Looking Into the Water by Unsupervised Learning of the Surface Shape
Authors: Ori Lifschitz
Tali Treibitz
Dan Rosenbaum
Venue: NeurIPS 2025 poster ()
Keywords: Underwater
refractive distrotion
unsupervised learning
SIREN
Primary area: applications
TL;DR: Underwater refractive distortion removal via unsupervised learning of the gradient of the water surface.

Abstract: We address the problem of looking into the water from the air, where we seek to remove image distortions caused by refractions at the water surface. Our approach is based on modeling the different water surface structures at various points in time, assuming the underlying image is constant. To this end, we propose a model that consists of two neural-field networks. The first network predicts the height of the water surface at each spatial position and time, and the second network predicts the image color at each position. Using both networks, we reconstruct the observed sequence of images and can therefore use unsupervised training. We show that using implicit neural representations with periodic activation functions (SIREN) leads to effective modeling of the surface height spatio-temporal signal and its derivative, as required for image reconstruction. Using both simulated and real data we show that our method outperforms the latest unsupervised image restoration approach. In addition, it provides an estimate of the water surface.

Looking Into the Water by Unsupervised Learning of the Surface Shape
Ori Lifschitz
Hatter Department of Marine Technologies
Charney School of Marine Sciences, University of Haifa Haifa, Israel
hwwp://b..comm/rrffchhheeeeee -uurad
Tali Treibitz
Dan Rosenbaum
Hatter Department of Marine Technologies
Department of Computer Science
Chamey School Marine Sciences, University of Haifa
University of Haifa Haifa, Israel danroêcs haifa. ac i1
Haifa, Israel
ttreibitz@univ.c haifa. ac.il
Abstract
We address the problem of looking into the water from the air, where we seek remove image distortions caused by refractions at the water surface. Our approach is based on modeling the different water surface structures various points in time, assuming the underlying image is constant. To this end, we propose model that consists of two neural-field networks. The first network predicts the height of the water surface at each spatial position and time, and the second network predicts the image color each position. Using both networks, we reconstruct the observed sequence of images and can therefore use unsupervised training. We show that using implicit neural representations with periodic activation functions (SIREN) leads to effective modeling of the surface height spatio-temporal signal and its derivative, as required for image reconstruction. Using both simulated and real data we show that our method outperforms the latest unsupervised image restoration approach. In addition, it provides an estimate the water surface.
Distorted Frame
NDIR
Ours
GT
Surface Height
112358
112358
112358
112358
Figure 1: Surface waves distort the appearance of underwater scenes viewed from the air due to refractions following Snell's law as seen in the distorted frame on the left. Our method aims at reconstructing the original scene and performs better than NDIR [I]. For example, the numbers marked in blue and the grid marked green. addition, our method outputs the surface height. The height presented on the right corresponds to the distorted frame on the left. Example taken from the elephant dataset from [9].
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
Observing objects in the ocean from aerial platforms can significantly increase the observation scale and speed since underwater vehicle operation is complex and expensive. Therefore, it is used in variety of scientific and operational applications. For example, measuring the scale of coral bleaching after warming event or storm [3]. However, the effects of refraction between the air and water can strongly distort the apparent position and shape of objects and features below the water's surface, hindering the observations. The distortion is directly related to the surface shape through its gradients, connecting the water surface with the underlying scene in a single image. Ocean wave measurements are very useful for coastal and ocean science and engineering and represent an active research field in physical oceanography [1 [5). Measurement of sea surface height also informs studies of the sea 25
surface microlayer
Here, using a short input sequence of an underwater object seen from above, we aim to reconstruct its fine details and undistorted structure, well as the surface height in each point. An example is shown in Fig. [ Real waves are a superposition of several types of wave from various sources with different wave periods and amplitudes. Large-scale ground truth for this problem is only available by simulations that do not encompass this range of surface waves. Thus, it is difficult for supervised methods to generalize real-world examples. However, distorted sequences contain wealth of information on the constant underlying scene that can be leveraged in an unsupervised method.
We formulate the unsupervised learning signal of reconstructing the observed distorted images by first estimating the water surface height and then using the estimation and its spatial derivatives to compute the pixel distortion map. We implement this using neural representation network based on periodic activation functions (SIREN (17), which has proven to be effective and efficient in modeling continuous signals and their derivatives.
Our method outperforms previous unsupervised methods using a simpler training setup and addition- ally provides surface height estimation. We demonstrate this both on real-world and simulated data. All our code and data will be made available upon publication.
2 Related work
2.1 Imaging through turbulent water.
The problem of looking through water has attracted attention since the earlier days of computer vision [14 as it poses interesting and applicative poysics-based challenges. Early works [5] [ 24 were based on finding and stitching together distortion-free patches from the distorted image sequence. In ( the authors formulate the reconstruction problem as a manifold embedding problem and propose a modified convex flows technique to robustly recover global distances on the manifold. 55] the authors suggest multistage clustering algorithm combined with frequency domain measurements. In [24] the authors propose to first find an ensemble of distortion free ("lucky") patches and then proceed to estimate the Fourier phase and the Fourier magnitude of the clean image.
different line of techniques is based on model-based tracking to reconstruct the clean image. In 23 the authors propose building spatial distortion model of the water surface using the wave equation. The model enables them to design tracking technique tailored for water surfaces. Using their method, they were able to use a shorter sequence of 61 frames instead of the long sequences required by the lucky patches techniques e.g. 800 g or 120 24
refracted image sequence contains strong physics cues on the underlying scene and the water surface. This was used by [9] who estimated optical flow between key feature points estimate object trajectories within the sequence. Using a compressive sensing solver they used these trajectories to estimate the entire motion field and reconstruct the scenes. Alternatively, [26] used the fact that water refraction changes the viewpoint to develop structure- from-motion like solver for an image sequence captured by a stationary camera. They are able to simultaneously retrieve the structure of the water surface and the static underwater scene geometry. Sulc et al. propose a parameter-fiee Snell's-law-band objective for monocular reconstruction of an arbitrary refractive surface from a single distorted view given known background texture and geometry. Unlike our setting (unsupervised restoration from short sequence), their method assumes a known background and directly optimizes surface geometry via a geometric ray-consistency error [18].

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Supervised deep learning methods require training dataset. In [12 a dataset was acquired using computer monitor displaying images from ImageNet 4 placed under a transparent water tank with a pump to generate water surface movements. Their network consists of two parts, a warping net to remove geometric distortion and a color predictor net to further refine the restoration.
Thapa er al. [21] generated a synthetic dataset using the wave equation for three types of waves: ripple waves, ocean waves, and Gaussian waves. The dataset was then used to train the following network: three parallel CNNs that generalize features from each input (consecutive distorted frames), and then uses recurrent layers to refine the CNN- NNN-pprdicted distortion maps by enforcing the temporal consistency among them. Then, a GAN is used to predict the distortion-free image. FSRN [00 was trained estimate the water surface based on a known reference background in the water.
