Plenodium: Underwater 3D Scene Reconstruction with Plenoptic Medium Representation
Authors: Changguang WU
Jiangxin Dong
Chengjian Li
Jinhui Tang
Venue: NeurIPS 2025 poster ()
Keywords: 3D Gaussian Splatting
Underwater Imaging
Novel View Synthesis
Spherical Harmonics
Depth Prior
and Underwater Image Restoration.
Primary area: applications

Abstract: We present *Plenodium* (*plenoptic medium*),  an effective and efficient 3D representation framework capable of jointly modeling both objects and the participating medium.
In contrast to existing medium representations that rely solely on view-dependent modeling, our novel plenoptic medium representation incorporates both directional and positional information through spherical harmonics encoding, enabling highly accurate underwater scene reconstruction.
To address the initialization challenge in degraded underwater environments, we propose the pseudo-depth Gaussian complementation to augment COLMAP-derived point clouds with robust depth priors.
In addition, a depth ranking regularized loss is developed to optimize the geometry of the scene and improve the ordinal consistency of the depth maps.
Extensive experiments on real-world underwater datasets demonstrate that our method achieves significant improvements in 3D reconstruction.
Furthermore, we construct a simulated dataset with GT and the controllable scattering medium to demonstrate the restoration capability of our method in underwater scenarios.

Plenodium: Underwater 3D Scene Reconstruction with Plenoptic Medium Representation
Changguang Wu' Jiangxin Dong" Chengjian Li' Jinhui Tanga*
*Najjing University of Science and Technology, NNajjing Forestry University
{changguangwu, jxdong, lichengj inn) @njust, jnjjsst edu. en, tangjhōnjfu. edu. cn https://plenodi wweaanodiii..iiituut github. io/
Abstract
We present Plenodium (plenoptic medium), an effective and efficient 3D represen- tation framework capable of jointly modeling both objects and the participating medium. In contrast to existing medium representations that rely solely on view- dependent modeling, our novel plenoptic medium representation incorporates both directional and positional information through spherical harmonics encoding, enabling highly accurate underwater scene reconstruction. To address the initializa- tion challenge in degraded underwater environments, we propose the seeudo-depth Gaussian complementation to augment COL.AA-ddri point clouds with robust depth priors. In addition, depth ranking regularized loss is developed to optimize the geometry of the scene and improve the ordinal consistency of the depth maps. Extensive experiments on real-world underwater datasets demonstrate that our method achieves significant improvements 3D reconstruction. Furthermore, we construct simulated dataset with GT and the controllable scattering medium to demonstrate the restoration capability of our method underwater scenarios.
Introduction
Underwater imaging plays critical role in diverse ap- plications, including underwater construction, marine sciences, etc. However, its efficacy is significantly hin- dered by the complex optical properties of the aquatic environment. These properties lead to wavelength- and distance-dependees attenuation and scattering of light, resulting in degraded image quality characterized by the color cast, diminished contrast, and loss of detail. Given the expanding scientific and industrial focus on oceanic exploration, the reconstruction of scattering- -affeeeeen--feeee un- derwater scenes becomes increasingly important.
Restoration
SS/M
cana
26422
PSNK
Reconstruction
mores
Suree
PSNR
SSIM
24.444
a
Teay
Pioneering works [3-7] based on Neural Radiance Fields (NeRF) [8] and 3D Gaussian Splatting (3DGS) [9] have significant contributions to 3D reconstruction. These methods achieve effective surface modeling by constrain- ing their representations to scene surfaces, assuming a vacuum-like medium between the observer and the ob- jects. However, such approaches neglect the influence of light scattering in participating media, limiting their applicability in real underwater environments.
Train Time
FPS
Efficiency
Plenodium
WaterSplatting
SeaThmu-NcRF
Figure 1: Comparison of Plenodium, Wa- terSplatting [1], and SeaThru-NcRF [2] reconstruction and restoration perfor- mance (PSNR, SSIM), as well as effi- ciency (FPS, training time).
Jiangxin Dong and Jinhui Tang are corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

To achieve underwater 3D scene reconstruction, SeaThru-NeRF [2] extends the NeRF framework by introducing an additional medium volume field, which is parameterized by an MLP and charac- terizes the color and density attributes of the medium, enabling accurate modeling of light-medium interactions. WaterSplating [1] leverages 3DGS as an alternative geometric representation to replace the computational NeRF in SeaThru-
[2], while preserving the core medium representation capability, achieving more efficient rendering. However, there are three significant limitations affect- ing its accuracy, efficiency, and robustness: 1) Existing methods estimate medium properties based exclusively on viewing directions, failing to account for the spatial relationship between camera positions and scattering effects in heterogeneous media; 2) Despite its advantages, WaterSplatting still employs an implicit MLP for medium representation. which introduces substantial computational costs limiting its efficiency; 3) The 3DGS-based approaches rely COLMAP [10, 11] for initial- izing Gaussian primitives, but underwater image degradation severely impairs COLMAP's feature extraction and matching, compromising the reliability of the initialization process.
In this paper, we present an effective and efficient method for underwater 3D reconstruction. Different from existing methods that rely on the medium representation with limited directional information, we are the first to take positional information into account and develop plenoptic medium representation. Notably, the proposed plenoptic medium representation is modeled by explicit Spherical Harmonics (SH), rather than implicit MLPs. Specifically, we positionally encode the SH coefficients via a trilinear interpolation mechanism to capture accurate scattering effects in arbitrary positions, while achieving faster rendering than MLP-based methods. Then, to address the limitations of COLMAP in degraded underwater scenes, propose a pseudo-depth Gaussian complementation method that enriches the
sparse point clouds with pseudo-depth estimated from the Depth Anything Model [12, 13). improving the robustness of the initialization for 3DGS. Furthermore, we introduce depth ranking regularized loss to optimize the geometry of the scene, enhancing the ordinal stability of the depth maps. Taken together, the proposed approach can effectively improve the reconstruction quality while speeding up rendering. In addition, we created a simulated dataset for validating the restoration performance of our approach across various types of media and different degradation intensities, as well as analyzing degradation impacts on 3D reconstruction.
The contributions can be summarized follows: 1) We propose Plenodium, which introduces a novel plenoptic medium representation that characterizes both the directional and positional information and then incorporates it with 3DGS for effective underwater 3D reconstruction. 2) To improve the robustness of 3DGS-based reconstruction in underwater scenarios, we introduce a pseudo-depth Gaussian primitives and a depth ranking
Gaussian complementation regularized loss to enhance the geometric consistency. 3) We construct a simulated dataset with ground truth (GT) and a controllable scattering medium, which enables systematic evaluation of image restoration performance across degradation levels. 4) Extensive experiments demonstrate the effectiveness and efficiency of our approach. As shown in Fig. Plenodium outperforms prior methods, increasing the PSNR by at least 0.872dB and speeding up the rendering efficiency by 47% % in real-world reconstruction scenarios.
enrich
2 Related Work
3D Gaussian splatting. 3DGS [9] constructs a 3D scene representation with a set of 3D Gaussians, where the i-th Gaussian is defined by center position μr; e R a 3D covariance matrix E, e 3 an opacity a; E IR, and color features A,. Specifically, the rendered color Ć is computed by a blending process that combines the color contributions [C, from N individual Gaussians:
i-1
Č= C Σ co,Ti where T, III (1)),),, 1=1
(I)
j=1
where Gaussian color c: SH(d, A,) is derived from spherical harmonics [14] with ray direction d
and its color features A,, and a; is computed by multiplying its o, and its projected 2D Gaussian.
3DGS addresses limitations of the reconstruction efficiency in 3D scene modeling by leveraging explicit 3D Gaussian primitives for real-time rendering [5, 6) and minute-level training [15, 16] on consumer GPUs. 3DGS has been proven to be effective in a wide range of applications, including digital human reconstruction [17, 18), Artificial Intelligence Generated Content [19-21], and au- tonomous driving [22, 233. In computational imaging, 3DGS has also shown significant improvements

---

in super-resolution [24], deblurring [25, 26], derain [27]. and low-light enhancement [28]. These advancements demonstrate the capacity of 3DGS to invert ill- posed imaging problems, transforming low-quality inputs into high-quality 3D reconstructions [29-33] with photometric consistency.
Computer vision with scattering medium. Underwater computer vision faces significant challenges due to complex optical phenomena, particularly light scattering and wavelength-depender attenuation. These effects degrade image quality by introducing color distortion, reduced contrast, and haze, rendering traditional computer vision methods (designed for clear-air environments) ineffective in underwater applications. To address the ill-posed nature of the problem, earlier work introduces domain-specinn priors to restore the scenes [34-37]. The method in [38] proposes general image formation model in scattering media under ambient illumination, expressing per-pixel color C' as:
C
obj
(e (e-a"
med
direct
backscatter
where coعi denotes the intrinsic color of the object at depth 2, c.eed represents the ambient medium color at infinite distance, gatt and ts are the attenuation coefficients for the direct and backscatter components, Building on this framework, SeaThru [39] leverages depth maps to decouple attenuation and backscatter estimation, achieving robust restoration by explicitly modeling depth-dependent light propagation. Osmosis [40] adopts an unsupervised diffusion framework that iteratively refines images using priors derived from unpaired clean and degraded datasets. Furthermore, Seathru-NeRF [2] and WaterSplatting [1] extend NeRF and 3DGS architectures by embedding the physical model into their rendering equations, enabling simultaneous 3D scene reconstruction and water removal.
Preliminaries
In contrast to vanilla 3DGS, our Plenodium incorporates explicit modeling of medium-induced light attenuation through absorption and scattering effects, following [1]. The transmittance T2(x) at a given depth along the ray, situated between the (i-1)-th and i-th Gaussian splat is formulated as:
T((=) T (2) T.0bj
represents the exponential attenuation due medium absorption, char- acterized by the medium's extinction coefficient med along the path from the camera to depth and Toobi [1 ay) captures the cumulative transmittance through all preceding Gaussian primitives, quantifying their occlusion effects downstream geometry.
where (2)) medd
Meanwhile, the medium's contribution to color Eined between these Gaussian splats is computed as:
Caned #1
med o meddrobi (z) dz = modd (e o -=0
where denotes the depth of the i-th Gaussian in the camera coordinate system (zg is set to 0).
Following [1, 21, we utilize two sets of parameters: object attenuation gall for object color (obj and
medium backscatter o for medium color (med The comprehensive rendering equation is:
N
Ô - + Emred
Coob
Equed Emned
1=1
im
(5)
nit
meedroohi
(e-oMzz-) c = + mnedroob -
N+1
where (med presents the medium's color contribution from the last Gaussian to infinitely far.
4 Plenodium
We aim to develop an efficient and robust 3D reconstruction method for underwater scenarios. Specifically, approach begins with explicit plenoptic medium representation (i.e., Fig. 2(b))

---

Pscudo-Depth Gaussian Complementations
(b) Plenoptic Mediuum Representarion
(c) Depth Ranking Regularized Loss
Pscado Depth Order
00090
G &
Sphariea Hammonic
Paeado- Depth
Render Depti Under
Lieg Cg
Leg zus detm
doptt
COLMAP
Di
Ag
02
Render
Rendered Depes
Pscudo Depth
Underwater Images
Rondored Tiiage
Figure 2: Overview of our Plenodium. We first employ the pseudo-depth Gaussian complementation to enrich the primitives initialized by COLMAP. Then we utilize the plenoptic medium representation to estimate the medium parameter and render the underwater images following Eqn. 5. The primitives are optimized with the loss function in Eqn. 12, including a new depth ranking regularized loss.
to accurately model the scattering medium in Sec. 4.1. We then present a pseudo-depth Gaussian complementation (i.e., Fig. 2(a)) that leverages robust depth priors to enhance Gaussian primitive initialization in Sec. 4.2. Finally, depth ranking regularized loss (i.e. Fig. 2(c)) is introduced to enhance the geometric consistency in Sec. 4.3. The whole framework summarized in Fig.
4.1 Plenoptic Medium Representation
Scattering effects heterogeneous media exhibit complex dependencies on both ray direction d and the observer's is spatial coordinates (xr, v). While existing methods only account for directional de- pendency while neglecting positional variations, we propose a novel plenoptic medium representation that explicitly incorporates both directional and positional information. Specifically, the properties of the medium along each ray (i.e., the medium color emed the object attenuation coefficient gatt, and the medium backscatter coefficient gh in Equ. 5) by Spherical Harmonics (SH):
parameterize
mod SH(d, A 2
o = SH(d, A gh = SH(d, A2
(6)
where A Ag.y. A denote the SH coefficients for medium color, object attenuation, and medium backscatter at position (2r, y, 2). respectively.
To enable efficient learning of spatially varying medium parameters from sparse camera observations, store eight fundamental SH coefficients at each corner of the normalized 3D space [-1, 1 Through trilinear interpolation [41] of these, we can reconstruct the SH coefficient set at any arbitrary spatial position:
Σ d.
(( #w 2)A where E mede att 0 (7)
8
The proposed plenoptic medium representation employs explicit SH encoding [14], reducing the time required for medium parameter retrieval during inference to less than 5% of that needed by implicit baseb methods [1, 2], while simultaneously improving the accuracy scattering simulations in heterogeneous media (as illustrated in Sec. 6).
4.2 Pseudo-Depth Gaussian Complementation
Underwater 3DGS initialization is challenged by severe light attenuation and scattering, which degrade conventional SIM pipelines [10] like COLMAP [11]. To address this, we propose Pseudo- Depth Gaussian Complementation (PDGC). which builds on COLMAP by inheriting its initial Gaussians and augmenting them with additional ones guided by monocular pseudo-depth priors.
First, for a given camera view, we render the pixel-wiss wixe depth ò via a-blending according to:
D
1 I (1 (1-aa)))/l
a,))) -
(8)

