I2-NeRF: Learning Neural Radiance Fields Under Physically-Grounded Media Interactions
Authors: Shuhong Liu
Lin Gu
Ziteng Cui
Xuangeng Chu
Tatsuya Harada
Venue: NeurIPS 2025 poster ()
Keywords: 3D Reconstruction
Primary area: applications

Abstract: Participating in efforts to endow generative AI with the 3D physical world perception, we propose I2-NeRF, a novel neural radiance field framework that enhances isometric and isotropic metric perception under media degradation. While existing NeRF models predominantly rely on object-centric sampling, I2-NeRF introduces a reverse-stratified upsampling strategy to achieve near-uniform sampling across 3D space, thereby preserving isometry. We further present a general radiative formulation for media degradation that unifies emission, absorption, and scattering into a particle model governed by the Beer–Lambert attenuation law. By matting direct and media-induced in-scatter radiance, this formulation extends naturally to complex media environments such as underwater, haze, and even low-light scenes. By treating light propagation uniformly in both vertical and horizontal directions, I2-NeRF enables isotropic metric perception and can even estimate medium properties such as water depth. Experiments on real-world datasets demonstrate that our method significantly improves both reconstruction fidelity and physical plausibility compared to existing approaches. The source code is available at https://github.com/ShuhongLL/I2-NeRF.

-e-NRRF: Learning Neural Radiance Fields Under Physically-Grounded Media Interactions
Shuhong Liu', Lin Gu Ziteng Cui', Xuangeng Chu', Tatsuya Harada
'The University of Tokyo, TThhoku University, PRKKNN
(s-liu,lingu,c cui, xuangeng. chu, harada) @mi wer.i..uutton u-tokyo. jc.
Abstract
Participating in efforts to endow generative AT with the 3D physical world percep- tion, propose -2-NeRF, novel neural radiance field framework that enhances isometric and isotropic metric perception under media degradation. While existing NeRF models predominantly rely on object-centric sampling, 12-NeRF introduces a reverse-stratified upsampling strategy to achieve near-uniform sampling across 3D space, thereby preserving isometry. We further present a general radiative formulation for media degradation that unifies emission, absorption, and scattering into a particle model governed by the Bambert attenuation law. By com- posing the direct and media- induced in-scatter radiance, this formulation extends naturally to complex media environments such as underwater, haze, and even low-light scenes. By treating light propagation uniformly in both vertical and horizontal directions, Ne-NeRF enables isotropic metric perception and can even es- timate medium properties such as water depth. Experiments real-world datasets demonstrate that our method significantly improves both reconstruction fidelity and physical plausibility compared to existing approaches. The source code is available at https:://// / thub. com/ ShuhongLL/IIS M
Introduction
Recent breakthroughs in generative models [20, 12, 59] have sparked growing belief that Artificial General Intelligence (AGI) may be within reach. However, these models primarily operate on virtual data and often lack grounded understanding of space, time, and causality [24, 1, 28, 50], limiting
their applicability to real-world tasks [62]. To bridge this gap, World Models [30, 29, 65, 31] have been introduced in navigation [5], multi-task control [32], long-horizon planning [73, 47], and robot embodiment [78]. Incorporating physical constraints has also been shown to enhance continuous-time prediction [37], enable thysically-consiseenn generation [9, 53], and facilitate the development of foundation models for simulation, education, entertainment, and embodied AI [19].
In this work, focus integrating two fundamental physical principles- isometry and isotropy-inn Neural Radiance Fields (NeRF), particularly for modeling volumetric media outside the object. Classical NeRF [56] and its variants [6, 8] assume clear-air medium, where radiance is sampled or accumulated between the camera and the object surface. While this assumption simplifies computation, it discards nearly 93.36% of the 3D volume, thereby failing capture the full metric structure of the space. Recent efforts [16, 81] relax this assumption by introducing virtual attenuation in the surrounding air to simulate illumination effects, enabling robustness under low-light and overexposed conditions, In parallel, [45, 63] address non-air media by incorporating absorption and
Corresponding author.
Average space occupancy ratio across eight synthetic indoor scenes from the Replica dataset [67]. The ratio computed ground-truth meshes divided by the total grid size.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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General Radiative Formulation
Observation
Emission
Absorption
Scattering
Revised Underwater image Formation
Atmospheric
Scattering Model
Virtual Absorption Field Model
expl
(1 expl- =)
expl
expl
22))
eorp
Underwater Condition
Hazy Condition
Low-light Cond
Sunlight
Diffuse Downwell Attenuation
Media
B exp (o-"""""" )=²))))))))))))
Downwelll
Estimated Water Depth 2 scale = 7.2 m
Downwel Depth
obj-centrie
ours
10, 1/ 6 Real-world world
Real
LoS
Recorded Water Depth
Horiznntl Depth
Figure The proposed general radiative formulation accommodates diverse media conditions, including underwater, hazy, and low-light environments. The scene shown here was captured in the Pacific Ocean near Okinawa. As a result of isometric and isotropic metric perception, the estimated depth closely matches the actual depth of the scene.
scattering based on the Beer-Lambert Law and do not explicitly disentangle object geometry from volumetric media, limiting interpretability and physical fidelity.
phase functions. However, they
Existing NeRF-based methods predominantly rely on object-centric sampling, which places most sampling points near high-density object surfaces. As shown in the bottom row of Figure 1, SeaThru- NeRF [45] concentrates samples around rock surfaces while leaving large portions of the surrounding medium undersampled. This imbalance limits the representation of the full volume and compro- mises spatial consistency. To address this, we propose -ttaaie-tr upsampling strategy that explicitly allocates samples within the medium. Our method adopts a two-phase process: we first perform standard sampling in high-density regions, such the rocks illustrated in orange. We then compute reverse weight of the object density to guide stratified sampling in low-density regions, placing additional points in the trni-trrnsparent medium, shown blue points. This enforces the isometric property of the radiance field by ensuring that spatial sampling reflects the actual spatial extent of the scene geometry. By treating the medium approach enables a more faithful mapping between the physical real-world and the radiance space.
equal component of the radiance field, our
Building on the formulation. This formulation models the observation as the composition of attenuated direct radiance J and backscattered ambient radiance B, illustrated at the top of Figure 1. It unifies emission, absorption, and scattering in a direction-independeet manner generalizes naturally to a variety of degradation conditions. In underwater scenes, the coefficients oetl and oeest governing direct and backscattered radiance differ and exhibit wavelength dependence reflecting the spectral sensitivity of the camera. When absorption and scattering share common coefficient the formulation reduces to classical atmospheric scattering models [60]. Remarkably, this formulation even explain low-light conditions by introducing virtual absorption medium, where darkness emerges from radiance attenuation along the viewing direction.
prreeerrii particle sampling, we further introduce general radiative
Moreover, existing scattering-ave aware NeRFs [45, 63, 14, 83] perform radiative modeling only along horizontal line of sight (LoS), neglecting downwelling attenuation from ambient illumination. This effect is particularly important in media, where the radiance at each point physically depends on its vertical depth relative the medium surface. We address this by explicitly modeling downwelling attenuation at vertical depth 2 for each ray. This allows the
Law to apply uniformly

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in both horizontal and vertical directions, forming an isotropic radiative model. As a result, our method enables metric perception across the full 3D space. For instance, with known scale, our model estimates the water depth in Figure as 7.2 meters, closely matching the real depth, 7.5 meters, shown on the diving watch.
With the general radiative formulation established, we apply our model to various media-degraded applications, including low-light, hazy, and underwater scenes. On the low-light benchmark [16], our method achieves state-of-the-art (SOTA) performance, outperforming Gaussian Splatting-based approaches [17. 84] by approximately dB in PSNR. For haze and underwater datasets [45], we deliver competitive results that closely match current SOTA methods. These improvements stem directly from the integration of isometry and isotropy as core physical principles within the radiance field. Unlike previous methods that rely on heuristic tuning or pixel-wise manipulation, our model ensures high-fidelity reconstruction while preserving physical plausibility.
Overall, we make the following contributions:
We propose a general radiative formulation that unifies the modeling of underwater, hazy, and low-light environments through an isotropic modeling.
We introduce novel reverse-stratified upsampling strategy that enables sampling in NeRF space. Combined with absorption modeling, our method extends spatial representation beyond the one-dimensional line of sight to recover real-world scene structure.
Experiments on real-world datasets demonstrate that Ie-NeRF substantially improves both reconstruction fidelity and physical plausibility compared to existing approaches.
2
Related Works
Neural Radiance Field Neural Radiance Fields (NeRF) [56] and 3D Gaussian Splatting (3DGS) [40] have achieved remarkable performance in novel-view synthesis (NVS). Building this, physi- cally grounded formulations have been introduced to improve fidelity and robustmess under real-world conditions. For realistic image formation, [64] reinterprets neural fields probabilistically simulate lens effects, while PAC-NeRF [49] adopts a hybrid Eulerian-Lagrangian framework for dynamic media. Mip-NeRF and its successors [6-8] reduce aliasing via conical frustum sampling. Ref-NeRF [72] and PBR-NeRF [79] model view-dependent reflectance using BRDFs. DP-NeRF [43] and Deblurring-GS [42] address motion and defocus blur. Atmospheric scattering models are used in [63, 70, 14, 83] to dehaze scenes. RawNeRF [57] handles low-light inputs in linear space, while LL-NeRF [74] and LL-GS [68] apply Retinex-basedd decomposition. Aleth-NeRF [16] introduces a concealing field, and Luminance-Gss [17] and LITA-GS [84] leverage clumination-adaptiii pri- ors. In underwater settings, SeaThru-NeRFF [3], Proposed-T [69], and Watersplatting [46] model wavelength- dependent attenuation and backscatter. NeuroPump [27] accounts for lens refraction to improve realism.
Single-Image Restoration Recent progress in single image restoration tackles the challenges of low-light, haze, and underwater conditions through deep learning architectures and novel learning strategies. Low-light enhancement has shifted toward end-to-end learning [77, 71, 38, 211, utilizing techniques such as direct curve estimation [26, 15] and self-calibration [54] to improve visibility in darkness. Haze removal has evolved from prior-bace based methods [33] to data-driven approaches with a focus handling complex atmospheric degradations [13, 10, 48, 18]. Underwater image restoration
addresses unique optical distortions using generalized priors [23, 11, 51], physics- modeling [61, 3), and unsupervised techniques [22, 52,34.. 34].
3 Isometry and Isotropy NeRF
Preliminaries NeRF [56] implicitly represents scene with continuous function fe : (x, d) - (c,a) that encodes the 3D position x E R&& and viewing direction to predict the density a and view-dependent color e = (r.g, y, b). This color is interpreted as the radiance emitted by the objects along direction d. For a ray r(1) = o + emitted from the center of camera o and range & IR NeRF uses numerical quadrature to approximate the integral of volume rendering as
3

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C(r)== ( is the cumulative transmittance, and ò; is the distance between two points.
where T(r:) exp( ΣØ=1 (r,)),)
3.1 General Radiative Formulation via Matting
Traditional image matting [44] refers to the process of compositing target image / from a foreground and background component B, using blending coefficient [0, 1]. In this classical problem, a is typically estimated empirically and determines the mixing ratio between J and B at each pixel.
In participating media such as fog, haze, or water, light is subject to volumetric scattering, blur, and exponential attenuation. These effects result in an observed view that also arises from the combination of two components: the direct scene radiance J and the ambient backscatter light B. This similarity in structure allows us reinterpret media-induced degradation as a physically grounded extension of matting. In our isotropic radiative formulation, the blending coefficient is no longer an abstract mixing weight but a transmittance function derived from the Beer-Lambert Law, relative to the scene depth This yields general radiative formulation as:
I= J=J-ch B a1 - = = exp(-oottha atia
B (1 exp(-o scat
The coefficients øattn and øeett respectively encode the medium's is direct extinction and in-scattering properties under the single-scattering assumption.
Haze Condition Haze arises from aerosol particles in the atmosphere, causing both scattering and absorption. Koschmieder's Law [41] introduces a single extinction coefficient, implicitly assuming equal scattering and absorption contributions. In our general formulation, setting gatin scat regresses Equation (1) to the classical Atmospheric Scattering Model (ASM).
Underwater Condition underwater scattering, scattering and absorption differ due to distinct optical mechanisms. Scattering depends on particle size and concentration, while absorption is influenced by molecular composition and the inherent optical properties of water [36, 58). Therefore, we define o gattn * scat and generalize Equation (1) to the Revised Underwater Image Formation (RUTF) model [2].
Low-Light Condition Underexposed images can be interpreted through simplified pixel-scaling model - / K-J, where J represents the signal of well-lit scenes and K is per-pixel scaling factor. introduce virtual absorption medium
To incorporate this model into radiative formulation, that attenuates the photon flux reaching the sensor. This corresponds to special case of Equation (1), where the backscatter component B and the scaling factor K exp( -gattm 2) gains a physical interpretation as the transmittance through the medium. Further details are provided in Appendix A.3,
3.2 Proposed General Particle Model
In our neural radiance model, we explicitly represent both the objects and the intervening medium as volumetric particles characterized by two separate spatial density fields. As shown in Figure 2, these particles may emit, absorb, or scatter light according to the same radiative transfer rules [39].
Emission Under clear-air conditions, only object particles of density ob) emit radiance directly toward the camera. Therefore, the volume rendering formation of direct clear randiance J is identical to the vanilla NeRF:
N Gob) Σ T:(1 expl-o oc where T, =exp(- - Σ 11
j =
(2)
Absorption Absorption reduces transmitted radiance without re-emitting energy. The received degraded radiance at the camera is attenuated by the absorption density o atta.
NV Σ r. sop(-obb) obj where T.P exp( Σ (0 + + (gttm)6,). (3)
dooi
i=1

