Image Stitching in Adverse Condition: A Bidirectional-Consistency Learning Framework and Benchmark

Thank you for your valuable feedback. I have carefully considered your suggestions and concerns, and will revise the manuscript accordingly. Please find my detailed responses to your comments below:

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Answer for Q1&Q2: Thank you for your suggestion. Our method can also serve as a general-purpose image stitching method under normal conditions. To demonstrate this, we conducted additional comparison experiments on the standard UDIS dataset. As shown in Table 1, the proposed method is quantitatively compared with other stitching methods on the UDIS dataset.

It is worth noting that since the UDIS dataset features normal lighting conditions without rain or fog, it differs from the adverse environments discussed in the main paper. Therefore, unlike the comparisons in the main text that involve combining task-specific restoration methods with stitching algorithms, here we directly compare pure stitching methods.

To ensure a fair comparison, and in contrast to the experimental protocol described in the manuscript (which uses synthetically generated pairs from adverse-environment datasets), we re-trained our method on the UDIS dataset using the Adam optimizer. The training was conducted for 100 epochs with a learning rate of 1e-4, and the retrained model was used for testing to validate the effectiveness of the proposed method under normal conditions.

Due to NIPS rebuttal policy restrictions, we are unable to provide visual comparisons. However, as shown in the table, our method still achieves a slight advantage under normal conditions, with a 1% improvement in PSNR, 2% in SSIM, 2% in NIQE, and 12% in SIQE compared to the best-performing existing methods. This demonstrates the generalizability of our proposed approach.

Table 1: Quantitative comparison for image stitching under normal environment (UDIS dataset).

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Answer for Limitation: Thank you for your suggestion. Regarding the applicability of our model in normal conditions, please refer to our response to Q1 and Q2. The quantitative results in Table 1 demonstrate the effectiveness of the proposed architecture for image stitching under normal conditions.

Thank you for your valuable comments. In response to your suggestions and concerns, I will provide detailed explanations and revise the manuscript accordingly. Please find my responses below.

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Ans for W1: Thank you for your feedback. The proposed motion constraint currently improves stitching performance in dynamic scenes to a certain extent. Taking pedestrians in road scenarios as an example: when a person moves during the acquisition of the image pair, our method can effectively suppress visual ghosting in the stitched result—but only if the motion remains within the overlapping region of the two images. If the pedestrian's movement exceeds this overlapping area, the network cannot recognize them as the same target, resulting in duplicated appearances in the final stitched image. This is because the core of our motion loss lies in capturing moving content within the overlap, and it cannot handle motion beyond that scope.

Addressing high-speed motion with large displacements (beyond the overlapping area), while ensuring that only non-redundant targets remain in the final output, remains highly challenging. This may require integrating explicit object detection modules with generative models to inpaint the occluded background around repeated targets using contextual information. We will include a discussion of this limitation in the Limitations section of the manuscript.

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W2(1): “Why the bidirectional optimization approach can enhance alignment reliability more effectively”

Ans: The proposed optimization framework is proposed to address the issue of inconsistent restoration. In image alignment tasks under adverse conditions, we aim for the backbone network to produce restoration results that are equivariant under spatial transformations. This objective can be formally expressed as:

$\Phi\left(\mathcal{W}\left(I_{\text{tar}} ; \mathbf{H}\right)\right) = \mathcal{W}\left(\Phi\left(I_{\text{tar}}\right); \mathbf{H}\right),$

where $\mathcal{W}$ denotes the warping operation based on homography $\mathbf{H}$, $I_{\text{tar}}$ is the target image, and $\Phi$ is the restoration module.

In this ideal case, the restored features from corresponding positions would perfectly match. However, in practice, it is difficult for restoration networks to maintain equivariance under homography transformations, which involve translation, rotation, scaling, shearing, aspect ratio change, and perspective distortion. This leads to inconsistent features between corresponding points after enhancement [1], ultimately degrading the performance of homography estimation—an observation consistent with the results shown in Fig. 1(a) of the manuscript.