---

where T N+1 represents the accumulated object transmission behind all N Gaussians.
Then, estimate the corresponding pseudo-depth map D using the RGB image C' under this camera view with the Depth Anything Model [12, 13], chosen for its superior generalization ability across diverse scenarios. To address the scale ambiguity and offset biases in monocular depth estimation,, we formulate an affine correction to calibrate the pseudo-depth:
D' ='= b, where k. b = arg min
Σ -k((,,) - (2.0)ER..
(9)
b,b
The k and are optimized via least-squares over well-initialized regions Sw {(z, v) T (x, < Tw refining D to reduce scale ambiguity and offset, and aligning it with the initialized scene.
Subsequently, we determine the region 22, n R2p to insert new Gaussian primitives, specifically targeting regions exhibiting both proximal camera distance (Pn, {(.,)) y) Thear max(D)3 and elevated transmittance values (L2p = {(z, y) (z, y) 2 )w)) which minimizes background interference and oversampling, thus improving efficiency and reconstruction accuracy.
Finally, we add new Gaussian primitives each pixel (a, y) in the defined region D, n S2p with depth (x y). More details on the Gaussian primitive insertion process and the other attributes of the inserted Gaussian primitives can be found in the Sec. A.2.
Our pseudo-depth Gaussian complementation method enriches the initialized Gaussian primitives across diverse scenes (Tab. 4), improving the robustness of 3DGS initialization against degradations.
4.3
Loss Function
Building upon differentiable 3DGS frameworks, we develop multi-objective optimization pipeline for primitive refinement, jointly enforcing photometric accuracy, structural coherence, and depth consistency. Following [1, 42], we incorporate weighting matrix W sg(C)+e (with 10 6.
sg(+) means stop gradient) to emphasize dark regions during optimization, aligning with human perceptual sensitivity to dynamic range. Then, based on the L.1 loss and the multi-scale differentiable SSIM loss [43], we employ two regularized losses:
freg L, (W @ Ć, W ④ C)2 Lreg -sim -.ms (W + C, W @ C).
(10)
for photometric accuracy and structural coherence, respectively. Notably, we utilize the regularized multi-scale differentiable SSIM loss Ereg-ms-ssim rather than the single-scale version Ereg [44] used previous works [1] for a larger perceptual field.
In addition, to enforce the ordinal stability on depth maps [45, 46] for 3DGS, we first downsample the pseudo-depth map D and the rendered depth map D to low-resolution variants D and D of size N x N pixels using bilinear pooling, which suppresses high-frequency noise while preserving relative depth ordering. We then introduce new depth ranking regularized loss that penalizes violations of ordinal relationships between every pair of pixels in the downsampled depth estimates:
N
Cespth
Σ
Σ
max(-(D" (.) (# v,)) (D) - D' 1))), (11)
N
This loss function maintains scale invariance and reduces dependence on fine-grained structural details by operating on the downsampled representations. Benefiting from this loss function, our approach achieves robust depth optimization even when initialized with imprecise pseudo-depth estimates, demonstrated in Tab. 6.
The final loss function is given as:
L= >c, Crog-C, + Assim >ssim mesm + Adepti
(12)
where the parameters Ac Assim and Adopth are utilized to balance the different loss components.
5 Experimental Results
In this section, we first describe the implementation details of our approach and the datasets we used. Then evaluate the proposed method on both real-world and simulated underwater scenarios.
5

---

Table 1: Reconstruction performance on the SeaThru-NeRL [2] dataset. We report PSNR1. SSIMT. and LPIPS|, scores for the four underwater scenes. The average FPSt and Training Time. on an RTX4090 also provided. The best and second-bes results are bolded and underlined, respectively.
Methods
IUT Red Sea
Curaçan SSIM
J.G. Red Sen
Panama SSIM
Avg. FPS
Avg.
PSNR
SSIM
LPIPS
PSNR
LPIPS
PSNR
SSIM
LPIPS
PSNR
LPIPS
Time
ZipNeRF [4]
16.937
0.474
0.412
19.956
0.442
0.421
19.022
0.349
0,483
19.012
0,349
0.482
0.17
5h
SeaThru-NeRR [2]
26.755
0.826
0.168
30.959
0.915
0.133
23,282
0.876
0.111
31,276
0.937
0.071
0.68
2h
3D Gauss. [9]
22,980
0.843
0.246
28.313
0.873
0.221
21.493
0.854
0.216
29.200
0.893
0.152
318
13min
WaterSplatting [1]
29.840
0.889
0.203
32,203
0.948
0.1
24.741
0.892
0.116
31,616
0.942
0.080
169
6.9min
Plenodium
30.275
0.895
0.205
34.120
0.953
0.110
25.058
0.896
0.121
32,435
0.946
0.074
249
7.0min
Table 2: Restoration performance on our simulated dataset. We report PSNR1. and SSIM for each subset scenes. The best and second-best results are bolded and underlined, respectively.
Beach
Street
Methods
PSNR medium
SSIM medium
PSNR medium
SSIM
easy
hard
easy
hard
eas
hard
easy
medium
hard
FOG
SeaThhu-NcRRF [2]
28.416
24.799
16.439
0.9228
0,8888
0.7856
27.672
23.562
17.730
0.8697
0.8286
0.7244
WaterSplatting [1]
17.725
16.724
15,492
0.8549
0.7728
0,7475
26.595
24.816
22.510
0.8924
0.8551
0.8003
Plenodium 26.372
26.248
25.275
0.9435
0.9259
0,9051
27.978
26.071
23.060
0.9107
0.8791
0.7982
WATER
SeaThru NeRF
25.938
19.500
16.495
0.8590
0,8085
25.268
19.420
0.7919
0.7467
WaterSplatting [1]
17.592
15.892
15.021
0.8198
0.7725
0,7450
24.936
22.
205
0.8793
0.8240
0.7546
Plenodium 26.360
24.723
23.636
0.9406
0,9119
0.8867
25.731
22.392
20.285
0.8594
0.7983
0.7556
5.1 Implementation and Datasets
Implementation details. Our implementation is based the Nerfstudio [16, 47]. After COLMAP
initialization, we use the pseudo-depth Gaussian complementation with Tw = 0.99 and Tocar = 0.5 to enrich the initial set of 3D Gaussians. During training, we empirically set Ac 0.8, Assim 0.2. and Adopth = 5 in Eqn. 12. The patch number N is set to 16. The maximum degree of the SH coefficients for the medium and Gaussian primitives set as We accumulate the absolute gradient norms of for finer densification following [48]. For the reconstruction task, we train the model and render novel views using Eqn. 5, whereas for the restoration task, we reuse the learned parameters to generate de- scattered images via Eqn. 1, focusing exclusively on the objects. All the experiments are conducted on an RTX 4090 GPU.
Seathru-NeRF dataset. The SeaThru-Nerf dataset [2] includes four real underwater scenes: IU13 Red Sea, Curaçao. Japanese Gardens Red Sea, and Panama. There are 29, 20, 20, and 18 images in each scene, respectively, where 25, 17, 17, and 15 images are used for training and the rest of the images are for testing. These images are captured in RAW format by a Nikon D850 SLR camera in underwater conditions. Following [1, 21, these images are downsampled to an averaged resolution of 900 1 1400 pixels and COLMAP [10, 11] is employed determine the camera poses and produce sparse point clouds for the initialization of 3DGS-based methods.
Our simulated dataset. We utilize Blender to simulate a dataset with precise GT for restoration evaluation. The dataset includes two scenes (beach and street), each degraded by two types of media (fog [49] and water) at three incremental intensity levels (easy, medium, and hard), yielding 12 systematically structured subsets. Each subset contains 100 images at a resolution of 512x512 pixels. We split them evenly into 50 training and 50 testing samples to ensure a balanced evalua- tion. Compared to existing simulated datasets [1, 21. our dataset provides enhanced accuracy, scale, and diversity, enabling robust evaluation across different media types and degradation intensities. Notably, we achieve heterogeneous media modeling by controlling the Density parameter within the Principled Volume, making our dataset more representative of real-world underwater environ- ments. To isolate restoration quality from exposure, we preprocess restored images by linearly scaling their intensity to align with the GT's mean luminance before computing evaluation metrics. Since Blender provides accurate camera poses, we use COLMAP solely to generate sparse point clouds for initializing the set of 3D Gaussians. More details regarding dataset construction procedures and comprehensive dataset analysis are provided in Sec. B.

---

Zip-NeRF
SeaThhu-NNRR
3DGS
WaterSplatting
Plenodium
GT
Figure 3: Rendering performance comparison of our Plenodium against existing methods on the "Curaçao" and "IUI3 Red Sea" scenes. Rendered images and depths are presented for comparison. The pseudo-depth for ground truth is estimated using the Depth Anything Model [12, 13] for reference purposes. Compared to competing methods, Plenodium enhances clarity for medium and distant objects, as highlighted in the red boxes, while simultaneously yielding more reasonable depth maps.
Reconstruction
Restoration
Reconstruction
Restoration
Reconstruction
Restoration
SeaThru-NeRF
WaterSplatting
Plenodium
GT
Figure 4: Restoration performance comparison our Plenodium against existing methods on the "aapnneeeGadden Red Sea" and "Panama" scenes. As shown in the red boxes, the proposed Plenodium generates results with more reasonable exposure and accurate colors.
5.2 Quantitative Results
We compare our approach against several state-of-the-art methods, including NeRF-based ones (Zip-NeRF [4] and SeaTThruNNRRF [2]) and two Gaussian splatting-based ones (3DGS [9] and WaterSplatting [1]). Note that SeaThru-NeRF and WaterSplatting are specifically tailored for underwater scene reconstruction. We use PSNR, SSIM, and LPIPS as metrics to evaluate the rendering quality. In addition, we benchmark the total training time and FPS (frames per second) on a machine with an RTX 4090 GPU to provide a comprehensive comparison of computational efficiency.
We first examine the 3D reconstruction performance of Plenodium the SeaThru-NeRF dataset. As shown in Tab. 1, Plenodium performs favorably against state-of-the methods, increasing the PSNR and SSIM values by 0.872dB and 0.047 on average and improving the rendering speed by 47% (from 169FPS to 249FPS) over the best-competing method. Our approach substitutes the computationally expensive MIPs used in conventional methods with lightweight SH-based spectral decomposition, significantly accelerating inference while preserving representational accuracy. We then evaluate the restoration performance of Plenodium on our simulated dataset with controllable scattering media in Tab. 2. Compared to state-of-the art methods [2, 1]. our Plenodium achieves better results, especially in challenging cases. This improvement stems from two key factors. First, benefitting from the proposed plenoptic medium representation, our approach is able to reconstruct 3D scenes more accurately. Second, the enhanced robustness of our approach originates from the integration of learned depth priors extracted from the Depth Anything Model, which supports: (i) pseudo-depth complementation to densify sparse points for initialization, and (ii) a ranking- depth loss that enforces ordinal consistency during optimization. 'Tkeen together, these components allow Plenodium to achieve high-fidelity reconstructions under heterogeneous medium conditions and maintain reliable performance across varying levels of visual degradation.
7

---

Seathru-NeRF
WaterSplatting
Plenodium
GT
easy
hard
easy
hard
easy
hard
26.41/0.908
19. 19.58/0.860
7977777
14. 788
14.4500,888
14. 3/0.733
27. 967.377
25.38/0.905
23.67/0.878
PSNR/SSIM
27.18/08881 22.63/0.827 16.88AU.716 26.39708887 24.63/0841
23.05/0.788
28.2900917 26.34/0.879
Restoration performance comparison of our Plenodium against existing methods on "Beach- Water" and "Street-Fog"" scenes from our simulated dataset. Quantitative evaluations, including PSNR and SSIM metrics for each image, are beneath the corresponding figures. Among these methods, Proposed Plenodium produces results with more coherent textural details and superior color accuracy.
Figure 5:
5.3 Qualitative Results
We provide visual assessment of the 3D reconstruction capabilities of our proposed Plenodium against other state-of-the-art methods on the SeaThru-NeRR dataset in Fig. 3. Conventional methods, 3DGS and ZipNeRF, exhibit significant limitations when operating in scattering media, resulting in visually incoherent outputs marked by dense floaters and depth inconsistencies underwater environments. SeaThru-NeRR and WaterSplatting show improvements by MLP-based medium modeling, thereby improving the rendering quality with enhanced photometric consistency. However, they still fail to accurately reconstruct fine details in water volumes and distant objects, shown in the red boxes of Fig. 3. In contrast, our Plenodium yields visually superior results with clear water volumes and well-defined distant objects. As discussed in Sec. 6, our improved results stem from the proposed plenoptic medium representation, pseudo-depth Gaussian complementation, and depth ranking regularized loss. In addition, Plenodium produces the most accurate depth maps among the compared methods, validating its effectiveness in addressing the complexity of scattering media.
Due to the lack of de-watered GT in the SeaThru-NeRF dataset, conduct visual horizontal com- parison of the de-water results across different methods. Fig. presents qualitative comparisons on the "Japanese Garden Red Sea" and "Panama" scenes, where Plenodium achieves superior underwater restoration quality compared to other methods. Specifically, SeaThru-NeRR often produces underex- posed images, leading to visually unappealing outputs with poor detail preservation. WaterSplatting introduces color distortions, such as greenish or yellowish tints on object surfaces, compromising the realism of restoration scenes. In contrast, Plenodium generates well-exposed outputs with effective medium separation, ensuring that submerged objects are rendered with natural color fidelity.
We further validate the restoration performance of Plenodium on simulated dataset, which provides ground-truth, clear images for evaluation. Qualitative comparisons of the restoration performance on our simulated dataset are visualized in Fig. 5. SeaThru-NeRF suffers from severe color distortions, most prominently manifested as unnatural yellow discoloration of sand in "Beach- Water".. " It also frequently generates underexposed images, especially in the "Strret-Fog"" scene. WaterSplatting exhibits hollow reconstruction artifacts in the "Beach- Water" scene, due to COLMAP's s failure under degraded visibility. Additionally, it retains residual fog windows in the "Street-Fogg" scene. Plenodium, by comparison, achieves more accurate color restoration and preserves fine textures, demonstrating greater robustness across diverse underwater scenes.
Analysis and Discussion
In this section, present ablation studies to evaluate the contributions of key components in framework, including the plenoptic medium representation, pseudo-depth Gaussian complementation, and the loss function design. Additional discussion is provided in Sec. C.
Effect of the plenoptic medium representation. To assess the effect of position information, as well as spherical harmonics (SH) encoding, in our plenoptic medium representation, we conduct an ablation study on the WaterSplatting framework, as shown Tab. 3. We first compare the ofate-of- the-art WaterSplatting [1], which parameterizes the medium by MLP with only the direction input
8