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in-scatter
(a)
Emission
Absorption
Scattering
2
Clear Scene
Absorption Media
Scattering Media
(b) NeRF's object-centric sampling
under-sampling
(c)
obj
object encoding
coarse
fine
reverse stratified sampling
up-sampling
med
view encoding
media hash encoding
med
linear layer+ ReLU
linear layer sigmoid
linear leyer softplus
CDF
media samples
Figure 2: Illustration of our particle model and pipeline. (a) depicts three types of particles in the media field that emit, absorb, or scatter radiance. (b) presents the media upsampling strategy designed to prevent media field collapse. (c) shows the model architecture, in which the object and the upsampled media points are processed by hash encoders followed by separate MLPs to predict density, color, and downwelling depth (in the case of scattering).
Scattering Particles such as suspended aerosols in haze colloidal particles in water can contribute additional backscattering radiance Émed by scattering ambient illumination into the viewing direction. Under single-scattering approximation, the scattered radiance from each sampled point along the ray is:
i-1 (o + )o)
Equed T.B (1 11--ey -ep((-op (cat d.))eeedd where T. exp(
(4)
j=1
Here, scat represents the scattering coefficient, med denotes the backscattered color contributed by ambient illumination, and 7 is the accumulated backscatter transmittance, Building upon our isotropic radiative formulation, we further model the backscatter color c qmed via Bembert attenuation of sunlight traveling vertically from the media surface. This approach reflects empirical observations, such as the progressive darkening with increasing water depth. At a sampled point i, the in-scattered medium color can be modeled as:
qmed 4 exp(-(o,,tua + occat) )
(5)
where is a learnable sunlight constant 2 2 denotes the downwelling distance to the medium surface, and ø + gest represents the diffuse attenuation coefficient [66]. This formulation further disentangles the formerly dew-dependent medium color into an explicit vertical attenuation model, enabling our radiance field to perceive the scene geometry both horizontally through LoS and vertically. Because d is expressed in the same metric units as the NeRF sampling space, our model maintains isometric relationship to real-world distances through a global scale factor. Although this scattering model allows per-sample specification of gatta ofeat and 2. such fine-grained parameterization significantly enlarges the optimization space. To make the problem tractable while preserving physical interpretability,
adopt the simplified RUIF model [2] that assumes horizontal rays with constant scattering coefficients and downwelling depth along each ray, as further described in Section 4. The detailed derivation of Equation (5) is shown in Appendix C.
Equal the empirical measurement of irradiance E(z, the medium surface (z 0).
5

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Final Model Considering all particle behaviors, the total radiance I received by the camera comprises the sum of direct radiance and potential in-scattered components:
N
N
Co
Emed
obj
T, (1- o, (,), c,red (6)
1=1
In Appendix B, we demonstrate that our volume rendering formulation in Equation (6) is equivalent the generalized image formation in Equation (1) across all degradation scenarios.
3.3 Reverse-Stratifeed Upsampling
Original NeRF [56] and its variants [63, 45, 16] employ a hierarchical coarse-to- to-fine sampling scheme [56, 6, 7] designed capture object densities in clear-air conditions. In real-world scenes, however, media particles reside exclusively along the LoS in front of objects, absorbing or scattering incoming light before it reaches the camera. This object-centric sampling thus under-samples the medium volume, which can cause the medium field to collapse into the object color during decomposition.
To realize the surrounding media in the NeRF model, propose novel reverse-stratified upsampling (RSU) strategy. As illustrated in Figure 2, our method upsamples media particles near-uniformly in regions where the object density is low solid object, we perform an additional sampling phase tailored specifically for media points. this phase, each current interval gobj is assigned a reverse weight derived from the object density oojj that favors low-density gaps:
Specifically, to sample media positions outside the
W,
A: max Jobj ISJSN
(obب) +,,
0i
1 A;
obi (1) dt,
(7)
jobi
where A, = yobj zob is the interval length, and is a small constant to prevent zero weight. Next, we normalize [weeed into cumulative distribution function (CDF) F and perform stratified sampling over [0, to draw Nadd new media points:
Uj U 1-1
obj
whenever F(i - 1) < uy F(1),
(8)
where U denotes uniform distribution. Finally, we merge these new media samples with the original object samples {1ob),, sort the union (1x), and obtain the upsampled set of ray-marching positions.
3.4 Objective Functions
We employ the reconstruction loss Crecon proposed by RawNeRF [57], which integrates inherent onnemapping to reduce sensitivity to scale variations during loss computation as:
2
1 M
i 1s
Lrccon
sg(1c)
+
where sg(-) denotes the stop-gradien operator, is the number of pixels, and c = 10-3 to avoid division by zero. To ensure geometric consistency, we introduce geometry loss Zreo between the normalized rendered depth D and pscudo-depth map D, obtained from a pretrained model [82] using:
Lgeo
1 M
Σ
D
(10)
To effectively recover the clean radiance structure . from the degraded observation I, we utilize compensated structure similarity loss Lcomp that accounts for ideal illuminance Vy and contrast factor R. This loss is calculated over H stochastic ray sub-patches following [80], expressed as:
Lcomp
1
1
Σ
LESIM
(11)
H
h=1

---

where Ph. denotes the h-th randomly extracted patch. Each patch-wise loss employs the SSIM index [76], adjusted for the desired mean and variance.
Considering the physical constraint that space is occupied either by objects or media, we apply a mutual exclusion loss Lmutex prevent simultaneous high densities of object and media the same spatial location:
N Σ N
Linttex
(0, obj n)) x medd
(12)
where N is the number of sampled points in ray, and the threshold 7) 0.1 helps avoid the trivial solution of zero media. Moreover, if a media transmittance prior T available, we define the media transmittance loss Lmedia to constrain media density at the object's 's surface depth z:
M Σ
Lmedia =
Σ Th Txl
1 M
exp(
Ei0 + toyood)8)) - TEl..
(13)
Additionally, to ensure a physically plausible monotonic decay in media density. which par- ticularly critical in nonhomogeneous media, we introduce a monotonic decay loss Lmono = MN k= E ReL ORi-i1 ) Thus, the total media transmittance regularization loss is defined as Liras Lemedia L.mon- The complete optimization objective is thereby expressed as:
Lrecnn = L + Ccop Ageofigeo + Amutex Luttex Atraus Ctrans:
(14)
where the hyperparameters Acomp. Ageo Amutexx and Aurans are specific to application scenarios. Media density a med in the above context subject to gattn or gueat, as applicable. Detailed derivations and justifications for the loss components are provided in Appendix E.
4 Applications
Underwater Scene To reflect the near- homogeneouu distribution of water particles and make the computation of scattering radiance tractable, adopt the RUIF model [2] which assumes horizontally propagating rays (i.e., an inclination angle of 90" the nadir direction) in Equation (4). Under this simplification, the attenuation and scattering coefficients are treated as constant along each ray r, i.e., ofttm (r) = a ( (r) and o scat (r) = (r). Consequently, each point along the ray is approximated cqued(r (r) = eimed The clean radiance J is obtained by rendering the scene with the scattering field removed. The model is optimized by minimizing Equation (14), with the À hyperparameters set to 0, 10 10 and respectively.
having an identical downwelling depth =f) =*(r) and media color
Hazy Scene We apply the identical settings and assump- tions used for underwater scattering the case of air-based scattering. The model is optimized using Equation (14), with the hyperparameters to 10-2, 10-4 and respectively.
Rendered Crear Imagh
SCF tranemot. Map
Low-light Scene In low-light conditions, spatially varying illumination necessitates modeling the absorption medium as nonhomogeneous along each ray. To regularize this inher- ently ill ill-posed setting, we incorporate an external supervi- sion signal Tp derived from the Bright Channel Prior (BCP) [75]. BCP estimates 2D illumination map Tp from the bright channel of each local patch P C I, and models the low-light image as:
objjett media a
object media
3.2 0.4
0.8
0.4 0.4
Fay Sarppl (anean coln
RtySSnp/eerod point)
Figure 3: Visualization of virtual ab- sorption fields on the LOM dataset [16]: (a) restored clean radiance J; (b) illumination map Tp estimated unsu- pervisedly via the BCP: (c,d) Particle density profiles along the rays, corre- sponding to the green and red points illustrated in (a).
1 I max 9EP
I= Tp J, and Tр
max cE(r.g.)
B
(15)
Within our volumetric framework, where attenuation solely attributed to the absorption field, this illumination
7

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Watersplattng SeaThru-NeRF
SeaThru-NeRf
Ours
Watersplatting
med
Distribution
Ours
Novel-view Synthesis
Backscatter
Object
Media Color
Vertical Depth
Figure 4: Visualization of NVS and media decomposition the SeaThru-NeRF dataset [45]. Our method precisely estimates the vertical water depth, which inaccessible in baseline methods. Top- right comner displays the mean RGB values of the medium color cmned from test views, alongside the real-world ranges simulated in [4] across various Jerlov water types [35] within depths 1-20 meters.
Table Quantitative comparison of hazy and underwater scenes on SeaThru- NeRFF dataset [45].
"Hazy Fern"
"Curaçao"
"TUI3 Red Sea"
"J.G. Red Sea"
"Panama"
Model
PSNR SSIM LPIPS PSNR SSIM LPIPS PSNR SSIM LPIPS PSNR SSIM LPIPS PSNR SSIM LPTPS
MipNeRF360 [7]
30.23 0.880 0,150 28.23 0.683 0.571 19.55 0,510 0,520 19.62 0.624 0,492 18.32 0.556 0.595
ZipNeRF [8]
30.34 0.875 0.142 19.96 0.442 0.421 16.94 0.474 0.412 19.02 0.349 0.483 19.01 0.349 0.482
3DGS [40]
25.96 0.782 0.303 28.31 0.873 0,221
22.98 0.843 0.249
21.49 0.854 0,216 29.20 0.893 0.152
NeaFh.NeRF [45]
30.75 0.870 0.160 30.96 0.915 0.133
26.76
0.826
0.168
23.28
0.876
0,111 31.28 0.937 0.071
Proposed-T [69]
30.03 0.828 0.238 22.70 0.624 0.348 25.81 0.853 0.183 23.75 0.687 0.263
Watersplat, [46]
29.35
0.880
0.181
32.20 0,948 0.116 29.84 0.889
0,203
24.74 0.892
0.116 31.62 0.942 0.080
Ours
30.59 0.862
0.139
32.70 0.947 0.144 27.33 0.870 0.269
24.11 0.884
0.168
31.55 0.938 0.096
map acquires a concrete physical interpretation as the accumulated transmittance of each ray through the medium up the object surface. This allows the BCP-derived illumination map Tp to physically grounded transmittance prior T in Equation (13) that constrains the transmittance object surfaces. Leveraging this BCP-derived supervision, the media density converges toward a physically plausible distribution that maintains clear spatial separation from the object geometry, shown in Figure 3. To incorporate this constraint during training, the model is optimized using Equation (14) with À hyperparameters
10-2, 2, 10-4, and 10-3, respectively.
Experiments
5.1 Implementation Details
Our model is built upon the ZipNeRF codebase [8], leveraging hash-based encoding for efficient training. For NeRF sampling, use 64 points for the object and 32 additional points for upsampling the media field. The global sunlight constant initialized to CIE D65. Additional hyperparameter details and visualizations of experimental results are provided in Appendices G and
Datasets For underwater environments, we use the SeaThru-NeRF dataset [45]. For low-light conditions, we conduct evaluations on the LOM dataset [16]. Both datasets follow the original train-test split. In addition, we captured two real-world underwater scenes in Okinawa, Pacific Ocean, using OLYMPUS Tough TG-6 underwater camera and recorded the corresponding water depths.
Metries To assess reconstruction quality, we adhere to common metrics including PSNR, SSIM, and LPIPS. The best results are shaded as first. second and third for each metric.

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"chair"
Lowlight// / Ground truth
IAT 3DGS
SCI- 3DGS
Aleth NcRF
Luminance GS
Ours
Figure 5: Qualitative comparison of NVS on the LOM dataset [16].
Table 2: Quantitative comparisons of low-light restoration performance on the LOM dataset [16].
"bike"
"buu"
"chair"
"shrub"
"sefa"
Model
PSNR SSIM LPIPS PSNR SSIM LPIPS PSNR SSIM LPIPS PSNR SSIM LPIPS PSNR SSIM LPIPS
ZipNeRF [8]
6.64 0.083 0.611
7.72
0.291
0.445
6.19
0.151 0.590
8.48 0.037 0.658 6.30
0.212 0.553
3DGS [40]
6,38 0.071 0.822
7.74
0.292 0.459
6.26
0.146 0.761
8.74 0.039 0.604
6.21
0.201 0.918
SCIIS4]+NeRI
13.44 0.658 0.435
7.76
0.692
0.525
19.77
0.802
0.674
18.16
0.503 0.475
10.08
0.772 0.520
[AT[15)+NeRF
13.65 0.616 0.528
14.46
0.705 0.386
18.70
0.780 0.665
13.87 0.317 0.536 17.88
0.829 0.547
SCI[54]+GS
13.67
0.677 0.324
7.95
0.695
0.501
21.77 0,866 0.350
18.67 0.657 0.153
9.99 0.750 0.452
IAT[15]+GS
11.55 0,570 0.593
14.23
0.727
0.207
17.59 0.858 0.344
14.26
0.517 0.366
16.96
0.841 0.347
Aleth-NeRF [16]
20.46
0.727 0.499
20.22
0.859 0.315
20,93
0.818
0,468
18.24
0.511
0.448
19.52
0.857 0.354
Lumin-GS [17]
18.27 0.749 0.412 18.09 0.878 0.193 19.83 0.836
0.367 15.41 0.666 0.242
20.12
0.259
LITA-GS [84]
22.75
0.819
0.282
20.59 0.897
0.175
22.60 0.873 0.223
19.35
0.659
0.217
20.43
0.895 0.268
Ours
22.87 0.803
0.278
22.35
0.845
0.203
23.82 0.847
0.280
19.44
0,674
0.249
25.89
0.859 0.234
Baselines For underwater scenes, we compare against SeaThru-NeRF [45], Proposed-T [69], and Watersplatting [46]. For low-light scenarios, we compare our method with end-to-end reconstruction approaches, including Aleth-NeRF [16], Luminance-Gr [17], and LITA-GS [84]. We also evaluate hybrid pipelines that incorporate 2D low-light enhancement models [15, 54].
5.2 Evaluation of Underwater Scenes
Table reports quantitative results of NVS on the SeaThru-NeRU dataset [45], where our method achieves competitive performance. Figure 4 illustrates both NVS and scattering decomposition results. While Watersplatting [46] produces visually compelling scene reconstructions, it struggles to capture volumetric scattering effects and erroneously attributes object radiance and shadows to the scattered media component. Compared to SeaThru-NeRRF [45], our method additionally estimates downwelling water depth. By incorporating downwelling attenuation modeling that accounts for water depth, our predicted medium color more accurately reproduces the spectral characteristics of natural oceanic water, where red light attenuates more rapidly than green and blue [4].
To evaluate the accuracy of the predicted downwelling depth, we applied our model to scenes captured in the Kerama Islands National Park, northwestern Pacific Ocean. As shown Figure 1, the subsea anchor has an approximate scene footprint of six meters. Using this as reference, we compute scaling factor that maps the NeRF sampling space [0, 1] to real-world metric units. Multiplying the predicted depth value in the region of the vanishing line by this factor yields an estimated downwelling distance of 7.2 meters. This result closely matches the recorded water depth of 7.5 meters as measured by the diving computer, demonstrating the accuracy and physical consistency of our model.

