Title: Looking Into the Water by Unsupervised Learning of the Surface Shape
Venue: NeurIPS 2025
Accepted: yes
Keywords: Underwater

refractive distrotion

unsupervised learning

SIREN
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

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.

Distorted Frame

NDIR

Ours

GT

SurfaceHeight

112358

112358

112358

112358

Dan Rosenbaum

1 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 a variety of scientific and operational applications. For example, measuring the scale of coral bleaching after a warming event or a 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, 15]. Measurement of sea surface height also informs studies of the sea surface microlayer [25].

Here, using a short input sequence of an underwater object seen from above, we aim to reconstruct its fine details and undistorted structure, as well as the surface height in each point. An example is shown in Fig. 1. 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 to real-world examples. However, distorted sequences contain a 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 a 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 additionally 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 physics-based challenges. Early works [5, 8, 24] were based on finding and stitching together distortion-free patches from the distorted image sequence. In [8] 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. In [5] the authors suggest a 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.

Adifferent line of techniques is based on model-based tracking to reconstruct the clean image. In [23] the authors propose building a spatial distortion model of the water surface using the wave equation. The model enables them to design a 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 in [8] or 120 in [24].

A 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 to 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 a 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-free, Snell's-law-based 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 a short sequence), their method assumes a known background and directly optimizes surface geometry via a geometric ray-consistency error [18].

Supervised deep learning methods require a training dataset. In [12] a dataset was acquired using a 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 et 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-predicted distortion maps by enforcing the temporal consistency among them. Then, a GAN is used to predict the distortion-free image. FSRN [20] was trained to estimate the water surface based on a known reference background in the water.

Li et al . [11] 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 distortionfree image. The optimizer for generating the distortion-free image by minimizing pairwise differences between the captured input images, the network's predicted distorted images, and resampled distorted images from the distortion-free image. Our model is also based on unsupervised reconstruction, modeling the image and the distortions using different networks, however we use a single SIREN [17] 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 a 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 [27] and as a basic representation for different downstream tasks [7].

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 h 0 below a water surface. The scene is fronto-parallel 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 [9, 16, 21, 22] we also assume small fluctuating water-waves, i.e ., the maximum surface fluctuation, max x,t | h ( x, t ) -h 0 | , is small compared to the average water-height h 0 . This is a reasonable assumption for many marine environments such as river beds and shallow coral reefs. If the camera exposure time is not sufficiently short in 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 Real1 dataset [9] which is considered a

xreg

Input

Xreg

Height model

Hg

Surface Height

h(x,t)

Distortion

Distortions

Calculation

d(x,t)

1

Distorted

Distorted

Gradient

×

Predicted

Images

Measurements

Observed

PE

It

Surface Height

Average Water

Mult. With

Constant

Multiplication

h(x,t)

ho·(1-

PE

Positional Encoding

x,t

Reconstructed

Clean Image

1g(xreg)

ForwardPropagation

hard dataset for underwater refractive distortion removal due to large frame-to-frame motion and motion-blur. In Fig. 7 we present real-world results where our assumptions do not fully hold and show that our method is able to reconstruct a plausible underlying clean image, see Sec. 5 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 on Snell's law (illustrated in Fig. 3). 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 h ( x, t ) at the 2D spatial position x and time t :

where h 0 is the average water height above the scene, and n 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 are used as neural fields to model both the water surface height at different times points h ( x, t ) , and the fixed underlying image.

Surface height model H θ . 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 t , and predicts the surface height at that position and time H θ ( x, t ) . Using a SIREN architecture is well-suited for modeling distortions through surface height as it allows for the efficient prediction of a signal and its spatial derivatives simultaneously. We use a single SIREN to 1) predict the water surface height h ( x, t ) which is used to compute h 0 by averaging the outputs across the 2D space x and time t ; and 2) predict ∇ h ( x, t ) by computing the gradients of the output of the network with respect to its spatial input x . Given the computed h 0 and ∇ h ( x, t ) we compute the pixel distortions d ( x, t ) due to light refraction for each observed image at time t using Eq. 1 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 I ϕ . This is implemented using a standard neural field SIREN where each pixel position is fed to the network along with a positional encoding using random Fourier features [19],

n1

h(x,t)

0r.1

ho

and is trained to predict the pixel values I ϕ ( x ) . Feeding this model with a set pixel positions on the image's regular grid x reg will output the set of pixel values for the distortion-free image I ϕ ( x reg ) , and feeding the model with a set of distorted pixel positions x t = x reg + d ( x reg , t ) will result in a distorted image which we denote by I t θ,ϕ , since it is generated using both models H θ and I ϕ and therefore depends on both sets of weights. To formulate this explicitly,

where d ( H ( · )) corresponds to using Eq. 1 on the height prediction.