---

Table 3: Effect of the plenoptic medium presenta- tion, All methods are evaluated on the SeaThru-
Table 4: Results of our method wo PDGC. Su- perscript values mark the differences in metrics when PDGC is disabled.
NeRF [2] dataset.
Metbod
PSNR
SSIM
LPIPS
FPS
Time
Scene
init. #G
PSNR
MLP w/ dir [i]
29.600
0.918
0.129
179
6.9miin
TU13 Red Sea
21, 1,907 7622
30. 176 0.0891
SH w/ pos
SH w/o dir&pos
w/
29.796
29.503
30.124
0.917
0.920
0.919
0.133
0.129
0.129
287
265
284
5.6min
6.0mmin
5.6min
Curaçao
JupaneseCraden Red Sea
25,837
21,140 2,1902
24,947 0-111g
33,996 0.1241
dir&ppo
0.921
0.127
6.0min
Panama
22,501 901
32.434 0.0011
Table Effect of the PDGC.
Table 6: Effect of the loss functions.
Initialization
PSNR
SSIM
LPIPS
FPS
Time
Loss Configuration
PSNR
SSIM
FPS
Time
CALMAP
30.388
0.9207
0.1274
238
7.0min
Cieg E1 Leogssinn
30.307
0,9216
6.0min
COLMAP Rand.
30.236
0.9218
0.1268
209
7.2min
Lug- & &mmppnnn Carph
30.389
0,9204
253
6.1min
COLMAP- PDGC
30.472
0.9225
0.1276
249
7.0min
Cup Cj Ling an Lepe
30.472
0.9225
249
7.0minn
Mlrnaptcc
MI.P
step 1000
step 2000
step = 15000
Forward
Badlward
wlo PDGIC
1000
2000
X000
Tomer
1500
3000
1000
3,00
200
PDGIC
Figure 6: Efficiency comparison of our plenoptic medium representation against MLP-based rep- resentation in forward and backward.
Figure 7: Rendering image comparison between w/ PDGC and w/o PDGC when different steps (1000, 2000, 15000).
(i.e., MLP w/ dir), with a modified version that replaces the MLP with SH (i.e., SH w/ dir). This substitution yields a 0.524 dB improvement in PSNR and an 86 FPS speedup, demonstrating SH's superior representational power and computational efficiency. To further investigate the contribution of position information, we begin with a shared SH parameterization across the entire volume using only degree-zero coefficients (i.e, SH w/o dir&pos), which lacks both directional and spatial awareness. Building upon this, we introduce trilinear interpolation over the eight voxel corners to encode position (i.e., SH w/ pos), leading to noticeable performance improvements. Finally, we combine the strengths of both directional and positional information, as well SH encoding, in our plenoptic medium representation (i.e., SH w/ dir&pos), which yields the highest rendering accuracy.
Furthermore, to validate the heterogeneous modeling capability of our plenoptic medium repre- sentation, we conducted systematic investigation into the relationship between our learned SH coefficients and the physical properties of heterogeneous media using the "Beach-Fog Fog-Hard" scene of our simulation dataset. Specifically, we examined the relationship between the learned SH coefficients for medium backscatter A and the Density parameter set for the medium. As depicted in Fig. 8, analysis reveals statistically significant and strong correlation (P 0.0001) between the learned SH coefficients and the ground-truth density values. This result provides compelling evidence that our representation is capable of modeling the complex, heterogeneous properties of scattering media.
Efficiency of the plenoptic medium representation. To assess the computational efficiency of our plenoptic medium representation compared to MLP-based representations, quantified the forward and backward propagation latencies across varying pixel counts. The results, illustrated in Fig. 6, reveal that our plenoptic medium representation achieves significant speed improvements. During forward propagation, it requires only 5% of the time needed by the MLP baseline, while during backward propagation, it is less than half time-consuming, which highlights the computational benefits of our plenoptic medium representation.
Effect of the pseudo-depth Gaussian complementation. To demonstrate the effectiveness of our pseudo-depth Gaussian complementation (PDGC) method, we remove PDGC and train this baseline using the same settings ours. The quantitative results in Tab. 4 show that our PDGC supplements

---

-46
Welux
fosT
Pooesoon CUrDe dtiion exdfft CiRCE
1,000
R'-07704
48
00200
Proditoon
0,366
700R
0,000
R R-000008, P-0,0001
#Pinl
-32
Curiicinnon
6000
0L000
-34
Pociition Bard
4000
340B
-36
R 08E6,, P-2L0001
Lizeer
Corfictrmn Dord
2000
0U983
-58
Prodiumn Bord
01900
01087
0.000
0:000
8000
01272
01677
heer
mm//im
4905)
59
mediam
herl
Dansity
Degradation
Figure Correlation between learned coeffi- cients and medium physical properties.
Figure 9: Influence of degradation on COLMAP and depth estimation.
762, 453, 2190, and 90 Gaussian primitives for each test scene, improving the PSNR value by 0.099dB, 0.124dB, 0. IdB, and 0.001dB, respectively. To further analyze the effect of the proposed PDGC, we compare it with a baseline method that supplements Gaussians by randomly selecting positions rather than by our PDGC. The comparison results in Tab. demonstrate the effectiveness of the proposed PDGC. Furthermore, Fig. visually validates that the PDGC effectively improves the reliability of the initialization for 3DGS in degraded scenarios, producing high-quality reconstructions with significantly enhanced clarity compared to the baseline without using PDGC.
Effect of the loss function. To show the effect of our improved components in the loss function Eqn. 12, we compare with two baseline methods that respectively replace our loss with Xe, Leg.E, Assim Lieg-siim (which contains single-scale structural similarity loss and is used in prior work [1] or Xe, Creg-h, + Assim Cre--simm + Atepth Table 6 reveals that both the improved multi-scale SSIM loss and the proposed depth ranking regularized loss yield significant improvements in terms of PSNR and SSIM while imposing minimal additional computational overhead during training.
Robustness of the pseudo-depth against degradation. To quantitatively evaluate the robustness of the pseudo-depth estimation against various degradation levels, we plot the Pearson correlation coefficient Fig. 9, which measures the agreement between pseudo-depth maps from degraded images and those from clean reference images on the "Street" scene of our simulated dataset. Simultaneously, we chart the number of 3D points estimated by COLMAP under different degradation conditions for comparison. As degradation intensity increases, COLMAP's point cloud density drops sharply, whereas the pseudo-depth consistently maintains high correlation values (e.g.. r >> 0.99), demonstrating its strong robustness and medium-agnostic properties. These results indicate that the depth prior well-suited for initialization and supervision challenging, degraded scenes.
7 Conclusion and Limitations
Conclusion. In this paper, we propose Plenodium, an efficient and robust framework for underwater 3D reconstruction. Our innovative plenoptic medium representation effectively integrates positional information to enhance medium modeling accuracy. Utilizing spherical harmonics-batd based encoding, we achieve 47% speedup relative to WaterSplatting. Using pseudo-depth Gaussian complementation, we significantly improve the robustness of the initialization process. The proposed depth ranking regularized loss further improves the geometry by using depth order. Extensive evaluations both real-world and simulated datasets with -fate-of-the-art methods demonstrate the effectiveness of our approach in reconstructing 3D underwater scenes and restoring underwater images.
Limitation. Despite the state-of-the -hertrt-rt performance achieved in underwater 3D reconstruction, the proposed Plenodium framework still faces several limitations. First, its perceptual consistency remains suboptimal. As shown in Tab. 1, Plenodium underperforms SeaThru--Neh on the LPIPS metric in certain scenes, indicating that the reconstructed results may not always align well with human visual perception. Second, the water model in Eqn. is inherently approximate and cannot fully capture the complex physical properties of heterogeneous media. This restricts our method to empirical fitting and limits its robustness and generalization in challenging environments.
10

---

Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 62332010 and 62272233).
References
[1] H. Li, W. Song, T. Xu, A. Elsig, and J. Kulhanck, "WaterSplatting Fast underwater 3D scene reconstruction using gaussian splatting," International Conference on 3D Vision, 2025.
[2] D. Levy, A. Peleg, N. Pearl, D. Rosenbaum, D. Akkaynak, S. Korman, and T. Treibitz, "Seathru- nerf: Neural radiance fields in scattering media," in IEEE Conference on Computer Vision and Pultern Recognition, 2023, pp. 56-65.
[3] J. T. Barron, B. Mildenhall, M. Tancik, P. Hedman, R. Martin-Brualle and P. P. Srinivasan, "Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields," International Conference Computer Vision, 2021, pp. 5855-5864.
[4] T. Barron, B. Mildenhall, D. Verbin, P. P. Srinivasan, and P. Hedman, "Zip-nerf: Anti-aliased grid- neural radiance fields," in International Conference on Computer Vision, 2023, pp- 19797-19 705.
[5] G. Fang and B. Wang, "Mini-splatting: Representing scenes with constrained number of gaussians," in European Conference on Computer Vision. Springer, 2024, pp. 165-181.
[6] S. S. Mallick, Goel, B. Kerbl, M. Steinberger, V. Carrasco, and De La Torre, "Taming 3dgs: High-quality radiance fields with limited resources," in ACM SIGGRAPH Asia, 2024, pp. 1-11.
[7] T. Müller, A. Evans, C. Schied, and A. Keller, "Instant neural graphics primitives with multiresolution hash encoding," ACM Transactions on Graphics, vol. 41, no. 4, pp. 102:1- 102:15, Jul. 2022.
[8] B. Mildenhall, Representing scenes as neural radiance fields for view synthesis," Communications of the ACM, vol. 65, no. 1, pp. 99-106, 2021.
Srinivasan, M. Tancik, J. Barron, R. Ramamoorthi, and R. Ng, "Nerf:
[9] B. Kerbi, G. Kopanas, T. Leimkühler, and G. Drettakis, "3d gaussian splatting for real-time radiance field rendering." ACM Transactions on Graphics, vol. 42, no. 4, pp. 139-1, 2023.
[10] J. L. Schönberger and J.-M. Frahm, "Structurefrrommmotio revisited," in IEEE Conference on Computer Vision and Pattern Recognition, 2016.
[11] J. L. Schönberger, E. Zheng, M. Pollefeys, and J.-M. Frahm, "Pixelwise view selection for unstructured mueti-view stereo," in European Conference on Computer Vision, 2016.
[12] L. Yang, B. Kang. Z. Huang, X. Xu, J. Feng, and H. Zhao, "Depth anything: Unleashing the power of lcrge-scale unlabeled data," in IEEE Conference on Computer Vision and Pattern Recognition, 2024, pp. 10 10371-10338..
[13] L. Yang, B. Kang, Z. Huang, Z. Zhao, X. Xu, J. Feng, and H. Zhao, "Depth anything v2," Conference Neural Information Processing Systems, vol. 37, pp. 21 875-21 911, 2025.
[14] S. Fridovich-Keil A. Yu, M. Tancik, Q. Chen, B. Recht, and A. Kanazawa, "Plenoxels: Ra- diance fields without neural networks," IEEE Conference on Computer Vision and Pattern Recognition, 2022, pp. 5501-5510.
[15) S. Durvasula, A. Zhao, F. Chen, R. Liang, P. K. Sanjaya, and N. Vijaykumar, "Distwar: Fast differentiable rendering on raster-based rendering pipelines," arXiv preprint 5405022401.05345, 2023.
[16] V. Ye, R. J. Kerr, M. Turkulainen, B. Yi, Z. Pan, O. Seiskari, J. Ye, J. Hu, M. Tancik, and A. Kanazawa, "gsplat: An open-source library for gaussian splatting." Journal of Machine Learning Research, vol. 26, no. 34, pp. 1-17, 2025.

---

[17] M. Kocabas, J.-H. R. Chang, J. Gabriel, O. Tuzel, and A. Ranjan, "Hugs: Human gaussian splats," " in IEEE Conference on Computer Vision and Pattern Recognition, 2024, pp. 505-
[18] S. Qian. T. Kirschstein, L. Schoneveld, D. Davoli, S. Giebenhain, and M. Nießner, "Gaussiana- vatars: Photorealistic head avatars with rigged 3d gaussians," in IEEE Conference on Computer Vision and Pattern Recognition, 2024, pp. 20 209-999-2 20 309.
[19] T. Yi. J. Fang. J. Wang, G. Wu, Xie, X. Zhang, W. Liu, Q. Tian, and X. Wang. "Gaussian- dreamer: Fast generation from text to 3d gaussians by bridging 2d and 3d diffusion models," in IEEE Conference on Computer Vision and Pattern Recognition, 2024, pp. 6796-6807.
[20] Z. Chen, F. Wang, Y. Wang, and H. Liu, "Text-to-3d using gaussian splatring," in IEEE Conference on Computer Vision and Pattern Recognition, 2024, pp. 21 401-21 412.
[21] J. Zhang, Z. Tang, Y. Pang, X. Cheng, P. Jin, Y. Wei, X. Zhou, M. Ning, and L. Yuan, "Re- paint123: Fast and high-quality one image to 3d generation with progressive controllable repainting," in European Conference on Computer Vision. Springer, 2024, pp. 303-320.
[22] X. Zhou, Z. Lin, X. Shan, Y. Wang, D. Sun, and M.-H. Yang. "Drivinggaussian Composite gaussian splatting for surrounding dynamic autonomous driving scenes," in IEEE Conference on Computer Vision and Pattern Recognition, 2024, pp. 21 634 21 643.
[23] M. Li, S. Liu, H. Zhou, G. Zhu, N. Cheng, T. Deng, and H. Wang, "Sgs-slam: Semantic gaussian splatting for neural dense slam," in European Conference on Computer Vision. Springer, 2024, pp. 163-179.
[24] Y. Wan, Y. Cheng, M. Shao, and W. Zuo, "S2gaussian: Sparse-view super-resolution 3d gaussian splatting," IEEE Conference Computer Vision and Pattern Recognition. 2025.
[25] L. Zhao, P. Wang, and P. Liu, "Bad-gaussians Bundle adjusted deblur gaussian splatting," in European Conference on Computer Vision Springer, 2024, pp. 233-250.
[26] O. Seiskari, J. Ylilammi, V. Kaatrasalo, P. Rantalankila, M. Turkulainen. Kannala, E. Rahtu, and A. Solin, "Gaussian splatting on the move: Blur and rolling shutter compensation for natural camera motion," " in European Conference on Computer Vision. Springer, 2024, pp. 160-177.
[27] S. Liu, X. Chen, H. Chen, Q. Xu, and M. Li, "Deraings: Gaussian splatting for enhanced scene reconstruction in rainy environments," in Association for the Advancement of Artificial Intelligence, vol. 39, no. 5, 2025, pp. 5558-5566.
[28] X. Jin, P. Jiao, Z.-. Duan, X. Yang, C. Li, C.-L. Guo, and B. Ren, "Lighting every darkness with 3dgs: Fast training and real-time rendering for hdr view synthesis," Conference on Neural Information Processing Systems, vol. 37, pp. 80 191-80219, 2025.
[29] Y. Tang, C. Zhu, Wan, C. Xu, and B. Shi, "Neural underwater scene representation." in IEEE Conference on Computer Vision and Pattern Recognition, 2024, pp. 11 780-11 789.
[30] I. Ma, X. Li, J. Liao, Q. Zhang, X. Wang. J. Wang, and P. V. Sander, "Deblur-nerf: Neural radiance fields from blurry images," in IEEE Conference Computer Vision and Pattern Recognition, 2022, pp. 12 12861-12870 870.
[31] X. Huang, Q. Zhang, Y. Feng, H. Li, X. Wang, and Q. Wang, nedr-nerf: High dynamic range neural radiance fields." in IEEE Conference on Computer Vision and Pattern Recognition, 2022, pp. 18 398-18884444 408.
[32] N. Pearl, T. Treibitz, and S. Korman, "Nan: Noise-aware nerfs for burst-denoising" " in IEEE Conference Computer Vision and Pattern Recognition, 2022, pp. 12 12672-122 12 681.
[33] C. Wang, X. Wu, Y.-C. Guo, S.-H. Zhang, Y.-W. Tai, and S.-M. Hu, "Nerf-sr: High quality neural radiance fields using supersampling." " in ACM International Conference on Multimedia, 2022, pp. 6445-6454.
[34] D. Berman, D. Levy, S. Avidan, and T. Treibitz, "Underwater single image color restoration using haze-lines and a new quantitative dataset," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 8, pp. 2822-2837 2020.
12