---

5.3 Evaluation of Low-light Scenes
For low-light restoration, we conduct experiments on the LOM dataset [16]. As shown in Table 2, our method achieves state-of-the-arr PSNR performance across all scenes, outperforming both NeRF-based and GS-based approaches [16. 17, 84]. Figure 5 presents qualitative results on three representative scenes. Our physically grounded volumetric model enables consistent and balanced color restoration across views by explicitly modeling media degradation. In contrast, pixel-scaling- based baselines exhibit noticeable color inconsistencies. Appendix G.4, we include a low-light underwater case study where our physically grounded model decomposes multiple media components and reconstructs clean radiance under hybrid conditions
5.4 Ablation Study
Effect of RSU We demon- strate the effectiveness of our upsampling strategy. Figure shows two views from low- light and underwater scenes, displaying the restored radi- ance and corresponding den- sity distributions in terms of sampling positions. Our strat- egy recovers the pace-filling media in front of objects by explicitly allocating samples, in contrast to object-centric methods that neglect these regions and cause media field collapse to near-zero densities.
W/
W/O
w/
w/o
W/
rands
w/o
from oceanic water
J from low-light
Figure 6: Ablation study of RSU upsampling strategy.
Effect of Loss Terms We present ablation analyses for each loss term under low-light underwater scenar- ios in Table and Table 4. Due to the inherent ill posedness of reconstruct- ing scenes through media, our pro- posed loss terms specifically de- signed to enforce physical plausibility. While omitting Liuttx permitting a non-homogencous scattering field may enhance the rendering quality of the observation I, it hinders the accurate recovery of the clean radiance J due to the lack of explicit density regulation, leading media field collapse. More analysis and visualizations are provided in Appendix F.
Table 3: Ablation of absorp- tion field on the "bike" [16].
Table 4: Ablation of under- water field on our captured scene in Okinawa.
Method
PSMRSSIMS
w/o upsampling
20.92 0.792 0.284
Method
PSNRSSIMI PIPS PIPS
w/o Egoo
20.66 0.776 0.297
inconstant m3d.a333..70.9133...
w/o Leomp
6,55 0.078 0.712
w/o upsampling
$2.080.8850.215
w/o Lanutex
22.71 0.793 0,281
w/o Egso
0.920.83
w/o Ltrans
21.87 0,790 0.285
w/o Lmutex
33.110. 178
Full model
222877 0.803 0.278
Full model
31.250.8870.201
6 Conclusion
We propose [2-NeRF, physically grounded volumetric model for radiative interactions in par- ticipating media. The model preserves isometry and isotropy through explicit sampling of dense objects and semi-transparent media, and with unified attenuation model applied consistently across viewing and vertical axes. This design enables metric-preserving scene reconstruction that faithfully reflects real-world spatial structure. Experiments across diverse media conditions demonstrate the effectiveness of our approach in achieving high reconstruction quality and physical plausibility.
Limitations While 12-NeRF demonstrates competitive performance in various degraded media conditions, it has several limitations. First, compared to rasterization-base methods [40, 17, 46]. our NeRF model requires longer training time due its neural implicit representation. Second, our model assumes static media with fixed optical properties, limiting its applicability to dynamic scenes such as moving water or drifting fog. Moreover, under scattering conditions, media properties such as downwelling depth have dependency on the encoded viewing directions, leading to variations that may not be strictly tied spatial position. In low-light settings, varying light across views can also degrade performance, our static virtual absorption medium cannot adapt dynamic illumination.
10

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Acknowledgement
This work was partially supported by JST Moonshot R&D Grant Number JPMJPS2011 I, CREST Grant Number JPMJCR2015 and Basic Research Grant (Super AI) of Institute for AI and Beyond of the University of Tokyo. In addition, this work was also partially supported by JST SPRING, Grant Number JPMISP2108.
The authors sincerely thank Mr. Zonggi Pan and the DeepSea Diving Center (Okinawa, Japan) for their valuable assistance in capturing the underwater scenes used in this study.
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Appendix -
Table of Contents
Image Formation Under Media Degradation
16
A.1
Degenerated Atmosphere Scattering Model (ASM)
16
A.2 Revised Underwater Image Formation (RUIF) Model
17
A.3 Simple Low-light Scaling Model
17
A.4
Low-light Bright Channel Prior (BCP) Model
18
Relation of Radiative Formulation and Particle Model
19
B.1 Low-light Conditions
19
B.2 Haze and Underwater Conditions
20
C Downwelling Attenuation Model
20
D Reverse-Stratified Upsampling
21
Objective Functions
21
E.1
Reconstruction Loss Creson
22
E,2
Geometry Loss Leen-..
22
E.3
Compensated Structural Similarity Loss Loomp
22
F
Additional Ablation Study
23
F.1
Underwater Scene
23
F2
Low-light Scene
24
G More Experimental Results
25
G.I Underwater Scene
25
G.2 Hazy Scene
25
G.3 Low-light Scene
28
G.4 Low-light and Underwater Hybrid Scene
28
H Downstream Applications
28
H.l Single-Image Volume Estimation
28
H.2 Physically-Groudder Synthesis
30
I Implementation Details
30
J Sanity Check
31
K Multiple Running
31
Training Time Analysis
32
M Dataset Diversity
32
Future Works
32
A Image Formation Under Media Degradation
In Section 3.2, introduced radiative model describing image formation under media degradation conditions. Here, we provide a detailed explanation of the typical image formation process in such environments. Specifically, and described clearly as a matting process, which combines direct radiance from objects and ambient illumination scattered by particles present in the medium.
show that image formation under media degradation can be simplified
A.1 Degenerated Atmosphere Scattering Model (ASM)
In hazy atmosphere, airborne particles such as water droplets, dust, and aerosols scatter and absorb incident light. These effects form veil that reduces contrast and desaturates color [55]. Under the
16

---

single-scattering assumption of the Atmospheric Scattering Model (ASM), the intensity observed each pixel of observation composed of two components: direct radiance from the object attenuated exponentially with distance, and ambient illumination scattered toward the camera by airborne particles. This is formulated as:
direct
bookscatter
B
(16)
observed object radiance
atternation
airlight
accumatiaiion
where z denotes the horizontal distance from the object surface the camera. J represents the radiance of clean image without media degradation, and 8 indicates the ambient airlight origi- nating from distant illumination sources. ASM, a single attenuation coefficient characterizes both direct transmission and backscatter. This shared attenuation coefficient exhibits wavelength independence due to the dominance of Mie scattering. Mie scattering occurs when particle sizes in haze significantly exceed the wavelengths of visible light, resulting in nearly equal scattering across all wavelengths.
A.2 Revised Underwater Image Formation (RUTF) Model
Unlike in air, image formation underwater is strongly dependent on wavelength X. This occurs because water molecules and suspended particles selectively absorb and scatter different wavelengths of visible light. Define the beam absorption coefficient as a()). the beam scattering coefficient as b( ()), and the beam attenuation coefficient B(A) a(A) b(A). Assuming horizontal line-of-sight (LoS), the narrow-sense underwater image formation model can be expressed as:
backscatter
direct
b(A) a(A) b(A)
(e (
A(z,
(1 - (o()++)(((
obsorved radiance object
attenaation
Irvadiance
accumuiation
(17)
where E(2, A) denotes the ambient irradiance at distance 2 along horizontal viewing directions. Moreover, due differences in optical pathways and directional sensitivity of the imaging system, the camera response to direct and scattered radiance signals differs significantly. As a result, two distinct coefficients, (At for direct signal attenuation and (X) for backscattered signal accumulation, are introduced. Incorporating these separate coefficients simplifies Equation (17)) into the Revised Underwater Image Formation (RUIF) model proposed by [2]:
direct
backscatier
(e-o + B000 (A)
(2)-2)
(18)
observed radionce
object radionce
altensation
ambient Hight
accumialation
In this context, _ (A) denotes the veiling light originating from ambient illumination at an infinite viewing distance, defined as:
B(A)
BeS (A) F F(2 A)- a(A) + B(A)*
(19)
where ② represents the vertical downwelling distance from the water surface. Although similar in form to the ASM, this underwater model differs in two critical ways. First, the direct attenuation (A) are distinct values. Second, values, accurately reflecting the selective absorption
coefficient (atta()) and the scattering accumulation coefficient scat(()
both coefficients exhibit and scattering characteristics of underwater media across different color channels.
A.3 Simple Low-light Scaling Model
As shown in Section 3.1, under low-light conditions, the image formation can effectively approxi- mated using simple scaling model. This simplification is valid because, in low-light conditions,
17

---

veiling light is negligible relative to the significantly reduced direct radiance. The simplified scaling model can thus be expressed as:
direct
buckscutter
K
(20)
observed color
object color
scaling factor
where K' denotes scaling factor and the backscatter component set to zero (B% 0). In the general radiative formulation, this simplified scaling scenario can be physically interpreted by introducing an absorbing medium positioned between the camera and the object, attenuating the photon flux along the viewing ray. Given the attenuation coefficient gtta and the object depth the lig-light image formation can then be represented explicitly as:
direct
backscatter
(21)
observed nadionce
object radiance
attenuation
A.4 Low-light Bright Channel Prior (BCP) Model
Inspired by the Dark Channel Prior (DCP) model [33], which was originally developed for modeling hazy environments, the Bright Channel Prior (BCP) model [75] was introduced to characterize illumination degradation in low-light images and to support local exposure correction. BCP formulates low-light image formation using an image matting approach. Specifically, the observed low-light image / is modeled as:
direct
compensation
Tp
B
(1-Tp)
(22)
observed color
object color
illumination intensity
ambient color
illumination compensation
Here, Tp represents the local illumination intensity computed over a patch centered at each pixel. Compared to the simple scaling model introduced in Equation (20). this formulation additionally includes global ambient term that accounts for veiling light in underexposed regions.
BCP is based on the assumption that in well-fit images, the bright defunne as the maximum intensity value across color channels within local patppaapttpeeeeeee approaches one. Formally, for clean image J, the bright channel is:
JBC
max J PEP
(23)
cE(r.g.b)
Empirically, JBC for well-lit images. In contrast, for a low-light image the corresponding bright channel I BC << 1 due to suppressed illumination.
To derive the illumination map Tp from low-light observation I, we first express Equation (22) in channel-wise as:
= J Tp B (1-Tp), ce {r.g.b}
(24)
Solving for Tp yields:
1 B Tp B
(25)
To estimate Tp, maximum operator is applied over the patch P C T:
1: Be
Tp max CE (E
max PEP
(26)
J
Be)
Assuming JBC = 1 and that Tp is constant within the patch, this simplifies to:
B
Tp = max cEfr.g.b)
max V
q
(27)
1
B
18

---

Rewriting this expression leads to the final BCP formulation:
1 I 1 B
Tp = 1
max (E.g.)))
max 9EP
(28)
The ambient constant B can estimated empirically as the average of the darkest 0.1% pixels the bright channel Ine [75]. Since B is typically small, we can approximate B as O, which simplifies Equation (22) to:
J-
(29)
This simplified form is equivalent to our low-light radiative formulation in Equation (21) with veiling light B = 0. Consequently, the BCP-derived local illumination map Tp acquires a physical interpre- tation as the transmittance through a virtual absorption medium. We leverage this transmittance map to supervise the estimation of the medium density in our training process, as described in Section 4.
B Relation of Radiative Formulation and Particle Model
In Sections 3.2 and 3.3, we introduced a general radiative formulation for modeling image degra- dation in participating media, along with volumetric particle model that incorporates emission, absorption, and scattering processes. In this section, we establish the equivalence between the two by demonstrating how our particle-based volumetric rendering aligns with the radiative formulation.
Using isometric sampling for the participating medium, we discretize the volume along each camera ray into intervals [&t, 81+1]. and assume uniform spacing where i ō and 8 denotes the constant sampling step. Suppose a single opaque object lies along the ray at the end of the interval [sk; sk+1], the object depth is then given by k 6. The ray terminates at index le when it intersects the object surface, and the transmittance drops to zero beyond this point.
Under this setting, we define the object density gobj to be nonzero only at index i == k, and zero for all i < kt Conversely, the medium densities, such as the absorption coefficient atta or the scattering coefficient g are defined only for intervals prior to the object surface, i.e., g gcat for 2 k. This setup reflects a spatial separation between the opaque object and the participating medium, capturing the physical intuition that dense objects and sparse media do not occupy the same space along the ray.
B.1 Low-light Conditions
Under low-light conditions, we simulate reduced visibility by introducing a virtual absorption medium. In this case, Equation (3) simplifies to:
Cobi k = TP. (1 (1- (1-exp(-obbin) bbbj
(30)
direct radiance
exp
obi (og
( exp(-ox -bbi 6x) ck ogtm))6)
obi
(31)
Assuming oj = 0 for all j < k. and taking both the interval length 6, = and the attenuation
coefficient gittm s gattn as roughly constants, the expression simplifies to:
obj Č = exp(-oo k:)) (1 exp(-o -0bb1)) c%
(32)
In typical low-light scenarios, the object density of sufficiently large that the ray terminates at the object surface, resulting in exp( -opp-ophii ohis) ~ 0. Therefore, we further simplify the expression to:
ck abj
exp( attn k5)
(33)
cx
obj
exp( aattn 2)
(34)
19

---

This result corresponds to a special case of our general radiative formulation under low-light con- ditions, as presented in Section 3.2, where the observed color is modeled as the attenuated object radiance with = Cj and no ambient component (B = 0).
B.2 Haze and Underwater Conditions
In scattering dominant environments, where backscattered radiance contributes significantly to the observed signal, we follow the derivation approach of [45] to formulate Equation (6) as:
Ö =
Cooj Σ
Emed
+
Emed
(35)
1=1
i=1
TR
- exp( (1-exp(- x 5k))
obi
obj
T. (1 (1-expp
exp ofpa 0;)) ond
(36)
direct radiance
backscatter radiance
The direct radiance term Equation (36) identical to the expression derived in (30), and can be simplified using the result in (34). We now focus on the backscatter term:
h Σ
i Σ j=1
Cmed
Σ exp
(ogh) + ogcue)o8 (1 exp( (xcaat 5,)) mned
(37)
im1
exp (-oscat scat i8) (1 exp(- - (opp--occttpp )ecat 8)) c,ued
(38)
Assuming the single scattering approximation holds and that the medium properties are approximately uniform along the ray, we treat cfudd constant value emed and obtain:
Σ Xmed = (1-exp(-- expp(oocat scat 8)) med
Σ ex -ca0- scat i8)
(39)
exp( expp-oaen J k5)
= - exp( - 8)) mod.
(40)
exp( expllosccat
= 1 -expp- acat c
(41)
Substituting (41) back into (36) gives:
obj k
exp(
attn kō) + c med (1 exp( - g -k))
(42)
direct
backscatter
obj exp( atta 2) + med (1 exp(-oo cosp--oscat. 2))
(43)
This expression consistent with our general radiative formulation, where J c and = med In atmospheric environments, the absorption and scattering components often combined into a single extinction coefficient, such that gttta = aaatt, due to the relatively uniform interaction between light and small airborne particles. In contrast, underwater environments exhibit distinet optical behaviors, where gattn # scat.
C Downwelling Attenuation Model
In Equation (19), the ambient light at infinity 8 (A) is proportional the irradiance E(2 X). which models the downwelling light reaching the medium along vertical paths. This irradiance accounts for the cumulative attenuation of sunlight as travels downward through the medium. According to [66], the downwelling irradiance at a vertical distance 2 can be modeled as:
E(z 4 A) E(O, A) exp(-K K (A) 20)
(44)
20

