Uncertainty-Aware 3D Reconstruction for Dynamic Underwater Scenes
Authors: Rui Liu
Zhibo Duan
Jianzhe Gao
Yi Yang
Wenguan Wang
Venue: ICLR 2026 Poster (2026)
Keywords: Underwater Reconstruction
Dynamic Reconstruction
Primary area: applications to robotics, autonomy, planning

Abstract: Underwater 3D reconstruction remains challenging due to the intricate interplay between light scattering and environment dynamics. While existing methods yield plausible reconstruction with rigid scene assumptions, they struggle to capture temporal dynamics and remain sensitive to observation noise. In this work, we propose an Uncertainty-aware Dynamic Field (UDF) that jointly represents underwater structure and view-dependent medium over time. A canonical underwater representation is initialized using a set of 3D Gaussians embedded in a volumetric medium field. Then we map this representation into a 4D neural voxel space and encode spatial-temporal features by querying the voxels. Based on these features, a deformation network and a medium offset network are proposed to model transformations of Gaussians and time-conditioned updates to medium properties, respectively. To address input-dependent noise, we model per-pixel uncertainty guided by surface-view radiance ambiguity and inter-frame scene flow inconsistency. This uncertainty is incorporated into the rendering loss to suppress the noise from low-confidence observations during training. Experiments on both controlled and in-the-wild underwater datasets demonstrate our method achieves both high-quality reconstruction and novel view synthesis.

Published as a conference paper at ICLR 2026
UNCERTAINTY-AWAS 3D RECONSTRUCTION FOR DYNAMIC UNDERWATER SCENES
Rui Liu"
Zhibo Duan'
Jianzhe Gao
Wenguan Wang
Yi Yang
The State Key Lab of Brain-Machin Intelligence, Zhejiang University, Hangzhou, China
https://underwart deserr-ddyniiiiiiiee beleed.githuul www.ggithh..oooo io/UDF
ABSTRACT
Underwater 3D reconstruction remains challenging due to the intricate interplay between light scattering and environment dynamics. While existing methods yield plausible reconstruction with rigid scene assumptions, they struggle to capture temporal dynamics and remain sensitive observation noise. In this work, we propose an Uncertainty-awes awaree Dynamic Field (UDF) that jointly represents under- water structure and view-dependent medium over time. A canonical underwater representation is imitialized using a set of 3D Gaussians embedded in volumetric medium field. Then we map this representation into a 4D neural voxel space and encode features, a deformation network and a medium offset network are proposed to model transformations of Gaussians and line-conditioned updates medium properties, respectively. To address input-dependent noise, we model per-pixel uncertainty guided by surface-vies radiance ambiguity and inter-frame scene flow inconsistency. This uncertainty is incorporated into the rendering loss to suppress the noise from low-confidence observations during training. Experiments on both controlled and in-the-wild underwater datasets demonstrate our method achieves both high-quality reconstruction and novel view synthesis.
features by querying the voxels. Based on these
INTRODUCTION
Background. Underwater 3D reconstruction is foundational yet underexplored problem across diverse applications, including marine ecological monitoring [1] and autonomous navigation [2-4]. Recent advances in 3D reconstruction, such neural radiance fields (NeRF) [5] and 3D Gaussian Splatting (3DGS) [6]. have demonstrated remarkable ability to recover geometry and synthesize photorealistic views across both static and dynamic scenes. However, these methods are typically developed for clear-air environments, assuming zero-density medium [7]. In underwater imaging, both object surfaces and the participating water volume affect image intensities [8]. a result, directly applying vanilla NeRF or 3DGS to underwater data confuses geometric cues with medium- induced attenuation, leading to degraded reconstruction quality.
Motivation. Underwater imaging involves complex interplay between light scattering and en- vironment dynamics [9]. Specifically, the radiance along camera ray comprises direct reflection from scene surfaces and accumulated scattering from surrounding water volume. Recent studies on underwater reconstruction either adopt learnable medium parameters during rendering [10, 11]. employ binary motion masks for moving objects [12-14]. While these methods yield promising results, two key challenges remain (Fig. 1). Underwater environments often exhibit complex dy- namic phenomena, such as object motion, surface deformations, and time-varying medium properties. As the participating medium induces wavelength-depenin scene geometry and appearance under such non-rigid dynamic scenes is non-trivial [15]. @ Real- world underwater observations, especially from in-the-wild videos, suffer from degraded visibility and random perturbations [14, 16, 17]. Due to varying noise levels across viewpoints and frames, recovering geometry from such uncontrolled data will introduce ghosting artifacts and temporal in-
attenuation and scattering, modeling
'The first two authors contribute equally to this work.
1 "Correspnndigg author: Wenguan Wang.

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Published as a conference paper at ICLR 2026
water surface
backscattering
surface ambigurty
attenuation
camera
underwater imaging
moving objects and dynamic medium
mation-induced uncertainty
Figure 1: Challenges in dynamic underwater reconstruction. Underwater scenes contain moving objects and dynamic participating medium, where wavelength-udeeedeen attenuation and backscattering jointly degrade visibility. Our UDF explicitly models surface ambiguity and indion-induued uncertainty, which highlight regions where observations are unreliable. The rays schematic and do not depict exact physical light paths (sce $1).
consistency [18-20]. However, most reconstruction methods [10-12, 14] in underwater environments overlook this input-dependent uncertainty, limiting their adaptability ambiguous regions.
Method. To address these challenges, we propose an Uncertainty-wware Dynamic Field (UDF) for underwater reconstruction, built upon three key designs: unified dynamic underwater field that jointly represents time-varying 3D geometry and the participating medium, ii) motion-aware medium dynamics conditioned scene motion, and iii) an underwater-speciff heleroscedastic uncertainty formulation that explicitly models input-dependent ambiguity. For O, our unified dynamic underwater field captures the evolution of both Faussian-bbsee structure and view-dependent medium properties. Specifically, canonical underwater representation is initialized using a set of 3D Gaussian ellipsoids embedded within volumetric medium field ($3.1). Each Gaussian serves as an explicit geometric primitive, while the surrounding water volume is modeled by spectral neural field conditioned on ray directions. encode spatial-temporal features of underwater dynamics, we map this representation into a compact 4D neural voxel space via planar factorization [21]. Built upon this representation, a deformation network is proposed to predict both spatial motion and shape transformation of the 3D Gaussians. Meanwhile. the time- varying volumetric medium properties updated based motion vectors via a medium offset network ($3.2). This design enables a consistent representation of dynamic geometry and motion-aware medium for underwater reconstruction.
For @, we incorporate the heteroscedastic uncertainty into the rendering loss to mitigate the impact of input-dependent noise ($3.3). To estimate per-pixel confidence, we analyze two physically grounded cues, i.e., surface-view radiance ambiguity and inter-frame scene flow inconsistency. The first factor captures radiance ambiguity when the ray direction is closely aligned with the surface normal. In this case, scattering contributions are hard to disentangle from direct radiance, and high-free figh-frequency appearance variations can be misinterpreted as geometry [22-24]. To quantify this vien-dependent factor, we estimate pixel-wise radiance confidence using the angle discrepancy between the ray direction and a pseudo-norma derived from the depth gradient. The second factor accounts for temporal instability caused by inter-frame inconsistencies. Appearance shifts non-uniform motion across views result in ambiguous correspondence along motion trajectories. We estimate this factor using Horn-Sete Schunck flow-guided [25] approximation of scene dynamics. These two cues combined into a per-pit per-pixel variance term within a probabilistic rendering loss. This allows the model adaptively suppress the noise in ambiguous regions while maintaining physical plausibility.