---

[35] Y.-T. Peng, K. Cao, and P. C. Cosman, "Generalization of the dark channel prior for single image restoration," IEEE Transactions on Image Processing, vol. 27, no. 6, pp. 2856-286666 2018.
[36] Y.TT. Peng and P. C. Cosman, "Underwater image restoration based image blurriness and light absorption," IEEE Transactions on Image Processing, vol. 26, no. 4, pp. 1579- 11949,11,,,411 2017.
[37] Y. Xie, L. Kong, K. Chen, Z. Zheng, X. Yu, Z. Yu, and B. Zheng. "Uveb: large-scale bench- mark and baseline towards real-world underwater video enhancement," in IEEE Conference Computer Vision and Pattern Recognition, 2024, pp. 22 358-22.34 367.
[38] D. Akkaynak and T. Treibitz, "A revised underwater image formation model," in IEEE Confer- ence on Computer Vision and Pattern Recognition, 2018, pp. 6723-6732.
[39]
"Sea-thru: method for removing water from underwater images," in IEEE Conference on Computer Vision and Pattern Recognition, 2019, pp. 1682-1691.
[40] O. B. Nathan, D. Levy, T. Treibitz, and D. Rosenbaum, "Osmosis: Rgbd diffusion prior for underwater image restoration," in European Conference on Computer Vision. Springer, 2024, pp. 302-319.
[41] H. Zeng, J. Cai, L. Li. Z. Cao, and L. Zhang, "Learning image-adaptive 3d lookup tables for high performance photo enhancement in real-time," " IEEE Transactions on Pultern Analysis and Machine Intelligence, vol. 44, 04, pp. 2058-2073 2022.
[42] B. Mildenhall, Hedman, R. Martin-Brualla, dark: High dynamic range view synthesis from noisy raw images," in IEEE Conference on Computer Vision and Pattern Recognition, 2022. pp. 16 190-16 199.
Srinivasan, and T. Barron, "Nerf in the
[43] Z. Wang, E. P. Simoncelli, and A. C. Bovik, "Multiscale structural similarity for image quality assessment," in The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, vol. 2. Ieee, 2003, pp. 1398-1402.
[44] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: from error visibility to structural similarity," IEEE Transactions Image Processing, vol. 13, pp. 600-612, 2004.
[45] K. Xian, J. Zhang, O. Wang, L. Mai, Z. Lin, and Z. Cao, "Structure-guide ranking loss for single image depth prediction," in IEEE Conference on Computer Vision and Pattern Recognition, 2020, pp. 1-620.
[46] G. Wang, 7. Chen, C. C. Loy, and Z. Liu, "Sparsenerf: Distilling depth ranking for few-shot novel view synthesis," in International Conference on Computer Vision, 2023, pp.
[47] M. Tancik, E. Weber, E. Ng, R. Li, B. J. Kerr, T. Wang, A. Kristoffersenn, Austin, K. Salahi, A. Ahuja, D. McAllister, and A. Kanazawa, "Nerfstudio: A modular framework for neural radiance field development," in ACM SIGGRAPH, 2023.
[48] Z. Ye, W. Li, S. Liu, P. Qiao, and Y. Dou, "Absgs: Recovering fine details in 3d gaussian splatting," in ACM International Conference on Multimedia, 2024, pp. 1053-1061.
[49] Y. Y. Schechner, G. Narasimhan, and S. K. Nayar, "Instant dehazing of images using polarization," in IEEE Conference on Computer Vision and Pattern Recognition, vol. 1. IEEE, 2001, pp. I-I.
[50] H. C. Karaimer and M. S. Brown, "A software platform for manipulating the camera imaging pipeline," in European Conference Computer Vision. Springer, 2016, pp. 429-444.
[51] G. Buchsbaum, "A spatial processor model for object colour perception." " Journal of the Franklin institute, vol. 310, no. 1, pp. 1-26, 1980.
[52] Z. Zhu, Z. Fan, Y. Jiang, and Z. Wang, "Fegs: Real-time few-shot view synthesis using gaussian splatting." " in European Conference on Computer Vision. Springer, 2024, pp. 145-163.
13

---

Summary of the Supplementary Materials
This appendix presents supplementary materials and analyses. We first present the implementation details of our method in Sec. A. We then detail the construction of our simulated dataset and analyze the effect degradation on COLMAP initialization in Sec. B. Sec. C, we conduct further ablation studies and provide an in-depth analysis of our findings. Section D provides additional qualitative visualizations to better illustrate the performance of our method. Finally, we consider our work's broader implications and potential societal impact in Sec. E.
A Implementation Detail
This section outlines our implementation details, including the training settings (i.e., Sec. A.1), supplementary information for pseudo-depth Gaussian complementation (i.e., Sec. A.2), and the depth gradient computation under scattering media (i.e., Sec. A.3).
A.1 Training Settings
We train our model using a volumetric extension of 3D Gaussian Splatting. For reconstruction tasks, train for 15,000 steps, while for restoration tasks, which require higher accuracy, extend training to 30,000 steps. Following the progressive training strategy introduced in 3DGS [9], training begins 1/4 resolution and gradually doubles every 3,000 steps to increase spatial detail. To prevent unstable updates in the early training phase, we apply a 500-step warm-up before the Gaussian refinement. After warm-up, Gaussian refinement (including densification and culling) is performed every 100 steps. Densification is triggered for a Gaussian primitive when its gradient norm exceeds 0.0008. In this case, if the Gaussian scale is below 0.001, it is copied expand coverage: otherwise, it is split into two samples to preserve fine-grained structure. In parallel, culling is applied at each refinement step to remove Gaussians with opacity below 0.5. To prevent opacity saturation and encourage stable convergence, all opacities are reset to 0.5 every five refinement steps. Together, these refinement steps first densify improve coverage, then cull to remove floaters, ensuring compact and effective representation.
Table 7: Optimizer and scheduler configurations for each parameter group.
Parameter Group
Initial LR
Final LR
Notes
Means
1.6e44
Se-5
Position updates
DC Features
2.5e-3
2.5e-4
Direct color channels
Rest Features
1.25e-4
1.25e-5
Non-DC channels
Opacities
5.0e-2
5.0e-2
No decay
Scales
5.0c-3
5.0c-3
No decay
Quaternions
1.0c-3
1.0c-3
Rotation parameters
Medium DC Features
2.5e-3
2.5e-4
For volumetric medium
Medium Rest Features
1.25e-4
1.25e-5
For anisotropic scattering
We employ the Depth Anything Model [12, 13] as an external image depth estimator to generate the pseudo-depth maps. We use the latest version, V2, and the largest model variant, VIT-L, which is pretrained on diverse datasets and applied in inference mode without further fine-tuning. Following the official implementation, each image is first resized to a fixed resolution (518 x 518) before passing through the model. This resizing ensures compatibility with the model's ViT backbone, which performs best under fixed input sizes due to its patch- based architecture. The predicted depth map is then upsampled via bilinear interpolation to match the original image resolution and stored as dense pseudo-depth prior for further use in our pipeline.
Each parameter group is optimized using the Adam optimizer with = 10-15 and exponential decay scheduling. For instance, the 3D means trained with initial learning rate of 1.6 x 10"4, which decays to 5 x 10 55 over time, while opacities are optimized using a fixed learning rate of 0.05. Additional learning rates and scheduler configurations details are provided in Tab. 7.
A.2 More Details of the Pseudo-Depth Gaussian Complementation
14

---

Algorithm Pseudo-Depth Gaussian Complementation
Input:
The set of the input cameras V. and corresponded images C:
COLMAP initialized Gaussian primitives. G;
Output:
The final Gaussian primitives, G';
1:
G'
= 0
2: for V C
D, &- render from V using Eqn. 8.
4:
S2p + {(x, 9) (x, y) 2 Tw)
5:
get D by Depth Anything Model with image input C
6:
In - (<a,,)) v)) y) Taearmax (D))
7:
D' from D using Eqn.
for v) Qn 22 do
get μ. using Eqn.
10:
get Σ using Equ. 14
11:
< 0.1
12:
G {u, A,or
13:
G' G' G' (9}
14: end for
15: end for
16: G' GUG
17: return G'
In this section, detail the procedure of our Pseudo-Depth Gaussian Complementation (PDGC), as summarized in Alg. 1.
Based on the pixel regions selected by Ωn and Q2p (as defined in Sec. 4.2), we determine where new Gaussians should inserted. For each selected pixel (Ir, y), we project into space as a Gaussian using its calibrated pscudo-depth D'(x, y). The 3D mean position μ and the spherical harmonics-encode color feature A are computed as:
D' v) x D' D'(x,))
1 W
+
Me Zc
A RGB2SH(C(x,,)) v)), where (x, Ωn n Spp (13)
here, W is the intrinsic matrix, and [ze, Ye. zc] is the camera position. The function RGB2SH maps RGB values to Oth-order spherical harmonics coefficients for compact color representation.
To represent the shape and orientation of each Gaussian, we define its covariance matrix Σ via isotropic scaling S and random rotation R:
D'(I, (fz fy) h +
Σ = RSS RT. S diag(s, 8,8).
(14)
where diag(s, (s, s, constructs a diagonal matrix S that uniformly scales the Gaussian along all three spatial axes, resulting in isotropic shape. The scalar adapts the Gaussian size the scene depth, while considering focal lengths [y) and image dimensions (h, w).. The rotation matrix R is randomly initialized promote diversity in orientation and mitigate optimization bias.
A.3 Backward Pass
Unlike standard 3DGS, where the depth mainly affects the rendered depth D, in medium- aware formulation, 2, also influences the final rendered color Ô through scattering and attenuation. The loss gradient concerning z; becomes:
ac
AL
a ac
ac
+
(15)
0z,
aD
0z,
ac
Oz,"
15

---

The first term corresponds to the direct contribution of 2; to the depth rendering, which follows the standard 3DGS formulation:
aD 0z; =,,T!"
(16)
The second term accounts for the influence of 2; on color rendering, which stems from the medium- aware compositing process:
Č= Σ C e
Σ meddpphi (e (e-0" -
- + moddrobh -
N+1 e
(17)
Thus, 2 appears in the following terms of the color computation:
C = c,a,l, e --== where 2, affects attenuation the object.
Equed mmadgeet -0 -e-o"s.), where 2; appears in the second exponential term.
Cmed = emoodraai (e- (e-o - - e-0 where appears in the first exponential term.
Combining these, we get:
aC
-0o""aao Tebbl e 0= e0== oh medd -d== (Tre)) Toty
(18)
where, the difference in transmittance simplifies as: T.th| Troyj T.ati (1 a,) ax T,T
Then, we substitute it back into the gradient of the loss:
OC Oc TT
+ OC (o ot== med - -00t a T.o
(19)
2z, aD
ac
This formulation captures depth's 's dual role in geometry and appearance, enabling more informative gradient flow in scattering environments.
B More Details of Our Simulated Dataset
In this section, we present additional details about our simulated dataset. We first describe the dataset construction process (i.e., Sec. B.1), including medium configurations and rendering settings. We then analyze the impact of different degradation levels on COLMAP- initialization (i.e., Sec. B.2).
Figure 10: Blender interface used for dataset rendering.
B.1 Dataset Construction
As shown in Fig. 10, we simulate a scattering medium using Blender's Principled Volume shader, rendered with the Cycles engine to achieve high-fidelity light transport. vertical density gradient is introduced along the Z-axis by combining the Texture Coordinate, Mapping, and Separate XYZ nodes, followed by Col Color colorRamp node to control the falloff. For fog, we adopt a white absorption color and low anisotropy (0.001) simulate uniform scattering, For water, we use bluish absorption
16