Li el al. present a two-stage unsupervised network. The first stage consists of a grid deformed for every input image that estimates the distortion field. Then, an image generator outputs the distortion- free image. The optimizer for generating the distortion-free image by minimizing pairwise differences between the captured input images, the network's 's predicted distorted images, and resampled distorted images from the distortion-frre image. Our model is also based on unsupervised reconstruction, modeling the image and the distortions using different networks, however use single SIREN [77 network conditioned on time that outputs the surface height. Using the height we compute the offset of each pixel in order to reconstruct the observed images. The advantage is that the predicted distortion is grounded in the temporal process of moving waves, and in addition this enables direct prediction of the water surface.
2.2 Neural fields
Representing data using neural fields has gained significant focus in recent years. These models, also known as implicit neural representations are used to model a continuous signal by predicting the value of the signal given a position in space as input. For example in images this corresponds to predicting pixel color given the 2D pixel position. This representation has proven effective for image compression [6), 3D modeling [13] PDE dynamics forcasting 22 and as a basic representation for different downstream tasks 77.
One implementation of neural fields that we adopt in this work is SIREN 17 This model is an MLP with sinusoidal activation functions, which was proven to be both effective and efficient for image modeling, achieving high accuracy with smaller networks and faster training times. One advantage of using periodic activation functions, is that the signal and its derivatives become similar in nature. To demonstrate this Sitzmann et al. [17] train a model to predict a signal by supervising the training loss with the gradients of the signal. In our work we show that this arises naturally from the physical formulation of the problem, as the image distortion caused by the water surface is directly related to the spatial derivatives of the surface height.
3 Method
Fig. 2 summarizes our method. Given an arbitrary number of video frames taken from air, we train our model per sequence to reconstruct the distorted frames and can then use our model structure to remove the distortion caused by the water surface. This is achieved by modeling the underlying image and the water surface separately.
3.1 Assumptions
We assume a static planar underwater scene at an unknown depth ho below a water surface. The scene is Prnto--paaalle to an orthographic camera and the camera is held in air outside of water. The interface between the refractive medium (water) and air is dynamic, i.e., wavy water-surface. Like 19. 16 21 22] we also assume small fluctuating fluctuation, max,, e [h(x, t) hol. is small compared to the average water-height hg. This is a reasonable assumption for many marine environments such as river beds and shallow coral reefs. the camera exposure time is not sufficiently short relation to the wave phase-velocity then the resulting image will suffer from motion-blur. While we do not make explicit assumptions regarding shutter speed, camera frame rate and the water-surface waves phase speed, our proposed method can handle the motion-blur commonly occurring in James Reall dataset [9] which is considered
waves, i.e., the maximum surface
3

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Forward and Sladward Prosagation
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Forward Propagation
From the left, regularized 2D spatial grids Freg and time / inputs to a SIREN [17] network that outputs surface height per frame. The gradient the output heights, along with its average across f, is used for calculating distortions in Eq. []] These are then used in another SIREN network to output the reconstructed image 1& (Zreg) and the distorted images 1 The predicted distorted images and the observed distorted images I are used in the loss calculation.
Figure 2: Our architecture.
hard dataset for underwater refractive distortion removal due to large Frame-to-franee motion and motion-blur. In Fig- 7 we present real-world results where assumptions do not fully hold and show that our method is able to reconstruct a plausible underlying clean image, see Sec. [ for further discussion.
3.2 Surface Gradient
By modeling the surface of the water above the image we can compute the refraction offset of every pixel based Snell's law (illustrated in Fig. 33. According to Snell's law, under first-order approximation [22], the distortion function (warping) d(x,, t) can be related to the height of water surface hxx, t) the 2D spatial position x and time t:
d(x, - No V)),))
where ho is the average water height above the scene, and is the relative refraction index between air and water.
3.3 Architecture
The architecture (Fig. 2 of our model consists of two parts. Both parts are implemented using SIREN models [17 which used as neural fields to model both the water surface height different times points (xx (), and the fixed underlying image.
Surface height model Ha. The first part of our model is a SIREN neural field that models the 2D surface height signal across different time points. This model takes as input a two dimensional position in the image space x, and one-dimensional point in time and predicts the surface height that position and time Ho (x, t). Using SIREN architecture is well-suited for modeling distortions through surface height as it allows for the efficient prediction of signal and its spatial derivatives simultameously. We use single SIREN to 1) predict the water surface height h(x, t) which is used to compute hn by averaging the outputs across the 2D space x and time f; and 2) predict Vh(r, t) by computing the gradients of the output of the network with respect to its spatial input x. Given the computed hg and Vh(x,, t) we compute the pixel distortions d(ar, t) due light refraction for each observed image at time f using Eq. and use it to reconstruct the observed images. We then compare this prediction with the observed images to compute the loss that we use to optimize the weights of the networks.
Image model Ta- This implemented using a standard neural field SIREN where each pixel position is fed to the network along with positional encoding using random Fourier features [19].

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Xrag:
Nrog.2
h(x, E)
ko
Xta
d2
d2
Figure 3: According to Snell's law light passing through an interface between media with different refraction indices changes its angle (refracts). Thus, when an orthographic camera views an object submerged in water from air, the object changes its geometrical appearance a function of the normals to the surface.
and is trained to predict the pixel values lo (z). Feeding this model with set pixel positions on the image's s regular grid Freg will output the set of pixel values for the distortion-free image I (Freg)- and feeding the model with set of distorted pixel positions Fe Zzeg d(Zreg. t) will result in distorted image which we denote by I2.s0 since it is generated using both models Hg and Lg and therefore depends on both sets of weights. To formulate this explicitly,
To (Freg + d (Ho(Treg. f)))
(2)
where di d-)( corresponds to using Eq.
| on the height prediction.
3.4 Training
Given set of distorted frames across time It we follow the training paradigm in [1]] consisting of two stages. The first training stage can be seen as an initialization of the weights, by training the height network Hg to output a height that corresponds to zero distortion for all pixels, and training the image network I to predict the average distorted image. This is implemented using the loss ( represents the L norm):
Linit (0, )) = ||d (Ha 1)) + Σ ls (Zrrgg)
It]
In the second stage of training the loss is computed by the reconstruction of all the distorted images. The loss is given by:
C(B, Φ) Σ Ig. It]
This is significant simplification compared 11 which required 3 different loss terms for training. We note that both the reconstructed and observed images inherently involve the gradient of the surface height signal computed through Eq. for the reconstruction and through the physical process of refraction in the observed image. Therefore this loss forms a real world application of the ability of SIREN to model signal by supervising it with the derivatives.