---

Here, (( denotes the ambient light at the surface of the medium, and K (A) is the diffuse downwelling attenuation coefficient. As derived Equation (43), we can establish connection between the medium radiance e. (X) in our volume rendering framework and the downwelling irradiance at depth via:
b(A)E(=*) med (A) = (A) a(2) + b(A)
((A)((O) a(A) B(X) exp( exp((-K*(0) - (A). =*).
(45)
According to [25], the diffuse downwelling attenuation coefficient A *h (A) can be approximated as function of the beam attenuation coefficients and the solar incident angle 8%
(A) ~ (a(2) - b(A)) cos 0
(46)
In practical scenarios, the beam absorption coefficient ({A) and scattering coefficient 6(A) are difficult
to estimate directly due their dependence local environmental and optical conditions. As alternative, we approximate them using the learned attenuation coefficients o g (A) and o scat (A)
obtained from our neural radiance field. Assuming direct overhead sunlight with cos 8
substituting Equation (46) into Equation (45) yields:
mod (A) ~ (()) A)
:xp( (xpp(((oatti() + o scat (A)) =0)
(47)
a(A) + b(A)
= Φ (sp(-(ontti(>> + scat (2))
(48)
Here, & denotes an ambient light coefficient at the medium surface. Following the setup in [2].
where E(0 A) is empirically initialized to solar illumination, similarly initialize T the CIE D65
daylight spectrum. This per-scene constant then optimized jointly with the parameters of our NeRF model during training.
D Reverse-Stratifeed Upsampling
In Section 3.4, we introduce media upsampling strategy designed to explicitly model the media field as spatially separate from the object geometry. this section, we provide a detailed explanation the subsequent stratified sampling and merging procedure. Specifically, given the reverse weights womedd over the original N intervals derived from Equation (7), we compute their cumulative distribution function (CDF) as:
T; TN
r
W med
F(i)
i= N.
(49)
We then draw Nadd stratified uniform samples:
Uj U
Nada N
1, 1,..., Nadd.
(50)
Invert the CDF by identifying the unique index i such that F(i 1) < uj F()), and sample within that interval as:
emed u (1ob) (
(51)
The complete set of sampled positions is formed by merging and sorting the object-centric and media-centric samples:
[tx} = sort ((eDbig y
(t Nadi |==1
(52)
The resulting sorted set {4x is then forwarded to our neural radiance model.
E
Objective Functions
In this section, we provide detailed formulations of the reconstruction loss Creom- the geometry loss Ego,, and the revisited structural similarity loss Lamas which were introduced in Section 3.4.
21

---

E.1 Reconstruction Loss Lrecon
In degraded images exhibiting low contrast, the standard L2 reconstruction loss employed in vanilla NeRF [56] often fails to emphasize differences in inw-intessity regions. To address this limitation, we follow [57] to incorporate tone curve linearization that places greater emphasis on reconstruction fidelity in low-intensity pixels. Specifically, we use the loss:
Ln Is
2
Freecm
Σ k=1 +c(C))++))
(53)
M
where sg(:) denotes the stop-gradient operator, M is the number of pixels in the batch, and e 10-3 avoid division by zero. This loss implicitly applies gradient supervision of the tone-mapping curve log(x + c) and produces high reconstruction quality in degraded conditions.
E.2 Geometry Loss Cgeo
To regularize scene geometry under visually degraded conditions, we utilize the pretrained DeepAnything-Vi V2 model [82] to generate pseudo depth maps as a geometric prior. Since the predicted depth is the relative depth map, we normalize the rendered depth to the range [0, 1]. The geometry loss is then defined as
M
Lgoo
D2
D2
(54)
M
k=1
where D2 denotes the normalized depth rendered from our NeRF model, Dy is the corresponding depth prior from the pretrained model, and M is the number of pixels in the batch.
E.3
Compensated Structural Similarity Loss feomp
The Structural Similarity Index (SSIM) is perceptual metric that evaluates image quality by comparing local patterns of pixel intensities. It decomposes similarity into three components: luminance, contrast, and structure. Formally, SSIM measures local means to assess luminance consistency, variances for contrast similarity, and normalized covariance to evaluate structural alignment.
However, in severely degraded conditions, especially under low-light environments where the ob- served radiance is strongly attenuated by the absorption medium, the observed image I often deviates significantly in luminance and contrast from the rendered object radiance J. To mitigate this dis- crepancy, we propose a revised structural similarity loss that compensates SSIM using the ideal luminance V and contrast scaling factor K, Such prior information can be derived from common well-lit images or tuned as hyperparameters during experiments. Specifically, let G' be a Gaussian kernel. We first compute local means of the rendered object radiance . and the observation I:
ò G J. V1, G I,
(55)
along with the global mean of the observation I as:
(56)
M
Here, M denotes the number of pixels within the batch. We then compensate the observation's
luminance and contrast using the prior Dy and R, as follows:
v comp
(vr - mm) R.j + DJ. (o = R3 (G 12 12 -
(57)
For the rendered radiance J. we compute local contrast and cross-correlation as:
of G * j²2 13 σ.I = G (J (J-1) - V1, With constants Ci = (0.01) 3 and C2 = (0.03)2, the compensated SSIM index is then derived as:
T comp = kj OJJ.
(58)
2 20 v comp + C1
20 comp + +C2 + (o) +
SSIM comp =
(59)
03 + (u) compps
comp y2 C
luminance
contrast-structure
22

---

And the SSIM loss is given by:
LSSIM SSIM (J, (J,
(60)
Since NeRF training randomizes ray sampling and disrupts spatial correlations, we adopt the strategy from [80] and apply our revised SSIM loss over stochastic image patches. Specifically, we define the final structural similarity loss as
1 H
Coomp
(ssi
(61)
where P extracts the /-th randomly partitioned ray patch, and repeat // times obtain averaged loss.
F
Additional Ablation Study
Underwater Scene
In Section 5.4, we present a quantitative ablation study on each component of our NeRF model. Specifically, for the LOM dataset [16], the evaluation was performed by comparing the restored object radiance against the ground-truth well-illuminated images. In contrast, for the Thruu-NRRRF dataset [45], the evaluation was based on the rendering quality of degraded novel-view images, since obtaining clean object radiance free from scattering infeasible in real-world underwater conditions. Due to this unavoidable difference in evaluation protocols between low-light and underwater scattering settings, the quantitative results reported in Table 4 do not fully capture the model's ability to disentangle and reconstruct scene components.
In this section, we elaborate on the ablation study for underwater scattering scenes and provide more intuitive qualitative and quantitative evaluations. As shown in Figure 7, we visualize novel-view synthesis results differences under well-illuminated yet challenging conditions, where backscattering is intensive. In such environments, backscattered radiance tends to collapse into object radiance, making the separation between the two more difficult. This radiance blending may superficially improve novel- view synthesis quality from the observed image perspective, as it effectively ignores the backscatter component and simplifies the task to resemble clear-air scenario. However, doing so leads to inaccurate estimation of the media field, undermining the physical plausibility of the model.
underwater scene captured by ourselves in Okinawa to highlight performance
We observe that omitting reverse-stratee stratified upsampling (RSU), the geometry loss faea or the mutual exclusivity loss femutex results in the collapse of scattered radiance into the object radiance, as evident in the rendered object and backscatter components. Furthermore, this collapse leads to erroneous depth estimations in both horizontal and vertical directions, making the recovered scene geometry physically unreliable.
We also examine the case where spatially varying scattering coefficients attn and scas are used along each ray. In Section 4, we discuss that, to accommodate the hear-homogeneous nature of the scattering medium and simplify the problem. we follow [45, 63] to assume constant media densities along the ray. While allowing inconstant scattering coefficients offers greater flexibility, it introduces extreme ill- ill-posedness in the absence of prior knowledge about the water medium. In practice, real-world underwater conditions are highly complex, and acquiring reliable priors for water properties is challenging. Without such constraints, the decomposition of scene radiance becomes physically inconsistent and results severely degraded reconstruction quality.
Table 5: Mean Chromatic Dissimilarity Metric (MCDM) between the restored object radiance J and the original underwater observation I for each ablation component of our model. Higher MCDM values indicate a greater chromatic separation from the original scatter-degraded image.
Ablation w/o RSU
w/o Liutex
w/o Egoo
full model inconstant
Object
6.06
11.64
13.94
15.88
24.22
To quantitatively assess the discrepancy between the recovered object radiance j and the observed image 7, we employ the Mean Chromatic Dissimilarity Metric (MCDM). MCDM measures the average perceptual difference chromaticity between two images, where higher values indicate greater deviation in color. Importantly, MCDM is not designed to reflect reconstruction fidelity;
23

---

Schine Images.
Obsarvation
Disarvation
Observation
Test
Test View 2
Test View 3
Full Model
Inconst M exdia
w/o RSU
w/o Epo
w/o Emu Ab
Novel-view Synthesis
Object
Backsratter
Horizontal Depth
Vertical Depth
Figure 7: Visualization of the ablation study underwater captured in Okinawa. In this well-illuminated environment, stronger backscattering occurs due to the increased ambient light being scattered by suspended particles. As result, distinguishing between the object radiance and the backscattered radiance becomes more challenging, especially when foreground objects exhibit colors similar the background water body.
rather, it provides an objective measure of chromatic separation. As shown in Table 5, in the ablated components, lower MCDM values indicate that the recovered object radiance closely resembles the observed image, suggesting collapse of the media field in which backscattered radiance is incorrectly absorbed into the object signal. On the other hand, excessively high MCDM values, such using inconstant scattering coefficients, reflect a failure case in scene decomposition.
F.2 Low-light Scene
Table 3, we present an ablation study on the application of our model low-light environments, In this section, we further investigate the effect of two critical hyperparameters: the ideal illumination ūy and the contrast factor R,, both of which are used in the compensated structural similarity loss Coomp defined in Equation (61).
24

---

j= 0.3
A=j= 0.4
A== 0.5
A=
Increase contrast
RJ PJ=10 10
KJ== 14
Increase illumination
Figure 8: Ablation study on the hyperparameters for ideal illumination vy and contrast factor R. in model, conducted on the "bike" scene from the LOM dataset [16].
As shown in Figure 8, Vy primarily controls the brightness of the restored clean object radiance J. with higher values leading to increased pixel intensities. R. governs the contrast of J, with higher values enhancing edge sharpness. The yellow pentagram indicates the selected hyperparameter values used in final model, which are close to the appearance of naturally well-lit images.
G More Experimental Results
G.1 Underwater Scene
As shown in Figure 9, we compare our method against SeaThru-NeRF [45] and Watersplatting [46] on the SeaThru-Nett dataset [45]. In the case of SeaThru-NeRF, the horizontal depth maps are truncated at regions with low accumulated radiance weights, and the oceanic background is removed during depth map rendering. Compared to the baseline methods, our model produces more accurate depth estimation along LoS and enables spatial perception that extends beyond the typical one-dimensional ray to incorporate vertical distance.
While Watersplatting [46] achieves state-of-the-an performance in full-image rendering. it struggles to accurately decompose scene radiance. Consequently, its backscatter component often contains erroneous elements from the object signal, such shadows or textures. In contrast, our approach yields more physically faithful geometry and radiance decomposition, leading to superior scene reconstruction under media degradation.
G.2
Hazy Scene
For the hazy environment, we conduct experiments on the synthetic hazy Fern scene provided in the SeaThru-NeRF dataset [45], as capturing real-world multi-view hazy scenes challenging. The synthetic scene is generated by first estimating the depth along the LoS and then applying the ASM to synthesize haze-induced degradation. Such hazy conditions present notable challenges for degradation removal, as the additional backscattered radiance significantly increases pixel intensity. As a result, the strong backscatter signal is often misinterpreted by models as part of the scene geometry, leading inaccurate estimation of the medium properties.
25

---

IUB3-RedSea
Watersplatting Sea Thru NeRF
Not Applicable
Applicable
Ours
JapaneseGurdens-Reeseee
Watersplatting SeaThru- NeRF
Not Applicable
Not Applicable
Ours
Panama
Waterrspl cettrrpplcting letting SeaThhu NcRF
Applicable
Applicable
Ours
Novel-view Synthesis
Backscatter
Object
Media Color
Horizontal Depth
Vertical Depth
Figure 9; Visualization of our method and baseline approaches on the SeaThru-NeRI dataset [45].
As shown in Figure 10, SeaThru-NeRF [45] exhibits media field collapse, where the estimated backscattered radiance is nearly zero and the restored image fails remove haze-induced degradation. In contrast, Watersplatting [46] suffers from an opposite failure case, which overestimates backscatter and erroneously attributes object radiance the medium component. This results in underexposed restorations with blurred boundaries and degraded structural fidelity, as shadows and fine edges are inaccurately absorbed into the backscattered signal.
In contrast, our model achieves well-balanced decomposition by incorporating physically grounded constraints and a metric-preserving perception strategy, producing sharper restorations and more accurate scattering estimation. Furthermore, our isotropic attenuation model with downwelling distance enables more realistic prediction of medium color, better capturing the color pattern of haze compared to SeaThru-Nee [45].
It is worth noting that the synthetic scene is constructed using globally constant scattering coefficient a, which differs from real-world scattering environments where the scattering varies spatially with medium depth and thickness. Consequently, model predicts uniform vertical depth map, which
26

