Train Once, Deploy Anywhere: Edge-Guided Single-source Domain Generalization for Medical Image Segmentation

Authors: jun  jiang
shi  gu
Venue: MIDL_io_2024_Conference
Published: 2024-02-01 08:08:42

Abstract: In medical image analysis, unsupervised domain adaptation models require retraining when receiving samples from a new data distribution, and multi-source domain generalization methods might be infeasible when there is only a single source domain. These will pose formidable obstacles to model deployment. To this end, we take the "Train Once, Deploy Anywhere" as our objective and consider a challenging but practical problem: Single-source Domain Generalization (SDG). Meanwhile, we note that (i) the medical image segmentation applications where generalization errors often come from imprecise predictions at the ambiguous boundary of anatomies and (ii) the edge of the image is domain-invariant, which can reduce the domain shift between the source and target domain in all network layers. Specifically, we borrow the prior knowledge from Digital Image Processing and take the edge of the image as input to enhance the model attention at the boundary of anatomies and improve the generalization performance on unknown target domains. Extensive experiments on three typical medical image segmentation datasets, which cover cross-sequence, cross-center, and cross-modality settings with various anatomical structures, demonstrate our method achieves superior generalization performance compared to the state-of-the-art SDG methods. The code is available at https://github.com/thinkdifferentor/EGSDG.