Results. Our method is evaluated on both controlled underwater datasets [10] and in-the-wild video sequences [12, 26] ($4). UDF achieves high-fidelity reconstruction across diverse scenes, e.g., 30.17 PSNR and 0.885 SSIM on DRUVA[26], and 27.72 PSNR and 0.883 SSIM on NUSR[12]. Furthermore, UDF enables high-quality novel view synthesis under adverse visibility conditions.
RELATED WORK
NeRF and 3DGS for Static/Dynamic Scenes. NeRF [5] and its extensions [27-29] have demon- strated remarkable performance in static scene reconstruction and generation [30-36], but suffers
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from high rendering cost and slow optimization. Later, 3DGS [6, 37] is proposed as explicit alter- native, enabling real-time rendering via rasterization of Gaussian primitives. While early NeRF and 3DGS focus static scenes [38], recent efforts extend them to dynamic scenarios [39-41]. Dynamic NeRF approaches either encode time as input [42, 43] or decouple scene motion via deformation fields [44, 45J. 4D Gaussian Splatting (4DGS) methods [20, 46-58] model temporal dynamics by either deforming static Gaussian primitives or directly learning continuous spatial-tempora fields. Some works are further proposed to enhance these frameworks, including dynamic surface model- ing [59-62], temporal embeddings [63], and tracking- based correspondence [64, 65]. Despite these advances, most existing approaches operate under the clear-air assumption and fail to explicitly model medium-induced effects, thereby limiting their generalization to real-world underwater environments.
Underwater Scene Reconstruction. Underwater environments present unique challenges for 3D reconstruction due to light attenuation and scattering [66]. Traditional approaches address these degradations via model-free color correction [67-69] or physics-based enhancement [8, 16, 70, 71] on single images without explicit scene geometry modeling. Existing methods [10, 72-74] incorporate underwater light propagation into the volume rendering process. They adopt the revised underwater image formation model [9] to separate direct radiance from backscattering components within the NeRF pipeline. To improve reconstruction efficiency, some studies [11, 75-77] combine 3D Gaussian primitives with learnable medium features in underwater settings. Beyond static modeling, recent advances adopt dynamic NeRF [12, 13] or motion-aware 3DGS with binary masks [14] to handle dynamic elements. UDR-GS [78] directly employs 4DGS [46] with depth priors for basic motion modeling, yet ignores the influence of the participating medium during rendering. In this paper, we propose a unified dynamic field that jointly models underwater structure and medium over time, while incorporating uncertainty- optimization for underwater reconstruction.
Uncertainty in Reconstruction. Quantifying uncertainty essential to improve the robustmess of 3D scene reconstruction [18, 79-81]. For NeRF-based methods, early efforts adopt Bayesian formu- lations to estimate per-ray predictive variance [18, 82-85], providing probabilistic interpretations of scene geometry. Recent methods attempt to integrate uncertainty into 3DGS- frameworks, including variational inference [86-88], Fisher information [89], deep feature- based estimation [19], and uncertainty aware regularization [20, 90]. However, few methods address uncertainty under dynamic conditions, where both geometry and appearance evolve over time. In contrast, our method incorporates per- per-pixel uncertainty modeling by combining surface-vier radiance ambiguity and inter- frame flow inconsistency. These cues are integrated into a heteroscedastic rendering loss, allowing the model suppress the noise from low-confidence observations during training.
3 METHOD
Overview. Given set of RGB images with camera poses and normalized timestamps, our goal is to reconstruct dynamic underwater scenes by jointly modeling scene geometry, medium effects, and their temporal evolution. UDF contains 3D Gaussians G, a neural medium module Jmm spatial- temporal encoding, a deformation network D and a medium offset network D (Fig. 2). A canonical underwater representation is initialized using a set of 3D Gaussian ellipsoids G embedded within a encode this representation
volumetric medium field Fm ($3.1). ) To model temporal dynamics, into a -eataal-eemporl space. The come-conditionedd networks DE and Dm are used to predict the evolution of Gaussians and medium attributes, respectively ($3.2). To address observation noise, we incorporate heteroscedastic uncertainty into the rendering loss based on surface-view radiance ambiguity and inter-frame flow inconsistency ($3.3). Implementation details are provided in $3.4.
3.1 CANONICAL UNDERWATER REPRESENTATION
Volume Rendering with Medium. To model the underwater scenes, the physically realistic medium term is incorporated into the volume rendering equation [10, 91, 92]. Given an image pixel 2d e IR? the corresponding camera ray is defined r(s) + sws, where denotes the camera center and w is the ray direction. The color radiance C(r) along this ray results from the accumulated contributions of both underwater structure surfaces and surrounding water medium [10, 91, 92]:
C(r) = (r) + (.med()) =f0 T(s)( (s)c (s) + med (s)c med (s))
(1)
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Canonical Underwater Representation
Underwater Dynomics Modeling
Uncertainty Aware Optimization
AM(()
Spatial- Tempord Encoding
Deformation Network
Fig 8
55G)
AR(O)
Output
SFM Initializaaiinn Goussions 5
Equ
Eq. 12
Eq, 9 v(()
Rendering Loss with Uncertainty
Eq. 15
Eq. 13
do (1)
Neural Medium
grod
Medium Offset Network
Eq.
do sitt
Shored 4D Neural
Ar (t)
Roy
Vaxel Space
Ground Truth
Figure 2: Overview of UDF ($3). UDF begins with canonical underwater representation composed of 3D Gaussian primitives G initialized from SfM, and neural medium F conditioned on the ray direction w ($3. 1). This representation is then encoded into a shared spatial-tempora space as F and groed To model scene dynamics, deformation network D and a medium offset network D are introduced to predict the evolution of both Gaussians and medium attributes ($3.2). To mitigate observation noise, uncertainty-awarc rendering loss incorporated based on surface-view radiance ambiguity E.. and inter-frame flow inconsistency Eyz (63.3).
where (str(s) and (s)) represent the density and emitted color of scene structure at distance s, while or o (s) and (m are for the volumetric medium. The transmittance term T(s) encodes the attenuation of light due to the participating medium:
T(s) = exp (- (((((" o a (s)) ds' - T-meed (s).
This formulation captures the interplay between geometry-induced occlusion and medium-induced scattering. In the following, we parameterize (s) and (s)) using Gaussian primitives, and model mnd (s) and emed(s (s) via a learnable neural field (see Eq. & 5).
Underwater Representation Initialization. Given the input underwater images, we first calibrate camera poses and recover sparse 3D point cloud using cencturr-frommmttieee (SfM) [93]. Based on this point cloud, a set of 3D Gaussian ellipsoids G is initialized to represent the canonical scene geometry. This SfM-based initialization sufficient for our method (see Appendix $A.1), while recent work [20] provides additional Gaussians for dynamic regions. Each Gaussian primitive is based on a 3D Gaussian kernel ((x)) with a central position μ E IR and covariance matrix Σ E 3x3x3,
G(æ 3d ) = exp (- 2 (ax - (x
m)), Σ RSS R
where 3d E R33 denotes a 3D location. Σ is decomposed into two learnable components, i.e., a rotation matrix R E R333 and diagonal scaling matrix S R3333 For the pixel x associated with ray r, N depth-ordered points {s J along the ray intersect with the pixel using a-blending:
(ar( (r) = Σ Ta(saaanc where an = exp(
1 (at
2d (xd
(xx"
24 )),
(4)
where an denotes the opacity, and the color on is modeled via spherical harmonics. The 3D Gaussian ellipsoids discretize the ray r(s) into a set of intervals, i.e., {10, $1]. .... [sN-1, sy], [sN, sc]]. where
(sN,o0) accounts for background contributions beyond the last Gaussian.