---

Object Radiance
Object
Object
Object
SeaThru-NeRF
Watersplatting
SeaThru-NeRf
Not Applicable
Watersplatting
Applicable
Ours
Novel view Synthesis
Backscatter
Media Color
Horizontal Depth
Vertical Depth
Figure 10: Visualization of our method and baseline approaches on synthetic hazy scene from the SeaThru-NeRF dataset [45]. The top shows the restored clean object radiance, while the bottom row compares full image rendering, backscattered radiance, estimated medium color e med and depth maps.
"sofa"
"shrub""
Low-light/ Ground-truth
|AT + 3DGS
SCI + 3DGS
Alath-NoRF
Lumina nce-GS
Ours
Figure Low-light restoration results of our method compared baseline approaches on the LOM dataset [16].
actually reflects the characteristies of this synthetic setup. This outcome also serves as a sanity check, reinforcing that our model provides physically plausible interpretation of the scene.
27

---

Low-light Scattering
Obscrvations
Test View 1
Test View
Test View 3
Decomposed NVS
Object
Scattering
Scattering
Object
w/o Absorption Medium
Backscatter
Object
Vertical Depth
Figure 12:
Visualization of a real-world low-light underwater scene captured Okinawa. We also present the decomposed radiance components, such removing the virtual absorption medium used to model low-light conditions, the direct object radiance, and backscattered ambient light.
G.3 Low-light Scene
As shown in Figure 11, we present visual results on the remaining two scenes from the LOM dataset [16]. Our method achieves more color-consistent restoration compared to both NeRF-based and Gaussian Splatting based approaches.
G.4 Low-light and Underwater Hybrid Scene
Benefiting from our general radiative formulation, the proposed model supports the simultaneous incorporation of multiple types of media, making it adaptable complex real-world environments. As case study, we captured low-light underwater scenes using an OLYMPUS Tough TG-6 camera under short-exposure settings. Within particle-based neural radiance framework, we jointly model both low-light and scattering effects. As shown in Figure 12, our method effectively decomposes the scene and reconstructs clean object radiance under hybrid low-light and scattering conditions, demonstrating its robustness in real-world physical settings. Although the vertical depth estimation becomes less precise due to interference from multiple interacting media, it still faithfully reflects the depth property of the scene.
H Downstream Applications
[45] demonstrates that modeling both the object and the participating medium in 3D space enables range of downstream applications, such as scene geometry reconstruction, clear radiance restoration, and medium property estimation. Building on this foundation, we explore several physically grounded applications enabled by our Ne-NeRF framework, particularly in underwater environments.
H.1 Single-Image Volume Estimation
Benefiting from metric-preserving framework, model enables the estimation of real- world physical quantities. In this section, we demonstrate how the volume of subsurface water can be estimated from single underwater image, based certain valid approximations and simplified geometric assumptions.
We begin by assuming an orthographic camera model, where all rays emitted from image pixels are parallel to the horizontal axis. For each pixel Ptj an image of size H, x W,, the emitted ray travels horizontally until it
intersects with object surface. The horizontal distance from the camera
28

---

Zi
A 2 Volume
AW
Parallel Rays
Image Plane
V
x
AW
2
Figure 13: Illustration of subsurface water volume estimation under orthographic projection assumption. Left: Each image pixel corresponds to non-overlapping 3D cuboid, defined by its horizontal extent Zs.j. vertical height A=,"; and pixel-aligned width Aw. Right: All rays are assumed to be parallel and aligned along the horizontal axis, consistent with an orthographic camera model.
denoted as zi.j. Meanwhile, the downwelling attenuation module estimates the vertical distance from the ray the water surface, denoted =
To convert image coordinates into real-world dimensions, we assume that a physical scale prior is available-that is, the real-world width corresponding to the image field of view is known estimated. In our case, for the underwater scene captured in Okinawa, we set the real-world width to six meters based on rough field measurement of subsea anchor present in the scene. As illustrated in Figure 13, each pixel is thus associated with a unique cuboid 3D space, defined by its horizontal extent zij- vertical height A and lateral span Aw. where Aw Wrea//W WW is the real-world width per pixel assuming uniform spacing. Since adjacent rays may penetrate to different depths, compute the Aeú; of each vertical water column by taking the difference in downwelling depth between vertical neighboring pixels:
be
fi=
A
(62)
max (0, 2..j
z4- 15)s
otherwise
The resulting per-pixel water volume is given by:
ViJ zi. b
Aw
(63)
Summing over all pixels across the image yields the total visible subsurface water volume:
H1 Wi
Vistal
Z
Aw
(64)
Applying this formulation to our underwater scene, and using the anchor-based scale prior of six meters image width, we estimate the total traversed water volume visible in the field of view to be approximately 330.68 cubic meters.
Although we introduce certain approximations and simplified assumptions, our method retains the ability to recover physically interpretable quantities. Unlike previous approaches that operate entirely within virtual space, 12-NeRF incorporates geometric alignment with physical measurements. This enables the estimation of real-world metries, such as volumetric quantities, a manner consistent with the physical structure of the environment.
29

---

Curasao
IU13-RedSea
J.G RedSea
Panama
Decrease Depth
Original Scene
Increase Depth
synthesis under varying water depths. By modifying the downwelling depth estimated in our model, we simulate the same scene under shallower (left) and deeper (right) water conditions.
Figure 14:
H.2 Physically-Gronnde Synthesis
Our framework reveals interpretable physical properties such as attenuation and scattering coefficients, sunlight parameters, and distances in the 3D volume, which enables controllable and physically grounded scene synthesis. In this example, we simulate the same scene under shallower and deeper water by scaling the downwelling depth by factor of one-third and three, respectively. These changes affect scattering and ambient illumination, resulting in noticeable variations in color tone, contrast, and visibility. As shown in Figure 14, our model enables realistic appearance modulation that reflects physically plausible modulation in underwater conditions. This supports the potential of our approach not only for geometry-ave rendering but also for physically grounded scene editing aligned with underwater optics.
I Implementation Details
our implementation based on Zip-NeRF codebase [8], we set number of proposal sampling
points to 128, the number of NeRF sampling points to 32, and the number of media upsampling points 32, treating them equally to object samples. The sampling hierarchy level is set 2. We employ two separate hash grid encoders for object and media components, which introduces slight
30

---

increase in training time but is necessary to preserve their distinct geometry and spatial distributions. The output dimensionality of both hash encoders is set 256.
Under scattering conditions, to enforce per-ray constant medium properties (i.e. a o and 2²)) in the RUIF simplification [2], we pool the per-sample predictions along each ray and the pooled values in subsequent volume rendering. For low-light conditions that favor spatially varying medium distribution, we instead preserve the per-sample media densities, allowing each sampled point to maintain its distinct value during volume rendering.
For the LOM dataset [16], batch size is set to 2048, and for our captured underwater scenes, it is set to 1024. Each batch size is scaled proportionally to the total number of pixels in the respective dataset. The maximum number of training steps is set to 25,000. We use the Adam optimizer with an initial learning rate of 10-2 and final learning rate of 10-4
batch size of 4096. For the SeaThru-NeRF dataset [45], the
Input images are loaded into the NeRF model at their original resolutions. We follow the same train-test splits provided by the datasets. For the SeaThru-NeRF dataset [45], we adopt the common practice in previous studies by assigning every 8th view as the test view. All experiments are conducted on single NVIDIA RTX A6000 Ada GPU. Training time are provided in Appendix L.
J
Sanity Check
(a) ZipNeRF [8]
(b) Our direct radiance
(c) Our backscatter radiance
Figure 15: Sanity check on clear-air Fern scene from NeRF dataset [56].
(a) ZipNeRF [8]
(b) Our direct radiance
(c) Our backscatter radiance
Figure 16: Sanity check on clear-air bike scene from LOM dataset [16].
Following SeaThru-NeRR [45], we conduct similar sanity check by applying our model to clear-air scenes while enabling the media branch. As shown in Figure and Figure 16, we compare the novel-view synthesis of direct radiance and backscatter radiance of our method with the ZipNeRF [8] baseline. Our approach produces no backscatter component when scattering is absent in clear-air scenes.
K
Multiple Running
Table 6: Multiple running statistics on the bike and Curasao scenes.
Metrics
PSNR
SSIM
LPIPS
bike
22.82 = 0.05
0.798 + 0.01
0,279 + 0.00
Curasao
30.55 = 0.04
0.860 + 0.01
0.142 0.00
31