3.4 Training

Given a set of distorted frames across time I t , we follow the training paradigm in [11] consisting of two stages. The first training stage can be seen as an initialization of the weights, by training the height network H θ to output a height that corresponds to zero distortion for all pixels, and training the image network I ϕ to predict the average distorted image. This is implemented using the loss ( | · | represents the L 1 norm):

In the second stage of training the loss is computed by the reconstruction of all the distorted images. The loss is given by:

This is a significant simplification compared to [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. 1 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 a signal by supervising it with the derivatives.

4 Experiments

To test our method we use three datasets. We use the James Real1 dataset [9], which contains 7 sequences of images acquired in a water tank using 50 fps acquisition rate (examples in Fig. 4). Additionally, we use the TianSet , which is also a real captured dataset by Tian and Narasimhan [23] using a 125 fps camera. We note that Real1 is considered a more challenging dataset as it has larger frame-to-frame motion and includes motion blur (due to water-waves). We also generate a synthetic dataset using the method in [20], with 3 wave types, resulting in 11 sequences of images. We compare our method to NDIR [11], which is our unsupervised baseline and to Li et al . [12] which is the

Distorted Frame

NDIR

Ours

GT

1123588

112358

Cartoon

112358

112358

12358

D

O

Checkers

state-of-the-art 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 all experiments we use a 2-layer network for H θ and a 3-layer network for I ϕ , both trained with the Adam optimizer. The input to I ϕ is augmented with random Fourier positional encoding with the bandwidth factor set to 8. We use two sets of hyperparameters. One set for both real datasets ( Real1 and TianSet ) and the other for the synthetic dataset. More details on 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 [11].

4.1 Image restoration

A qualitative comparison of our results on the Real1 dataset is shown in Figs. 1 and 4 where green and blue rectangles mark areas of interest. In the cartoon sequence our method better aligns several

DistortedFrame

NDIR

Ours

GT

OurEstimated

Distortion

品

2

areas, e.g., the numbers, elephant, hand, and as a 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 in the acquired frame.

Tab. 1 summarizes quantitative results for all three methods, ours and [9, 11], 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 [11]. In all other sequences in both datasets, our method achieves the best LPIPS, while also providing surface-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 is thus less indicative of perceptual quality, whereas LPIPS aligns more closely with sharpness and fidelity, as can be seen in the qualitative comparison (Fig. 4). Finally, Tab. 2 shows results on the simulated dataset, where our method is superior in all metrics compared to the baseline method on every wave-type.

b

Z

Z

Z

Y

X

y

X

X

X

Z

Z

X

X

X

4.2 Water surface estimation

In addition to reconstructing the underlying image, our method estimates the water surface height of every frame in the sequence. Examples are shown qualitatively on sequences from the Real1 dataset [9] in Figs. 1, 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 of [26]. Fig. 6b shows surface height estimations on a ripple sequence evolving with time. We see that our estimations closely follow the ground-truth height shape over time.

4.3 Ablations.

All ablations were performed using the more challenging Real1 dataset. The quantitative results presented in Tables 3 and 4 are the average over the entire dataset.

Modeling surface-height and spatio-temporal information. We compare our final architecture with two ablations of our method (Tab. 3). In ablation 1 , we predict per-frame pixel distortions x t using separate networks for each time step instead of a single, time-conditioned network. Ablation 2 employs a shared network across time while still predicting x t , ignoring surface height. Both ablations use SIRENs for sub-networks and neglect refraction modeling, precluding surface height estimation. The key distinction is that ablation 2 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. 3). In NDIR [11] the authors use in the second stage of training a loss function composed of three terms which are based on two different ways to compute predictions of the distorted images. The first way is computing I t θ,ϕ using Eq. 2, and the second way is to generate the regular image I ϕ ( x reg ) and then use the distortion to warp the image W t θ,ϕ = warp( I ϕ ( x reg ) , d ( H θ ( x reg , t ))) . Using these two predictions and the observed image, they compute the loss by comparing the three possible pairs for each observed frame

in time:

We test different combinations of these 3 loss terms, and find that for our model, using only the first term as formulated in Eq. 4 results in better performance. This shows that our model can attain better results while using a simplified training setup compared to NDIR, for which it was shown that all 3 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, our 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 in a real-world setting (Fig. 7) without an orthographic camera and with a nonfronto-parallel 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.