To address this issue, we depart from the conventional sequential paradigm of restoration followed by warping. Instead, we propose an alternating scheme within our recursive homography estimation framework, referred to as restoration-guided warping. As illustrated in Fig. 1(b), the image warping module and restoration module are interleaved during the iterative process, which can be formulated as:

\hat{\mathbf{H}}^{n+1} = \Psi\left(I_{\text{ref}} ; E_{\text{tar}}^n\right),$$ where $\Psi$ denotes the homography estimation module, and $E_{\text{tar}}^n$ and $\mathbf{H}^n$ represent the enhanced warped image and the estimated homography at the $n$-th iteration, respectively. As the iteration proceeds, the warped image $I_{\text{tar}}^w$ becomes increasingly aligned with the reference image $I_{\text{ref}}$, allowing the DIR module to produce more consistent restoration in the overlapping regions, which in turn improves the accuracy of homography estimation. The effectiveness of this mechanism is demonstrated in Fig. 1(b) of the main text. It is also important to note that although the framework performs multiple iterations, the restoration network (DIR) shares weights across iterations, and thus does not incur any additional parameter overhead. [1] Gift: Learning transformation-invariant dense visual descriptors via group CNNs. --- **W2(2)**: “How the homography estimation module gradually approximates the true homography transformation during the iterative process.” **Ans**: The iterative process in our homography estimation network can be summarized in three main steps to better clarify the mechanism: 1. In each iteration, disparity candidates are sampled using the current mean $\mu$ and standard deviation $\sigma$. Specifically, at the $i$-th iteration, candidates are uniformly sampled within the interval $[ \mu_i - \sigma_i, \mu_i + \sigma_i ]$. For the initial iteration, $\mu_0$ is initialized to 0 and $\sigma_0$ is set to 32 (as mentioned in the experimental details of the manuscript). 2. The matching cost is computed based on the sampled disparities of the current iteration, which is then used to predict the update step $\Delta_i$. 3. According to Equation (3) in the manuscript, the predicted step $\Delta_i$ is used to update the current $\mu$ and $\sigma$ according to follows formulation: $$\qquad\qquad\sigma_i^{t} =\sigma_i^{t-1}-\frac{1}{2}\left(\frac{(\sigma_i^{t-1})^2-\sigma_G^2-(\Delta^{t-1})^2}{ (\sigma_i^{t-1})^3}-\frac{1}{\sigma_i^{t-1}}+\frac{\sigma_i^{t-1}}{\sigma_G^2}\right), \mu_i^{t} =\mu_i^{t-1}-\left(-\frac{\Delta^{t-1}}{2}\left(\frac{1}{(\sigma_i^{t-1})^2}+\frac{1}{\sigma_G^2}\right)\right).$$       where $\sigma_G$ is a predefined parameter. After $N$ iterations, the final updated $\mu_N$ is taken as the predicted displacement. A direct linear transformation is then applied to obtain the final homography matrix. Meanwhile, $\sigma$ progressively decreases throughout the iterations, making the sampling more concentrated and thus improving the accuracy and stability of the final prediction. The advantage of this approach lies in its ability to maintain differentiability throughout the sampling and matching process during training. Moreover, by introducing JS divergence, the distribution gradually converges toward a standard Gaussian, which further accelerates model convergence and enhances generalization. The optimization process can be formulated as: $$\mathcal{J}_i=\frac{1}{2}\left(F\left(\mathcal{N}_G \| \mathcal{N}_i\right)+F\left( \mathcal{N}_i \| \mathcal{N}_G\right)\right),$$ where $\mathcal{N}_i$ is the short form of $\mathcal{N}\left(\mu_i, \sigma_i^2\right)$. $\mathcal{N}_G=\mathcal{N}\left(\mu_G, \sigma^2_G\right)$ denotes predefined Gaussian distribution, where $\mu_G$ represents the ground truth offset. $F\left( \cdot \|\cdot\right)$ represents KL divergence. This combination of random modeling and differentiable optimization effectively addresses the limitations of traditional methods. --- **Ans for W3**: Thank you for your suggestion. Multi-iteration optimization is a widely adopted strategy in current deformation estimation networks. Since image stitching tasks often involve handling large-baseline scenarios, a coarse-to-fine iterative deformation process is crucial for achieving satisfactory stitching performance[1-2]. Although single-iteration strategies can indeed improve runtime, they often lead to a significant drop in final stitching quality. To ensure practical applicability, our method is designed to strike a balance between stitching accuracy and computational efficiency, aiming to meet real-time requirements. During the design phase, we introduced the following optimizations: *1. Convergence Acceleration via Gaussian-Encoded Optimization:* We ensure the differentiability of the sampling and matching process during training. By introducing a JS divergence constraint, the distribution gradually converges to a standard Gaussian, which accelerates model convergence and improves generalization. This combination of probabilistic modeling and differentiable optimization effectively addresses the limitations of traditional methods. *2. Lightweight Image Restoration Module:* The module is designed to be lightweight, consisting of only 5 convolutional layers. It is solely responsible for predicting the hyperparameters used in restoration. With a computational cost of just 0.07 Gflops. To further validate the efficiency, we conducted runtime comparison experiments under identical settings. Tables below show the processing time per image pair for all methods. The average runtime per pair for our method is 0.336s (low-light), 0.322s (underwater), and 0.344s (foggy). Across all three scenes, the proposed method performs competitively, with runtime only slightly higher than VFIS and its enhanced variant (restoration + VFIS). In future work, we will explore further simplifications of the module architecture and investigate low-iteration optimization strategies. ||||LLI|||||HBLALS|||||NeRCo|||| |-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-| || APAP|VFIS|LPC|UDIS|UDIS2| APAP|VFIS|  LPC|UDIS|UDIS2|APAP|  VFIS|  LPC|UDIS|UDIS2|Ours| |time(s)|2.282|**0.283** | 1.550 | 0.692|0.351|2.313|*0.302*|  1.577|0.710|0.380|2.291|  0.299|  1.562|0.704|0.360|0.336| --- ||||UI|||||HBLALS|||||WFlow|||| |-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-| || APAP|VFIS|LPC|UDIS|UDIS2|APAP|VFIS|  LPC|UDIS|UDIS2|APAP|  VFIS|  LPC|UDIS|UDIS2|Ours| |time(s)|2.262|**0.304**|1.602|0.699|0.350|2.274|*0.313*|  1.623|0.710|0.366|2.382|  0.400|  1.695|0.804|0.362|0.322| --- ||||SI|||||HBLALS|||||WGWS|||| |-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-| || APAP|VFIS|LPC|UDIS|UDIS2|APAP|VFIS|  LPC|UDIS|UDIS2|APAP|  VFIS|  LPC|UDIS|UDIS2|Ours| |time(s)|2.174|**0.262**|1.499|0.660|0.295|2.180|*0.273*|  0.520|0.679|0.348|2.262|  0.331|  1.573|0.759|0.390|0.334| --- [1] Learning edge-preserved image stitching from multi-scale deep homography[J]. Neurocomputing, 2022. [2] Unsupervised deep image stitching: Reconstructing stitched features to images[J]. IEEE TIP, 2021.