For the volumetric medium, we introduce a neural medium model Fm conditioned on spherical harmonic [23] encoded viewing directions w for medium properties med and med along each ray (see Eq. 10 for dynamic medium properties). To model wavelength-dependeen underwater effects, gmdd is three-channel density vector corresponding RGB channels. The accumulated contribution (r) is calculated by integrating within each ray segment [11]:
from the volumetric medium ('meed
m (r)
Σ
( mnd c
med ds.
(5)
In Eq. 4&5, the transmittance Tr (s) is factorized into two terms [1I], Le., accumulated occlusion from previous Gaussians T (s) and the exponential attenuation from the volumetric medium m (s):
T, (+) T med (s) II (1 ag) exp(-on _ s).
(6)
For compactness, the above expression uses a single medium coefficient o med In our actual formulation, this term is explicitly decomposed into attenuation coefficient att and backscatter coefficient o hs following underwater imaging models [9, 10]. Both gtth and o are parameterized RGB-channel vectors, the transmittance and emission computed per color channel.
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3.2 DYNAMIC FIELD FOR UNDERWATER SCENES
Features. To model temporal changes in both underwater structures and surrounding medium effects, rather than assuming statie scene [11, 12], we extend the canonical underwater representation into a shared 4D neural voxel space via planar factorization [21]. This 4D space serves as a shared ppatio-tempone and the time-varying participating medium. Given a 3D spatial coordinate x = (I, z) and a normalized timestamp & [0. 1]. we decompose the 4D space-time domain into six orthogonal 21) planes {<x, v), (ar, 2). (y,2), (I. t). (v, }. For both the Gaussian- -basad scene structure and the neural medium field in underwater representation space, each plane is respectively associated with learnable feature maps f: and fiued. Given spatio-temporal query Q(x="d)))
Underwater
backbone that jointly represents dynamic geometry
(), bilinear
interpolation dbb is performed on each plane to retrieve local features:
F (a 2d .) = II the (ft", Qu(a" .t), (p .t) Ih (Jt"m Qu(e" .)),
(7)
where Qx 1) denotes the 4D query point of the k-th plane. These interpolated features from different planes are fused by element-wise multiplication. Fstt () and Fmme( (æx, () encode spatio- temporal features of geometry and medium properties for dynamic motion and appearance modeling.
Joint Geometry and Medium Dynamics. To capture the dynamics of scene geometry and motion- aware medium, we introduce a time-conditioned deformation module built upon the spatio-temporal features F and Funed Different from vanilla 4DGS [46], this module estimates both geometric transformations of the 3D Gaussian primitives and the updates of the medium attributes. For each canonical Gaussian centered at μu, we employ deformation network DE to predict temporal offsets in translation (1) E RR$, scaling (S) E RR$, and rotation A (() E R respectively:
Au((), AS(1) AR()) = Dd (F (H, t), Fumeed t)).
(8)
These parameters define the deformation of each Gaussian from the canonical space its time- dependent state. By conditioning on both structural and medium-aware features, the deformation network is able to model plausible underwater dynamics. For the evolving state of the participating medium, a medium offset network 2 is introduced to estimate dynamic properties, A 2D scene flow vector (f) is calculated by projecting temporal difference of Gaussian centers on the image plane:
(t) Proj( + Au(t + AC)) - Proj(μ + Ap(())
(9)
åt
where Proj(-) denotes the projection function from the 3D world space to the 2D image plane. v(() encodes the motion cues of the underwater structure (represented by 3D Gaussians) on the image plane. The medium offset network D yields time-varying medium properties at location x, where two MLPs are used to integrate the motion cues based on vt)) and w, respectively:
mee (f), Rthh (t), o (t) = D (Fitedd (ax, f), v(t),
(10)
This enables complete modeling of environment tlyamiics,thereby improving reconstruction accuracy.
3.3 UNCERTAINTY- OPTIMIZATION
In underwater environments, degraded visibility and random perturbations often introduce noise into observations. Such noise is inherently input-dependent and varies with surface geometry and scene motion, leading to inconsistent geometry and appearance. To address this, we incorporate an uncertainty-awan aware rendering loss that adaptively modulates per-pixel supervision based on surface- view radiance ambiguity and inter-frame flow inconsistency (see visualization in Appendix $A.1).
Surface-Viee Radiance Ambiguity. This factor captures radiance ambiguity when the ray direction closely aligned with the surface normal. In such cases, scattering contributions are hard to disentangle from direct radiance, and high-frequency appearance variations are misinterpreted as geometry cues [22, 23, 94-96). To approximate this ambiguity, we compute a pseudo-normal vector based on the gradient of the corresponding depth map D [97]. Each pixel of D is calculated by the expected distance d(r) using a-blending (similar to Eq. 4):
|-
aD 8s
aD
d(r) = ΣN= (t)t)and
n2 R3
0y
(11)
0D
+ 02 +1
ΣN, Tn())an
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We define the surface- view uncertainty based on the pseudo-normal and the ray direction
(max(0, w n)))²
(12)
Sav is used only soft cue in the variance term of Eq. 15: it modulates the weight of the photometric loss, but does not directly change the rendered color or geometry. Furthermore, the ablation study in Table 5 indicates the overall robustness of UDF does not rely on perfect pseudo-normal estimates.
Frame-Frame Flow Inconsistency. Non-rigid scene or appearance shifts often lead to inter-frame inconsistencies, resulting in artifacts during reconstruction. To measure such inconsistencies, we estimate a per-pixel motion vector Upisel by aggregating the scene flow of visible Gaussians in Eq. 9, and evaluate its alignment with image gradients inspired by the Horn-Schunck optical flow [25]:
c (VI Upixel aI)² 2
ΣN (t)
Eu;
Upixel
I Tr(()an
(13)
where V denotes the spatial image gradient, al is the temporal derivative of intensity, eg is a small constant for numerical stability, and v, is the motion vector of the n-th Gaussian.
Probabilistic Rendering Loss. We formulate the rendering objective as probabilistic regression, where each pixel color is modeled as a normal distribution [18, 19]. The total uncertainty E combines both E2, and En- The rendering loss Le is defined as the negative log-likelihood of the ground truth color ((r) under a predicted normal distribution with mean ((r) and variance Stoaa=
L. (((r)-C(r))
log Sooal. where Sinal = Syy + Eh-
(14)
2C
This probabilistic formulation enables the model to down- weight ambiguous observations, instead of applying a uniform deterministic per-pixel loss to all measurements as in prior methods [11, 12, 78], leading to more stable and temporally consistent reconstruction over time. A total variation term Liv is applied to the total loss L for smoothness of the predicted color sequence [46, 61]:
C == Lc + Lev.