DistortedInputImage

ReconstructedImage

Acquisition Setup

5 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 are a 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 our method has numerous applications in ocean surveys, fish farm monitoring, and also drowning detection both in the ocean and in swimming pools. Future work includes evaluating our restoration as a 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 of reconstructions in safety-critical scenarios. Our work is primarily foundational and aimed at environmental, marine research and safety applications. 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 / 23 , Israeli Ministry of Science and Technology grants #1001577600 & #1001593851 , EU Horizon 2020 research and innovation programme GA 101094924 (ANERIS), and the Maurice Hatter Foundation.

References

R. Almar, E. W. Bergsma, P. A. Catalan, R. Cienfuegos, L. Suarez, F. Lucero, A. N. Lerma, F. Desmazes, E. Perugini, M. L. Palmsten, et al. Sea state from single optical images: A methodology to derive wind-generated ocean waves from cameras, drones and satellites. Remote Sensing , 13(4):679, 2021.

N. Benbarka, T. Höfer, H. ul Moqeet Riaz, and A. Zell. Seeing implicit neural representations as fourier series. 2022 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) , pages 2283-2292, 2021. URL https://api.semanticscholar.org/CorpusID: 237371659 .

V. Chirayath and R. Instrella. Fluid lensing and machine learning for centimeter-resolution airborne assessment of coral reefs in american samoa. Remote sensing of environment , 235: 111475, 2019.

J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition , pages 248-255. Ieee, 2009.

A. Donate and E. Ribeiro. Improved reconstruction of images distorted by water waves. In Advances in Computer Graphics and Computer Vision , volume 4, pages 228-235, 01 2006. ISBN 978-3-540-75272-1. doi: 10.1007/978-3-540-75274-5_18.

E. Dupont, A. Goli´ nski, M. Alizadeh, Y. W. Teh, and A. Doucet. Coin: Compression with implicit neural representations. arXiv preprint arXiv:2103.03123 , 2021.

E. Dupont, H. Kim, S. M. A. Eslami, D. Rezende, and D. Rosenbaum. From data to functa: Your data point is a function and you can treat it like one, 2022. URL https://arxiv.org/ abs/2201.12204 .

A. Efros, V. Isler, J. Shi, and M. Visontai. Seeing through water. In NeurIPS , volume 17, 2004.

J. G. James, P. Agrawal, and A. Rajwade. Restoration of non-rigidly distorted underwater images using a combination of compressive sensing and local polynomial image representations. In ICCV , pages 7839-7848, 2019.

W. Jiang, V. Boominathan, and A. Veeraraghavan. Nert: Implicit neural representations for unsupervised atmospheric turbulence mitigation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops , pages 4236-4243, June 2023.

N. Li, S. Thapa, C. Whyte, A. W. Reed, S. Jayasuriya, and J. Ye. Unsupervised non-rigid image distortion removal via grid deformation. In CVPR , pages 2522-2532, 2021.

Z. Li, Z. Murez, D. Kriegman, R. Ramamoorthi, and M. Chandraker. Learning to see through turbulent water. In Proc. IEEE Winter Conference on Applications of Computer Vision (WACV) , pages 512-520, 2018.

B. Mildenhall, P. Srinivasan, M. Tancik, J. Barron, R. Ramamoorthi, and R. Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In ECCV , 2020.

H. Murase et al. Surface shape reconstruction of a nonrigid transparent object using refraction and motion. IEEE TPAMI , 14(10):1045-1052, 1992.

N. Sawada, D. Inazu, L. Wu, T. Ikeya, and A. Okayasu. Air-borne stereo observation of ocean wave height using two independent cameras from a single unmanned aerial vehicle. J. Marine Science and Technology , 2024.

K. Seemakurthy and A. N. Rajagopalan. Deskewing of underwater images. IEEE Transactions on Image Processing , 24(3):1046-1059, 2015. ISSN 10577149. doi: 10.1109/TIP.2015. 2395814.

V. Sitzmann, J. Martel, A. Bergman, D. Lindell, and G. Wetzstein. Implicit neural representations with periodic activation functions. NeurIPS , 33:7462-7473, 2020.