---

Figure 11: Sampled images from our simulated dataset.
Water
Fog
hard
easy
easy
hard
2988
5569
6043
8371
6454
5569
3707
2805
4326
7239
9931
7819
6072
3406
Figure 12: Sparse point clouds obtained by COLMAP under varying degradation conditions. The numbers below each image indicate the number of points. For both the Beach (top) and Street (bottom) scenes, we show the impact of different levels of fog and water degradation (from easy to hard) compared to the clean ground truth. Severe degradation results in significantly sparser points, illustrating the challenge of reliable initialization of 3DGS.
tint and increased anisotropy to better approximate underwater light propagation with enhanced forward scattering. Three degradation levels (easy, medium, and hard) are realized by scaling the base density using adjustable Multipliere piliesllssssieell (e.g., 0.005, 0.01, 0.02). All images our dataset are rendered with linear color management to allow for accurate exposure adjustments during post-processing. Specifically, we set the view transform to Standard and turn off gamma correction (gamma = 1.0). We do not user-defined curve adjustments, ensuring no tone mapping nonlinear operations alter the image. This enables consistent and physically meaningful exposure control during procceso....ig. The dataset comprises two distinct scenes (Beach and Street), illustrated in the ground truth (GT) visualizations shown in Fig. 11, supporting robust and comprehensive benchmarking. Additional details, including exact shader setups and scene configurations, are provided in the supplementary Blender source files.
B.2 Dataset Analysis
To evaluate the impact of image degradation caused by scattering media on the crructurefrrommmotion (SIM) [10] initialization process in COLMAP [10, 11], we analyze the density and completeness of the generated sparse point clouds under degraded imaging conditions. When image quality is compromised due to fog or water, COLMAP struggles with reliable feature extraction and matching. resulting in significantly sparser and less accurate point clouds. As visualized in Fig. 12, specific regions, particularly those with strong scattering effects, exhibit apparent gaps or absences in geometry. This degradation-induuel sparsity directly hinders the quality of subsequent reconstruction stages, especially for methods relying on accurate geometry priors, such as 3DGS. These findings highlight the sensitivity of COLMAP-based initialization pipelines to visibility degradation, under-
17

---

Water
Fog
GT
hard
easy
easy
hard
0.999
0.999
1.000
1.000
1.000
1.000
0.999
0.994
0.996
0.997
1.000
0.998
0.996
0.995
Figure 13: Pseudo-Depth estimated from various degraded images by [13]. Numbers below each map denote the Pearson correlation coefficient concerning the GT-based pseudo-depth. The consistently high values (close to 1.0) validate its effectiveness as a reliable depth in different environments.
scoring the need for complementary initialization strategies recover missing geometry in severely degraded scenes.
C More Analysis and Discussion
In this section, we provide a comprehensive analysis of our method under various settings. We supplement a ColorChecker-based evaluation to verify the color fidelity of our approach for restoration (i.e., Sec. C.I) and assess the robustness of the pseudo-depth estimation under diverse degradation types (i.e., Sec. C.2). We then compare our Pseudo-Deptl Gaussian Complementation (PDGC) with a graph-bases densification strategy (i.e., Sec. C.3) and further analyze the effects of the regularization weight (i.c.. Sec. C.4), COLMAP initialization (i.c., Sec. C.5), and depth ranking regularized loss (i.e.. Sec. C.6). Furthermore, we examine how critical hyperparameters affect performance(i.c. Sec. C.7) and analyze statistical variance across different runs and degradation levels to establish result consistency (i.e., Sec. C.8). Finally, we analyze the limitations of our method with respect to the LPIPS metric (i.e., Sec. C.9).
C.1 Colorchecker-basee Evaluation
To validate the color fidelity of the proposed Plenodium, we supplement ColorChecker-basee evaluation. Following SeaThru [39], restored images are converted to a standard color space via the camera-pipeline manipulation platform [50], and white balance is an identity matrix derived from the Gray-World Hypothesis [51]. Color accuracy is quantified as the mean RGB angular error:
1lCall
Σ COS -( 1=1
(20)
V31
between the six grayscale patches for each chart, following [34]. Table 8 demonstrates that our Plenodium attains the lowest angular error, further confirming the superior color fidelity. However,
18

---

Table 8: Comparison of RGB angular error across methods.
SeaThmi-NRRF
WaterSplatting
Plenodium
RGB angular error
13.039
11.527
8.288
Table 9: Effectiveness of the PDGC.
Table 10: Effectiveness of the regularized losses.
Methol
PSNR
SSIM
G (inil/linal)
Losses
PSNR
SSIM
Lez + Lus
Plenodium wis PooG.
30.176
0.890
21.907 887
Leg + Lepomnsii
29.60
0,910
Plenodium w/rU
30.210
0.890
77,830/ 861,567
Canp
Leog
30.41
0.923
Plenodium (ours)
30.275
0.891
22,669/ / 860,219
Coce C)
Loog moessan
30.47
0,923
note that the SeaThru-NeRF dataset is not fully designed for color checker evaluation: only the "Curaçao" scene contains an unobstructed color chart, while the others suffer from occlusions or lack such references entirely, limiting the application of the color-checker-based metric.
C.2 Robustness of Pseudo-Depth
Our pipeline leverages the Depth Anything Model [12, 13], state-of-the-art monocular depth estimator, to compute robust pseudo-depth maps from media-degraded images. These maps serve as essential guidance for both our Pseudo-Depth Gaussian Complementation (PDCG) and the depth ranking regularized loss. As shown in Fig. 13, a key advantage of this approach is its robustness to medium-induced degradations. Despite varying levels of scattering and absorption in both water and fog, the pseudo-depth maps remain visually consistent across different input conditions and align well with those derived from clean ground- ground-truth images. To quantitatively support this observation, we report the Pearson [52] correlation coefficient below each depth map. comparing each pseudo-depth the one predicted from the clean (GT) image. The consistently high correlation values (e.g., >0.99) validate the robustness and medium- aagnostic nature of the predictions by [13], making it well-suited for initialization and supervision in degraded scenes.
C.3 Comparison Between PDGC and Graph-based Densification
We provide a comparison between our Pseudo-Depth Gaussian Complementation (PDGC) with graph-based densification strategy (i.., Gaussian Unpooling, GU used in FSGS [52]). To quantita- tively compare PDGC against GU, we conduct controlled experiments on the "IUI3-RedSea" scene and compare our Plenodium with two baselines that respectively remove our PDGC (i.e., Plenodium w/o PDGC) and replace our PDGC with GU (i.e., Plenodium w/o PDGC & w/ GU) for providing additional Gaussian during initialization while keeping all subsequent training settings identical. Compared to GU only using the information estimated by COLMAP, our PDGC further leverages an additional depth prior, thereby delivering superior quantitative results illustrated in the Tab. 9. Moreover, GU introduces large number of Gaussians at initialization, yet yields negligible gains in final reconstruction quality and leaves the final Gaussian count almost unchanged.
C.4 Effect of the Regularized Losses
We further provide ablation evaluations the effectiveness of the regularized in Eqn. 10 (i.e., the effectiveness of the weighting matrix W = sg(C)+e on two losses in Eqn. 10). We compare our
approach with the losses Eqn. 10 (i.e., Creg-Li + Lrog-ms-ssim) with three baseline methods that respectively remove the weighting matrix W from the Li loss (i.e., Lc, + -rgg-m--ssim) remove the weighting matrix W from the multi-scale differentiable SSIM loss (i.e., Lreg-C, Lmss ), remove the weighting matrix W from both the LI loss and the multi-scale differentiable SSIM loss (i.e., Le, + Lim)) The comparison results in Tab. 10 show that our approach outperforms all the baselines, which demonstrates the effectiveness of emphasizing dark regions during optimization.
19

---

Table 11: Effect of the COLMAP initialization. We compare it with a random initialization with 50,000 points.
Table 12: Effect of the depth ranking regularized loss. We compare it with the Pearson correlation loss from [52].
Initialzation
LPIPS
I
PSNR
SSIM
T.PTPS
FPS
Time
Random
25. 198
0.7983
0.2235
116
6.4min
w/o Caepus
30.305
0,9212
0.1272
252
7.0min
COLMAP
30.388
0.9207
0.1274
7.0min
Leytt w/ Caeqeh
30.384
0.9209
0,1292
246
7.7min
COLMAP & PDOC
30.472
0.9225
0.1276
249
7.0minn
30.472
0.9225
0.1276
249
7.0minn
316
30,44)
30:472
30,401
30,48
30,472
30.4
PSINR (dB)
PSNR (dB)
30,42
30.
30.36
30.0
30.30
23.700
30:351
29.8
30.24
4
16
32
64
128
Degree
N
Figure 14: Effect of varying the maximum SH degree used for the plenoptic medium represen- tation.
Figure 15: Effect of varying the number N of patches used in the depth ranking regularized loss.
C.5 Effect of the COLMAP Initialization
To evaluate the role of COLMAP- A-aaed initialization within our framework, we compare three variants: (1) our method with COLMAP initialization but without PDGC, (2) our method with random initialization using 50,000 uniformly sampled 3D points, and (3) our full pipeline combining COLMAP with PDGC. COLMAP provides strong geometric prior that aids reconstruction; however, under severe degradation (e.g.. fog or water), its output often becomes sparse and contains missing regions. In contrast, random initialization does not rely scene-specific priors but ensures uniform spatial coverage, even areas where COLMAP fails to generate points. As shown in Tab. 11, despite the degraded visibility, COLMAP initialization still leads to better performance than random initialization, validating the utility of its geometric prior. Moreover, our full method (augmenting COLMAP with PDGC, COLMAP PDGC) further improves results, indicating that while COLMAP provides a solid foundation, complementary strategies can effectively enhance geometric priors under a degraded environment.
C.6 Effect of the Depth Ranking Regularized Loss
To further evaluate the effectiveness of our proposed depth ranking regularized loss Ldepth: we compare our method (i.e., w/ Ldepb) against two baselines: one trained without any depth supervision (i.e., w/o Leppt)), and another using the Pearson correlation-
depth loss L'spahh adopted FSGS [52] (i.c., w/ Ca As shown in Tab. 12, while Cleeuhh provides marginal improvements over the no-depth baseline, our method that leverages Luepth achieves superior performance, which shows that our depth ranking regularized loss offers more effective geometric supervision with imprecise pseudo-depth supervision.
C.7 Effect of Hyperparameters
In our experiments, we investigate two critical hyperparameters that affect the performance of our plenoptic medium representation and the efficacy of the depth ranking regularized loss.
First, in Fig. 14, we control the maximum spherical harmonics (SH) degree for our plenoptic representation in our method. Adjusting this parameter determines the level of angular complexity captured the medium field, thereby influencing the fidelity of volumetric effects such as scattering and color absorption. A higher maximum SH degree model more detailed angular variations.
20

---

WatesSgaating
Plenodimm
WaterSpltting
Plenodium
28.8
PSNN (dB)
PSNR (dB)
14.4
28
9.6
26
4.8
24
0.0
IUISR So6
Cunoga
J.G. R. Sen
Panama
Beschfog
Bexch weler
Street fog
Strott watte
Scane
Soene
Figure 16: Mean and variance of reconstruction quality over four runs on real-world scenes.
Figure 17: Performance variation on simulated data across different degradation levels.
SeaThru-NeRF's LPIPS
Our LPIPS
GT
Noise in Background
Figure 18: Visual comparison of LPIPS maps between SeaTThu-NeRRi and Plenodium. The primary difference appears in the background regions corrupted by GT noise.
Still, it may also increase computational cost and risk of overfitting, whereas lower degree results in a smoother but potentially oversimplified medium representation. To achieve an optimal trade-off' between computational efficiency and representational fidelity, we fix the SH degree to 3.
Second, we vary the number N of downsampled patches used the depth ranking regularized loss for our method in Fig. 15. This loss plays crucial role in enforcing depth consistency during training. larger N provides finer granularity for capturing local depth variations, but it also introduces more noise and increases computational overhead, even out-of-memory issues during training. In contrast, a smaller simplifies the loss calculation but may not capture sufficient spatial detail. Empirically, setting N = 16 yields the best performance while maintaining reasonable computational load.
C.8 Statistical Analysis
To ensure the robustness and stability of our quantitative results, we conduct four independent training runs on real-world scenes and report the average performance in Tab. of the main manuscript. As shown in Fig. 16, we visualize the mean performance across runs and the corresponding variance to reflect consistency.
For our simulated dataset, we compare the average PSNR across scenes under water and fog degra- dation. As shown in Fig. 17, our method (Plenodium) consistently outperforms WaterSplatting across all conditions. The error bars represent the standard deviation across different degradation levels, reflecting both the effectiveness and robustness of each method under challenging visual environments.
C.9 Limitation
While our method underperforms SeaThru-NeRR terms of LPIPS in some scenes (as reported in Tab. 1 of the main manuscript), we conduct visual analysis to better understand this discrepancy. As shown in Fig. 18, the LPIPS maps indicate that the main difference arises the medium regions, where our method yields higher LPIPS values. We further observe that background areas in the GT contain visible noise, which may act as confounding factor in LPIPS evaluation, limiting its reliability in degraded scenes.
21

---

Fog
Water
easy
hard
easy
hard
GT
Low Quality
19.26/0.575
Sea SeaThru-Te NeRF
28.22/0.877
23.42/0.800
17.21/0.722
558
19.81/0.746
Water- Spt Splatiing
25. 25.16/0.866 1600.662
24.760.83 834
22. 169.779
24 24.000.853
21. 21.72/0.815
20.31/0.748
Menodium
27.58/0.902
25.41/0.873
22,71/0.794
25.82/0.851
21. 21.9000,73
19.73/07748
Fog
Water
easy
hard
easy
hard
Low Quality
24.44/0.921
21.13/0.873
18.31/0.800
22.04/0.910
18.72/0.856
16.89/0.810
PSNR/SSIM
SeaThru- NeRF hre-h---NR
28. 29.66/009925
8/9
14.49/0.760
26.71/0.915
20.05/0.863
17. 17.1070.117
Water- Splatting
1W.2700.88
14.87N0.78
16. 16.76/0.770
15.19/0.442
Plenodium
25.59/0.945
25. 25.96/0.933
25.12/0.912
25.32/0.942
23.90 23.99/0.916
23.60/0891
Figure 19; Visual comparison on our simulated dataset.
D More Visualizations
In this section, we present additional visualizations on our simulated dataset, comparing SeaThru-
NeRF [2], WaterSplatting [1], and our proposed Plenodium, shown in Fig. 19. We also include
22

---

video results in the supplementary material, rendered at 24 FPS using camera trajectories interpolated from the evaluation poses with step size of 10.
E
Broader Impact
Our method offers accurate and efficient solution for underwater 3D reconstruction, which positively impact fields such as marine ecology, environmental monitoring, underwater archacology. and infrastructure inspection. By improving scene recovery in visually degraded environments, approach may assist in documenting underwater habitats, tracking pollution effects, and preserving submerged cultural heritage. Furthermore, the proposed simulated dataset provides benchmark for evaluating underwater image restoration methods, promoting reproducibility and transparency. How- ever, with any enhanced visual sensing technology, there exists potential for misuse in surveillance or unauthorized mapping. We encourage responsible use and recommend that applications of this technology follow appropriate ethical and legal guidelines.
23