4 Experiments
To test our method we use three datasets. We use the James Reall dataset 9 which contains 7 sequences of images acquired water tank using 50 fps acquisition rate (examples in Fig. Additionally, we use the TianSer. which is also a real captured dataset by Tian and Narasimhan 23 using a 125 fps camera. We note that Real/ is considered more challenging dataset as it has larger frame-to-fre tormme motion and includes motion blur (due to water- We also generate synthetic dataset using the method 200). with wave types, resulting 11 sequences of images. We compare method to NDIR M. which is our unsupervised bascline and to Li et al. [12] which is the
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Distorted Frame
NDIR
Ours
GT
Cartoon
112358
112358
112358
E
Dice
Ö
Checkers
Figure 4: Results on the Real/ dataset 99. Marked squares indicate areas where our results are sharper than the baseline. Note sharper details in the cartoon and dice sequences, as well straighter squares in the checkers sequence in our method.
state-of-the-are supervised method on single images. In all experiments we use a sequence size of 10 frames (except for the batch-size ablation). We conduct ablation studies to validate benefits of modeling surface-height and spatio-temporal information, to examine design choices and to evaluate the impact of the input sequence size (Sec. 4.3 Additional results and videos are provided in the supplementary material.
Implementation details. In experiments we use a 2-layer network for Ha and a 3-layer network for Ig. both trained with the Adam optimizer. The input to Lo is augmented with random Fourier positional encoding with the bandwidth factor set 8. We use two sets of hyperparameters. One set for both real datasets (Reall and TianSer) and the other for the synthetic dataset. More details the configurations of the hyperparameters, the amount of iterations on each training stage, hardware setup, memory usage, runtime, and reproducibility scripts are provided in the supplementary material ("Implementation Details",, "). Our implementation is based on the code of [1].
4.1 Image restoration
qualitative comparison of our results on the Reall dataset is shown in Figs. Tand where green and blue rectangles mark areas of interest. In the cartoon sequence method better aligns several

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Our Estimated Distortion
Distorted Frame
NDIR
Ours
GT
C
2
C
E
B8
R
R
O
R
C
C
CV
R
V
R
e
V
V
O
C
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0
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Figure 5: Examples from the simulated dataset following 20]. Our results have less distortions, manifesting in straighter lines. The estimated distortions match the apparent distortions in the acquired frames.
Table 1: Quantitative comparison results the Reall dataset from [9] and TianSet 23 our method with NDIR [I]], Li et al. [[2), and NeRT [10]. Our method achieves the best overall performance Reall, with the best SSIM and LPIPS across both datasets. It outperforms prior methods on most individual sequences and metrics, demonstrating consistent superiority. Minor exceptions include NDIR achieving slightly higher PSNR and SSIM Math, Li el al. obtaining the best SSIM in isolated TianSet cases, and NeRT occasionally strong in PSNR and SSIM but substantially worse LPIPS.
We compare
NDIR
Lf [X
NeRT 10
Dutinct Sequence
PSNR
SSIM 1
PSNR
55IM
Bricks
20.83
0.55
0.21
19.71
0.55
0.18
20.43
0.66
0.35
21.34
0.59
0.16
Castoon
21.85
0.77
0.16
18.75
0.71
0.19
21.63
0.84
0.37
22.37
0.79
0.12
Chacker
14.10
0.55
0.12
12.06
0.45
0.76
16.00
0.77
1.09
14.27
0.58
1.10
Dirrs
18:50
0.51
0.11
16.23
0.4]
0.24
15.27
0.50
0.21
19:15
8.57
EL09
Explunt
15.63
0.31
0.19
14.63
0.23
0.26
15.01
0.41
0.38
15.95
0.33
IL17
Reall
Eye
Muth
21.10
24,07
0.82
0U62
0.50
0.11
18:36
19.92
0.75
0.55
0.12
0.13
23.34
15.75
0.5L
0.53
0.21
0.39
23.98
21.42
0.83
0.60
0.10
0.11
19:44
0.59
0.14
17.14
0.61
0.29
19.78
0.12
Midele
Average
0.37
0.30
13.13
0.29
18.90
areas, e.g., the numbers, elephant, hand, and result reconstruct more details in these drawings. In the dice sequence our method compensates better for the distortion and as a result reveals more fine details in the letters. In the checkers sequence the motion of the squares in the bottom right corner is better compensated. Fig. 5 displays results from two simulated scenes where our result shows straighter lines and less distortions. The estimated distortion matches the apparent distortions the acquired frame.
Tab. |ummarizes quantitative results for all three methods, ours and III on the real datasets [9] 23). Our approach achieves the highest overall metrics. Detailed per-sequence evaluations are also presented along with the standard deviation for each sequence. In Eye and Math our method is on-par with NDIR [II. In all other sequences in both datasets, our method achieves the best LPIPS, while also providing height prediction. Our method achieves the best PSNR and SSIM values, with only one exception on the Math sequence. We note that PSNR often favors overly smooth reconstructions and thus less indicative of perceptual quality, whereas LPIPS aligns more closely with sharpness and fidelity, as can be seen in the qualitative comparison (Fig. Finally, Tab. 2 shows results on the simulated dataset, where our method superior in all metries compared baseline method on every wave-type.
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Table Quantitative comparison results on simulated dataset following 20 Our method performs better than NDIR [TT] as can also be seen in Fig.
on three wave types.
Wave type
Method
SSIM
LPIPS
NDIR M
20.70
0.64
0.12
Gaussian
Ours
20.92
0.65
0.11
Ripple
Ours
23.07
0.92
0.05
NDIR
I||
15.52
0.54
0.15
Ocean
Ours
16.07
0.58
0.14
Figure 6: Examples of surface height reconstructions. a) Checkers set from the Reall datáset (9) The strong curvatures in the surface match the strong distortions in the input image. b) A ripple wave from the simulated dataset based on [20]. We show reconstructions of four frames evolving with time, where reconstruction closely matches the ground truth used for simulation.
4.2 Water surface estimation
In addition to reconstructing the underlying image, method estimates the water surface height of every frame in the sequence. Examples are shown qualitatively on sequences from the Reall dataset [9] in Figs. I 6a. The estimated surface curves match large distortions and blurs in the input image. For a quantitative comparison, we use the estimated depth in the Synthetic dataset. The average root mean square errors (RMSE) and absolute relative errors (Abs Rel) are 0.115 and 0.0635, respectively. These results are on par with previous methods shown in the supplementary [26]. Fig. 66p shows surface height estimations estimations closely follow the ground-truth height shape over time.
ripple sequence evolving with time. We that
4.3 Ablations.
All ablations were performed using the more challenging Reall dataset. The quantitative results presented in Tables and and are the average over the entire dataset.
Modeling surface-height and spatio-temporal information. We compare final architecture with two ablations of our method (Tab. 3). In ablation 1, we predict per-frame pixel distortions 2; using separate networks for each time step instead of a single, time-conditioned network. Ablation employs shared network across time while still predicting Tt, ignoring surface height. Both ablations SIRENs for sub-networks and neglect refraction modeling, precluding surface height estimation. The key distinction that ablation incorporates temporal conditioning. Our final proposed method (Our method) integrates surface-height prediction and temporal conditioning, achieving the best PSNR, LPIPS and SSIM, aligning well with qualitative results.