A. Sulc, I. Sato, B. Goldluecke, and T. Treibitz. Towards monocular shape from refraction. In 32nd British Machine Vision Conference 2021, BMVC 2021, Online, November 22-25, 2021 , page 6. BMVA Press, 2021. URL https://www.bmvc2021-virtualconference. com/assets/papers/0195.pdf .

M. Tancik, P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoorthi, J. Barron, and R. Ng. Fourier features let networks learn high frequency functions in low dimensional domains. Advances in neural information processing systems , 33:7537-7547, 2020.

S. Thapa, N. Li, and J. Ye. Dynamic fluid surface reconstruction using deep neural network. In CVPR , pages 21-30, 2020.

S. Thapa, N. Li, and J. Ye. Learning to remove refractive distortions from underwater images. In ICCV , pages 5007-5016, 2021.

Y. Tian and S. Narasimhan. The relationship between water depth and distortion. CMU TechReport RI , 2009.

Y. Tian and S. G. Narasimhan. Seeing through water: Image restoration using model-based tracking. ICCV , pages 2303-2310, 2009. ISSN 15505499. doi: 10.1109/ICCV.2009.5459440.

Z. Wen, D. Fraser, A. J. Lambert, and H. Li. Reconstruction of underwater image by bispectrum. ICIP , 3:III - 545-III - 548, 2007. URL https://api.semanticscholar.org/CorpusID: 11016621 .

O. Wurl, W. Ekau, W. M. Landing, and C. J. Zappa. Sea surface microlayer in a changing ocean-a perspective. Elem Sci Anth , 5:31, 2017.

J. Xiong and W. Heidrich. In-the-wild single camera 3d reconstruction through moving water surfaces. In ICCV , pages 12558-12567, 2021.

Y. Yin, M. Kirchmeyer, J.-Y. Franceschi, A. Rakotomamonjy, and P. Gallinari. Continuous pde dynamics forecasting with implicit neural representations, 2023. URL https://arxiv.org/ abs/2209.14855 .

Z. Zheng, Z. Xin, Z. Yu, and S.-K. Yeung. Real-time gan-based image enhancement for robust underwater monocular slam. Frontiers in Marine Science , 10:1161399, 2023.

NeurIPS Paper Checklist

1. Claims

Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?

Answer: [Yes] .

Justification: The claims established in the abstract and introduction are supported by the technical sections (Sec. 3) and validated through experiments and analysis (Sec. 4). Assumptions are discussed (Sec. 3.1) and real-world applicability is tested (Sec. 4.4).

Guidelines:

The answer NA means that the abstract and introduction do not include the claims made in the paper.

The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.

The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.

It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.

2. Limitations

Question: Does the paper discuss the limitations of the work performed by the authors?

Answer: [Yes] .

Justification: Assumptions and limitations are discussed in a separate section (Sec. 3.1). We perform a qualitative experiment to validate the applicability of our proposed solution when our assumptions are only partially fulfilled in a real-world setting (Sec. 4.4). As discussed in the paper, for real-world setting it is very difficult to produce ground truth data of the water-surface geometry paired with a distorted image caused by refraction due to wavy air-water interface, as far as we know no such dataset exists yet.

Guidelines:

The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.

The authors are encouraged to create a separate "Limitations" section in their paper.

The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.

The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.

The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.

The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.

If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.

While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.

3. Theory assumptions and proofs

Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?

Answer: [NA] .

Justification: [NA] .

Guidelines:

The answer NA means that the paper does not include theoretical results.

All the theorems, formulas, and proofs in the paper should be numbered and crossreferenced.

All assumptions should be clearly stated or referenced in the statement of any theorems.

The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.

Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.

Theorems and Lemmas that the proof relies upon should be properly referenced.

4. Experimental result reproducibility

Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?

Answer: [Yes] .

Justification: We fully describe our architecture and provide all hyperparameters used. See Sec. 3 in the main paper and in the supplementary material under "Implementation Details" . We provide code, datasets and scripts to run exeperiments in the supplementary material .zip file.

Guidelines:

The answer NA means that the paper does not include experiments.

If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.

If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.

Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.

While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example

(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.

(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.

(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).

(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.

5. Open access to data and code

Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?

Answer: [Yes] .

Justification: We provide as much information as possible in supplemental material (appended to the paper), an online repository will be made available online upon publication of the paper. The repository will contain the code, datasets and script provided in the supplementary material submitted for review.