---

NeurIPS Paper Checklist
The checklist is designed encourage best practices for responsible machine learning research, addressing issues of reproducibility, transparency, research ethics, and societal impact. Do not remove the checklist: The papers not including the checklist will be desk rejected. The checklist should follow the references and follow the (optional) supplemental material. The checklist does NOT count towards the page limit.
Please read the checklist guidelines carefully for information on how to answer these questions. For each question in the checklist:
You should answer [Yes], [No]. or [NA].
[NA] means either that the question Not Applicable for that particular paper or the relevant information is Not Available.
Please provide short (1-2 sentence) justification right after your answer (even for NA).
The checklist answers are an integral part of your paper submission. They are visible to the reviewers, area chairs, senior area chairs, and ethics reviewers. You will be asked to also include (after eventual revisions) with the final version of your paper, and its final version will published with the paper.
The reviewers of your paper will be asked use the checklist as one of the factors their evaluation. While "[Yes] is generally preferable to "[No]" ", it is perfectly acceptable to answer "[No] providedd proper justification is given (e.g.. "error bars are not reported because it would be too computationally expensive" or "we were unable to find the license for the dataset we used"). In general, answering binary way, we
"[No] or "[NA]" is not grounds for rejection. While the questions are phrased acknowledge that the true answer is often more nuanced, please just use your best judgment and write justification to elaborate. All supporting evidence can appear either in the main paper or the supplemental material, provided in appendix. If you answer [Yes] to a question, in the justification please point to the section(s) where related material for the question can be found.
IMPORTANT, please:
Delete this instruction block, but keep the section heading "NeurIPS Paper Checklist",
Keep the checklist subsection headings, questions/answers and guidelines below.
Do not modify the questions and only use the provided macros for your answers.
1. Claims
Question:
Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: Abstract and Introduction (Sec. 1).
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results be expected to generalize other settings.
is fine include aspirational goals as motivation long is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: Limitation (Sec. 7and Supplementary Material (Sec. C)

---

Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, c.g., if the approach was only tested few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
Justification:
The main results of this paper are experimental results.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proofs can either appear in the main paper the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should complemented by formal proofs provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions the paper (regardless whether the code and data are provided or not)?
Answer: [Yes]
Justification: Experiment (Sec. 5)
Guidelines:
The answer NA means that the paper does not include experiments.
25

---

If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g.. with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors welcome describe the particular way they provide for reproducibilityy In the case of closed-source models, it may be that access to the model is limited in some way (e.g., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification: Experiment (Sec. 5), Supplementary Material (Sec. B), and our project website: https: https://plenodium um, .ei.gggtuuu github.ii i
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (c.g., for a new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https: /ttpsscccppbblcc////eeccppppppcp hwwbbliccguiidee guwdee/ /CodeSubmis ssionPolicy for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
26

---

Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Question:
Answer:
[Yes]
Justification: Experiments (Sec. 5) and Supplementary Material (Sec. A)
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented the core the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: Experiments (Sec. 5) and Supplementary Material (Sec. C)
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results accompanied by enror bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
OK to report 1-sigma error bars, but one should state The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that out of range (e.g. negative error rates).
If error bars reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: Experiments (Sec. 5)
Guidelines:
The answer NA means that the paper does include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
27

---

The paper should provide the amount of compute required for each of the individual experimental runs as well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https: //ttrr//e....peee wwwpsurips.ccpppppppeeeeoo Spppblic//thissuuddeeep.p.eppeee
Answer: [Yes]
Justification: conform
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. if there special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: Introduction (Sec. 1) and Supplementary Material (Sec. E)
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility ML).
11. Safeguards
Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, scraped datasets)?
Answer: [NA]
Justification: This paper poses no such risks.
Guidelines:
The answer NA means that the paper poses such risks.
28

---

Released models that have high risk for misuse or dual-use use should be released with necessary safeguards to allow for controlled use of the model. for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g.. code, data, models), used in the paper, properly credited and the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: Reference
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g.. website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if has changed) should be provided.
this information is not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: Experiment (Sec. 5), Supplementary Material (Sec. C)
Guidelines:
The answer NA means that the paper does not release assets.
Researchers should communicate the details of the dataset/code/modde part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: This work entirely completed by the authors and does not involve research with human subjects.
29

---

Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation,
other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: This work does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with
human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods this research? Note that if the L.M used only for writing, editing, or formatting purposes and does not impact the core methodology. scientific rigorousness, or originality the research, declaration is not required.
Answer: [NA]
Justification: this research does not involve LLMs any important.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs any important, original, non-standard components.
Please refer to our LLM policy (https : http///eurrpp.ppp htt////riis.cc//offeeeeeeeeeeeee ww/coofeeeenccsscccccoooccos//.. /etpeencccee/2////// for what should or should not be described.
30