Design choices. We conduct ablation studies to validate our design choices (Tab. Bp. In NDIR
the authors use in the second stage of training loss function composed of three terms which are based on two different ways to compute predictions the distorted images. The first way is computing 4h using Eq. 2 and the second way is to generate the regular image I& (Freg) and then use the distortion to warp the image W warp (Z d (( (Ho (Zreg t))). Using these two predictions and the observed image, they compute the loss by comparing the three possible pairs for each observed frame

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Table 3: Design-choice ablations. We examine the loss terms. No init skips the first training stage (initialization). No positional encoding replaces the positional encoding module with another SIREN layer as suggested by 12 Ablations and are discussed in 4.3 The results are the average results
on Real/ dataset.
L1 +
L1
Ablation
Ablation
Our Method
No init
positional encoding
PSNR
19.42
19.07
SSIM
0.613
0.54
0.49
0.60
0.58
0.57
0.59
0.59
0.77
0.19
Table 4: Comparison of different batch sizes. Presented are the average results on Reall.
Batch size
PSNR f
S
LPIPS
NDIR
Ours
NDIR
Ours
NDIR
Ours
17.81
17.69
0.54
0.17
6
17.90
18.56
0.55
0.55
0.16
0.15
7
18.04
18.87
0.56
0.57
0.16
0.15
8
18.15
18.98
0,56
0.57
0.15
0.15
9
18.18
19.15
0.57
0.58
0.16
0.15
10
0.613
0.14
0.121
in time:
[(0,6) - E 16.. 4el W - [1| + 11.0. - W
(5)
We test different combinations of these 3 loss terms, and find that for our model, using only the first formulated in Eq. results in better performance. This shows that our model can attain better results while using simplified training setup compared to NDIR, for which it was shown that all loss terms are required for training stability. We also test against training without the initialization phase and without positional encodings and find them beneficial.
Input sequence size, We perform batch size ablations (Tab. 4). showing our method consistently achieves the best LPIPS and SSIM across all tested sizes. For PSNR, approach also outperforms NDIR 11] starting from six frames. Interestingly, for a batch size of five, the competing method achieves higher PSNR but 0.03 worse LPIPS. Given LPIPS' stronger correlation with perceptual quality, even a 0.03 difference is often visually noticeable.
4.4 A Real- World Scene with Partial Fulfillment of Assumptions
We test our method real-world setting (Fig. 7 without an orthographic camera and with non- Pronto-paralled scene due to complex object geometry. Motion blur is present (e.g., green rectangle), yet our method reconstructs both the planar grid-like structure and non-planar corals, demonstrating robustness to assumption violations.
Distorted Input Image
Reconstructed Image
Acquisition Setup
Figure 7: Real-world scene in coral tank, in which distortions in 3D objects are corrected. Some loss of detail stems from limited network resolution.

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Summary
Looking into the water from air is an interesting physics-based problem where image distortion is tied to the surface shape through Snell's law. Since the water surface is changing temporally, a sequence of images acquired from the same viewpoint provides different distorted views of the same scene. Our method leverages this information to reconstruct a single image of the undistorted scene.
Real-world acquisition of such scenes and their ground-truth is very challenging. Several methods simulated datasets using different formulations of wave equations. Nevertheless, in the real-world the actual waves super position of different wave-forms with multiple amplitudes and periods, and also depend on the bottom type. Thus, there is strong advantage for developing unsupervised methods that leverage the physical cues from the image sequences and do not rely on pre-training.
We present an unsupervised method that both reconstructs the underlying distorted scene and the surface shape in each temporal frame. With the exploding popularity of aerial drones method has numerous applications ocean surveys, fish farm monitoring, and also drowning detection both in the ocean and in swimming pools. Future work includes evaluating restoration pre-proceee pre-processing step for downstream feature matching and monocular SLAM (28)
Beyond these positive impacts, potential negative implications may include misuse for unauthorized surveillance in underwater settings or misinterpretation reconstructions in safety-critical scenarios. Our work is primarily foundational and aimed environmental, marine research and safety applica- tions. Such concerns highlight the need for responsible deployment and further investigation into failure modes.
Acknowledgments. The research was funded by Israel Science Foundation grant # #1951/25 Israeli Ministry of Science and Technology grants # #1001577600 & #1001593851, EU Horizon 2020 research and innovation programme GA 101094924 (ANERIS), and the Maurice Hatter Foundation.
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Reviews:
[{"review_id": "ugFrqEqUt7", "reviewer": "Reviewer_uWFv", "summary": "This paper proposes to remove the image distortion when taking images from the air through the turbulated water. Taking as input consecutive distorted frames, the presented method adopts the neural field SIREN to implicitly learn the water surface height and uses the spatial derivatives of water height to compute the pixel distortion map. Fed with distortions and positional encoding, another SIREN network predicts the restored image. The training procedure penalizes the discrepancy between the predicted distorted images and the observed ones, requiring no ground-truth distortion-free images. Experiments shows the proposed method outperforms the previous method NDIR and baseline network settings.", "questions": "1. In the ablative experiments, why does the first SIREN network predicting surface height help to reconstruct images? Does predicting height benefit produce more accurate distortion maps? Since this network design is the core contribution of the paper, the quantitative evaluation in Table 3 may be insufficient, and further analysis about this problem should be conducted.\n2. Could the proposed method work in the wild scenes?  As most smartphones can capture live photos, it is easy to obtain water-distorted image sequences. I suggest testing the proposed method on more real-world data to comprehensively discuss the application scope of the method.\n3. Since this paper is titled ‘… Learning of the Surface Gradient’, how about predicting the surface normal/gradient by the first SIREN network instead of surface height?", "limitations": "As mentioned in Weaknesses and Questions, the setup limitation and application scope of the proposed method should be discussed comprehensively. Besides, the proposed method relies on many assumptions in section 3.1, such as small fluctuating water waves. The impact of these assumptions is supposed to be discussed.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "[Strengths]\n\n- This paper is well written with enough clarity.\n- Two interesting results are displayed in the experiments of the paper:\n    - For the water distortion removal task, learning water surface height is a more effective way compared to directly predicting distortion maps.\n    - Simplifying the loss function seems to improve the SIREN network performance.\n- Experimental results show that the proposed method has superior performance on the publicly available datasets.\n- The code is provided in the supplementary material.\n\n[Weaknesses]\n\n- The motivation for learning water surface height for distortion removal is unclear. Experiments show that water surface estimation helps to solve the problem. However, few discussions in Section 4 convey insight about this design. Moreover, the writing of the Introduction section could be further improved to emphasize the main contribution of the paper.\n- According to [9] and Fig. 7 in this paper, the experimental setup is restricted in a lab environment: a fixed camera captures images in a coral tank with slightly waved water. As an application research paper, this limitation should be discussed.