---

Due to computational costs, we present statistical results based on multiple rums for two scenes: the low-light bike scene from the LOM dataset [16], and the underwater Curasao scene from the SeaThru-NeRe dataset [45]. As shown in Table 6, we report the mean and standard deviation of PSNR, SSIM, and LPIPS metrics across five independent runs.
L Training Time Analysis
In this section, we present a training time analysis of our method and baseline approaches on the low-light [16] and underwater [45] datasets. As shown in Figure 17, our method achieves fair training efficiency, benefiting from hash encoding to accelerate convergence. Gaussian Splatting based approaches demonstrate significantly faster training times due to their rasterization based rendering process.
Low-light
Underwater
Training Time
Training Time
3.15
1.23 h
0.86
0.20
0.16
AlethNeRF
Ours
Lum-GS
SeaTh.NeRF Ours
Watersplat.
Training time analysis of our method and baseline approaches low-light and underwater scenes. For each model, the training time recorded using a single NVIDIA RTX A6000 Ada GPU.
Figure 17:
M Dataset Diversity
In this study, we evaluate our method on benchmarks that encompass various types of media degradation. For low-light scenes, we use the LOM dataset [16], which contains five real-world scenes captured as underexposed multi-view images, along with corresponding ground-truth well-lit images. For underwater scenes, we employ the Sea SearhruNNRRF dataset [45], which includes four real-world underwater scenes without ground-truth clean object radiance. Additionally, we capture two underwater scenes ourselves- one under well-illuminated conditions and another exhibiting hybrid of low-light and underwater scattering. For hazy environments, we utilize the synthetic hazy Fern scene provided [45].
The datasets used in our evaluation cover wide range of degradation scenarios, allowing for fair comparison and clearly demonstrating the superior performance of our method over baseline approaches. Nonetheless, evaluating on larger number of scenes would further strengthen the generality of our conclusions. Given the limited availability of multi-view datasets with media degradation, collecting more real-world data, especially with paired degraded and ground-truth images, is considered as future work.
N Future Works
Apart from real-world paired datasets that facilitate the study of 3D reconstruction under degraded conditions, several key directions deserve further investigation. First, integrating physically grounded 3D representations into large-scale foundation models offers a promising path toward spatially and physically aware reasoning. Such integration could enhance the model's 's ability to understand geometry, material properties, and environmental interactions in complex scenes.
Second, there remains lack of evaluation metrics that reflect physical correctness. Existing image- based metrics such as PSNR and SSIM are limited to appearance similarity and fail to capture geometric fidelity or physical plausibility. While comparisons based point cloud or mesh complete- ness are more suitable for geometric evaluation, they require high-quality ground-truth data and are not applicable to implicit volumetric representations, which do not produce point- surface-based
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Developing evaluation metrics that account for radiometric consistency, media media- aware realism, and structural integrity is increasingly important as scene representations move toward physically based modeling.
outputs,
Finally, reconstruction pipelines assume access to accurate camera poses. However, in real-world degraded environments, such priors are often unavailable. Traditional structure- crructue-frommmeee from-moooooooon methods and deep learning-based pose estimators struggle under strong scattering, blur, and noise. Recent advances in pose-free methods alleviate this dependency by learning jointly from unposed images, but their performance remains limited heavily degraded conditions. Improving the robustness of such methods under physical degradation is critical for real-world deployment.
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Reviews:
[{"review_id": "R5X6LHiJqB", "reviewer": "Reviewer_sErE", "summary": "This paper presents I2-NeRF, a neural radiance field framework designed to improve 3D perception in challenging environments with media degradation such as underwater, hazy, or low-light conditions. The method introduces a reverse-stratified upsampling strategy for near-uniform 3D sampling to preserve geometric properties (isometry) and develops a unified radiative formulation based on the Beer-Lambert law that handles emission, absorption, and scattering effects in degraded media.", "questions": "N/A", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The paper is well-written, organized and easy to follow.\n- The paper takes into account absorption as well as scattering in volumetric rendering, allowing for improved performance in low-light condition or condition with semi-transparent medium.\n- Proposal of reverse stratified sampling (RSU) for modeling on semi-transparent medium is novel and intuitive, and is demonstrated to be effective in the ablation experiment.\n- Overall, the method is robust and clear in its objective, and the method seems well-designed and meets the objective well.\n\n**Weaknesses:**\n- The paper's main focus is on describing novel sampling strategy and volumetric rendering strategy in case of non-translucent medium, but the setting where the method achieves SoTA is low-light setting, in which external supervision signal $T_p$ plays a heavy role. In other settings, the method is unable to achieve complete SoTA. This makes me question whether the performance improvement of the method derives from incorporation of $T_p$ rather than its novel reverse stratified sampling or medium-modeling volumetric rendering. I ask the authors to clarify this question for me, demonstrating that its major performance gains come from the novel methodology the method proposes.\n- The method is designed to implicit neural representation-based settings where sampling of the network is conducted: can this method be extended to 3DGS for improved speed and rendering speed? What is the computation overhead and optimization time required to train a single scene? Please elaborate.", "was_revised": true, "final_justification": "My initail concerns, especially regarding the theoretical foundation of RSU in low-light conditions and the view-dependent density modeling, have been adequately addressed through the authors' detailed responses. For this I continue to recommend acceptance. The authors provided clear explanations that:\n\n- RSU in low-light settings is theoretically sound - the method models absorption (not scattering) in low-light conditions, where the \"density\" represents optical attenuation coefficients rather than physical density. The separation of absorption fields from object geometry allows proper restoration while preserving underlying scene structure.\n- View-dependent modeling is scientifically justified - the authors provided authoritative references, with detailed explanation, convincing me that that scattering phase functions are inherently view-dependent. Their statement that NeRF tries to recover *optical density* of the scene, not explicit geometrical density, was especially crucial in coming to this understanding. I agree with this statement, as NeRF ultimately is trained on photometric loss between the representation and its rendered image.\n\nThe rebuttal successfully resolved my primary theoretical concerns about the method's foundation. The authors demonstrated good understanding of light transport theory and provided appropriate scientific backing for their design choices. While some complexity remains in the view-dependent architecture, this appears to be a necessary component for handling real-world scattering scenarios rather than a fundamental flaw. In this light, I recommend acceptance for this paper.", "rebuttal": "**We are grateful for the valuable comments, especially the suggestion to extend the proposed method to 3DGS. Please find our detailed responses below. We look forward to hearing your opinion.** (Supp denotes supplementary matrial)\n\n### **W1. Ablation studies of $T_P$ and RSU**\n\nThank you for the question. As shown in Sec. 5.4 ablation study, we demonstrate that **while $T_P$ plays an important role in low-light conditions, the physical constraints and RSU sampling are also essential for accurate modeling**. Our ablation study in Tab. 3 shows that with $L_{trans}$ that incorporates external supervision signal $T_P$, the performance of our model on LOM dataset [1] increases for 1 dB in PSNR. RSU also proves crucial, and it increases PSNR for approximately 2 dB.\n\nIn low-light environments, the proposed method integrates several key elements to enhance restoration performance. Specifically, we incorporate an additional supervision signal $T_P$ derived from the Bright Channel Prior (Supp Sec A.4), which is used to define the transmittance loss. In addition, the model includes geometry-guided depth supervision (Line 193), a specially designed SSIM loss to compensate for luminance and contrast discrepancies (Line 196), and the RSU sampling strategy (Sec 3.4). By employing all of these components, the proposed method achieves SOTA performance on the competitive low-light restoration task [1].  \n\nThe importance of RSU is further illustrated in the right panel of Fig. 6. Without explicit media sampling, the estimated media field tends to spatially overlap with the object, as shown in the sub-figures of density distribution. This leads to noticeable artifacts in the restored novel views. \n\nOn the other hand, in real-world scattering environments, it is inherently difficult to remove the scattering medium from a scene to obtain clean ground-truth restoration views. As a result, datasets like SeaThru-NeRF [2] lack ground-truth images for evaluating restoration performance. Therefore, in this setting, we report novel view synthesis (NVS) results instead. As shown in Tab.2, $I^2$-NeRF achieves competitive performance in NVS under scattering conditions.\n\n**In scattering conditions, by incorporating our geometric constraints and RSU sampling strategy, we achieve notable improvements in both restoration quality and geometric accuracy compared to their counterparts without these components.** In scattering scenarios, we do not incorporate $L_{trans}$ as there is not external supervision signal on transmittance, i.e., $T_P$. To qualitatively evaluate the effect of RSU on restoration performance, we illustrate the restoration outcomes with and without  RSU in the left panel of Fig. 6. In scattering conditions, insufficient media sampling along the ray causes the backscatter radiance to collapse into the direct radiance emitted by scene objects. This collapse disrupts the separation between the media field and object geometry, leading to empty media field and visible artifacts in restored views.\n\nIn Supp Sec F.1, we provide more visualizations (Fig. 1) and a quantitative chromatic analysis for each key designs of $I^2$-NeRF under scattering conditions.\n\n### **W2.1 Training time and computation overhead**\n\nThe average training time of our model is 1.23 hours on the LOM dataset [1] (compare to Aleth-NeRF [1] of 8.25 hours) and 0.86 hours on the SeaThru-NeRF dataset [2] (compare to SeaThru-NeRF [2] of 3.15 hours). $I^2$-NeRF achieves substantially faster training speeds compared to previous NeRF-based approaches [1-2], benefiting from the hash encoding of spatially sampled features. Regarding computational overhead, compared to ZipNeRF [5] (our codebase), $I^2$-NeRF requires approximately 30% more training time (\\~20 minutes) on the low-light dataset [1], and approximately 25% more (\\~12 minutes) on the underwater dataset [2] on same device.\n\nIn Supp Sec. K, we provide detailed information for the training time of the proposed method and baselines on both low-light and underwater scenes using the same GPU. **We will add a sentence in Line 246 to indicate the training time and refer readers to the corresponding section in supplementary material for more details.**\n\n### **W2.2 Potential extension to 3DGS**\n\nWe greatly appreciate this brilliant idea. After investigation, we find that a potential solution lies in integrating rasterization-based rendering techniques with point/voxel-based representations derived from NeRF, such as the recently proposed Sparse Voxel Rasterization [6]. This hybrid approach would enable geometry-aware sampling for both objects and participating media, while leveraging the rendering efficiency of rasterization. By doing so, it has the potential to significantly accelerate training without compromising reconstruction quality, offering the best of both implicit and explicit representations. \n\nWe are particularly excited about the implications of this direction for real-time and resource-constrained applications. Achieving such efficiency would pave the way for deploying the proposed method on embedded systems, edge devices, and long-term environmental monitoring platforms, where both computational speed and physical realism are critical. We look forward to exploring this promising avenue in future work and believe it could significantly broaden the impact of physically-grounded neural rendering.\n\n### References:\n\n[1] Cui, Ziteng, et al. \"Aleth-nerf: Illumination adaptive nerf with concealing field assumption.\" Proceedings of the AAAI conference on artificial intelligence. Vol. 38. No. 2. 2024.\n\n[2] Levy, Deborah, et al. \"Seathru-nerf: Neural radiance fields in scattering media.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2023.\n\n[3] Cui, Ziteng, Xuangeng Chu, and Tatsuya Harada. \"Luminance-GS: Adapting 3D Gaussian Splatting to Challenging Lighting Conditions with View-Adaptive Curve Adjustment.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025.\n\n[4] Li, Huapeng, et al. \"Watersplatting: Fast underwater 3d scene reconstruction using gaussian splatting.\" arXiv preprint arXiv:2408.08206 (2024).\n\n[5] Barron, Jonathan T., et al. \"Zip-nerf: Anti-aliased grid-based neural radiance fields.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023.\n\n[6] Sun, Cheng, et al. \"Sparse Voxels Rasterization: Real-time High-fidelity Radiance Field Rendering.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025."}, {"review_id": "8wuCJxwstr", "reviewer": "Reviewer_sN9j", "summary": "This paper presents a method for learning NeRF representation in the presence of scattering media, which has applications in underwater, hazy, and low-light environments. A reverse stratified sampling technique is employed to focus sampling on the scattering medium along the ray. For underwater applications, a “downwelling distance” is predicted to guide the media color and is claimed to be related to the actual underwater depth.", "questions": "1. The concept of “downwelling distance” is confusing. From Figure 2, it indicates that $z^{\\Phi}$ is a function of a 3D position and viewing direction. Is this view-dependent? If it is view-dependent, how does it relate to the physical depth?\n\n2. In Figure 4, what is the difference between “Backscatter” and “Media Color”? If “Media Color” refers to $c^{med}(r)$ in equation 5, then at which point along the ray (of the pixel) is this color evaluated? Similarly, at which point is the “vertical depth” evaluated for each pixel? For a camera operating under perspective projection, rays are not parallel; therefore, they cannot all be parallel to the sea surface and maintain a constant depth.\n\n3. On the other hand, if the Media Color $c^{med}$ is constant for each ray, it doesn’t seem necessary to apply the proposed RSU strategy to sample more points in the scattering media for the underwater application. The assumption of homogeneous distribution already implies that the media density is constant (in lines 215-216). Together with the constant color, the NeRF’s volume gathering wouldn’t change with the number of samples. Moreover, in Figure 6 (left), what is the “media density distribution” if it is already held constant?\n\n4. As indicated in equation 5, $c^{med}(r)$ monotonically decreases as the “downwelling distance” increases. However, this does not correspond to Figure 4, where the bottom of the media appears brighter while the vertical depth is deeper. How is that interpolated?\n\nThe questionable concept prevents me from engaging with this paper; more technical details rather than just the formulation would help address my concerns.", "limitations": "yes", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Quality: The method is fairly sound; however, the claims are not well supported due to the ambiguous key concept of “downwelling distance,” as elaborated in the questions section.\n\nClarity: While the paper is structured, it is difficult to distinguish its novelty from previous work. In Section 3, it would be beneficial to incorporate existing models in the \"Preliminaries\" and then highlight the original modifications. The key novelty is not presented clearly enough.\n\nSignificance: The quantitative evaluation shows only marginal improvement. It is challenging to assess the physically-grounded properties given the ambiguity of the key concept.\n\nOriginality: The novelty of this work compared to, for example, SeaThru NeRF [1], is not very clear, as the formulation in Section 3.3 shares many similarities. Two noticeable original designs are the reverse stratified sampling and the use of “downwelling distance,” both of which lack robust evaluation.\n\n[1] SeaThru-NeRF: Neural Radiance Fields in Scattering Media", "was_revised": true, "final_justification": "After extensive discussion with the authors, several concerns were addressed and I raised my rating to borderline reject. Key agreements:\n\n* The RSU (Reverse-stratified Upsampling) alters training gradients by querying density values with positional embeddings and pooling to keep them constant per ray. While seemingly inefficient, this approach is acceptable.\n* View-dependent media densities: I accept this paradigm for underwater NeRF modeling despite limited justification. It is uncommon in other NeRFs and rare in volume-rendering literature, but plausible.\n\nRemaining issue:\n\n* View-dependent downwelling distance: As a central claim for demonstrating “isometry,” treating downwelling distance as view-dependent undermines its physical interpretation. The authors should either revise the model or provide experiments showing view consistency.\n\nOverall, technical details are clearer, but I remain negative due to limited and insufficiently justified technical contributions. Given other reviewers’ positive recommendations, I could accept the paper for its inclusion of low-light scenes and the completeness of the work, provided the authors address consistency in the downwelling depth analysis in a revision.", "rebuttal": "**We appreciate the feedback and questions, which help clarify our NeRF‑based model for a broader conference audience. Below, we provide our explanation and responses to each point of the questions and concerns.