Guidelines:

The answer NA means that paper does not include experiments requiring code.

Please see the NeurIPS code and data submission guidelines ( https://nips.cc/ public/guides/CodeSubmissionPolicy ) for more details.

While we encourage the release of code and data, we understand that this might not be possible, so 'No' is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).

The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines ( https: //nips.cc/public/guides/CodeSubmissionPolicy ) for more details.

The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.

The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.

At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).

Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.

6. Experimental setting/details

Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?

Answer: [Yes] .

Justification: We explicitly specify all training and test details in the main paper (Sec. 4).

Guidelines:

The answer NA means that the paper does not include experiments.

The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.

The full details can be provided either with the code, in appendix, or as supplemental material.

7. Experiment statistical significance

Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?

Answer: [Yes] .

Justification: We accompany the main results of this paper with statistical significance by reporting standard deviation on each sequence of each dataset, along with the standard deviation of the mean over the entire dataset. This statistical analysis supports the reliability of the core quantitative results reported in Table 1, and the calculation is based on training the parameters with different sets of observed images (i.e., no random seeds were involved).

Guidelines:

The answer NA means that the paper does not include experiments.

The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.

The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).

The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)

The assumptions made should be given (e.g., Normally distributed errors).

It should be clear whether the error bar is the standard deviation or the standard error of the mean.

It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified.

For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).

If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.

8. Experiments compute resources

Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?

Answer: [Yes]

Justification: We specify information regarding compute resources in the provided supplementary material (under "Implementation Details" ).

Guidelines:

The answer NA means that the paper does not include experiments.

The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.

The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.

The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).

9. Code of ethics

Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines ?

Answer: [Yes] .

Justification: We have read the NeurIPS Code of Ethic and declare that our reseearch and this paper fully conform in every respect with the NeurIPS Code of Ethics.

Guidelines:

The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.

If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.

The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).

10. Broader impacts

Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?

Answer: [Yes] .

Justification: The paper explicitly discusses both potential positive and negative societal impacts in the Summary section (Sec. 5).

Guidelines:

The answer NA means that there is no societal impact of the work performed.

If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.

Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.

The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.

The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.

If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).

11. Safeguards

Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?

Answer: [No]

Justification: All datasets used in this paper do not require any safeguards, no pretrained models were used thus making the work in this paper based purely on safe-to-use datasets. In this manner the authos discouraged possible misuse of the work in this paper. The risk for misuse lies with a future downstream application that deploys the proposed solution, generating safeguards against such misuse is difficult.

Guidelines:

The answer NA means that the paper poses no such risks.

Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.

Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.

We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.

12. Licenses for existing assets

Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?

Answer: [Yes] .

Justification: All original owners are properly credited and terms of use are explicitly mentioned where applicable.

Guidelines:

The answer NA means that the paper does not use existing assets.

The authors should cite the original paper that produced the code package or dataset.

The authors should state which version of the asset is used and, if possible, include a URL.

The name of the license (e.g., CC-BY 4.0) should be included for each asset.

For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.

If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.

For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.

If this information is not available online, the authors are encouraged to reach out to the asset's creators.

13. New assets

Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?

Answer: [Yes] .

Justification: Details regarding all new assets are thoroughly discussed in the paper, the provided supplementary material and the published code and datasets.

Guidelines:

The answer NA means that the paper does not release new assets.

Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.

The paper should discuss whether and how consent was obtained from people whose asset is used.

At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.

14. Crowdsourcing and research with human subjects

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?

Answer: [NA] .

Justification: [NA] .

Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.

Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.

According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.

15. Institutional review board (IRB) approvals or equivalent for research with human subjects

Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?

Answer: [NA] .

Justification: [NA] .

Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.

Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.

We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.

For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.

16. Declaration of LLM usage

Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.

Answer: [NA] .

Justification: [NA] .

Guidelines:

The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.

Please refer to our LLM policy ( https://neurips.cc/Conferences/2025/LLM ) for what should or should not be described.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nThe 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.\n\nQUESTIONS:\n1. 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?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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\n\nSTRENGTHS AND WEAKNESSES:\nQuality: 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.\n\nQUESTIONS:\n1. 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)?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nThe 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.\n\nQUESTIONS:\n1. 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)?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\n[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.\n\nQUESTIONS:\n1. 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?\n\nLIMITATIONS:\nAs 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.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}