Reviews:
[{"review_id": "dVAfQCsu88", "reviewer": "Reviewer_fBkD", "summary": "The work proposes to reconstruct 3D-GS representation from multi-view underwater images. Different from prior work, which usually exploit MLP to represent the medium, they exploit spherical harmonics encoding for better performance. The new medium representation incorporates both directional and positional information for more effective and efficient 3D representations, compared to MLP. They also exploit pseudo-depth Gaussian complementation for more robust depth priors. The experimental results demonstrate improved performance compared to prior baselines.", "questions": "Please see weakness section.", "limitations": "Does the proposed method could also be applied to other similar problems, such as dehaze etc.?", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths ## \n1. The paper is well written and easy to follow. \n2. The proposed method is rational and the experimental results demonstrate its effectiveness.\n\n## Weaknesses ##\n1. Parts of the technical details can be further improved:\n* the paper mentions that they exploit a medium volume field for SH coefficient interpolation, what is the size of the grid? It is selected based on which criteria? \n* eq (12), why the denominator is N^4, how many i, j pairs are chosen? \n* eq (11), what is the motivation to emphasize dark regions during optimization? Could the authors provide any ablation evaluations on its effectiveness? \n\n2. eq (12), the manuscript mentions that they downsampled the depth image to 16x16 pixels low-resolution from 512x512/900x1400 pixels. The reviewer wonders the necessity of the depth loss. It is also verified from the ablation studies, i.e. the loss only improves the PSNR by 0.099 dB, 0.124 dB, 0.111 dB and 0.001 dB, which could be considered a very marginal improvements since you might also get similar performance by repeat the training several times.  \n\n3. Line 2: participating media -> participating medium;", "was_revised": true, "final_justification": "The paper has addressed my concerns.", "rebuttal": "# Response to Reviewer fBkD\n\nWe sincerely thank the reviewer for the constructive comments. We provide the detailed responses to all the concerns below.\n\n> **W1:** Parts of the technical details can be further improved.\n\n> **W1.1:** What is the size of the grid and what is its selection criteria?\n\n+ The  grid spans $[−1, 1]^3$. As specified in Eq. 7, the  grid spans the 3D cube $[−1, 1]^3$, yielding a total volume of $2 \\times 2 \\times 2$.\n\n+ This selection refers to existing state-of-the-art methods and is based on the number of input images.\n\n  + Most open-source NeRF [8] and 3DGS [16] implementations adopt this selection criterion, which recenters all camera poses so that the resulting scene geometry is fully enclosed within the unit cube.\n\n  + Meanwhile, the stable optimization of parameters requires that the number of grid vertices be smaller than the number of input images. As the training set of the SeaThru-NeRF [2] dataset contains only ~20 views, we adopt a single 3D grid and bilinear interpolation. Note, when denser multi-view data are available, the representation can employ multiple grids and more sophisticated interpolation schemes.\n\n\n> **W1.2:** For Eq. 12, why the denominator is $N^4$ and how many $i$,$j$ pairs are chosen? \n\nIn Eq. 12 , the indices $i$ and $j$ enumerate all $N\\times N$ ($16\\times 16$) pixel locations, yielding $N^4$ (65546) unique pairs. Thus, the denominator is set as $N^4$ for normalization.\n\n> **W1.3:** For Eq. 11, what is the motivation to emphasize dark regions during optimization? \n \n+ We deliberately emphasize dark regions for two reasons: \n    1. to align human perception to compress dynamic range[43]; \n    2. to enhance 3DGS’s ability to reconstruct distant underwater structures [1]. \n\n    The human visual system is far more sensitive to faint light than to bright light. Emphasizing darker tones matches this non-linearity, yielding perceptually natural images. As shown in Fig. 3, distant objects appear darker in raw images due to water scattering and absorption. We increase their loss weight, prompting 3D Gaussian Splatting to refine long-range Gaussians and recover details.\n\n+ As suggested, we further provide ablation evaluations on its effectiveness (i.e., the effectiveness of the weighting matrix $W=\\frac{1}{\\text{sg}(\\hat C)+\\epsilon}$ on the two losses in Eq. 11) . We compare our approach with the losses in Eq. 11 (i.e., $\\mathcal{L}\\_{\\text{reg-}\\mathcal{L}_1}+\\mathcal{L}\\_\\text{reg-ms-ssim}$) with three baseline methods that respectively remove the weighting matrix $W$ from the L1 loss (i.e., $\\mathcal{L}\\_{\\mathcal{L}_1}+\\mathcal{L}\\_\\text{reg-ms-ssim}$), remove the weighting matrix $W$ from the multi-scale differentiable SSIM loss (i.e., $\\mathcal{L}\\_{\\text{reg-}\\mathcal{L}\\_1}+\\mathcal{L}\\_\\text{ms-ssim}$), remove the weighting matrix $W$ from both the L1 loss and the multi-scale differentiable SSIM loss (i.e., $\\mathcal{L}\\_{\\mathcal{L}\\_1}+\\mathcal{L}\\_\\text{ms-ssim}$). The comparison results in the following table show that our approach outperforms all the baselines, which demonstrates the effectiveness of emphasizing dark regions during optimization.\n\n| Losses                                                       | PSNR$\\uparrow$     | SSIM$\\uparrow$      |\n| ------------------------------------------------------------ | --------- | --------- |\n| $\\mathcal{L}\\_{\\mathcal{L}_1}+\\mathcal{L}\\_\\text{ms-ssim}$     | 29.35     | 0.892     |\n| $\\mathcal{L}\\_{\\text{reg-}\\mathcal{L}_1}+\\mathcal{L}\\_\\text{ms-ssim}$ | 29.60     | 0.910     |\n| $\\mathcal{L}\\_{\\mathcal{L}_1}+\\mathcal{L}\\_\\text{reg-ms-ssim}$ | 30.41     | **0.923** |\n| $\\mathcal{L}\\_{\\text{reg-}\\mathcal{L}_1}+\\mathcal{L}\\_\\text{reg-ms-ssim}$ | **30.47** | **0.923** |\n\n---\n\n>  **W2:** Necessity of the depth ranking loss\n\nThe depth ranking loss is necessary. After averaging over multiple runs, the depth-ranking loss delivers a modest 0.083 dB PSNR improvement on the reconstruction benchmark. More importantly, it effectively separates medium from object, suppressing color-weak semi-transparent floating Gaussians (i.e., the WaterSplatting in Fig. 3) and thereby markedly enhancing the quality of de-scattered images. To validate the efficacy of the depth-ranking loss $\\mathcal{L}\\_\\text{depth}$ for the restoration task, we conducted controlled experiments on our simulated dataset (which has the de-scatterred GT for quantitative evaluation), comparing the full model (w/ $\\mathcal{L}\\_\\text{depth}$) against a baseline (w/o $\\mathcal{L}\\_\\text{depth}$) and reporting the average PSNR$\\uparrow$ value across two scenes and two degradation types. As illustrated in the following tables, the inclusion of depth-ranking loss yields a noticeable improvement in restoration quality.\n| EXP | easy | medium | hard | \n| ------ | ------ | ------ | ------ |\n| w/o $\\mathcal{L}\\_\\text{depth}$ | 26.068 | 24.212 | 22.256 |\n| w/ $\\mathcal{L}\\_\\text{depth}$ | **26.610** | **24.859** | **23.064** |\n\n\n---\n\n>  **L1:** Does the proposed method could also be applied to other similar problems, such as dehaze etc?\n\nYes, the proposed method could be applied to the dehazing task, since the light propagation in both fog and water obeys Eq. 2. As mentioned in Lines 203–205 of the main paper and Sec. B of the supplementary material, our simulated dataset considers two types of media, including fog and water. Tab. 2 demonstrates our superior performance on the simulated dataset, while Figure 5 in the main paper and Fig. 17 in the supplementary material further validate the dehazing capability of our approach. In addition, the real-world 3D dehazing is worth future study."}, {"review_id": "Uy9OczHW5M", "reviewer": "Reviewer_Q9a1", "summary": "The manuscript presents an underwater 3D scene reconstruction method that models objects using a 3D Gaussian Splatting (3DGS) representation, while encoding view-dependent scattering properties of the medium on a voxel grid as opposed to WaterSplatting which represents the medium as an MLP. This grid is interpolated to enable continuous estimation of the medium’s spatio-angular optical characteristics. To initialize the 3DGS representation, the method leverages both COLMAP and monocular depth estimation techniques. The manuscript claims all these tricks enable faster and more accurate reconstructions compared to state-of-the-art methods such as SeaThru-NeRF and WaterSplatting. However, the fairness of the comparisons is questionable.", "questions": "Please answer the questions asked in the weakness section.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**strengths** \n\n1. The authors shared code in the supplementary. While I didn't try it out myself, I believe that they code runs fine. Assuming that the authors make the code publicly available, the technique is replicable. \n2. Quantitatively, the proposed technique is faster and results in better reconstructions.\n3. Ablation studies show that all three contributions: (i) Plenoptic medium representation (ii) monocular depth initialization (iii) depth regularized loss helps quantitatively. \n\n**weaknesses**\n1. Line 143-8: As monocular depth estimates are trained on clean images (non-underwater images), won't they get affected by degradation as well? So, I am unsure if it is fair to state that degradation affects colmap but not this technique. Instead, I guess that more independent estimates (one from colmap and another from depth priors) is helping this technique. As such, if one were to try this on non-underwater (non-degraded images), they probably will have better initialization and hence, better results as well. Not a negative point to the manuscript but the claim is probably not accurate and can be more generic. \n2. Eq. 9: Are these k and b voxel or Gaussian dependent? Given that underwater degradation varies from depth plane to depth plane, does it make sense to have this correction for each depth plane? If k and b are global, what are typical k and b values. Are they significantly different from 1 and 0?\n3. Fig 3: The depth map comparison is super unfair. Of course the proposed technique will result in better results given that the proposed technique uses depth anything for initialization, it has scaled it and the manuscript is using the same model for validation.A fairer comparison is to do an affine alignment between GT and the past methods (assuming that k and b are constant for all depths for Plenodium) and see if the error is just in affine alignment\n4. Fig 4: \"Plenodium generates results with more reasonable exposure and accurate colors.\"  I am unsure how the manuscript is claiming that without ground truth.- Also, I don't buy that Plenodium generates better results and natural color fidelity (Line 255). There is a standard color checkerboard in this scene. One can retrieve and check if the colors are accurate. The proposed Plenodium actually has poorly retrieved colors in the color checkerboard. \n5. Line 227-228: how is it simulated? Is multipath considered? If not there is no model mismatch and of course this technique works the best. \n6. In Fig 5. what does \"easy-->hard\" mean? Poor illumination? Is Poisson noise added when the illumination is reduced. \nLine 256-259: can't we do simple color and exposure correction before comparing? Also white balancing. \n\ntypos: Line 260: \"Additionally, it and retains\" --> \"Additionally, it retains\"", "was_revised": true, "final_justification": "The rebuttal answers the questions that I had, and I keep my original accept rating. \n\nHowever, the final version should consider (1) highlighting that ground truth comparisons of medium parameters are missing (though not required for novel view synthesis) as pointed by dxfw reviewer, and (2) compare the color reconstructions using the checkerboard pattern in Fig. 3. results.", "rebuttal": "# Response to Reviewer Q9a1\n\nWe sincerely thank the reviewer for the constructive comments. We provide the detailed responses to all the concerns below.\n\n> **W1:** Will the depth estimator get affected by degradation?\n\nThe monocular depth estimator (Depth Anything Model) exhibits negligible degradation-induced error. For systematically quantifying the effects of degradation on 3D reconstruction, we simulated a dataset with a controllable scattering medium as shown in Line 205 of our main paper and Sec B.1 of our supplementary material. While Fig. 10 in the supplementary material shows COLMAP’s progressive degradation under increasing medium density, Fig. 11 in the supplementary material reveals that the same degradation levels leave the depth predictor almost intact (despite being trained solely on clean images), and the accompanying Pearson-coefficient analysis ( > 0.99 across all conditions) further quantitatively confirms this robustness. These results establish the theoretical basis for employing depth priors within our Pseudo Depth Gaussian Complementation (PDGC) to refine COLMAP-derived initializations.\n\n\n---\n\n> **W2:** Details of $k$ and $b$ in Eq. 9. \n\n+ First, we would like to clarify that the pseudo-depth correction in Eq. 9 is only employed in our Gaussian initialization, which proceeds in two stages as shown in Fig. 2(a).\n  1. Stage 1: A sparse point cloud extracted by COLMAP from the input images yields initial Gaussians with positions and default opacity, which we immediately use to render depth by Eq. 8;\n  2. Stage 2: We then augment this set with additional Gaussians placed in poorly initialized regions, guided by corrected pseudo-depth (i.e., Eq. 9) from the Depth Anything  Model. \n\n+ Second, we clarify more details about  $k$ and $b$ in Eq. 9.\n  + $k$ and $b$ are dependent but not only dependent on the Gaussian. $k$ and $b$ are determined jointly by the pseudo-depth predicted by the Depth Anything model and the depth rendered from the Gaussians at the identical viewpoint, as prescribed by Eq. 10.\n  + It is necessary to correct each pseudo-depth. Because pseudo-depth values are metric (often hundreds of meters), whereas the Gaussian primitives reside in the canonical cube [−1, 1]$^3$. We therefore correct the pseudo-depth into this normalized space using the scaling transformation with the $k$, $b$ defined in Eq. 10.\n  + Each pseudo-depth map possesses its own unique $k$ and $b$ to ensure an accurate alignment with the canonical coordinate system.\n\n---\n\n> **W3:** In Fig. 3, the depth map comparison is super unfair. \n\nThis comparison is fair. Consistent with all baselines, we enforce no explicit alignment between depth planes and Depth-Anything predictions. The scaling by Eq. 9 is only used in the Gaussian initialization, which merely rescales pseudo-depth into the canonical cube, as detailed in **W2**. Meanwhile, the GT depth in Fig. 3 is supplied purely as a visual reference; higher similarity to GT does not indicate superiority. Instead, we conduct a horizontal evaluation, examining which depth map among all methods is most reasonable. This side-by-side evaluation confirms that our method yields noticeably cleaner backgrounds than WaterSplatting[1].\n\n---\n\n> **W4:** How to compare the visual result without GT?\n\n+ We conduct a horizontal evaluation. Since no ground-truth image is available for the restoration shown in Fig. 4, we compare the outputs of all methods under identical inputs. Relative to ours, WaterSplatting [1] retains a seawater tint (highlighted in the red box), whereas SeaThru produces an under-exposed result in distance. \n+ Color-checker evaluation is inherently unreliable on the SeaThru-NeRF [2] dataset, as the images were never white-balanced against the checker. As shown in the GT of Fig. 3, the first row of the checker (intended to run from white to black) exhibits a noticeable blue cast in its mid-gray patch. Our result has achieved the highest fidelity to the ground-truth, confirming the accuracy of our color correction.\n\n---\n\n> **W5:** How is the simulated dataset simulated?\n\n+ Our synthetic data were rendered in Blender (Line 203), while the scattering medium is simulated using the Principled Volume element; further details are provided in Sec. B.1 of our supplementary material.\n+ Each scene contains a single path, as shown in Fig. 8 in our supplementary material. \n+ We have a fair comparison. The dataset is built with Blender’s built-in functions rather than to match any specific model, ensuring a fair setting for all compared methods.\n\n---\n\n\n> **W6:** In Figure 5,  what does \"easy-->hard\" mean? & why not correct before visual comparison?\n\n+ The *easy*, *medium*, and *hard* present different intensity levels of medium (Line 205), which are obtained by setting the density parameter of the *Principled Volume*. \n\n+ To ensure a fair visual comparison in Fig. 5, all methods receive the same inputs, and no additional visual adjustments are performed for the qualitative comparison. While color casts and exposure shifts can affect quantitative evaluation as your concern, the Blender pipeline guarantees that the ground-truth and degraded images share identical white-balance matrices; their exposure parameters differ only to compensate for scene-specific luminance and maintain a consistent overall exposure value. Consequently, we retain the original white balance and merely apply a global luminance scaling to compute the metric between each restored image and its corresponding GT (Lines 210–211)."}, {"review_id": "ZT4QRbuDPc", "reviewer": "Reviewer_8g2B", "summary": "This paper proposes a novel view synthesis algorithm for underwater scenes. Compared to prior work, it uses a grid-based spherical harmonic spatial discretization (as opposed to an implicit neural network) to store medium information, encodes positional as well as directional dependences, and improves the initialization process. It is shown to improve or match the reconstruction accuracy of previously existing methods while cutting the runtime by a significant amount.", "questions": "- As someone who has not worked on this problem before, I was surprised to hear that that scattering effects were dependent on the viewing position as well as the direction (Sec. 1 and 4.1). I do not doubt that this is the case, but I would love to see (here and in the paper) a citation justifying this!\n- I would have appreciated more evaluation of the grid discretization. What is the grid size used in the results? Is it always a regular grid? In cases where the medium changes drastically and irregularly, can this method suffer due to not being able to concentrate resolutive power the same way that an MLP can?\n- This is probably my own limitation, but I was not able to follow Sec. 4.2. If this is about how the Gaussians are initialized, what does it mean to “render the pixel-wise depth”? If we are in the initialization step, isn’t alpha_i and z_i not defined yet? Also, if \\tilde{D} is estimated using Depth Anything, why does it depend on (x,y) in Eq. 10? I am sure I am missing something obvious, but I would really appreciate if this section was rewritten to be easier to follow.\n- In Fig. 1, what is the difference between reconstruction and restoration? Is one 3D and the other 2D? The figure is otherwise clear and a very helpful visualization, but those two words confused me a bit.", "limitations": "See “weaknesses”. Strangely, limitations are not discussed anywhere in the manuscript.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "It seems to be like the main strength of the paper is the spherical harmonic discretization of the medium parameters, as well as the performance improvements that result from it. Together with the produced dataset, I am confident that this work is an interesting contribution to this research problem that may inspire future work. In general, I think exploring differentiable discretizations different from implicit MLPs that encode problem priors to improve efficiency and accuracy is a worthwhile pursuit in many applications, and I am encouraged to see it applied here. It is possible that the initialization strategy is a fundamental novel contribution as well; unfortunately, I was not able to understand it very well (see “Questions”).