**\n\n### **Q1. Concept of downwelling distance**\n\nThank you for the question that helps clarify the description of our model design. The downwelling distance $z^{\\Phi}(r)$ is not explicitly a 3D function; instead, it is view-dependent and associated with each ray. Our model as well as previous studies [2-4] are all built upon the Revised Underwater Image Formation (RUIF) model [1] (Line 136/Sup Sec A.2), which plays an important role in forming the basis of scattering modeling. In precise underwater imaging, the line-of-sight (LoS) is not parallel in horizontal directions, and this introduces an inclination angle $\\theta$ in the nadir direction. This causes the backscatter radiance at every point along the LoS to depend on $\\theta$, which significantly increases the ill-posedness of the problem (Eq. 1 in RUIF paper). To make the problem tractable, RUIF makes a core contribution to the community by proposing a simplified formulation by setting $\\theta=90^{\\circ}$, which reduces to an inclination-free interpretation (Eq.2 in our Supp/Eq.2 in RUIF paper). **This simplification assumes all LoS are horizontal when computing the backscatter radiance** (also shown in Line 59 of our Supp). In this approximated model, each point along LoS will have the same downwelling depth. Note that this simplification only applies to backscatter radiance. **We will add this explanation in Sec 3.1 to emphasize horizon simplification, and revise the bottom-right portion of Fig. 1 to improve clarity.**.\n\n### **Q2. Backscatter and media color & Points of downwelling depth and media color**\n\nBackscatter describes a behavior that particles redirect incident light into the camera’s viewing direction. Backscatter radiance is the cumulative radiance (multiplying transmittance) collected from those scattering events along a ray. Media color is $c^{med}(r)$, represents the scattering albedo (of a scattering particle) quantifying how much ambient light is redirected toward the camera in a single scattering assumption (Line 127, and Supp Sec. A.1/A.2). Under RUIF model, rays are approximated to be parallel when computing backscatter radiance, and all sampling points on a ray is simplified to have the same $c^{med}(r)$ and $z^{\\Phi}(r)$.\n\n### **Q3.1 Clarification of $c^{med}(r)$**\n\nIn the scattering conditions such as underwater scenes, by adopting RUIF, the media color $c^{med}(r)$, scattering coefficient $\\sigma^{scat}(r)$, and downwelling depth $z^{\\Phi}(r)$ become constant along each ray. These coefficients are associated to each ray, and can vary across different rays. To accurately reflect this modeling, we revise Eq. 5 in our paper as follows:\n\n$c^{med}(r) = \\Phi\\ \\cdot \\exp\\bigl(-(\\sigma^{attn}(r) + \\sigma^{scat}(r))z^{\\phi}(r)\\bigr)$\n\nHere $r$ represents individual ray and $\\Phi$ is the scene constant global illumination.\n \n### **Q3.2 Necessity of RSU strategy**\n\nThank you for the comment. Under scattering conditions, where the medium color and scattering coefficients are constant, it is  possible to apply a closed-form solution to directly compute the backscatter radiance component of a ray. **We find that utilizing this closed-form approach can reduce GPU memory by approximately 4 GB (at a training batch size of 2048).** However, our spatial sampling design presents two advantages:\n\nFirst, inverse rendering in scattering conditions is an inherent ill-pose problem requires separating the direct and backscatter radiance given only the degraded observations. Explicit spatial sampling, such as provided by RSU, is therefore crucial for the successful optimization of the NeRF model. **Accurate media sampling helps prevent the collapse of the media field** (Line 177/292), a failure case where backscatter radiance is incorrectly attributed to direct object radiance, leaving the medium field empty (as demonstrated in Fig. 6 left and Supp. Fig. 1 w/o RSU). This collapse becomes particularly significant when the ambient light has close color to the scene color, such as in shallow underwater scene (Supp Fig. 1) and hazy scene (Supp Fig. 4). Geometrically accurate spatial sampling facilitates the proper separation and convergence of the two distinct fields (media and object), resulting in remarkably improved restoration quality, as demonstrated in Fig. 4, Fig. 6, and Supp Figs. 1, 3, and 4.\n\nSecond, in low-light environments (no scattering only absorption), a spatially variant absorption field is required (Line 226) due to the highly-dynamical scene illumination. As a result, **the media density becomes inconstant along each ray, and there is no closed-form solution.** We visualize the density distribution of two representative rays in Fig. 3. To employ a unified model architecture capable of handling all adverse media conditions, we adhere to the current design of spatially sampling media points along each ray. When a constant value is needed, we apply additional pooling to retrieve a scalar value (Line 220). Moreover, as shown in Tab. 3 and right panel of Fig. 6, RSU also plays a crucial role under low-light conditions. Without this geometrically accurate sampling, the absorption field tends to spatially overlap with scene objects, resulting in visible artifacts in the restored outputs.\n\n### **Q3.3 Explanation of Fig.6**\n\nFig. 6 shows the distribution of density $\\sigma^{scat}(r)$ for all rays from the entire image, plotted over sampling depth. As noted in Q3.1, $\\sigma^{scat}(r)$ varies across rays, and thus the distribution is non-uniform.\n\n### **Q4. Relation of media color and downwelling depth**\n\nAs noted in Q3.1, the medium color $c^{med}(r)$ depends on the global constant $\\Phi$, the attenuation and scattering coefficients $\\sigma^{attn}(r)$ and $\\sigma^{scat}(r)$, and the downwelling depth $z^{\\Phi}(r)$. Since these coefficients are ray-dependent, different pixels/rays can have different values. Consequently, $c^{med}(r)$ does not necessarily decrease monotonically with $z^{\\Phi}(r)$, as it is also dependent to $\\sigma^{attn}(r)$ and $\\sigma^{scat}(r)$. However, when these two coefficients are held constant, the backscatter radiance does decrease with increasing $z^{\\Phi}(r)$, as demonstrated in Supp Fig. 8.\n\n### **Relation to SeaThru-NeRF's formula on Section 3.3**\n\nVanilla NeRF models only the radiance contributed by scene objects, neglecting the non-contributive clear air in the space. SeaThru-NeRF [2] was the first to attribute radiance and weights to the surrounding 3D volume, extending the formula of RUIF [1] to multi-view underwater reconstruction. Formula of Section 3.3 in our work builds upon this physical model, further generalizes to a broader range of media scenarios including low-light, haze, underwater, and even hybrid conditions (as shown in Supp Sec G.4) using a unified model formulation. $I^2$-NeRF incorporates physical plausibility and enables interpretable estimation of media properties. Specifically, our work differs from SeaThru-NeRF [2] in the following aspects:\n\n- We propose a unified physically-grounded formulation that models both low-light and scattering effects within a single framework (Lines 7/50/56/76). This allows our model to handle diverse media conditions, even including hybrid scenarios combining low-light and scattering showing in Supp Sec. G.4. In contrast, SeaThru-NeRF models only scattering.\n- Our model applies the Beer-Lambert attenuation law along the vertical direction, enabling physically plausible recovery of media properties, including water depth (Lines 13/62/81). By comparison, SeaThru-NeRF yields implausible estimations, as illustrated in Fig. 4.\n- We introduce RSU, a precise media sampling strategy that facilitates the separation of medium and object geometry (Lines 5/36/78) and prevents collapse of the media field, which otherwise leads to artifacts and vanishing media content (Lines 177/292/304). Without this sampling strategy, the model can converge to a trivial solution with low/zero media field, shown in Fig.6 and Supp Fig. 1.3.4.\n\n### **Experiment performance**\n\nOn the highly contested low-light restoration task [5], the proposed method archive SOTA performance compared to recent approaches. On the challenging SeaThru-NeRF dataset [2], it demonstrates competitive results in novel view synthesis. Beyond numerical performance, our approach provides physically plausible reconstructions, as discussed above, including sampling, restoration, and media property estimation. Furthermore, in Supp Sec.H, we presented two potential applications of $I^2$-NeRF for scientific estimation and visualization, highlighting its potential to extend physically grounded neural rendering to a broader range of real-world and scientific domains.\n\nWe are willing to engage in further discussion.\n\n### References:\n\n[1] Akkaynak, Derya, and Tali Treibitz. \"A revised underwater image formation model.\" CVPR, 2018.\n\n[2] Levy, Deborah, et al. \"Seathru-nerf: Neural radiance fields in scattering media.\" CVPR, 2023.\n\n[3] Tang, Yunkai, et al. \"Neural underwater scene representation.\" CVPR, 2024.\n\n[4] Li, Huapeng, et al. \"Watersplatting: Fast underwater 3d scene reconstruction using gaussian splatting.\" 3DV, 2025.\n\n[5] Cui, Ziteng, et al. \"Aleth-nerf: Illumination adaptive nerf with concealing field assumption.\" AAAI, 2024."}, {"review_id": "0pUP5LMjMK", "reviewer": "Reviewer_teTt", "summary": "The paper proposes a new method for modeling non-clear air medium for 3D reconstruction through NeRFs. This is done through an explicit modeling of the medium, its density, absorbtion and emitted radiance and a stratified sampling mechanism that increases the number of samples taken outside of the surface of the object. The experimental results show a significant improvement in modeling under-water, hazy and dark scenes.", "questions": "- What is the runtime of the model for an average-sized scene (~50 images)\n- In table 3 the structural similarity loss seems to affect the rendering quality by a lot, why is that? Usually this loss adds <0.5 db when added to the photometric reconstruction loss.", "limitations": "The limitations are discussed.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The proposed model follows the physical modeling of the Beer–Lambert Law and allows for backscatter color and light absorbtion \n- The proposed model allows for isotrpoy and isometry that leads to prediction of actual depth, given the scale, in non-clear air medium.\n- The model achieves 3D reconstruction in challenging scenes with minimal additional supervision from depth foundation models.\n\n- Specifically the method improves on previous methods like Sea-Thru NeRF and Watersplatting by being applicable to different challenging mediums like hazey and dark settings (not just water), handling vertical attenuation on top of LoS, having a more effective sampling than object surface sampling, and the ability to predict actual depth that emerges from accurate physical modeling. These benefits show as qualitative improvement in the results.\n\nWeaknesses:\n- The stratified upsampling adds to the complexity and the rendering time needed for the NeRF. \n- I'm curious to see if the model still performs well in normal scenes with mostly having clear air medium. My concern is that the medium prediction branch of the network might add to the complexity of modeling simpler scenes and overfit.\n- The quantitative results are competitive with Watersplat, however the qualitative results show a better reconstruction and depth estimation. Why is the better rendering quality not reflected in the image quality metrics?", "was_revised": true, "final_justification": "All of my concerns were sufficiently addressed in the rebuttal. I believe the paper has practical contributions to the field, therefore I am still leaning toward acceptance.", "rebuttal": "**We sincerely appreciate the valuable comments and suggestions that help strengthen our paper. We conduct additional experiments below to show the efficiency of the proposed method.**\n\n### **W1. Complexity of RSU**\n\nThe additional GridEncoder for media position encoding and the media radiance in volume rendering process increases both the complexity and rendering runtime. However, in adverse media conditions, such complexity tradoff are necessary to maintain the high-quality restoration and geometry reconstruction of the clean scenes. We conduct additional experiments and demonstrate that **The incorporation of medium modeling introduces a managable computation overhead.**\n\nSpecifically, to investigate the computation overhead, we conduct experiments below by training ZipNeRF [1], which is our code base (Line 243), on both the \"bike\" scene in LOM dataset [2], and “Curaçao” scene in SeaThru-NeRF dataset [3] to compare the training and rendering time. $I^2$-NeRF introduces a reasonable computational overhead of approximately 20–30\\% (10–20 minutes) additional training time compared to the baseline, while achieving substantial performance improvements under adverse conditions such as low light, haze, underwater environments, and even hybrid cases like low light + underwater shown in Supp Sec G.4 and Supp Fig. 6. \n\n### Table 1: Computation and memory cost on \"bike\" of LOM dataset [2]\n| Method   | Train | Render | GPU Memory (training) |\n| -------- | -------- | --------- | --------- |\n| Baseline [1]  |    0.95 Hours      |     1.29 FPS      |    \\~ 10 GB   |\n| Ours     |     1.25 Hours   |    0.58 FPS      |     \\~ 22 GB     |\n(Training batch size of 4096, training epoch 20,000, image resolution 500 x 375)\n\n### Table 2: Computation and memory cost on \"Curaçao\" of SeaThru-NeRF dataset [3]\n| Method    | Train | Render | GPU Memory (training) |\n| -------- | ------- | ------- | ------- |\n| Baseline [1]  |  0.69 Hours  |  0.041 FPS  |  \\~ 5 GB  |\n| Ours |  0.88 Hours  |  0.028 FPS  |  \\~ 10 GB  |\n(Training batch size of 2048, training epoch 20,000, image resolution 1776 x 1182)\n\n### **W2. Performance in clear-air condition**\nWe sincerely appreciate this comment, as it highlights the importance of validating the generalization of our model to clear-air environments. We conduct additional experiments showing below. **In clear air condition, our model performs very close (< 1\\%) to the original baseline [1]**. Moreover, the backscatter radiance estimated by our model is nearly zero, indicating that **the media branch does not learn any signal when scattering is absent in the scene**.\n\nSpecifically, we conducted sanity checks by applying our model to well-lit images from the “bike” scene in the LOM dataset [2] and the original “fern” scene from the NeRF dataset [4], using ZipNeRF [1] as the baseline for comparison. \n\n### Table 3: Sanity check on \"bike\" of LOM dataset [2]\n| Method   | PSNR | SSIM | LPIPS |\n| -------- | -------- | --------- | --------- |\n| Baseline [1]  |  31.40 |  0.884  |  0.163 |\n| Ours     |  31.32  (-0.08) |   0.879  (-0.06)  |  0.166 (-0.03) |\n\n### Table 4: Sanity check on  \"fern\" of NeRF dataset [4]\n| Method    | PSNR | SSIM | LPIPS |\n| -------- | ------- | ------- | ------- |\n| Baseline [1]  |  24.95  |  0.807  |  0.169  |\n| Ours |  24.80 (-0.15) |  0.799 (-0.08) |  0.171 (-0.02) |\n\n### **W3. Experiment results**\n\nThank you for the comment. We would like to clarify the key differences in evaluation settings and the inherent challenges of the current community that hinder us from performing fair restoration evaluations.\n\nIn the low-light dataset [2], pixel-aligned (paired) low-light and well-lit images are available for testing. This allows us to render novel-view clean (well-lit) images and compute evaluation metrics directly against GT clean views. As shown in Tab. 2, the proposed method achieves SOTA performance under this setting.\n\nIn contrast, real-world haze and underwater datasets, such as the SeaThru-NeRF dataset [3], only provide degraded observations, and there is no pixel-aligned clean images for evaluation. It is difficult to remove haze or oceanic water from the real-world environment to capture pair-wised images of clean views. As a result, we can only render degraded novel views (with haze or water) and compare them against the degraded inputs. Such novel-view synthesis results are shown in Table 1.\n\nDue to the absence of pair-wised clean observations in real-world scattering datasets, **Tab. 1 reflects only how well each method reconstructs the appearance of degraded scenes, as visualized in the novel view synthesis results shown in the first columns of Fig. 4 and Supp Fig. 3. However, Table 1 does not capture the accuracy of restored scene geometry (i.e., depth) or clean image synthesis (i.e., novel-view restoration), which is illustrated in the remaining columns of Fig. 4 and Supp Fig. 3.** When solely look at the novel view synthesis results (first column of Fig. 4) of our model and Watersplatting [5], the differences appear subtle. However, the rest columns of qualitative results on geometry and scene restoration clearly demonstrate that the proposed method provides more accurate geometry reconstruction and physically plausible estimation of media properties.\n**We will add this description to clarify the evaluation settings for each dataset in Sec 5.1. Line 249.**\n\n### **Q1. Runtime of the model**\n\nFor an average-sized scene (\\~50 images) and a common resolution (\\~720x540), training for a commonly employed iteration (\\~20k), it will take roughly 1.2 \\~1.5 hours to train our model.\n\nThe average training time of our model is 1.23 hours on the LOM dataset [1] (compare to Aleth-NeRF [2] of 8.25 hours) and 0.86 hours on the SeaThru-NeRF dataset [2] (compare to SeaThru-NeRF [4] of 3.15 hours). The proposed method achieves substantially faster training speeds compared to previous NeRF-based approaches [2,4], benefiting from the hash encoding of spatially sampled features. In Supp Sec. K, we provide detailed information for the training time of the proposed method and baselines on both low-light and underwater scenes using the same GPU. **We will add a sentence in Line 246 to indicate the training time and refer readers to the corresponding section in supplementary material for more details.**\n\n### **Q2. Structure similarity loss**\n\nWe appreciate this question that helps improve the clarity of our paper. Structure Similarity Index Measure (SSIM) composes of luminance, contrast, and structure. It usually has limited effect on common reconstruction target. However, in the case of low-light restoration, the luminance and contrast between rendered well-lit images (by remove absorption field) and supervision signal from low-light observation are remarkably different. Low-light observations typically exhibit lower luminance (< \\~0.1) and lower contrast (< \\~1) compared to well-lit images, which generally have luminance \\~ 0.5 and contrast \\~ 10. These discrepancies cause the standard SSIM loss to struggle in recovering scene geometry from low-light inputs. Therefore, we design a **compensated SSIM loss** (Line 196) which takes into account the luminance and contrast discrepancy (Eq. 9). The detailed derivation of this $\\mathcal{L}_{struct}$ loss is provided in Supp Sec E.3, and the effect of the parameter chosen is provided in Supp Sec F.2, visualized in Supp Fig 2. Without this compensated SSIM loss, our model cannot effectively restore well-lit scenes from low-light observations. As a result, the performance drops significantly without this loss term, as shown in Tab. 3. To distinguish between the conventional SSIM loss, **we will rename this loss term to Compensated SSIM Loss in Line 196, and denoted as $\\mathcal{L}_{comp}$ for clearness**\n\n### Reference\n\n[1] Barron, Jonathan T., et al. \"Zip-nerf: Anti-aliased grid-based neural radiance fields.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023.\n\n[2] Cui, Ziteng, et al. \"Aleth-nerf: Illumination adaptive nerf with concealing field assumption.\" Proceedings of the AAAI conference on artificial intelligence. Vol. 38. No. 2. 2024.\n\n[3] Mildenhall, Ben, et al. \"Nerf: Representing scenes as neural radiance fields for view synthesis.