Dear Reviewer kt8k,

Please engage in the discussion with the authors and other reviewers as soon as possible.

Thank you.

Best,

AC

Thank you for your valuable comments. I will provide a detailed explanation based on your suggestions and concerns, and revise the manuscript accordingly. Below are my responses to your questions:

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Ans for W1: Thank you for your valuable feedback. Explicitly designing submodules for specific degradation types does indeed limit adaptability when dealing with unknown or compound degradations.

However, we have paid particular attention to modularity and scalability in the design of the DIR module. Each degradation-specific sub-module is implemented in a plug-and-play manner, allowing flexible extension or replacement to accommodate new degradation types without retraining the entire model. Moreover, all DIP modules are connected to a shared encoder that captures global contextual information. Even when a specific degradation type is not explicitly modeled, the shared features can still compensate for potential performance loss through semantic interaction.

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Ans for W2: Thank you for your suggestion. The core purpose of adopting uniform sampling is to construct a differentiable and robust optimization module that can model the uncertainty of the current offset distribution, thereby enhancing the model’s robustness to local minima and ambiguous regions.

To further evaluate the efficiency, we conducted a runtime comparison under the same experimental settings. The table below lists the processing time per image pair for all methods across low-light, underwater, and foggy scenes. It can be observed that our proposed method still performs competitively under sampling conditions, with runtime only slightly higher than VFIS and its enhanced variant (Restoration + VFIS). In future work, we will explore further simplifications of the module architecture and investigate low-iteration optimization strategies.

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Ans for W3 : Thank you for your question. First, BCDA and MSC are treated as two independent stages in the image stitching pipeline and are trained separately. The BCDA module focuses on estimating transformation parameters, typically supervised by geometric errors or positional discrepancies; in contrast, the composition stage emphasizes image blending quality and relies on pixel-level or perceptual losses. Due to the significant differences in their numerical scales, gradient directions, and convergence behaviors, end-to-end training cannot effectively optimize both tasks simultaneously. Therefore, similar to other learning-based stitching methods [1–2], we adopt a staged training strategy. For training BCDA and DIR, directly training BCDA disrupts DIR’s pixel-level supervision, reducing its enhancement. To avoid this, we pre-trained DIR for 200 epochs before joint training.

[1] Unsupervised deep image stitching: Reconstructing stitched features to images. TIP, 2021. [2] Parallax-tolerant unsupervised deep image stitching. ICCV, 2023.

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Ans for W4:: Thank you for your suggestion. Tab. 1 and Fig. 5 in the manuscript present the quantitative and qualitative comparison of the newly proposed dataset, covering image stitching performance under three challenging conditions.

Besides directly stitching degraded images for baseline comparison, we also restore them using task-specific methods before stitching to ensure fairer evaluation. The results highlight that our method is not just a simple combination, but a tailored solution for stitching under degradation.

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Ans for Q1:: Thank you for your question. The iterative process in our homography estimation network can be summarized in three main steps to better clarify the mechanism:

1. In each iteration, disparity candidates are sampled using the current mean $\mu$ and standard deviation $\sigma$. Specifically, at the $i$-th iteration, candidates are uniformly sampled within the interval $[ \mu_i - \sigma_i, \mu_i + \sigma_i ]$. For the initial iteration, $\mu_0$ is initialized to 0 and $\sigma_0$ is set to 32 (as mentioned in the experimental details of the manuscript).

2. The matching cost is computed based on the sampled disparities of the current iteration, which is then used to predict the update step $\Delta_i$.

3. According to Equation (3) in the manuscript, the predicted step $\Delta_i$ is used to update the current $\mu$ and $\sigma$.

After $N$ iterations, the final updated $\mu_N$ is taken as the predicted displacement. A direct linear transformation is then applied to obtain the final homography matrix. Meanwhile, $\sigma$ progressively decreases throughout the iterations, making the sampling more concentrated and thus improving the accuracy and stability of the final prediction.

The advantage of this approach lies in its ability to maintain differentiability throughout the sampling and matching process during training. Moreover, by introducing JS divergence, the distribution gradually converges toward a standard Gaussian, which further accelerates model convergence and enhances generalization. This combination of random modeling and differentiable optimization effectively addresses the limitations of traditional methods.

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Ans for Q2:: Thank you for your question. We have indeed considered the issue you raised. In the early stages of our work, we initially planned to design a conventional CNN-based restoration module. However, we ultimately chose to implement a differentiable restoration (DIR) module for the following three reasons:

First, our goal is stitching-oriented image restoration, which enhances visual quality while preserving structural consistency between image pairs. Although traditional data-driven CNN methods often perform well under visual metrics, they may introduce artifacts that impair correspondence, disrupting consistency in overlapping regions. DIR combines physics-guided enhancement with a bi-directional consistency framework, facilitating structural preservation and equivariant feature extraction.