\n\nThe main weakness of this manuscript is in its comparison to WaterSplatting, which has similar runtime requirements and very similar performance (in Table 1, one often has to go to the fourth significant digit to see an accuracy difference). There is a chance I misunderstood this and the result in Table 1 is of WaterSplatting combined with the SH discretization (Sec 7 says “a 47% speedup relative to WaterSplatting”, but it seems to me like this refers to rendering only, not training. Could one train WaterSplatting and then save the information on a grid to render efficiently?), and I will gladly listen to the authors’ response to see if this is the case.", "was_revised": true, "final_justification": "The method is technically solid and improves the state of the art for an important task. The authors have satisfied most of my concerns and I remain positive about this work", "rebuttal": "# Response to Reviewer 8g2B\n\nWe sincerely thank the reviewer for the constructive comments. We provide the detailed responses to all the concerns below.\n\n> **W1:** Comparison to WaterSplatting.\n\n+ As shown in Tab. 1, our method outperforms WaterSplatting by a large margin, increasing the PSNR by at least 0.317 dB and on average 0.872 dB.\n+ Compared to WaterSplatting, our Plenodium in the Tab. 1 replaces the view-dependent medium modeling (implemented by MLP) by our proposed plenoptic medium representation (implemented by multiple SH), improves the initialization with our Pseudo-Depth Gaussian Complementation, and trains them with our proposed loss terms. Note that the plenoptic medium representation improves both rendering and training efficiency (refer to “MLP w/ dir” vs. “SH w/ dir&pos” in Tab. 3). While as shown in Tab. 6, the regularized multi-scale differentiable SSIM loss (i.e., $\\mathcal{L}\\_\\text{reg-ms-ssim}$ in Eq. 13) raises training time by 0.9min yet delivers a fidelity improvement.\n+ The suggested approach to improve the rendering efficiency is technically feasible. However, converting WaterSplatting’s MLP into spherical-harmonics coefficients can introduce approximation errors. For practitioners who prioritize rapid convergence, we recommend the variant of our method that adopts the single scale regularized differentiable SSIM loss (i.e., $\\mathcal{L}\\_{\\text{reg-}\\mathcal{L1}}$&$\\mathcal{L}\\_\\text{reg-ssim}$&$\\mathcal{L}\\_\\text{depth}$ in Tab. 6), which trains faster than the original WaterSplatting pipeline, renders more efficiently, and simultaneously yields higher reconstruction quality.\n\n\n---\n\n> **Q1:** Citations to justify that scattering effects were dependent on the viewing position as well as the direction.\n\nPrior works [40, 41] assumed homogeneous media, whose optical properties are invariant to both the viewing position and direction. SeaThru-NeRF [2] then introduced the directional anisotropy. We further extend the model to account for the spatially-varying position, enabling full heterogeneous medium representation. Thus, as far as we know, we are the first to introduce the spatially-varying medium properties, whose effectiveness is discussed in Sec. 6 and validated in Tab. 3.\n\n---\n\n> **Q2:** More evaluation of the grid discretization. \n\n+ The grid spans the 3D cube $[−1, 1]^3$, as specified in Eq. 7, yielding a total volume of $2 \\times 2 \\times 2$.\n+ We use the regular grid in our manuscript; however, it could be extended. Note that the stable optimization of parameters requires that the number of grid vertices be smaller than the number of input images. As the training set of the SeaThru-NeRF [2] dataset contains only ~20 views, we adopt a single 3D grid and bilinear interpolation. Note, when denser multi-view data are available, the representation can employ multiple grids and more sophisticated interpolation schemes.\n+ Higher-order spherical harmonics allow our method to concentrate resolutive power adaptively, as an MLP can do. As illustrated in Fig. 12 of our supplementary material, raising the maximum SH degree captures finer angular detail and improves reconstruction. Yet it also raises computational cost and overfitting risk.\n\n---\n\n> **Q3:** How are the Gaussians initialized?\n\n+ First, we would like to clarify our Gaussian initialization, which proceeds in two stages as shown in Fig. 2(a).\n\n    1. Stage 1: A sparse point cloud extracted by COLMAP from the input images yields initial Gaussians with positions and default opacity, which we immediately use to render depth by Eq. 8;\n\n    2. Stage 2: We then augment this set with additional Gaussians placed in poorly initialized regions, guided by corrected pseudo-depth (i.e., Eq. 9) from the Depth Anything Model.\n\n+ Then we clarify more details.\n\n  + We render the pixel-wise depth map using the initialized Gaussian estimated from COLMAP-initialized point clouds. Each primitive is endowed with a 3D position and a default opacity of 0.1, enabling direct depth-map synthesis via Eq. 8.\n\n  + We obtain per-image correction coefficients via Eq. 10 to rescale $\\tilde D$ into the canonical space. Pseudo-depth values are metric (often hundreds of metres), whereas the Gaussian parameters reside in the canonical cube [−1, 1]$^3$. We therefore correct the pseudo-depth into this normalized space using the scaling transformation (i.e., Eq. 9) with the parameter defined in Eq. 10.\n\n  We will clarify them in the revised paper and rewrite Sec. 4.2 to make it easier to follow.\n\n---\n\n> **Q4:** What is the difference between reconstruction and restoration in Fig. 1?\n\n  The goal of 3D scene reconstruction is to create a novel 3D model approximating the real-world scene's structure and appearance, typically using sensor data (e.g., multiple 2D images). While the goal of restoration is to restore and enhance an existing 3D scene model that is degraded and corrupted (e.g., by severe weather or underwater effects).\n\n  In this paper, we jointly address these two tasks: 3D scene reconstruction and restoration. First, our approach constructs the 3D scene based on Eq. 5, which enables novel-view synthesis. After completing the 3D scene reconstruction, Eq. 1 can be invoked to disregard the medium and render de-scattered images, thereby accomplishing image restoration, as illustrated in Figs. 4 and 5. \n\n---\n\n> **L1:** Limitations are not discussed anywhere in the manuscript.\n\nWe have discussed the limitations of our method in Sec. C.6 of the supplementary material."}, {"review_id": "NqbQqvxtB4", "reviewer": "Reviewer_dXFw", "summary": "This paper proposes a novel-view synthesis method for participating media based on 3D Gaussian Splatting (3DGS). The primary contribution lies in modeling spatially-varying and directionally-dependent scattering coefficients using spherical harmonics (SH) encoding (Plenodium), which enables the representation of heterogeneous participating media. Compared to previous MLP-based approaches for participating media, Plenodium achieves superior scene reconstruction quality and faster rendering speed.", "questions": "- I suggest visualizing the learned SH coefficients, especially on synthesized heterogeneous media, to strengthen the claim that the method effectively models heterogeneous participating media.\n- Please clarify the input to PDGC. Does it require initial Gaussian primitives to be estimated? If so, does the reported training time include the time needed for this initial estimation?\n- If there are any novel aspects or design elements specific to underwater scenarios in PDGC or the proposed depth-ranking loss compared to prior densification techniques for sparse-view scenarios or existing depth-ranking losses (e.g., in FSGS and SparseNeRF), please clarify them. If not, I recommend refraining from presenting them as technical contributions (e.g, Line 67: \"To improve ..., we introduce a pseudo-depth Gaussian complementation ... and a depth ranking loss ...\").", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "[Strengths]\n\n- The main technical contribution lies in leveraging spherical harmonics (SH) encoding without relying on MLPs to model spatially-varying and directionally-dependent scattering effects in heterogeneous participating media. This design choice is simple yet well-motivated, given the established effectiveness of SH representations in prior works such as Plenoxels [CVPR’22] and TensoRF [ECCV’22]. (Originality, Quality)\n- The proposed method outperforms SeaThru-NeRF and WaterSplatting--state-of-the-art approaches for underwater novel-view synthesis--in both reconstruction quality and rendering efficiency. Since underwater imaging remains a challenging, these results may encourage further research and adoption in real-world aquatic vision systems.\n(Quality, Significance)\n\n[Weaknesses]\n- The primary weakness of the paper lies in the lack of detailed analysis to support its central motivation. While the use of spatially-varying SH encoding is intended to represent heterogeneity in participating media, the evaluation focuses solely on novel-view quality. Prior studies have already demonstrated that SH encoding improves scene representation compared to MLPs in natural scenes. As a result, it remains unclear whether the improvements are indeed due to modeling heterogeneous media or merely the general advantages of SH. To support the motivation more convincingly, further experiments--such as synthesizing clearly heterogeneous media (the current simulation dataset appears to depict homogeneous media) and visualizing the learned SH coefficients--would be valuable. (Quality, Originality)\n- The proposed pseudo-depth Gaussian Complementation (PDGC) in Sec. 4.2 is technically unclear. As shown in Fig. 2, PDGC initially increases Gaussian primitives derived from COLMAP based on monocular depth from DepthAnything. However, to compensate for the scale ambiguity, the scene depth should be computed as in Eq. (8), which requires Gaussian primitives with learned depth and opacity--not merely initial estimates--contradicting the inputs illustrated in Fig. 2. If the proposed method requires initial Gaussian estimates, does the reported training time include the entire training process? Additionally, the expression “COLMAP-initialized Gaussian primitives” (e.g., Line 69) is confusing. I recommend using “Gaussian primitives estimated from COLMAP-initialized point clouds.” It is also unclear what actual parameter values are assigned to the Gaussians inserted by PDGC. (Clarity, Quality)\n- Although the paper introduces PDGC and a depth-ranking loss, their novelty appears limited. The issue of insufficient initial SfM points has been addressed in the context of sparse-view reconstruction; to claim technical novelty, comparisons with existing approaches such as the graph-based densification in FSGS [ECCV’24] are necessary. Additionally, the proposed depth-ranking loss is nearly identical to that used in SparseNeRF [ICCV’23]. (Originality, Significance)\n- Minor errors\n    - Line 128 refers to (x,y,z) as the observer’s spatial coordinates, while Line 134 uses it to denote the backscatter position.\n    - In Fig. 3, “Depth Any Model” should be corrected to “Depth Anything Model.”", "was_revised": true, "final_justification": "After reading the rebuttal and engaging in further discussion with the authors, my main concerns have been largely addressed. Specifically, the authors provided an extended analysis demonstrating a statistically significant correlation between the learned SH coefficients and the density parameters of heterogeneous media in simulated scenes.  I am inclined to recommend acceptance.", "rebuttal": "# Response to Reviewer dXFw\n\nWe sincerely thank the reviewer for the constructive comments. We provide the detailed responses to all the concerns below.\n\n> **W1:** Lack of a detailed analysis to support the motivation of our plenoptic representation (i.e., the effect of heterogeneous media modeling vs SH encoding).\n\n+ The improvements of our approach stem from not only the advantages of SH but also modeling heterogeneous media. As shown in Tab. 3, compared to MLPs, SH encoding indeed improves the scene representation ability, increasing the PSNR by 0.524 dB (refer to \"MLP w/ dir\" vs. \"SH w/ dir\" in Tab. 3). In addition, compared to a homogeneous baseline (i.e., \"SH w/o dir&pos\" in Tab. 3), incorporating the directional anisotropy (i.e., \"SH w/ dir\" in Tab. 3) and the spatially-variant property (i.e., \"SH w/ pos\" in Tab. 3) increase the PSNR by 0.621 dB and 0.293 dB, respectively. When both the directional and positional information are jointly encoded (i.e., \"SH w/ dir&pos\" in Tab. 3), the cumulative gain reaches 0.754 dB, confirming that comprehensive heterogeneous modeling is essential for accurate scene reconstruction.\n+ Our simulated dataset explicitly models heterogeneous media, which is implemented by the *anisotropy* parameter of the *Principled Volume* as well as *Texture Corrdinate* using Blender (Lines 76–77 and Sec. B.1 in our supplementary material).\n\n+ We visualize the learned SH coefficients of Eq. 6 (only the direction current component) in the following table. Their non-uniform values at the eight grid vertices confirm that the learned medium is heterogeneous.\n\n  | Pos        | $A^{c^{med}}$ (SH for medium color)            | $A^{c^{att}}$ (SH for object attenuation)               | $A^{c^{bs}}$  (SH for medium backscatter)              |\n  | ---------- | --------------------------- | --------------------------- | --------------------------- |\n  | [-1,-1,-1] | [-0.8398, -0.5495, -0.2319] | [-4.4626, -5.1525, -5.4686] | [-3.5283, -3.7398, -3.9918] |\n  | [1,-1,-1]  | [-1.1547, -0.9677, -0.7678] | [-4.6882, -5.6180, -6.0288] | [-3.6346, -3.8946, -3.9502] |\n  | [-1,1,-1]  | [-0.7586, -0.8084, -0.6472] | [-4.5747, -5.7520, -6.0402] | [-4.5726, -4.2947, -4.2186] |\n  | [1,1,-1]   | [-1.1530, -1.0041, -0.8348] | [-5.4690, -6.3593, -6.5371] | [-4.2445, -3.6186, -3.2268] |\n  | [-1,-1,1]  | [-1.0325, -0.7321, -0.3701] | [-4.9317, -5.5160, -5.7383] | [-3.0611, -3.2200, -3.6581] |\n  | [1,-1,1]   | [-1.5311, -1.3408, -1.0695] | [-5.3027, -6.1486, -6.4818] | [-2.9159, -3.1454, -3.3973] |\n  | [-1,1,1]   | [-1.0523, -0.9408, -0.7582] | [-5.4642, -6.2606, -6.4235] | [-3.7325, -3.4505, -3.7295] |\n  | [1,1,1]    | [-1.4284, -1.0559, -0.8024] | [-6.0865, -6.6113, -6.6812] | [-3.4898, -2.9542, -2.8887] |\n\n---\n\n> **W2:** PDGC is technically unclear.\n\nFirst, we would like to clarify the procedure of our Pseudo-Depth Gaussian Complementation (PDGC), which is also detailed in Sec. A.2 and Alg. 1 in our supplementary material:\n1. Estimate the pseudo-depth and render the depth map based on Eq. 8;\n2. Correct pseudo-depth based on Eq. 9 and Eq. 10;\n3. Get the region to insert Gaussian (Lines 158-160 of the main paper);\n4. Add the Gaussian with attributions: 3D mean position $\\mu$ (Eq. 14), color feature $A$ (Eq. 14), covariance matrix $\\Sigma$ (Eq.15) and opacity $\\sigma$ (0.1).\n\nSecond, we clarify more details about our PDGC.\n+  In this process, we don't need the learned position and opacity for Gaussian. We adopt the 3D positions provided by COLMAP and an initialized Gaussian opacity  (default to 0.1). The factor $1/(1−T^{obj}_{N+1})$ in Eq. 8 compensates for this inaccurate opacity initialization, ensuring accurate rendering depth. \n+ The actual parameter values assigned to the Gaussians are detailed in the sec. A.2 of our supplementary material. And we also list it below:\n$$\\mu = W^T \\cdot\n    \\begin{bmatrix}\n        \\tilde{D}'{(x,y)}\\cdot x \\\\\\ \\tilde{D}'{(x,y)}\\cdot y\\\\\\ \\tilde{D}'{(x,y)}\n    \\end{bmatrix} +\n    \\begin{bmatrix}\n        x_c \\\\\\y_c\\\\\\z_c\n    \\end{bmatrix},$$\nwhere $(x,y)$ is the pixel position, $W$ is the camera transform matrix, and $[x_c, y_c, z_c]^T$ is the camera position, and $\\tilde{D}'$ denotes the corrected pseudo-depth map.\n$$A=\\text{RGB2SH}(C(x,y)),$$\nwhere the function RGB2SH maps RGB values to 0th-order spherical harmonics coefficients.\n$$\\Sigma = R S S^T R^T, \\quad S = \\text{diag}(s, s, s), \\quad s = \\frac{\\tilde{D}'(x,y)\\cdot(f_x + f_y)}{h + w},$$\nwhere $R$ is initialized randomly, the scalar $s$ adapts the Gaussian size to the scene depth, while considering focal lengths $(f_x,f_y)$ and image dimensions $(h,w)$.\n + PDGC takes pre-initialized Gaussian primitives, along with all input views and their corresponding RGB images as input.\n+  The process only takes a few seconds, including COLMAP estimating sparse points, Depth Anything model estimating pseudo-depth, and the other parts of PDGC. \n\n---\n\n> **W3:** The novelty of PDGC and a depth-ranking loss appears limited (i.e., lack of comparison with existing approaches [ref1, ref2]).\n\n+ Comparison between our PDGC and the graph-based densification (i.e., Gaussian Unpooling (GU)) in FSGS [ref1]. PDGC is executed once at initialization: it identifies undersampled or poorly initialized areas (mainly outside the initial point cloud) and inserts new Gaussians there based on the pseudo-depth. In contrast, graph-based GU densification runs throughout training, inserting a child Gaussian between each parent and its nearest neighbor, thereby densifying the existing Gaussian set. To quantitatively compare PDGC against GU, we conduct controlled experiments on the \"IUI3-RedSea\" scene and compare our Plenodium with two baselines that respectively remove our PDGC (i.e., Plenodium w/o PDGC) and replace our PDGC with GU (i.e., Plenodium w/o PDGC \\& w/ GU ) while keeping all subsequent training settings identical. Compared to GU only using the COLMAP information, our PDGC further leverages an additional depth prior, thereby delivering superior quantitative results as illustrated in the following table.\nMoreover, GU introduces a large number of Gaussians at initialization, yet yields negligible gains in final reconstruction quality and leaves the final Gaussian count almost unchanged.\n\n|  | PSNR$\\uparrow$ | SSIM$\\uparrow$ | # Gaussian (init./final) |\n| ------ | ------ | ------ |------ |\n| Plenodium w/o PDGC | 30.176 | 0.890 | 21,907/857,571|\n| Plenodium w/o PDGC \\& w/ GU | 30.210 | 0.890 | 77,830/861,567 | \n| Plenodium (ours) | **30.275** | **0.895** |  22,669/860,219  |\n\n\n\n+ Comparison between our depth ranking loss and the depth ranking regularization from SparseNeRF [ref2]. Unlike the depth-ranking regularization $\\mathcal{R}\\_{rank}=\\sum\\_{d^{k1}\\_{dpt}\\le d^{k2}\\_{dpt}} \\text{max}(d^{k1}\\_{\\textbf{r}}- d^{k2}\\_{\\textbf{r}}+ m,0)$, which employs a margin term $m$ to suppress overfitting to inaccurate pseudo-depth, we instead rely on downsampling. As shown in Fig. 13 of our supplementary material, experiments with varying resolutions reveal that a resolution of $N =16$ effectively filters unreliable pseudo-depth, whereas the SparseNeRF formulation (pair-wise loss) incurs an out-of-memory error at 256×256 (Line 135 in our supplementary material), underscoring the efficiency and practicality of our depth-ranking loss for high-definition scenes.\n  \n[ref1] Zhu Z, Fan Z, Jiang Y, et al. Fsgs: Real-time few-shot view synthesis using gaussian splatting[C]//European conference on computer vision. Cham: Springer Nature Switzerland, 2024: 145-163.\n\n[ref2] Wang G, Chen Z, Loy C C, et al. Sparsenerf: Distilling depth ranking for few-shot novel view synthesis[C]//Proceedings of the IEEE/CVF international conference on computer vision. 2023: 9065-9076."}]

Author rebuttal:

Meta-review: This paper proposes Plenodium, a framework for underwater 3D scene reconstruction that introduces a plenoptic medium representation based on spherical harmonics, a pseudo-depth Gaussian complementation (PDGC) for initialization, and a depth-ranking loss. The method shows improved accuracy and efficiency over comparison methods on synthetic and real-world datasets.

The reviewers’ main concerns were (1) the limited analysis of heterogeneous medium modeling, (2) the novelty of PDGC and the depth-ranking loss, (3) the evaluation of color fidelity, and (4) unclear explanations of some technical details. In the rebuttal, the authors provided additional experiments (e.g., color checkerboard evaluation, SH coefficient analysis on simulated heterogeneous media) and clarifications, which convinced the reviewers. After the discussion, all leaned toward acceptance.

The final version should incorporate the revisions outlined in the authors’ final remarks.
Decision: Accept (poster)