\" Communications of the ACM 65.1 (2021): 99-106.\n\n[4] Levy, Deborah, et al. \"Seathru-nerf: Neural radiance fields in scattering media.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2023.\n\n[5] Li, Huapeng, et al. \"Watersplatting: Fast underwater 3d scene reconstruction using gaussian splatting.\" arXiv preprint arXiv:2408.08206 (2024)."}, {"review_id": "rgiENGHIjp", "reviewer": "Reviewer_TDRQ", "summary": "The paper proposes a NeRF variant (built on ZipNeRF) that adjusts the sampling strategy along each ray, and the forward model, to flexibly model scenes with translucent media like seawater or fog. The paper also proposes to model low-light scenes in the same framework, by modeling a virtual absorptive medium. The paper also introduces several regularizers in the loss function, to encourage a clean separation of their separate models for objects and translucent media. This enables more physically plausible and separable (object vs medium) reconstructions compared to baselines that are designed separately for each task (underwater NeRF, hazy/foggy NeRF, and low-light NeRF).", "questions": "Some questions are embedded in the discussion of weaknesses; remaining questions are below. For the rebuttal, my primary concerns are the points mentioned under weaknesses.\n- Line 131: Should “regresses” be “reduces”? Similarly in equation 2 I think there is an $i$ that is supposed to be in the subscript instead of on the main level.\n- Are the $u_j$ in equation 8 and the $u_J$ in line 196 related to each other? I’m concerned this might be a notation clash because the former would appear to be a sample position and the latter would appear to be an illuminance value.\n- Will the novel underwater dataset be released? The authors state that code will be released, but do not specify release of data.", "limitations": "Limitations are adequately discussed. One question here is that the authors mention that their method takes longer training time than some others, but doesn’t specify a rough estimate of what the training time is or how it might be improved.", "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- Section 3.2 is very clearly written, and clarified many of my questions after reading the abstract and introduction. I also found the derivations and modeling descriptions in section 3.3 to be clear and elegant.\n- The experiments are comprehensive, including 3 types of challenging scenes (underwater, low light, and hazy) as well as ablation studies. The paper shows competitive and in some cases SOTA performance on these three types of scenes in terms of quantitative metrics, and shows qualitatively better scene decomposition into object vs medium layers, compared to baselines. \n- The evaluation includes both existing public datasets and a new underwater dataset; if this dataset is released it would also be a valuable contribution. \n\nWeaknesses / Suggestions for improvement:\n- The $I^2$ in the title would appear to be referring to “isometric” and “isotropic”, but (a) this title choice is never actually stated so I am just inferring it, and (b) I’m not sure that isometric and isotropic really describe the method clearly. As I understand it, “isometric” means having the same dimensions as something else, and “isotropic” means having some property remain fixed in all directions. It’s not clear how either of these is descriptive of the proposed method. I think the connection for “isometric” might be that the proposed method promotes metric consistency with the real world, up to some global scaling, but this is only demonstrated in the context of the depth of an underwater scene, not as a general property of the method. I’m not sure what is “isotropic” about the method, especially since it actively considers one-dimensional depth of a medium (water, mist, etc.) when modeling scattering, and this is a quantity that only makes sense in the vertical dimension, not all 3 dimensions. Note that this is not so much a weakness of the proposed method or results, as it is a concern over how the method is presented. Relatedly, the second bullet point contribution on line 78 describes the sampling strategy as “metric-preserving” but it’s not clear what this means (what’s the connection between the sampling strategy and the metric accuracy of the reconstruction? In the results it seems that sampling in the medium allows for better decomposition of the scene into medium and object layers, but I’m not sure why this is “metric-preserving”). \n- For most settings (at least for underwater and fog/haze scenes, perhaps also for low-light scenes?), it seems that the properties of the medium are fixed regardless of spatial position. This makes perfect sense as an approximation that is likely close to accurate in reality. But, if this is the case, it seems wasteful to spend a lot of ray samples in the medium, and to spend a lot of memory representing the density parameters throughout the medium. Why not just model the distance the ray travels between the camera and the object, and apply a closed-form estimate with a single set of spatially-invariant medium parameters instead of estimating an integral with individual samples?\n- The dependence of downwelling attenuation on vertical depth seems to be modeled based on a single depth $z^\\Phi$ per ray. For rays that are not perfectly horizontal, won’t the vertical depth vary along the length of the ray? Shouldn’t this be included in the model?\n\nMinor weaknesses / suggestions for improvement:\n- The term “matting” is used several times between the abstract and introduction, but not defined until the top of page 4. I thought this was a typo / misspelled other word until I had already read ⅓ of the paper.\n- Figure 1 uses blue points for samples in the medium, and orange points for samples of the object. This should be included in the caption rather than deferred to lines 42-44.\n- The discussion of related work is brief but generally sufficient. My suggestion here is to add a sentence or two in each paragraph explaining how the methods you just described are related to your proposed approach: what is similar and what is novel in your approach.\n- The sampling strategy in equations 7 and 8 should be augmented with a description of how they result in increased medium sampling only in front of the object (between the object and the camera) instead of on both sides of the object. It’s not obvious from the equations that this is the case.\n- $\\mathcal{L}_{recon}$ and $\\mathcal{L}_{geo}$ are losses borrowed from prior work, but their formulas should still be reproduced in the main text for the readers’ convenience.\n- Line 203 describes avoiding “the trivial solution”--please specify what this is. Is it both object and medium densities going to zero?\n- Line 206-207 describes a “monotonic decay in media density” but this statement is unclear without knowing what the monotonicity is with respect to. Similarly, the notation on line 208 is unclear; it uses a ReLU with 3 arguments but usually ReLU takes a single argument and returns $max(\\cdot, 0)$. \n- Line 212 is a sentence fragment; the meaning is not clear. I suspect a word is missing?\n- Can the authors provide some description/intuition for why $\\lambda_{struct}, \\lambda_{trans}$ are both zero for both underwater and hazy scenes?\n- What is the bright channel in a low-light scene? Is there a different color space being used other than RGB? What is $B^c$ in equation 13?\n- Line 260 describes a baseline as “the GS-based method” but in the associated figure (fig. 4) the label is “Watersplatting”--making these namings consistent would help readers understand the figure.", "was_revised": true, "final_justification": "The authors have engaged with my review during the rebuttal and discussion phase, and have promised to discuss some assumptions and inefficiencies in their method that may be removed in future work. My only remaining concern that was not fully addressed is about the paper naming/framing that focuses on isometry and isotropy, which I feel does not really reflect the focus of the work, which is on modeling absorptive and scattering media. However, this naming concern is not significant enough for me to change my score, so I continue to recommend acceptance.", "rebuttal": "**We would like to express our deepest gratitude for receiving such detailed and thoughtful review of our paper. We greatly appreciate the concrete comments and suggestions.**\n\n### **W1. Isometry and Isotropy**\n\nThank you for the insightful question. In our paper, we introduce the notation $I^2$ to denote two complementary desiderata in neural field modeling: isometry, the ability to recover metric distances in space, and isotropy, the capacity to model properties uniformly in all directions.\n\nIn vanilla NeRF, weights and density samplings concentrate exclusively on object surfaces, treating free space as void. This simplification makes rendering efficient, but it also erases any notion of “distance through air”: an object one meter away is treated identically to one ten meters away, and transmittance through the intervening volume is ignored. In situations where accounting for the space in between is essential, such as when optical scattering occurs in the surrounding medium, this becomes a critical limitation. Works such as Aleth-NeRF [1] and SeaThru-NeRF [2] attempt to mitigate this by assigning additional weights along the ray to capture radiance contributions beyond object.\n\nWe consider this challenge as an opportunity toward a fully metric-aware method by explicitly allocating samples in non‑object regions, thereby restoring optical length scales. In an absorption field in low-light scenes, distant objects appear darker in accordance with a distance‑dependent attenuation law; in a scattering field, further objects appear blurrier and shift toward the scattering color. By letting the model attend to these samples, we recover an approximate metric estimation (up to a global scale) under scattering conditions, and similarly reflect physical distance as low‑illumination in low-light scenarios.\n\nBy definition, isometry refers to a mapping that preserves distances. In our work, we want the neural field to recover physical length scales throughout the volume rather than collapsing all free space into an inert background. To achieve this, we allocate sampling points not only on object surfaces but also in the surrounding medium. The network then learns to accumulate attenuation and scattering along each ray, effectively measuring line‑of‑sight (LoS) distance and downwelling depth in scattering environments. Although we do not yet recover absolute metric units, this sampling lets distant objects exhibit the correct degree of blurring, color shift, or illumination loss that arises from true volumetric propagation.\n\nIsotropy denotes uniform behavior in all directions. In vanilla NeRF and existing scattering‑aware extensions [2–4], media properties (color) are learned implicitly along each viewing ray, without a coherent physical model for propagation in other directions. We extend the Beer–Lambert attenuation law both along the LoS and vertically toward the media boundary (i.e., the water surface), making the “downwelling distance” an explicit, learnable quantity. Although we cannot apply the optical attenuation in all 3 dimensions, the law is consistent along the ray and in vertical direction. \n\nBy combining these two concepts, we introduce the $I^2$ concept, aimed at enabling AI models not only to perceive the spatial positions of objects but also to sense and interpret whole space metric. This capability is critical for advancing current AI systems, particularly in the context of Embodied AI, World Models, and Generative Models. These areas demand a deeper integration of spatial awareness and metric understanding, which our $I^2$ concept seeks to provide.\n\nIn submitting this work to NeurIPS, a conference that brings together experts from Mathematics, Physics, Machine Learning, and Embodied AI, we hope to gather insights from diverse perspectives and engage in interdisciplinary discussions. We would like to discuss with NeurIPS's community and explore how the proposed $I^2$ concepts can contribute to encoding a complete metric perception of 3D space. Through constructive feedback, we seek to examine the potential for establishing a comprehensive framework encompassing key concepts, benchmark datasets, evaluation metrics, and technical methods for this emerging research direction.\n\n### **W2. Closed-form solution between camera and object**\n\nThank you for raising this important question. In scattering conditions, where the media color and media scattering coefficients are constant, we find it possible to apply a closed-form solution to directly calculate the backscatter radiance component and add it to the direct radiance to compute the pixel color. In this condition, we only need scalar values for each ray, and this will approximately reduces 4 GB of GPU memory given the training batch size of 2048 (Supp Line 377). We think the current sampling design has three advantages presented below, and we would like to hear your opinion.\n\nFirst, as noted in W1, the objective of our work is to explicitly model the entire 3D space, including both the dense object and the surrounding volume. This comprehensive modeling enables metric measurements and fosters a physically grounded understanding of the 3D space. Motivated by this intention, we explicitly allocate media sampling points throughout the space.\n\nSecond, the inherent ill-posedness of the inverse rendering problem requires separating the direct and backscatter radiance given only the degraded observations. Explicit spatial sampling, such as that provided by RSU, is therefore crucial for the successful optimization of the NeRF model. Accurate media sampling helps prevent the collapse of the media field during learning. Collapse can results a failure case where backscatter radiance is incorrectly attributed to object direct radiance, leaving the medium field empty (as demonstrated in Fig. 6 left and Supp. Fig. 1 without RSU). This collapse becomes particularly significant when the ambient light has close color to the scene color, such as in shallow underwater scene (Supp Fig. 1) and hazy scene (Supp Fig. 4). In such case, the guidance from media geometry positions becomes important for convergence.\n\nFinally, in low-light environments (no scattering only absorption), a spatially variant absorption field is required (Line 226) due to the highly-dynamical scene illumination. As a result, the media density becomes inconsistent along each ray; therefore, there is no closed-form solution in low-light conditions. We visualized the density distribution of two representative rays in Fig. 3, the absorption media field monotonic decays and terminate at the object surfaces.\n\n### **W3. Rays Assumption**\n\nWe appreciate your thoughtful question. Under scattering conditions, we build upon the Revised Underwater Image Formation (RUIF) model [5], which simplifies the computation of backscattered radiance by assuming that all rays are horizontal (as noted in Line 59 of our Supp).\n\nIn precise underwater imaging, rays are not parallel in horizontal directions, and this introduces an inclination angle $\\theta$ in the nadir direction. As a result, the backscatter radiance at each point along the ray becomes dependent on $\\theta$, substantially increasing the ill-posedness of the problem (Eq. 1 in RUIF paper [5]). To make the problem tractable, RUIF [5] proposes a simplified formulation by setting $\\theta=90^{\\circ}$, effectively removing the inclination dependence as shown in Supp Eq.2. (Eq.2 in RUIF paper as well). This approximation is widely adopted in previous studies [2-4]. Consequntly, each point along the ray will have the approximated same downwelling depth $z^{\\Phi}$. **We will add this explanation in Sec 3.1 to emphasize this horizon simplification**. More elaboration of RUIF [5] is provided in Supp Sec. A.2.\n\n### **Q1**\nShould be \"reduces\" and $\\hat{C}_i^{obj}$\n\n### **Q2**\nIt is a notation clash and we will change symbol.\n\n### **Q3**\nThank you for the reminder. We will definitely release the dataset.\n\n### **Minor: trivial solution**\n\nIt should be rephrased to \"helps avoid the trivial solution of zero media density\" in Line 203.\n\n### **Minor: monotonic decay**\n\nRefer to W2., we have spatially-variant absorption media in low-light conditions. We want this media field to be monotonic decay as shown in Fig.3 such that it ends on the object surface. Line 208 has typo, it should be $ReLU(\\sigma_{k,i}^{med}-\\sigma_{k,{i-1}}^{med})$.\n\n### **Minor:  $\\lambda_{struct}$ and $\\lambda_{trans}$ are zero in underwater and hazy scenes**\n\n$\\lambda_{struct}$ is weight of compensated SSIM loss, which takes into account the luminance and contrast differences, and are particularly important in low-light scenes where the rendered well-lit and low-light observations present large discrepancy. In scattering conditions, such SSIM do not really help to improve the scene reconstruction when there are no large illumination/contrast gaps. $\\lambda_{trans}$ is activated when there are any transmittance prior. In low-light scenes, we can unsupervisedly retrieve such prior from BCP to facilitate the learning of spatial-varient absorption media. In underwater/haze scenes, there is unfortunately no such prior available, so we disable this loss term.\n\n### **Minor: BCP definition in Eq. 13**\n\nWe provide detailed derivation of BCP in Supp Sec A.4. $B^c$ means the channel-wise value of ambient light, $c \\in (r,g,b)$ defined in Eq.13.\n\n**Due to the word limitations, we answer all questions, and will carefully revise the paper according to your rest of the suggestions.**\n\n### Reference\n\n[1] \"Aleth-nerf: Illumination adaptive nerf with concealing field assumption.\" AAAI, 2024.\n\n[2] \"Seathru-nerf: Neural radiance fields in scattering media.\" CVPR, 2023.\n\n[3] \"Neural underwater scene representation.\" CVPR, 2024.\n\n[4] \"Watersplatting: Fast underwater 3d scene reconstruction using gaussian splatting.\" 3DV, 2025.\n\n[5] \"A revised underwater image formation model.\" CVPR, 2018."}]

Author rebuttal:

Meta-review: The paper proposes a NeRF variant that considers media interactions along the rays. This enables modeling 3D scenes in underwater environments, in foggy conditions and in low light conditions. The paper demonstrates more physically plausible and separable reconstructions compared to baselines that are designed separately for each task (underwater NeRF, hazy/foggy NeRF, and low-light NeRF).

The reviewers agreed that the paper is well written and that the comprehensive presentation of the method provides useful insights to the community. 

There were a few issues that were discussed during the discussion period, including:

1. The level of contribution related to similar prior work.

2.  The RSU (Reverse-stratified Upsampling) mechanism and the flexibility in media parameters across the media. 

3. Should media densities be view dependent.

4. Assumptions made on the modeling of downwelling distance, its physical interpretation and its dependence on viewing angle.
 
5. The $I^2$ in the title and its importance in the method.

Most of the concerns including points 1, 2 and 3 were resolved. Points 4 and 5 remain in some level of disagreement. 
 
Based on the authors response most reviewers recommended acceptance, and the sole reviewer that was leaning for rejection agreed to accept the paper provided the authors address consistency in the downwelling depth analysis (point 4 above) in the final revision.
Decision: Accept (poster)