(15)
3.4 IMPLEMENTATION DETAILS
Network Architecture. UDF contains 3D Gaussians G, neural medium module J=M, spatial- temporal encoding, deformation network DE, and a medium offset network 2ndh ($3). The neural medium model .r adopts spherical harmonic encoding and employ an MLP with 128 hidden units and Sigmoid activation to predict per-ray medium properties. For ppaatal-temporal encoding, planar factorization and learnable 4D voxels implemented via K-planes [21]. For the deformation network DE (Eq. 8) and the medium offset network D (Eq. 10), use separate MLPs compute the temporal evolution of both 3DGS geometry and medium parameters.
use
Training and Inference. We first optimize Gaussian primitives g and the spectral medium field Jrl for warm-up. Then we jointly train the deformation network 2 and the medium offset module D" with the uncertainty-aware rendering loss ($3.3). We set ED = 1 x 4 for numerical stability (Eq. 13). To reduce the overhead of Horn-Schunck flow estimation, we approximate the second term of Eq. 13 using simplified inter-frame difference. We use the Adam optimizer with an initial learning rate of 1 x 10 which decays exponentially to 1.5 x 10-4, During inference, uncertainty modeling disabled and the rendering module is used to produce the final output.
Reproducibility. Experiments are conducted with an Intel 19-14900K and an NVIDIA RTX 4090 GPU. 3DGS rasterisation implemented in CUDA, while the remaining pipeline is developed using PyTorch. We use the gradient clip to stabilize training.
4 EXPERIMENT
Datasets. Our method is evaluated on both controlled and in in-the-wile wild underwater datasets:
NUSR [12] is collected from in wild captured clips from the Internet, containing four monocular underwater videos with dynamic objects: Turtle, Coral, Composite, and Sardine.

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DRUVA [26] includes video sequences of 20 different artifacts. All videos are captured under natural illumination at a depth of 3 - 6 m from the sea surface with a resolution of 1920 x 1080. SeaThru [10] contains real-world scenes from IUI3-Red Sea, Japanese Gardens, Panama, and Curaçao including 29, 20, 18, and 20 images respectively, each with a resolution of 900 x 1400.
Evaluation Metries. Following existing methods [11, 12], we primarily assess our experimental results using seak-signal-iee -to- no-noise ratio (PSNR), perceptual quality measure LPIPS [98], and structural similarity index (SSIM) [99]. All reported results are averaged over five runs on the same test set.
Baselines. We compare our UDF with recent approaches. For NUSR [12], we adopt static reconstruc- tion methods, such as Instant-NGP [100]. SeaThru-NeRF [10], as well as dynamic methods, including DynamicNeRF [13], NUSR [12], 4DGS [46], and WaterSplatting [1 [11]. For DRUVA [26], the baseline methods include SeaThru-NeRF [10], TiNeu Vox [101], 4DGS [46, 52], and WaterSplatting [11]. For SeaThru [10], we evaluate 3DGS[6], SeaThru-NeRF [10], NUSR [12], WaterSplatting [11], and
4DGS [46]. All methods are reproduced using their publicly available implementations.
4.1 QUANTITATIVE RESULTS
Performance on NUSR. Table 1 reports quantitative results of UDF NUSR [12]. Compared to the original NUSR model [12], UDF achieves consistently better reconstruction quality. For instance, in the Turtle scene, it improves PSNR from 28.10 to 33.73, increases SSIM from 0.899 to 0.965, and significantly reduces LPIPS from 0.216 to 0.051, demonstrating the effectiveness of our uncertainty-guice reconstruction strategy. Similar improvements are also observed in other scenes.
Table I: Quantitative results on NUSR [12] ($4.1).
Models
Sardine
Cora
Turtle
Compusite SSIM
PSNR
SSIM
LPIPS]
PSNR|
SSIM1
LPIPS.
PSNR1
LPISS
PSNR1
LPIPSI
Iastant-NGP [100] 2R
21.73
0.850
0,467
211.87
0.438
0.730
26.12
0.871
0.225
22.81
0.506
01371
DynamicNeRF [13] pec0vRo
19.70
0.676
0.690
17.77
0.542
0.826
23.31
0.837
0.426
16:27
0.738
0.476
SeaThro-NeRF/ [10] 2
21.37
0.578
0.606
23.89
0.618
0.105
27.06
0.881
0.191
16.21
0.105
0.828
4DGS [46] Jov
21.42
0.627
0.486
25.81
0.709
0.258
25.06
0.838
0.239
26.81
0.844
0.201
NUSR [12]
21.58
0.720
0.454
26.17
0.828
0.157
28.10
0.599
0.216
25.00
0.798
0.238
WaterSplatting [11] pav zoen
23.16
0,876
0.184
28.67 67
0,908
0.098
25,20
0.879
0.253
27. 20
0.910
0.124
Ours
24.41
0.847
0.168
28.72
0.890
0.085
33.73
0.965
0.051
27.53
0.911
0.090
Emor Bars (+)
(0.02)
(cle-3)
(cle:3)
(0.02)
(<le:3)
(<le-3)
(0.05)
(cle:))
(cle:3)
(0.01)
(<le.3)
(cle-3)
Performance DRUVA. Table 2 presents results representative scenes from the DRUVA dataset.
Compared to WaterSplatring [11], UDF consistently achieves superior performance across PSNR, SSIM, and LPIPS. Notably, in A11, UDF improves PSNR from 32.33 to 34.03 and SSIM from 0.962 to 0.964, and reduces LPIPS from 0.207 to 0.123, verifying the effectiveness of dynamic modeling. Similar improvements across other scenes further underscore the general applicability of UDF.
Table 2: Quantitative results on DRUVA [26] ($4.1).
Models
Al
A2
All
A12
PSNRT
SSIM
LPIPS
PSNR?
SSIM
LPIPS)
PSKRT
SSIM:
LPIPS.
PSNR
SSIM
LPIPSL
TiNeuVox [101] po0c8 bes
23.05
0.757
0.664
21.74
0.843
0.637
27.02
0.878
0.355
27.59
0.911
0.221
SesThru-NeRF [10] (023
26.27
0.778
0.336
20.23
0.681
01481
27.62
0.916
0.251
4DGaussian [52] pcua
22.84
0.688
0.535
20.83
0.386
0.638
26,84
0.882
0.273
25.84
0.906
0.244
4DGS [46] 2000
20.75
0.736
0.119
19.51
0.678
0.516
21.09
0.938
0.173
25.79
0.956
0.128
WaterSplatting [1 [] paw nen
28.71
0.830
0.376
26.33
0.800
0.406
32.33
0.962
0.207
30.86
0.958
0.201
Outs
29.29
0.842
0.300
27.35
0.801
0.384
34.03
0.964
0.123
31.01
0.969
0,100
Error Bars (+)
(0.12)
(<le-3)
(0.001)
(0.06)
(cle-3)
(cle-3)
(0.11)
(<le-3)
(<le-3)
(0.09)
(<le-3) (cle-3)
Performance on ThaT. Table 3 reports quantitative results of UDF on the SeaThru dataset. Compared to 4DGS [46], our method achieves substantial improvements across all metrics. For instance, in the Panama scene, UDF improves PSNR from 25.90 to 32.95, increases SSIM from 0.801 to 0.930, and reduces LPIPS from 0.277 to 0.065, which highlights the effectiveness of incorporating the MLP- -enedddd medium representation in improving underwater reconstruction quality. On average, our method achieves consistently higher PSNR and lower LPIPS than all baselines, while SSIM is slightly lower than WaterSplatting [11] on a few specific sequences. As SSIM primarily measures local structural similarity, the sequences where WaterSplatting [11] attains marginally higher SSIM scores typically contain static content. Therefore, this static-style method can already preserve most
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local background structures. In such cases, the advantages of UDF in dynamic modeling not fully reflected SSIM when the overall structural layout can be well reconstructed by a static method.