\n- The title of the paper is inaccurate, since the surface gradient is computed from the water height. Thus, ‘Unsupervised Learning of the Water Surface Height’ can be more suitable.", "was_revised": true, "final_justification": "The authors' feedback in the rebuttal resolves my concerns about the motivation of this paper. After reading the comments from other reviewers, I think this paper proposes an effective method for seeing through water surfaces, and some interesting conclusions are revealed in the experiment. Therefore, I give the rating at borderline acceptance. Besides, I suggest that the authors discuss the adopted assumptions and the application scope of the proposed method in the final version.", "rebuttal": "We thank the reviewers for their positive reviews and constructive feedback. \nOur response includes more detailed explanations and additional quantitative and qualitative results that further support our claims (see Additional Results below). \nWe believe our response addresses all the main issues and hope the reviewers will acknowledge this. \n\n## Clarification of contribution in the Introduction:\n\nWe agree that the introduction can better emphasize the main contribution. In the revised version, we will clearly highlight that our method introduces a physically-constrained unsupervised learning framework that jointly reconstructs the undistorted scene and estimates the time-varying surface geometry, improving interpretability and robustness compared to prior works.\n\n## Motivation and design insight for modeling surface height rather than the gradients directly:\n\nModeling the surface gradients directly would be closer to modeling the distortions,  which is the approach in NDIR (the baseline we compare to).  Rather than learning such unconstrained gradients or distortion fields, we propose learning a scalar surface height function, which is smoother, easier to regularize, and less prone to noise than directly learning gradients. This leads to more stable training (our simpler loss vs. previous baseline method), better reconstruction, and allows for physically interpretable outputs. Section 4.2 and the tables in the supplementary material demonstrate that the estimated height fields correlate well with visible distortions and achieve low depth error on synthetic data. We recognize the value of additional analysis and have therefore expanded our discussion and results, please see \"Additional Results\" for further evidence and a more in-depth evaluation.\n\n## Assumptions and application scope:\n\nWe agree that looking through large, highly dynamic water waves remains the holy grail of this application domain. Nevertheless, the case of small fluctuating surface waves is still unsolved, challenging, and actively researched, as evidenced by recent works we cite (e.g., [9, 10, 19]). Our method explicitly targets this regime, which is relevant in real-world scenarios such as shallow coral reefs, riverbeds, and coastal areas, particularly in tropical environments (e.g., [3]) where this assumption is often valid. These settings are important for ecological monitoring, marine biology, and safety applications, and we believe the problem remains both scientifically meaningful and practically impactful. As discussed in Sec. 3.1 and demonstrated in Sec. 4.4, our method shows robustness even when some assumptions are partially violated. We will make these points more explicit in the revised version.\n\nWe agree that adding results on images in-the-wild would be interesting, however, restoring such images typically involves more problems than just light refraction, such as foam, specularities, and dynamics. While these problems are outside our paper's scope, we believe that our work still makes a significant contribution towards a comprehensive solution for real-world settings.   \n\n## Paper title gradient vs. height:\n\nWhile we predict surface height, the supervision is entirely on its gradient, as image distortion is governed by Snell’s Law, which depends on surface slope (Sec. 3.2, Eq. 1). We use SIREN precisely for its strength in learning via derivatives. That said, we are open to renaming the title from \"...Gradient\" to “...Height” or “...Height and Gradient” if preferred.\n\n# Additional Results:\n\n### 1. Distortion metrics: \n\nThe already submitted supplementary contains a comparison of synthetic sequences with known ground truth distortion field between the intermediate distortion maps computed in our method and the baseline. As requested by reviewer uWFv, we are adding results of the intermediate distortion maps produced by Ablation 1 and Ablation 2 to further investigate the effect of height prediction. The results across all three quantitative tables indicate that Ablation 1 consistently performs slightly better than Ablation 2 on key metrics such as  End-Point Error (EPE) and Average Angular Error (AAE). \n\nFor example, when averaging across all waves, Ablation 1 achieves lower EPE compared to Ablation 2 (e.g., 0.78 vs. 0.80 on Wave1, 1.13 vs. 1.16 on Wave2, and 1.12 vs. 1.14 on Wave3), and similarly better AAE (27.2° vs. 27.8° on Wave1, 44.7° vs. 45.6° on Wave2, 54.9° vs. 55.5° on Wave3). [8] achieves slightly better RMSE, EPE and AAE than both Ablation 1 and Ablation 2. However, our method outperforms all alternatives, including [8], with the lowest EPE (0.78 on Wave1, 0.64 on Wave2, 0.40 on Wave3) and AAE (26.8° on Wave1, 23.9° on Wave2, 11.1° on Wave3). \n\nThis may be explained by the fact that Ablation 1 allocates a separate network per frame, increasing parameter capacity and flexibility, whereas Ablation 2’s single temporally-conditioned network reduces the parameter count by a factor of 10 but, without a physical constraint, acts mainly as a regularizer and does not generalize as well. Importantly, unlike [8], Ablation 1, or Ablation 2, our method also provides explicit surface height estimations, enabling physically interpretable scene reconstruction in addition to superior distortion removal. We will add this expanded analysis to the revised paper.\n\n| Method       | Wave1 RMSE ↓ | Wave1 EPE ↓ | Wave1 AAE ↓ | Wave2 RMSE ↓ | Wave2 EPE ↓ | Wave2 AAE ↓ | Wave3 RMSE ↓ | Wave3 EPE ↓ | Wave3 AAE ↓ |\n|--------------|:------------:|:-----------:|:-----------:|:------------:|:-----------:|:-----------:|:------------:|:-----------:|:-----------:|\n| Ours         | **0.64**     | **0.78**    | **26.8**    | **0.53**     | **0.64**    | **23.9**    | **0.33**     | **0.40**    | **11.1**    |\n| [8]          | 0.66         | 0.78        | 27.2        | 0.92         | 1.13        | 44.7        | 1.16         | 1.12        | 54.9        |\n| Ablation 1   | 0.67         | 0.78        | 27.2        | 0.93         | 1.13        | 44.7        | 1.17         | 1.12        | 54.9        |\n| Ablation 2   | 0.68         | 0.80        | 27.8        | 0.94         | 1.16        | 45.6        | 1.18         | 1.14        | 55.5        |\n\n### 2. Comparison to NeRT: \n\nAs suggested by reviewer vzUj we have revised Table 1 to include per-sequence results for NeRT [R1] on both the Real1 and TianSet datasets. The updated table reports PSNR, SSIM, and LPIPS for each sequence individually, alongside the dataset-level averages. Compared to our method, NeRT achieves similar average PSNR and SSIM—18.77 / 0.61 (our 19.78 / 0.61) on Real1 and 18.60 / 0.40 (our 18.50 / 0.40) on TianSet. However, NeRT significantly underperforms in LPIPS: 0.29 on both datasets compared to our 0.121 (Real1) and 0.174 (TianSet). \n\nThis suggests that our method better preserves high-frequency structures, leading to lower LPIPS and sharper, more visually faithful outputs. Given LPIPS's stronger correlation with perceptual quality, we believe our results more accurately reflect real-world restoration performance. We will also include qualitative visual comparisons between our method and NeRT in the supplementary material. These examples will help illustrate the perceptual differences discussed in the quantitative analysis, particularly highlighting cases where NeRT yields higher PSNR but visibly blurrier reconstructions.\n\n| Method | Dataset | PSNR ↑    | SSIM ↑   | LPIPS ↓   |\n| ------ | ------- | --------- | -------- | --------- |\n| Ours   | Real1   | **19.78** | **0.61** | **0.121** |\n| NeRT   | Real1   | 18.77     | 0.61     | 0.29      |\n| Ours   | TianSet | 18.50     | **0.40** | **0.174** |\n| NeRT   | TianSet | **18.60** | 0.40     | 0.29      |"}, {"review_id": "F6CX19DF8b", "reviewer": "Reviewer_5QwM", "summary": "This paper addresses the problem of 3D reconstruction of underwater scenes using a physically accurate and refraction-aware variant of Neural Radiance Fields (NeRF), termed R-NeRF. The key novelty lies in the explicit modeling of light refraction at the air-water interface using Snell’s Law, allowing for accurate tracing of rays distorted by a dynamic water surface. The authors propose a differentiable formulation of this refractive geometry and jointly optimize for both the radiance field and the water surface geometry from multiview images. Experiments on synthetic and real datasets demonstrate superior reconstruction accuracy compared to baseline NeRF variants that ignore refraction.", "questions": "1. How sensitive is the surface optimization to the initialization of the water surface normals? Can the method generalize to more complex or non-smooth surface waves?