Second, under our proposed bi-directional consistency framework, the restoration module is repeatedly invoked at each iteration. To ensure efficiency, we aimed to minimize its computational overhead. The proposed DIR module is highly lightweight, with a total cost of only 0.07 Gflops. The learnable part consists of just five convolutional layers and one feedforward layer, significantly reducing the burden on the overall network.

Lastly, as mentioned earlier, we placed strong emphasis on modularity and scalability when designing the DIR module. Each degradation-specific sub-module is implemented in a plug-and-play fashion, making it easy to extend or replace to accommodate new degradation types in the future.

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Ans for Q3: Thank you for your comment. The mACE metric evaluates the error between the estimated and ground truth corner displacements in homography estimation tasks. Therefore, it is only applicable to stitching methods based on homography transformations.

However, many stitching methods—especially traditional, non-deep-learning approaches—do not rely on projective transformations as their warping models. This includes the comparison methods used in our manuscript, such as LPC, APAP, and UDIS2, all of which cannot be evaluated using the mACE metric.

For this reason, we did not use mACE in our comparative experiments. Instead, we relied on PSNR and SSIM, which are applicable to all stitching methods, as the evaluation metrics to compare the performance of the proposed approach.

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Ans for Q4: Thank you for your valuable question. The Table presents the average training time in each epoch of our proposed method compared with other learning-based image stitching networks included in the manuscript. For a fair comparison, all methods were trained on the same device (NVIDIA RTX 4090 GPU) with a unified batch size of 8. Since our framework additionally includes a restoration subtask, the overall training time is longer than that of existing stitching networks. Specifically, our main network was trained for 160 epochs, taking approximately 66 hours in total, which is longer than the compared methods. In future work, we plan to improve training efficiency while maintaining performance.

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Ans for L1: Thank you for your insightful comment. The proposed network requires deformation parameters of a fixed size as output. To this end, the input images are resized to 128×128 during training. However, the predicted deformation parameters can be upsampled to match the resolution of the original image, enabling accurate warping at the full scale. This strategy is consistent with common practices in representative learning-based image stitching and optical flow estimation methods. Therefore, our approach is capable of handling image stitching tasks across varying input resolutions.

Thank you for your detailed answers, which have fully resolved all of my questions.

I believe the following strengths of this paper will have a impact on future research:

• It addresses the overconfidence problem by utilizing stochastic predictions rather than conventional deterministic ones.

• It introduces a scalable DIR module, moving beyond naive CNN architectures and integrating it into the stitching learning process.

• It presents a novel dataset for the community.

I will positively consider raising my rating during the next discussion phase.

Excellent work.

Thank you for your valuable comments. I will provide a detailed explanation based on your suggestions and concerns, and revise the manuscript accordingly.

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W1: “In sec 3.2, Eq. 5 is not related to Beer-Lamber law.”

Ans: Thank you for your valuable comment. We agree that Eq. 5: $t(x, \omega)=1-\omega \min _C\left(\min _{y \in \Omega(x)} \frac{I^C(y)}{A^C}\right),$ is not a direct analytical derivation from the Beer-Lambert law. Rather, it is an approximate estimation of the transmission map t(x).

Specifically, the haze imaging model used in our work: $I(x) = J(x) \cdot t(x) + A \cdot (1 - t(x))$ assumes that the transmission t(x) follows the exponential decay with respect to scene depth d(x), which directly reflects the Beer-Lambert principle. However, since depth d(x) is unknown in single image scenarios, the dark channel prior[1] is adopted to approximate the transmission via local statistics. Therefore, Eq. 5 is not a direct derivation from Beer-Lambert, but a practical formulation motivated by its physical behavior, designed for estimating transmission maps in the absence of ground-truth depth. We will revise the text in the manuscript to clarify this distinction.