Table 3: Quantitative results on SeaThru [10] ($4.1).
CURAÇAO
UeT--RedSen SSIM
Panama
Japanese Gardenss
Models
PSNR1
SSIM
LPIPS)
PSNRT
LPIPS.
PSNK
SSIM
LPIPS.
PSNK
SSIM.
LPIPS]
31Gauusiams [6]
(106
28.31
0.873
0.221
22.98
0.843
0.245
29.20
0.803
0.152
21.49
0.854
0.216
SeaThru NeRF [10] (099 sasq
30.19
0.873
0.210
25.90
0.785
0.304
27.84
0.834
0.224
21.84
0.767
0.240
NUSR
23.75
0,263
4DGS [46]
(0
21.75
0.706
0.195
22.51
0.630
0.473
25.90
0.801
0.277
22.42
0.779
0.323
WaterSplattig [1
paw samg
32.20
0.948
0.116
20.84
0.889
0:203
31.61
0.942
0.060
24.74
0.802
0.116
Ours
33.82
0.940
0.530
0.139
32.95
0.930
0.065
27.39
Emor Bars
(0.03)
(<le-3)
(<le.3)
(0.05)
(<le:3)
(<le.3)
(0.01)
(<le:3)
(<le-3)
(0.04)
(<le.3) (<le:3)
4.2 QUALITATIVE RESULTS
Rendering Quality. In Fig.3, compare method against SeaThru-NeRF [10] and WaterSplat- ting [1I] on DRUVA [26]. All scene, the yylllo--bxxe region highlights a calibration board. Our reconstruction closely resembles the ground-truth reference, preserving sharp edges and color fidelity. In A12 scene, the red-boxed area reveals a moving rope, and our method demonstrates better performance in reconstructing such dynamic structure (see more results in Appendix $A.1). I).
Woter-Splathing
411
SeRRhnu-NoRR
Ours
Groundrruth
Woter-Spletting
A12 SeoThru-NeeR
A12 Groundrruth
A12
Figure 3: Underwater scene rendering on DRUVA [26]. compare our method with SeaTThr-NNeRF [10] and WaterSplatting [11] on All and A12 scenes. For each method, we present four rendered images and provide two zoomed-in in views of representative regions below each image, focusing dynamic content and challenging areas. Our method produces consistently higher-quality results in both dynamic and static regions. ($4.2).
Medium Removal and Depth Maps. In Fig. provide medium-free renderings by disabling the neural medium module Jm and full rendered results] with zoomed-in views. To further present geometry accuracy, we include the rendered depth maps (Eq. 11), which exhibit structural consis- tency with the scene layout. In Turtle, our approach accurately recovers the natural appearance of muddy terrain, producing visually realistic outputs. In contrast, other methods [11, 12] generate distorted colors after "medium removal". which amplifies small estimation errors and pushes colors toward unrealistic hues. By explicitly separating dynamic geometry and medium in unified 4D field, and by using heteroscedastic uncertainty to down- ill-posed regions, UDF avoids such severe hue shifts and produces more plausible appearances (see more visualizations in Appendix $A.
User Study on Novel View Synthesis. To further validate the perceptual quality novel view synthesis, we conduct blind human evaluation study comparing the outputs of different methods. Concretely, 40 college students are invited to evaluate 1, 500 rendered images. In each session, participants randomly presented triplet of renderings generated by SeaThru-Nehh [10], Water- Splatting [11], and our UDF, respectively. Each triplet contains multiple novel views the same scene along with ground-truth reference. Across all sessions, method was selected as the top
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choice in more than 90% of cases. This indicates that UDF not only improves perceptual realism of underwater reconstructions but also maintains consistent visual quality across diverse viewpoints.
Snter-Splatiing
Turtle
SeaThrg Neet
Turtle
Ourr
Tur
Groundruth
Turlless
Water Splatting
Carol SeaThey Nes
Corol
Ours
Dard
Groundhrulhi
Caral
Figure 4:
Scene Rendering and Medium Removal on NUSR [12]. We compare our method with SeaThru- NeRF [10] and WaterSplatting [11]. Zoomed-in regions show the original rendering results]. Leveraging composite underwater representation, we can fremove medium effects by disabling the medium module (yellow boxes), recovering colors for both dynamic and static objects. We also include the rendered depth maps in the bottom-right corner of the groundtruth, where brighter values indicate greater distances (84.2).
4.3 DIAGNOSTIC EXPERIMENT
Model Design. Table 4 presents ablation study on the neural medium module (J"m), the offset net- work (D"), and the deformation network (D#) on NUSR [12]. Removing DD'h entirely leads to a no- table performance drop, with PSNR falling to 30.84, SSIM decreasing to 0.951, and LPIPS rising to 0.072. Excluding Jm results in moderate degradation, indi- cating that modeling temporal variation in medium properties contributes to reconstruction fidelity. In addition, removing DE causes a considerable decline in performance, with PSNR reduced from 33.73 to 31.46, highlighting the necessity of modeling dynamic geometry for accurate reconstruction. These results validate the importance of all three components in improving both photometric accuracy and temporal coherence across frames.
Table 4: Ablation study of model design ($4.3).
NUSR Turtle [12]
fu
DDR
D
PSNR1
SSIMI
LPIPS_
29.90
0.9188
0.075
31.46
0.953
0.068
31.53
0.954
0.052
33.73
0.965
0.051
Uncertainty-Awar Optimization. Table presents an ablation study the proposed uncertainty model- ing components (Eq. 14). Removing the entire uncer- tainty terms results in signiticant performance degra- dation, with PSNR dropping from 33.73 to 30.83, SSIM from 0.965 0.941, and LPIPS increasing from 0.051 to 0.070. Excluding the surface-view ra- diance ambiguity term E², leads to moderate decline (PSNR: 32.4 48 and SSIM: 0.951), while omitting the inter-frame flow inconsistency term & yields comparable degradation (PSNR: .52 and SSIM: 0.954). These results demonstrate that both < and c essential for improving image quality and ensuring consistent dynamics across frames.
Table Ablation study of uncertainty ($4.3).
NUSR Turtle [12]
$
PSNRT
SSIM
LPIPS
30.83
0.941
0.070
31.52
0.954
0.063
32.48
33.73
Parameter Sensitivity. We conduct sensitivity analysis to evaluate the impact of key hyperparam- eters across all test scenes. First, varying the hidden layer size of the neural medium module Jmm among {64, 128, 256) results in an average PSNR fluctuation of only 0.2 dB. Adjusting the weight of the uncertainty loss term (Eq. 14) within range leads PSNR variations of less than 0.5 dB. For 3D Gaussians G. hyperparameters such as the total number of Gaussians and the splitting threshold are loosely constrained by scene complexity. For example, decreasing the splitting threshold from le-4

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to 55-5 yields consistent performance with negligible impact reconstruction accuracy. These findings indicate that our model exhibits low sensitivity to hyperparameter settings, demonstrating stability and ease of deployment in diverse underwater reconstruction scenarios.
Initialization Strategy. In our experiments ($4.1), the traditional SfM method, i.e. COLMAP [93], proves effective for 3DGS ini- tialization. To further evaluate alternatives, explore the recent VGGT [102] and observe comparable reconstruction quality in Table This demonstrates that our pipeline remains robust across different initialization choices.