\n\n2. Have you considered extending your model to support dynamic scenes or refraction through multiple interfaces (e.g., glass + water)?", "limitations": "Yes.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper is both novel and technically strong. Modeling refraction in a neural rendering framework is a non-trivial extension and represents a significant step forward in bringing physical realism into NeRFs. The authors carefully integrate refractive geometry into the NeRF pipeline by tracing rays through a parameterized water surface and optimizing the associated surface normals. The optimization framework is differentiable and jointly learns the 3D scene and the water interface. The experiments are convincing and show marked improvements in both geometric and visual fidelity, especially in real-world underwater scenarios. The methodology is clearly presented and well-supported by theoretical justifications and ablation studies.", "was_revised": true, "final_justification": "This paper introduces an interesting learning-based method for addressing the problem of 3D underwater reconstruction. The results support the proposed approach, and I would encourage its publication.", "rebuttal": "We thank the reviewers for their positive reviews and constructive feedback. Our response includes more detailed explanations and additional quantitative and qualitative results that further support our claims (see Additional Results in response to reviewer uWFv). We believe our response addresses all the main issues and hope the reviewers will acknowledge this.\n\n## Robustness to Initialization and Relevance to the Small-Wave Regime\nThe approach is physically motivated for small, smooth wave regimes—an unsolved and impactful problem in scenarios such as shallow reefs and coastal monitoring. Performance may degrade for highly non-smooth or large-amplitude surfaces, which we acknowledge as an open limitation and will clarify in the revision. We thank the reviewer for highlighting these important aspects.\n\n## Extensibility to Dynamic Scenes and Multi-Interface Refraction\nThank you for this insightful suggestion. Our framework is readily extensible to multi-interface refraction scenarios (e.g., glass + water) whenever an analytical or differentiable distortion model is available. In such cases, additional SIREN modules could be incorporated to sequentially model each refractive surface between the scene and the sensor. For dynamic scenes, the network could be adapted by introducing a temporal conditioned segmentation model (inspired by CVPR 2024 Turb-seg-res). While these extensions are beyond the scope of the current work, they are promising directions for future research and illustrate the flexibility of our architecture."}, {"review_id": "uKQfhhoEWd", "reviewer": "Reviewer_bzDM", "summary": "The paper introduces an unsupervised method to remove refraction distortions in underwater imagery captured from above water. It models the dynamic water surface and reconstructs the undistorted scene by leveraging a sequence of distorted images. The approach relies on two SIREN (sinusoidal representation network) models, one to represent the water surface height over time and another to reconstruct the static underlying image. By predicting surface gradients and their impact on light distortion using Snell’s law, the method achieves impressive results without requiring ground truth data. It outperforms prior unsupervised and supervised baselines on both real and synthetic datasets, also producing accurate surface height estimations. The architecture is compact, the training process is simplified compared to existing methods, and the results are claimed to generalize well, even when assumptions like orthographic projection or small wave perturbations are partially violated", "questions": "1. Generalization Across Sequences: Your current method is trained independently per sequence. Do you foresee a way to extend this to a setting where a pretrained model can generalize across sequences without retraining from scratch?\nIt would be helpful to know whether amortized inference, meta-learning, or adaptation techniques were considered. A discussion on this could open the door to more scalable applications.\n\n2. Real-World Surface Height Evaluation: Have you explored the possibility of validating surface height predictions using real-world measurements (e.g., stereo imaging, depth sensors, or known surface profiles)? \nA stronger quantitative grounding on real data could meaningfully improve my assessment of the method's physical reliability and general significance.\n\n3. Scope of Applicability and Extensions: The method is designed for air-to-water scenarios. Do you think it could be adapted to other refractive scenarios (e.g., viewing through glass or submerged camera settings)?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Quality: The technical execution is solid. The authors propose a novel use of two SIREN-based neural fields to model surface height and image content, with image reconstruction grounded in physical principles (Snell’s law). The model is trained in an unsupervised manner, yet delivers results that outperform both unsupervised (NDIR) and supervised baselines across real and synthetic datasets. The ablations and evaluations are given, and the use of LPIPS, SSIM, and PSNR provides a complete picture.\n\nClarity: The paper is well-organized, with clear explanations of the method and assumptions. Figures are helpful. The training losses and architectural choices are explained concisely.\n\nSignificance: This work has strong applied value, especially with the rise of drone-based environmental monitoring. Its relevance spans coral reef health checks, shallow water surveys, and potentially even safety applications like drowning detection. The ability to reconstruct surface shape and correct refractions without supervised data is a meaningful step forward for both scientific and practical imaging tasks.\n\nOriginality: The core contribution: the use of SIRENs for joint spatiotemporal modeling of surface distortions and clean image reconstruction is innovative and well-motivated. While the components (neural fields, unsupervised loss) are known, their integration in this setting is novel and demonstrates strong insight.\n\n\nSome weaknesses to be noted:\n\nAssumptions and Limitations: The method assumes relatively small wave perturbations and a planar underwater scene, which may not always hold in complex real-world settings. While the authors do test their model on scenes that partially violate these assumptions, the performance under more drastic violations remains uncertain.\n\nScalability: Each sequence is trained independently, which could pose efficiency challenges for large-scale or real-time applications. It would be interesting to see future work explore amortized inference or meta-learning to generalize across sequences.", "was_revised": true, "final_justification": "I am keeping my original score, which already reflected a strong endorsement of the quality and significance of the work. The authors have addressed the questions raised during the rebuttal phase with clear and thorough responses. While the points brought up were relevant, they primarily served to validate the scientific rigor of the approach rather than reveal any substantive issues. The authors' answers confirmed a solid grasp of the subject matter and reinforced that the methodology is well-founded. I find no remaining concerns, and I continue to fully support the acceptance of this paper.", "rebuttal": "We thank the reviewers for their positive reviews and constructive feedback. Our response includes more detailed explanations and additional quantitative and qualitative results that further support our claims (see Additional Results in response to reviewer uWFv). We believe our response addresses all the main issues and hope the reviewers will acknowledge this.