[1] Single image haze removal using dark channel prior.

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W2: in section 3.2, how is removed the $\mu_{\mathrm{GT}}$ which is not known? ”

Ans:
Thank you for your comment. $\mu_{\mathrm{GT}}$ is not appear in Sec 3.2, but appears in Eq.3 in Sec 3.1. If you would like to know how it is eliminated during inference, please refer to Ans for Q1. If you would like to know why $\mu_{\mathrm{GT}}$ does not appear in Sec 3.2, I can explain it from the perspective of the dataset.

Our training dataset is synthesized based on adverse-scene datasets that include clean reference images. Specifically, we first sample the same spatial position from both the clean and degraded images to obtain the reference view image. Then, we apply random offsets (including synchronized endpoint translation and independent endpoint perturbations) to generate both the degraded and clean target view images. The random offset parameters used in this process correspond to $\mu_{\mathrm{GT}}$ as mentioned in the manuscript, which allows for supervised training for homography estimation during optimization.

As for the restoration task described in Sec 3.2, the loss function (Eq. 6) does not rely on $\mu_{\mathrm{GT}}$, since our synthesized dataset already provides clean images at both the reference and target positions, making deformation through $\mu_{\mathrm{GT}}$ unnecessary.

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W3: “The obtained results are not always convincing, like in Fig 14-15. It is only the two images stitching which is discussed and not the stitching of series of images.”

Ans: Thank you for your question. To date, representative image stitching algorithms(including all comparison methods in the manuscript) are all designed to compute correspondences between only two images. Therefore, when stitching more than two images, one must first input the first two images into the algorithm to obtain an initial stitched result, and then iteratively feed the resulting image and the next image into the algorithm to generate the updated stitched image. As a result, current stitching methods are incapable of learning or modeling the correspondence among multiple images simultaneously. Consequently, evaluating multi-image stitching essentially holds the same meaning as evaluating pairwise stitching performance, since each step still only involves two-image correspondence. Moreover, previous benchmark comparisons for representative stitching methods have only evaluated two-image stitching performance. Based on this, we did not conduct additional comparisons on multi-image stitching.

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Q1: “Explain the way the "RPHE" module is working.”

Ans: The iterative process in our homography estimation network can be summarized in three main steps to better clarify the mechanism:

1. In each iteration, disparity candidates are sampled using the current mean $\mu$ and standard deviation $\sigma$. Specifically, at the $i$-th iteration, candidates are uniformly sampled within the interval $[ \mu_i - \sigma_i, \mu_i + \sigma_i ]$. For the initial iteration, $\mu_0$ is initialized to 0 and $\sigma_0$ is set to 32 (as mentioned in the experimental details of the manuscript).

2. The matching cost is computed based on the sampled disparities of the current iteration, which is then used to predict the update step $\Delta_i$.

3. According to Eq. 3 in the manuscript, the predicted step $\Delta_i$ is used to update the current $\mu$ and $\sigma$ according to follows formulation:

\mu_i^{t} =\mu_i^{t-1}-\left(-\frac{\Delta^{t-1}}{2}\left(\frac{1}{(\sigma_i^{t-1})^2}+\frac{1}{\sigma_G^2}\right)\right).$$       It is worth noting that since the ground-truth mean \$\mu\_{G}\$ is unavailable during inference, we approximate \$\Delta^{t-1}\$ as \$\qquad\mu\_{G} - \mu\_i^{t-1}\$. $\sigma_G$ is a predefined parameter. After $N$ iterations, the final updated $\mu_N$ is taken as the predicted displacement. Meanwhile, $\sigma$ progressively decreases throughout the iterations, making the sampling more concentrated and thus improving the accuracy and stability of the final prediction. This approach ensures differentiability during training and uses JS divergence to guide the distribution toward a standard Gaussian, accelerating convergence and improving generalization. It effectively combines randomness with optimization to overcome traditional limitations. --- **Q2**: “Better explain the way the "BCLF" is working” **Ans**: The Bidirectional-Consistency Learning Framework is proposed to address the issue of inconsistent restoration caused by enhancement networks. In image alignment tasks under adverse conditions, we aim for the backbone network to produce restoration results that are equivariant under spatial transformations. This objective can be formally expressed as:

\Phi\left(\mathcal{W}\left(I_{\text{tar}} ; \mathbf{H}\right)\right) = \mathcal{W}\left(\Phi\left(I_{\text{tar}}\right); \mathbf{H}\right),

where $\mathcal{W}$ denotes the warping operation based on homography $\mathbf{H}$, $I_{\text{tar}}$ is the target image, and $\Phi$ is the restoration module. In this ideal case, the restored features from corresponding positions would perfectly match. However, in practice, it is difficult for restoration networks to maintain equivariance under homography transformations, which involve translation, rotation, scaling, shearing, aspect ratio change, and perspective distortion. This leads to inconsistent features between corresponding points after enhancement \[1], ultimately degrading the performance of homography estimation—an observation consistent with the results shown in Fig. 1(a) of the manuscript. To address this issue, we depart from the conventional sequential paradigm of restoration followed by warping. Instead, we propose an alternating scheme within our recursive homography estimation framework, referred to as *restoration-guided warping*. The image warping module and restoration module are interleaved during the iterative process, which can be formulated as:

E_{\text{tar}}^n = \Phi\left(\mathcal{W}\left(I_{\text{tar}} ; \hat{\mathbf{H}}^n\right)\right), \quad \hat{\mathbf{H}}^{n+1} = \Psi\left(I_{\text{ref}} ; E_{\text{tar}}^n\right),

where $\Psi$ denotes the homography estimation module, and $E_{\text{tar}}^n$ and $\mathbf{H}^n$ represent the enhanced warped image and the estimated homography at the $n$-th iteration, respectively. As the iteration proceeds, the warped image $I_{\text{tar}}^w$ becomes increasingly aligned with the reference image $I_{\text{ref}}$, allowing the DIR module to produce more consistent restoration in the overlapping regions, which in turn improves the accuracy of homography estimation. [1] Gift: Learning transformation-invariant dense visual descriptors via group CNNs. --- **Q3**: “How can be performed the stitching of series of images?” **Ans**: Most stitching methods only take two images as input and estimate transformations for stitching by computing the correspondence between these two images. This process can be described as $I^s = \mathcal{S}(I_{1}, I_{2})$, where $I_{1}, I_{2}$ denote the two input images, $I^s$ and $\mathcal{S}$ represent the stitched result and stitching network. To stitch more than two images $[I_{1}, I_{2}, \ldots, I_{t}]$, the network can only iteratively combine each new image $I_t$ with the previous stitched result $I^s_{t-1}$. The entire procedure can be expressed as $I^s_t = \mathcal{S}(I^s_{t-1}, I_{t})$, where $t \geq 2$. --- **Q4**: “The property of the YouTube video used for building the dataset ?” **Ans**: The proposed dataset includes three types of scenes, among which the foggy and underwater scene images were sourced from online videos. The fog data comes from 3 YouTube videos, which have been posted in supplementary details. All three videos have a frame rate of 30 fps and a resolution of 1280×720. The total number of frames across them is 192,266. The underwater scene data is sourced from the 2 YouTube videos. Both underwater videos also have a frame rate of 30 fps and a resolution of 1280×720. The combined total number of frames in both videos is 358,228. Since these videos were not originally recorded for image stitching, most consecutive frames contain excessive parallax or severe occlusions, making them unsuitable for stitching tasks. Therefore, we carefully selected 750 image pairs from each of the fog and underwater scenes. These pairs were chosen to ensure valid displacement while maximizing the diversity of scene deformations.

Dear Reviewer gzJT,

Please engage in the discussion with the authors and other reviewers as soon as possible.

Thank you.

Best,

AC