Table 6: Analysis on different initialization (64.3).
NUSR [12]
SeaThri [10]
Models
PSNR1
SSIM LPIPS)
PSNRT
SSIM LPIPSL
VGGT [102]
28.27
0.968
0.103
31.33
0.902
0.082
COLMAP [93]
28.59
0.903
0.098
31.31
0.809
0.087
Robustness Calibration Inaccuracies. We additionally organize an ablation study that per- turbs input camera poses with Gaussian noise in Table 7. We evaluate three noise levels (1%. 3%, 5%) and report the average performance under these perturbations. We observe that the
Table Robustness to Camera Calibration ($4.3).
DRUVA
A2 [66]
SeaThru
[10]
Panama
PSNK
SSIM
PSNR
SSIM
with Clussiaa noise
27.10
0.793
32.79
0.912
without moise (ours)
27.35
0.801
32.95
0,930
degradation under noisy poses is small, and UDF still maintains strong reconstruction quality, which further supports its robustness to calibration inaccuracies in underwater capture.
Runtime and Memory Analysis. We evaluate the runtime efficiency and memory usage of our method on DRUVA [26] in Table 8. Our method achieves 23.81 FPS while consuming 10.70 GB of GPU memory, with a parameter size of 33.67 MB. comparison, SeaThru-NeRF [10] operates slower at only 0.43 FPS. WaterSplat- ting [11] consumes even more memory (12.93 GB) while operating lower frame rate (18.55
Table 8: Efficiency analysis DRUVA [26] (84.3).
Models
Param, Size (MB)
GPU Mem. (GB)
FPS
SeaThru-NoRF [10]
201.32
11.70
0.43
WaterSplatting [11]
21.49
12.93
18.55
4DGS [46]
54.75
2.88
29.27
Ours
33.67
10.70
23.81
FPS). Although 4DGS [46] achieves the highest speed (29.27 FPS), it comes with a moderately larger parameter size (54.75 MB) and lower reconstruction metrics. In terms of training efficiency, our method converges in 18, 000 iterations. Overall, UDF provides favorable trade-off between speed, memory usage, and model size, making it suitable for real-time or resource-constrained deployment.
Failure Cases. In Fig. 5, we present failure case in NUSR [12]. A representative region| is cropped and enlarged for detailed inspection. The yellow and magenta] boxes highlight two failure modes: blurry reconstruction in distant regions and arti- facts in fine structures. These issues are primarily caused by severe depth-dependent light attenua- tion, which inherent to underwater environments. Such attenuation significantly reduces the visibility of distant scene content, increasing the difficulty of accurately modeling both geometry and appearance (see more failure cases in Appendix A.1).
Groak
Figure 5: Failure cases in NUSR [12] (84.2).
CONCLUSION
We presented uncertainty-aware dynamic field (UDF) for underwater 3D reconstruction, addressing the inherent challenges posed by light scattering and environmental dynamics. Our method jointly models dynamic geometry and medium properties using 4D encoding, and introduces per-pixel heteroscedastic uncertainty to adaptively mitigate observation noise. We quantify input-dependent uncertainty by leveraging surface-view radiance ambiguity and inter-frame flow inconsistency, and further incorporate it into the rendering loss. Experimental results demonstrate that UDF achieves high-fidelity reconstruction and novel view synthesis under adverse visibility conditions.
Acknowledgment. This work supported by Zhejiang Provincial Natural Science Foundation of China (No. LR26F020002), Fundamental Research Funds for the Central Universities (226-2025- 00057), and CIE-Tencent Robotics XRhino-Bird Focused Research Program.
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A APPENDIX
We first present additional visualizations ($A.1), including Uncertainty and Depth Maps (Fig. 6). Medium Decoupling and Removal (Fig. 7), More Failure Cases (Fig. 8), Dynamic Motion Trajec- tories (Fig. 9), and Point Clouds from SfM (Fig. 10). Furthermore, detailed discussion ($A.2) is provided with Terms of use, Limitations, Future Direction, and Broader Impacts. Finally, we present additional comparisons (Table 9) and supplementary videos ($A.5).
A.1 MORE VISUALIZATIONS AND ANALYSES
Uncertainty and Depth Maps. Fig. 6, we visualize the depth map D, surface-view ambiguity Sau inter-frame flow inconsistency $7,- and the corresponding input images. As shown on the right, the moving objects within the orange bounding box is clearly highlighted in the inter-frame flow inconsistency map, demonstrating the model's ability to capture dynamic motion cues. These areas typically exhibit high inconsistency due to non-rigid motion and temporal misalignment. Our method effectively distinguishes both geometry-induces and oation-induced uncertainty.
Depth
Surface View Ambigutty
Frame
Origina
Figure 6: Uncertainty visualization 'Coral', 'Sardine', and 'Composite' scenes of NUSR [12]. We show per-pixel uncertainty magnitude our model using surface-view ambiguity inter-frame flow inconsistency. Furthermore, the highlighted orange boxes outline dynamic regions in both the inter- frame flow inconsistency maps and the corresponding original images, which are then magnified and shown on the right.
Medium Decoupling and Removal. In Fig. 7, we visualize the decomposition of underwater rendering outputs for representative views in 'Coral' and 'Japanese Garden Red Sea' scenes. For each selected view, we display the estimated medium appearance, object appearance, restored appearance, the final rendered image, and the corresponding ground truth. Our model effectively disentangles medium-related effects, such scattering and attenuation, from the underlying object surfaces. The restored appearance reveals faithful color recovery, while the estimated medium maps capture plausible distributions of underwater light propagation. These results demonstrate the effectiveness of our medium modeling in separating rendering components and enhancing reconstruction realism.
Chaest
Thage
Tragge
J
Objjctt Imoge
7.5
Med un Erage
3 Sog
Recoar Image
Figure 7: Medium removal visualization for underwater rendering in 'coral' and 'Japanese Garden Red Sea' scenes. We show rendering results from a selected viewpoint in cach scene, including the estimated medium appcarance, object appcarance, restored appearance, final rendered image and ground truth. These visualizations demonstrate the effectiveness our medium modeling and its contribution accurate underwater reconstruction.
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More Failure Cases. In Fig. 8, present an additional failure from NUSR[12]. While method successfully captures the motion of the large foreground fish, it produces noticeable ghosting artifacts on smaller red fish undergoing rapid movement (highlighted in the red box)). This failure reveals a limitation in handling fast-moving, small-scale objects with high-frequency motion.
Our
Groundrruth
Figure 8: Failure cases in NUSR [12].
Dynamic Motion Trajectories. In Fig. 9, trajectories are densely distributed around dynamic objects such the turtle, while static regions like rocks exhibit minimal motion. This spatial distribution aligns with intuitive expectations and highlight the necessity of modeling underwater dynamics.
Figure 9: Motion trajectories in 'Turtie' scene of NUSR [12]. From left to right: input image, two-frame motion trajectories, and multi-frame motion trajectories.
Point Clouds from SIM. In Fig. 10, we present point clouds obtained from SIM [93] ($3.1). These point clouds exhibit high quality and faithfully capture the geometry of objects in the real scene, providing valuable priors for reliable Gaussian initialization.
Figure Point clouds for gaussian initialization.
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Assumption on Illumination Conditions. Our method assumes that underwater images are captured under natural sunlight instead of active lighting systems. This assumption holds for all datasets used in our experiments, where ambient daylight provides relatively uniform illumination. This design simplifies modeling of wavelength-deeeenden attenuation and scattering, and works well for these datasets where natural light is the dominant source. We consider extending this to handle non-uniform, active lighting promising direction for future work, potentially by inverse rendering with disentangled illumination representations [97, 1033.