\n\n## Assumptions and application scope:\nWe agree that looking through large, highly dynamic water waves remains the holy grail of this application domain. Nevertheless, the case of small fluctuating surface waves is still unsolved, challenging, and actively researched, as evidenced by recent works we cite (e.g., [9, 10, 19]). Our method explicitly targets this regime, which is relevant in real-world scenarios such as shallow coral reefs, riverbeds, and coastal areas, particularly in tropical environments (e.g., [3]) where this assumption is often valid. These settings are important for ecological monitoring, marine biology, and safety applications, and we believe the problem remains both scientifically meaningful and practically impactful. As discussed in Sec. 3.1 and demonstrated in Sec. 4.4, our method shows robustness even when some assumptions are partially violated. We will make these points more explicit in the revised version. \n\nWe agree that adding results on images in the wild would be interesting, however, restoring such images typically involves more problems than just light refraction, such as foam, specularities, and dynamics. While these problems are out of our paper's scope, we acknowledge that performance under severe violations of the assumptions remains an open limitation and an important direction for future work. We will clarify this in the revised version. However, we believe that our work still provides a significant contribution towards a comprehensive solution for real-world settings.   \n\n## Scalability and Generalizing across sequences:\nGeneralizing across sequences without per-sequence retraining is indeed an important and promising direction. Approaches such as amortized inference or meta-learning could be used to learn a mapping from sequence statistics to latent codes or meta-initializations, enabling our SIREN-based architecture to adapt to new sequences without full retraining. \nThe implementation could be based on works like [1] and [2]. While this extension is beyond the current scope, we agree it is a natural next step to improve scalability and practical deployment, and we appreciate the reviewer highlighting this opportunity.\n\n[1] Modulated periodic activations for generalizable local function representations. Mehta et al.\n\n[2] From data to functa: Your data point is a function and you can treat it like one. Dupont et al. \n\n## Towards Empirical Validation of Surface Height on Real-World Data:\nWe wholeheartedly agree with the reviewer. The ability to validate surface height predictions on real-world data would significantly enhance the empirical grounding and physical interpretability of our method. At present, however, there is no publicly available dataset that jointly contains (i) dynamic water surface ground truth, (ii) a corresponding distorted image sequence, and (iii) the associated clean (undistorted) imagery. This lack probably stems from the fact that stereo or depth sensing using NIR sensors do not perform well on transparent water surfaces with high NIR absorbance. That is why our ability to reconstruct the surface out of the sequence is important. We agree that constructing such a dataset would be of high value to the community. Indeed, while working on this research, we have also started planning the development of such a dataset as part of future work, and we thank the reviewer for emphasizing its importance. We aim to utilize a research wave tank with controllable surface dynamics, and additionally employing distributed wave gauges to obtain accurate ground truth water heights. These local measurements could be interpolated to provide dense water-surface measurements. \n\n## Extensibility to Multi-Layer Refraction and Submerged Imaging Scenarios\nThis is a very relevant and appreciated question. Our method is currently tailored to single-surface air-to-water refraction. However, the underlying framework can be extended to more complex refractive scenarios, such as multi-layered media (e.g., glass + water interfaces), provided the distortion model across layers can be approximated analytically or through differentiable simulation. In such cases, additional SIREN modules could be introduced to sequentially model the intermediate refractive surfaces between the scene and the sensor. This modularity makes the architecture naturally extensible.\nIn submerged camera scenarios (e.g., a camera underwater looking upward toward a dynamic water surface), similar principles apply, although some modifications are required. For instance, if the camera is viewing objects in air through the water surface, the algorithm would need to estimate the distance between the scene and the water interface instead of the average water height. Furthermore, care must be taken with camera housing: flat ports introduce ray deflections that violate the single viewpoint assumption, so a dome port (which preserves central projection) would be preferable to ensure consistent geometric modeling.\nWe thank the reviewer for encouraging us to elaborate on these points, and we will consider adding a dedicated discussion on this topic in the revised version of the paper."}, {"review_id": "NWZgC8RV48", "reviewer": "Reviewer_vzUj", "summary": "The paper aims to remove the image distortion caused by the refractions at the water surfact, with a SIREN implicit representation to learn the shape of the water surface in a self-supervised way.", "questions": "1. Can the authors provide the runtime of the baselines and the proposed method?\n2. Is the proposed method limited to modeling the surface of water? For example, can it be modified to mitigate the atmospheric turbulence?\n3. Can it model the water surface with dramatic slope?", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper defines the problem intuitively, with an illustration showing the Snell’s law. The scenes also have their names as labels, and the results are visualized in the supplementary material.\n\nThe weaknesses, in comparison, outweigh the strengths significantly, and I list my concerns below:\n1. A lack of comparison. The authors only compare with NDIR and Li et al., which is not enough. For example, as the authors mention the dataset proposed by Thapa et al. [19], their method is also worth comparing with. In addition, general-purposed turbulence mitigation methods (such as [R1]) as well as image restoration methods (such as Swin Transformer) should be taken into consideration.\n2. Doubts about the synthetic data. In the simulated distortion, The distorted image patch has black borders around it, which indicates the distortion of the original straight edges to some extent, which deviates from the real-world situation. Also, the size (both spatial resolution and temporal frames) of the dataset is very small, and the listed quantitative comparison are even limited to the single frames, which poses more doubts over the comparison. The Real1 dataset also seems to exhibit over-exposure, which again makes the result less reliable.\n3. A lack of study on the background. The fields of turbulence removal and refraction removal are both well-established, but the paper only cited 25 references.\n\n[19] Learning to remove refractive distortions from underwater images. In ICCV 2021.\n[R1] NeRT: Implicit Neural Representations for Unsupervised Atmospheric Turbulence Mitigation, In CVPR 2023.", "was_revised": true, "final_justification": "The paper itself needs further polishing, but I would not be surprised if it were accepted, given its current form.", "rebuttal": "We thank the reviewers for their positive reviews and constructive feedback. Our response includes more detailed explanations and additional quantitative and qualitative results that further support our claims (see Additional Results in response to reviewer uWFv). We believe our response addresses all the main issues and hope the reviewers will acknowledge this.\n\n## Addressing Comparison Scope with Additional Baselines and Related Work:\n\nWe agree with the reviewer that broader comparisons would strengthen the experimental section. One caveat is that, to the best of our knowledge, no code is publicly available for Thapa et al. [19], which limits our ability to include their method in a fair evaluation. That said, we acknowledge the relevance of general-purpose turbulence mitigation methods. To this end, we have taken two steps: (1) expand the related work section to include background and citations of prominent turbulence mitigation methods (such as ECCV 2022's TurbNET, ACCV 2024's DeTurb, and prior works, e.g. ICPR 2014's Atmospheric Turbulence Mitigation Using Optical Flow), and (2) expand Table 1 to include results from [R1]. We believe these additions will provide a more comprehensive context for evaluating our approach.