailed technical questions and some requests for additional information (e.g., comparison to some missing SOTA methods, some missing metrics in experiments, and some missing related works). The rebuttal addressed all these concerns, which the reviewers found satisfactory. AC agrees on the positive ratings and the novelty of the hybrid representation. Accordingly, an accept decision is recommended under the condition that the additional information provided in the rebuttals is included in the final version.
Decision: Accept (spotlight)