A.2 DISCUSSION
Terms of Use, Privacy, and License. We do not collect or use any private or personally identifiable information in our study. All datasets used are anonymized and publicly available for research purposes. The algorithms described in this work are made available exclusively for academic research purposes. We conduct experiments using three publicly available underwater datasets: SeaThru [10], NUSR [12], and DRUVA [26]. The terms of use and licensing details for these datasets are summarized as follows. SeaThru' released under the Apache License 2.0, which permits both commercial and non-commercial use, provided proper attribution and license preservation. NUSR provides data access through a public download link², but does not explicitly state a license. We use it solely for non-commercial academic research in compliance with common usage norms. DRUVA requires a signed release agreement and approval via request form prior to access." 3 We obtained the dataset through the official process and comply with its academic-use conditions.
Limitations. While our method achieves strong performance in modeling dynamic underwater scenes with uncertainty-awan rendering, it has several limitations. (1) Real-world underwater environments, such as occans, rivers, and lakes, exhibit diverse dynamics and medium properties. To fully assess the generalization of our method, more datasets covering a wider range of scenarios are needed. (2) Our method uses heteroscedastic aleatoric uncertainty to handle input-dependent noise but does not model epistemic uncertainty [79], which captures uncertainty in model parameters arising from limited data. Incorporating epistemic uncertainty could improve reliability in out-of-distribution settings. (3) Some bluish tint may still be observed in scenes, suggesting incomplete disentanglement between object appearance and medium effects. This residual tint arises primarily from relying exclusively on photometric supervision, which provides only pixel-level intensity information. The datasets used in our experiments are collected from in-the-wild Internet videos and lack auxiliary supervision, such as medium-free reference images or known transmission profiles. Without such prior knowledge, our model may struggle to fully decouple medium scattering effects, particularly in spectrally biased regions (e.g. red-light attenuation in deeper water). This limitation highlights a valuable direction for future work: introducing auxiliary supervision via synthetic data with ground-truth albedo and transmission would provide explicit guidance, improving separation of object and medium. (4) As discussed in the failure cases (Appendix Fig. 8), model can still produce artifacts around small, fast, highly deformable fish. These objects undergo rapid non-rigid motion at very fine spatial scales and often observed from only few viewpoints under strong scattering, making accurate reconstruction extremely challenging. Our primary goal is to jointly model dynamic geometry and dynamic underwater medium at the scene level. And extending the framework with fine-scale, object-aware motion modeling for such cases remains an important direction for future work.
Future Direction. A promising direction is to more explicitly address calibration inaccuracies that are typical in underwater capture (e.g.. refraction at the housing interface, mechanical tolerances, and slight pose drifts). A natural idea for future work to jointly refine camera poses and refractive parameters within the dynamic field optimization, potentially coupled with uncertainty over camera extrinsics, to further improve robustness in severely miscalibrated settings. Beyond calibration, another important direction is the principled integration of physical priors into dynamic scene representations, enabling stronger generalization beyond the training data distribution. Incorporating multi-modal sensory signals-such as acoustic measurements or inertial priors- may further improve robustness in visually degraded or sensor-limited limited underwater settings. Moreover, uncertainty could be modeled more holistically, not only at the observation level but also within the representation and
Dataset page: 2 NNSR download:
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com/ fi /e///// httee////AAArPPPrC AKPUPPKIN cowTFOORVd 1
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Dataset access via: https: / //i thub. sha shava 5/DRUVA
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rendering stages. This could be achieved through Bayesian modeling variational inference [84], enabling the capture of epistemic uncertainty arising from model ambiguity. Furthermore, while the revised underwater image formation model [9] is designed for linear input data, our results, along with prior work [11, 12], suggest that neural approaches to medium modeling remain effective to both RGB images (e.g., from NUSR [12] and DRUVA [26]) and linear data (e.g., from SeaThru [8]).
Further exploration is needed to generalize these findings across different datasets.
Broader Impacts. Our work enables reliable and physically grounded reconstruction in challenging underwater environments by jointly modeling geometric structures, medium dynamics, and observa- tion uncertainty. This advancement holds significant potential for critical domains such as marine ecology, underwater archaeology, and autonomous robotics, where robust scene understanding is essential under degraded visual conditions. The deployment of such technologies in ecologically sensitive areas needs careful consideration. Ensuring transparency in data collection, fairness in system behavior, and adherence to ethical standards is crucial to prevent ecological disturbance or operational bias. We encourage the community to continue examining the environmental, safety, and ethical implications of exploration underwater ecosystems such as the ocean.
A.3
MORE RESULTS
Table 9: Quantitative results SeaThru [10] (SA.3).
CURAÇAO
[U]3-RedSen
Japanese Gardens
Models
PSNRT
SSIM
I.PISS)
PSNRT
SSIM1
1.PIS]]
PSNRT
SSIMF
LPIPS.
PSNRT
SSIM1
I.PIPS]
UW-GS [14]
31,77
0,943
0.144
28.65
0.933
0.125
31,79
0.936
0.115
23.04
0.860
0.189
ScaSplat [76] (104 2014
30.30
0.900
0.190
26.67
0.870
0.210
28.76
0.900
0.150
22.70
0.870
0.180
Gaussian Splashing [77] Bosk sing
31,26
0.920
0.170
24.73
0.920
0.110
31.35
0.940
0.1
24.73
0.920
Ours
33,82
0.940
0,071
31.09
0.830
0.139
32,95
0.930
0.065
27.39
0.899
0,073
Error Bars (#)
(0.03)
(<le-3)
(<le-3)
(0:05)
(<lo-3)
(<lo-3)
(0.01)
(<lo-3)
(<le-3)
(0.04)
(<lo-3)
(<le-3)
Comparison SeaThru. In Table 9, we further compare against several recently proposed methods on SeaThru [10], including UW-GS [14], SeaSplat [76]. and Gaussian Splashing [77]. Our method consistently outperforms these approaches across most metries. For instance, in CURAÇAO, method achieves a PSNR of 33.82, significantly higher than UW-GS [14] (31.77), and obtains the lowest LPIPS score (0.071). Similar performance gains observed across the other scenes, demonstrating the effectiveness and generalizability of our design.
A.4 USE OF LARGE LANGUAGE MODELS
We did not use any large language models this work.
A.5 SUPPLEMENTARY MATERIAL
Supplementary Videos. We provide additional video visualizations in the supplementary material (filename: 'Supplementary Videos") to further demonstrate the effectiveness of our method. For each of three representative scenes, i.e., RedSeR, Japanese Gardens from SeaThru [10], and Composite from NUSR [12], we render sequence of images along the camera trajectories provided in the dataset and compile them into videos. Each video contains two side-by-side views: the left shows the final rendered results, while the right displays the estimated mediums. These visualizations highlight that our neural medium temporally adaptive and effectively captures dynamic changes over time, contributing to improved scene reconstruction under diverse and challenging underwater conditions.