\n\n[R1] NeRT: Implicit Neural Representations for Unsupervised Atmospheric Turbulence Mitigation (CVPR 2023).\n\n**Expanded Table 1 and more detailed descriptions (See also in Additional Results #2 in response to reviewer uWFv):**\n\nThe updated table reports  PSNR, SSIM, and LPIPS on both the Real1 and TianSet datasets for each sequence individually, alongside the dataset-level averages. Compared to our method, NeRT achieves similar average PSNR and SSIM—18.77 / 0.61 (our 19.78 / 0.61) on Real1 and 18.60 / 0.40 (our 18.50 / 0.40) on TianSet. However, NeRT significantly underperforms in LPIPS: 0.29 on both datasets compared to our 0.121 (Real1) and 0.174 (TianSet). \n\nThis suggests that our method better preserves high-frequency structures, leading to lower LPIPS and sharper, more visually faithful outputs. Given LPIPS's stronger correlation with perceptual quality, we believe our results more accurately reflect real-world restoration performance. We will also include qualitative visual comparisons between our method and NeRT in the supplementary material. These examples will help illustrate the perceptual differences discussed in the quantitative analysis, particularly highlighting cases where NeRT yields higher PSNR but visibly blurrier reconstructions.\n\n| Method | Dataset | PSNR ↑    | SSIM ↑   | LPIPS ↓   |\n| ------ | ------- | --------- | -------- | --------- |\n| Ours   | Real1   | **19.78** | **0.61** | **0.121** |\n| NeRT   | Real1   | 18.77     | 0.61     | 0.29      |\n| Ours   | TianSet | 18.50     | **0.40** | **0.174** |\n| NeRT   | TianSet | **18.60** | 0.40     | 0.29      |\n\n\n## Clarifying Simulator Usage and Synthetic Data Limitations\n\nWe use the same simulator originally introduced by Tian et al. [21] and later adopted by Thapa et al. [19], without modification. This was done intentionally to ensure a fair and direct comparison with prior work. We report single-frame quantitative comparisons as representative examples to illustrate our evaluation process for distortion and height prediction, rather than as exhaustive summaries over the synthetic dataset. The spatial and temporal sizes of our synthetic data are on par with prior works, ensuring methodological alignment and fair comparison. \n\nWhile we did not explicitly state it, we do mask the loss in the black border areas introduced by the distortion process. We agree that without this masking, the height prediction network could exploit strong gradient cues at the artificial boundaries.  We chose to use this simulation setup rather than redesigning the simulator in order to preserve comparability with prior methods. We will make this implementation detail and its motivation explicit in the revised version, as we agree it is a crucial point for interpreting the results and understanding the limits of the current experimental design.\n\nRegarding the Real1 dataset, we note that it has been widely used in the community since its publication, with most subsequent works employing it for benchmarking. Real1 is considered a particularly challenging benchmark, as it contains not only strong refractive distortions but also significant motion blur. While the issue of over-exposure is present, it has not been directly addressed by prior work, so we have chosen to conduct a fair comparison under the same conditions. We acknowledge the reviewer’s point, and agree that if over-exposure is to be systematically addressed, it would require a careful re-implementation of all baseline methods for consistency.\n\n## Runtime of the baselines and the proposed method:\n\nThe following tables describe the running time of our method vs. NDIR. We will add it to the supp. material.\n\n| BatchSize | Runtime \\[min] Ours | Runtime \\[min] NDIR \\[8] |\n| --------- | ------------------- | ------------------------ |\n| 5         | **4**               | 5                        |\n| 6         | **4**               | 5                        |\n| 7         | **5**               | 6                        |\n| 8         | **6**               | 7                        |\n| 9         | **6**               | 8                        |\n| 10        | **6**               | 9                        |\n\n## Applicability to Other Distortion Regimes and Extensibility Beyond Water Surfaces:\n\nOur proposed method is specifically designed to model refractive distortions caused by dynamic water surfaces. This is achieved by embedding physics-based priors, derived from Snell’s Law, directly into the network architecture, including surface height estimation and its gradient-based contribution to image distortion.\nAtmospheric turbulence, in contrast, arises from different optical principles, primarily small-scale random index-of-refraction changes over space and time due to thermal gradients, and typically lacks a closed-form deterministic model like that of refraction through a water-air interface.\nThus, while our current formulation is not directly applicable to atmospheric turbulence, it can in principle be extended to handle more complex refractive scenarios where an analytical distortion model is available (e.g., layered refractive media). For example, the architecture could be adapted to multi-stage refractions by introducing additional SIRENs between the surface estimator and the image reconstruction module. That said, atmospheric turbulence may require a separate modeling paradigm due to its stochastic and volumetric nature, which goes beyond the surface-based refractive model we use.\n\n## Modeling Limitations, Assumptions, and Validity for Large Surface Slopes:\n\nAs discussed in Section 3.2, Equation 1 relates surface height and its gradient to the pixel-wise distortion via Snell’s law. However, this formulation relies on a small-angle approximation, which introduces a theoretical bound on the maximum slope (i.e., surface-height gradient magnitude) that can be accurately modeled.\nWe acknowledge that this limitation is not sufficiently emphasized in the main text and will clarify this in the revised version. Specifically, we will include the complete derivation of Equation 1 and formally state the required assumptions (e.g., small surface tilt) for its validity. This derivation, along with the theoretical slope bounds, will be added to the revised appendix of our paper. We are grateful to the reviewer for pointing this out, as it improves both the clarity and rigor of the paper."}]

Author rebuttal:

Meta-review: The submission proposes a physically grounded, unsupervised method for removing refractive distortions caused by viewing underwater scenes from above the water surface. It uses SIREN-based implicit neural representations to model the water surface height and the distortion-free underlying image. The key strengths of the paper are a well-grounded methodology that tackles a challenging problem to produce good results. The key weaknesses are a range of limitations that are understandable for a challenging problem and the need for additional validations, many of which are addressed in the rebuttal phase. uWFv notes the need for more analysis, lack of in-the-wild testing and that the title suggest learning the gradient instead of height. The authors respond by clarifying the motivation, noting that in-lab testing is the only feasible option given modeling limitations and including additional ablations and comparisons, which are satisfactory responses. 5QwM questions sensitivity to initialization, extension to non-smooth waves and multiple interfaces. The authors acknowledge them all as limitations, however, 5QwM remains overall positive. bzDM is strongly supportive based on the methodology, but raises the important question of generalization across sequences, which the authors note might be possible in future extensions.  Lack of comparisons to baselines and a runtime in minutes are cited by vzUj as reasons for leaning to reject. The authors provide analysis for NeRT and note the runtime as reasonable, while also noting the lack of baselines in this area. The AC deems the author feedback as valid arguments. Overall the AC agrees with the majority opinion that the problem is a challenging one and while limitations exist, the solution is a well-motivated one that extends the state-of-the-art. Thus, the submission is recommended for acceptance. The authors are encouraged to reword the title, include clearer statements on limitations, discuss the possibility of generalizable extensions in future work and include the additional comparisons and ablations from the rebuttal discussions.
Decision: Accept (poster)