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Reviews:
[{"review_id": "q7srYt91gz", "reviewer": "Reviewer_mECr", "summary": "This paper introduces Uncertainty-aware Dynamic Field (UDF) for 3D reconstruction of dynamic undetwater scenes. UDF jointly models scene structure and view-dependent medium properties over time. UDF initializes with 3D Gaussians in a volumetric medium field, maps them to a 4D neural voxel space, and employs deformation/medium offset networks to handle spatio-temporal dynamics. To suppress noise from low-confidence observations, UDF incorporates per-pixel uncertainty estimation based on surface-view radiance ambiguity and inter-frame flow inconsistency, and further integrates the uncertainty into the rendering loss. Experiments on controlled and in-the-wild underwater datasets demonstrate UDF achieves superior reconstruction quality and novel view synthesis for dynamic underwater scenes.", "questions": "-- The gradient-induced pseudo-normal, used in modeling surface-view radiance ambiguity, is particularly prone to significant errors at object edges and in rapidly moving regions. Consequently, failures in uncertainty modeling can occur, potentially adversely affecting the robustness of the entire approach. Can the authors provide some analysis on this aspect?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "++ The shared 4D neural voxel space based on planar factorization extends the 3D canonical representation to a spatial-temporal space, which further enables the dynamics modeling of scene structure and medium in a physics-informed manner.\n\n++ UDF estimates per-pixel uncertainty using physical cues and integrates it into the rendering loss to suppress noisy data during training. The effectiveness of this design is validated in the ablation study (Table 5).", "weaknesses": "-- The fundamental contributions and differentiating aspects of the underwater dynamic modeling approach proposed in this paper compared to existing methods require clearer articulation. The authors may need to emphasize these points in their writing.\n\n\n\n-- Regarding the distorted colors shown in WaterSplatting and SeaThru-NeRF after medium removal: could the authors provide insight into the root cause? It would be helpful to know if UDF is immune to this artifact across the entire tested cases and, crucially, what specific aspect of its design confers this advantage.\n\n-- From the supplementary videos (especially composite.mp4),  we can see significant artifacts around dynamic objects (fishes). This indicates that the method's performance in modeling moving objects is not satisfactory.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "m6vIFuOSSG", "reviewer": "Reviewer_TEeD", "summary": "This paper presents a method for reconstructing dynamic underwater scenes by using an uncertainty module to discard low-quality pixels in the measurements as well as dynamics modules to model the time-varying nature of both the scene and the medium. The authors demonstrate improved results on several benchmarks compared to baselines, and extensively validate components of their methods.", "questions": "Could the authors rerender the supplement videos with smooth trajectories? I won't make my score conditional on the response to this question, since I think it's against the policies to ask authors to do excessive work or provide new results, particularly graphics, but I think it would just be nice.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "The problem is well-motivated because dynamics are almost unavoidable underwater, since currents and wildlife are commonplace in captured data. The qualitative results are compelling and show clear improvement, especially for dynamic objects and medium recovery, as can be seen in Figures 2 and 3, which show that both the scene and medium reconstructions are better than prior works. The quantitative metrics are also improved by relatively significant margins for most of the scenes. Finally, the evaluation is fairly comprehensive, covering pipeline as well as module design, and illustrates clearly some of the limitations of the method, shown in Figure 4.", "weaknesses": "About the videos in the supplement, the paper claims there are four of them but there are only three in the folder. Maybe this is a typo? Furthermore, the trajectories in IUI3RedSea and JapaneseGarden are relatively choppy. I know that the authors are just rendering at the positions provided by the original dataset, but I think it would be helpful to regenerate smooth trajectories with which to render the result.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "03GyNTIJYH", "reviewer": "Reviewer_JbgZ", "summary": "This paper proposes UDF, a dynamic scene representation that jointly models underwater structure (via 3D Gaussian primitives) and the participating medium (via a neural, view-conditioned medium field). A canonical scene (Gaussians embedded in a volumetric medium) is mapped into a 4D neural voxel space (K-Planes) to extract spatio-temporal features. Two heads then evolve the scene over time: a deformation network that predicts per-Gaussian offsets, and a medium-offset network that updates attenuation/backscatter conditioned on motion cues. The paper introduces a heteroscedastic rendering loss with per-pixel variance derived from surface-view radiance ambiguity and inter-frame flow inconsistency. Experiments on NUSR, DRUVA, and SeaThru show gains in PSNR/SSIM/LPIPS with qualitative  visualizations.", "questions": "I hope the authors can address Weaknesses 1–5 in the rebuttal, and I remain positive about this work's contribution to the community.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. The pipeline overview is clear and visual results further aid understanding. These choices make the method and evidence easy to follow.\n\n2. The combination of 3DGS geometry + learnable medium + 4D K-Planes provides a clean factorization of structure vs. medium over time. The two cues (surface-view ambiguity and flow-based inconsistency) are well-grounded and integrated in the NLL loss.\n\n2. The paper reports consistent improvements on NUSR, DRUVA, and SeaThru with both quantitative and qualitative evidence (novel views, medium-free renderings, depth maps).", "weaknesses": "1. Eq. (6) uses a single σ_med inside T_med(s), yet later the paper separates σ_med into σ_att (structure) and σ_bs (backscatter). The derivation would benefit from writing the explicit separated transmittance and emission terms to avoid ambiguity, and clarifying wavelength-dependent parameterization (RGB-channel σ_med).\n\n2. Consider adding a teaser in the introduction, e.g., a before/after comparison on a challenging underwater scene, to foreground the key difficulties and to show how your method addresses them. Without this, your advantages are not immediately clear to readers.\n\n3. User study details. The 40-person, 1,500-image study is promising, but lacks description of the protocol (randomization, rating scale, inter-rater reliability).\n\n4. You report VGGT vs. COLMAP with comparable results. Could you add experiments with noisy to quantify robustness to calibration inaccuracies typical in underwater capture?\n\n5. Some typos:\n- \"Japanese Gradens\" -> \"Japanese Gardens\"\n- \"a uncertainty-aware rendering loss\" -> \"an uncertainty-aware rendering loss\"\n- L226 \"enotes the projection function\" -> \"denotes the projection function\"\n- \"Zoomed-in regions shows\" -> \"Zoomed-in regions show\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "JqZNue0f4i", "reviewer": "Reviewer_9Jh1", "summary": "The paper introduces UDF (Uncertainty-aware Dynamic Field), a novel framework for underwater 3D reconstruction that models dynamic geometry and medium properties while incorporating uncertainty. The framework builds on 3DGS and targets underwater scenes by \n1) Initializing a set of 3D Gaussians embedded in a volumetric medium. \n2) Encoding spatial-temporal features in a 4D neural voxel space via planar factorization.\n3) Using a deformation network to model dynamic geometry and a medium offset network to capture evolving medium properties \n4) Incorporating uncertainty into the rendering loss guided by surface-view radiance ambiguity and inter-frame flow inconsistency. \n\nThe authors evaluate the effectiveness of their method in multiple underwater datasets and showcase a significant improvement over prior methods.", "questions": "As noted in Weaknesses.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "The paper is very well written and the authors provide deep insights in their design choices. \n1) The integration of dynamic medium modeling with uncertainty-aware rendering is a substantial advancement over prior work \n2) The radiance ambiguity and flow inconsistency are physically motivated and well-integrated into the loss function\n2) Strong results across all datasets \n3) The method achieves a good balance between rendering speed and memory usage.", "weaknesses": "1) In the experimental evaluation, the method improves over all metrics. The only metric that watersplatting outperforms the current is in SSIM. Can you comment on why that might happen?\n\n2) While the paper is technically rich, some sections are very dense in information. Even figure 1. Is very technically dense. The paper could benefit from additional diagrams and moving details to supplementary material.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)