Main paper: 
 introduction: 
 Medical image segmentation is a crucial task in clinical applications. In recent years, deep segmentation networks have achieved remarkable progress (Butoi et al., 2023; Isensee et al., 2021) . However, when there is domain shift between the training and testing data, the performance of data-driven deep models degrades dramatically, like scanning technique, acquisition parameters, device manufacturers, etc. Recently, many efforts of Domain Generalization (DG) and Unsupervised Domain Adaptation (UDA) have been made to improve the model's generalization ability on the target domain (Su et al., 2023; Feng et al., 2023) . Further, domain generalization can be divided into Multi-source Domain Generalization (MDG) and Single-source Domain Generalization (SDG). On the one hand, MDG models (Dou et al., 2019; Li et al., 2019) are designed with multiple source domains to learn domain-invariant representations, and it may not work when there is only a single source domain. On the other hand, the high cost of medical image labeling and the strict regulations of privacy protection make it difficult to obtain large amounts of medical data. Besides, previous UDA works (Feng et al., 2023; Chen et al., 2019) require retraining when receiving the samples from a new data distribution, which leads to the high cost of model deployment. To this end, we take the "Train Once, Deploy Anywhere" as our objective and consider a challenging but practical setting: single-source domain generalization.For segmentation tasks, models often make inaccurate predictions at target boundaries. This weakness is more pronounced for domain generalization or adaptation segmentation tasks in medical images due to the domain gap and ambiguous boundary of anatomies. Recently, some works have proposed corresponding solutions and made significant progress (Liu et al., 2022; You et al., 2023; Feng et al., 2023) . However, there are several limitations to them. First, they do not directly take the image edge as the model input, which weakens the supervision of edge information during the training process. Second, they acquire the image edge or shape priors by learning, which will take lots of training time. Based on these insights, we employ the edge detection algorithm to get image edge maps and use them as input to train the model directly. This effectively filters out domain-specific information and significantly improves the generalization ability. The major contributions of this work are as follows: (i) We make a comprehensive analysis to the impact of image edge on the model generalization ability, including the positions of edge supervision signals, such as shallow, deep, or output layers; the fusion strategies of edge map and feature map, such as concatenating it with shallow or deep features and directly as network input. (ii) For the challenging yet essential SDG problem of medical image segmentation, we propose a simple yet effective approach EGSDG, which significantly improves the generalization performance on unknown target domains. (iii) We conducted extensive experiments on three typical medical image segmentation datasets that cover various anatomical structures. With only a single source domain, our method achieves superior generalization performance on the unknown target domain compared to the state-of-the-art SDG methods. 
sdg of nature image: 
 SDG models of nature images can be divided into two mainstream methods: (1) the imagelevel method, which improve the model generalization by data augmentation with the help of existing large datasets (e.g. ImageNet) (Yue et al., 2019; Lee et al., 2022) , and (2) the feature-level method, which aims to learn domain-invariant segmentation network by removing the style information of feature maps with normalization or whitening strategy (Choi et al., 2021; Peng et al., 2022) . However, these models may not work well on grayscale medical images, because there are significant differences in texture, structure, and data privacy policies between medical and natural images.In medical images, there are fewer works on the SDG segmentation task compared to natural images. Most of these models (Liu et al., 2022; Ouyang et al., 2021; Su et al., 2023) conduct data augmentation on the source domain to improve the model's robustness. Different from the previous works, we introduce an edge-guided model, which filters the domain-specific information effectively and improves the generalization ability significantly.Recently, many efforts of edge-guided methods have been made to raise attention to the segmentation boundary and improve the generalization ability of models. Cardace et al. (Cardace et al., 2021) presented a novel low-level adaptation strategy with semantic edges and displacement maps from shallow features to obtain sharp predictions. CIConv (Lengyel et al., 2021) exploited a visual inductive prior derived from physics-based reflection models and cast a number of color-invariant edge detectors as trainable layers for domain adaptation. In contrast to existing methods, we utilize the edge detector to extract edge maps of images and take them as input to train the model directly. 
preliminaries: 
 Edge detectors significantly filter out useless information, while preserving the important structural properties of an image. There are a large number of edge detection algorithms available, each designed to be sensitive to specific types of edges like edge orientation, noise environment, and edge structure. We take the most classic ones for exploring, including Canny (Canny, 1986) , AutoCanny (Rong et al., 2014) , Roberts (Roberts, 1963) , Prewitt (Prewitt et al., 1970) , Sobel (Kittler, 1983), and Laplacian (LeCun et al., 1998) . For an image, its gradient at (x, y) is defined as vector ▽f (x, y), which is composed of the partial derivative of the image in the X and Y directions:EQUATIONThe modulus and direction of the gradient are defined by:|▽f (x, y)| = G 2 x + G 2 y , θ(x, y) = arctan( G y G x ) (2)For Laplacian, the second derivative is defined as:▽ 2 f (x, y) = ∂ 2 f (x, y) ∂x 2 + ∂ 2 f (x, y) ∂y 2 (3)Note that the digital images are discrete and different edge detection algorithms differ in the way of G x and G y calculation, which are provided in Appendix A. The details of Canny and AutoCanny algorithms can be found in Appendix B and (Rong et al., 2014) . Compared to Canny algorithm, AutoCanny does not need to manually set Gaussian smoothing parameters and the double thresholds.In single-source domain generalization, we are given a single source domainD s = {(x s i , y s i )} Ns i=1, where s represents the domain ID, x s i ∈ R H×W ×3 is the i-th image in the source domain s. y s i ∈ R H×W is the corresponding ground truth mask, and N s is the total number of samples.Given unseen target domainD t = x t i , y t i Nt i=1, which is not accessible during the training process, we aim to minimize the error between prediction ŷt i and ground truth mask y t i .Edge or gradient information is one of the most important features of an image. The edge of image is domain-invariant, which can reduce the domain shift between the source and target domain in all network layers (Lengyel et al., 2021) . Different from previous works, TASD (Liu et al., 2022) establishes the dictionary learning to extract the explicit shape priors and CIConv (Lengyel et al., 2021) derived from the complex Kubelka-Munk theory to build a learnable edge detector layer, our model is borrowed from the classical edge detection algorithm with less computational complexity and more stable performance. Visualization comparison of classical edge detection algorithms and CIConv refer to Appendix C. In addition, data augmentation can enrich the gradient information of the training samples, which will bring huge performance gains to our edge-guided model's generalization ability (Details refer to Appendix D). For medical images, we expect to map the source image to diverse grayscale value distribution and keep the appearance of the anatomic structures perceivable at the same time. Motivated by Model Genesis (Zhou et al., 2019) , we employ the Bézier Curve (Mortenson, 1999) as our data augmentation method, which is generated from two end points (P 0 and P 3 ) and two control points (P 1 and P 2 ), defined as:B(t) = n i=0 n i P i (1 -t) n-i t i , n = 3, t ∈ [0, 1] (4)where t is a fractional value along the length of the line.The learning process of our EGSDG is shown in Figure 1 . Firstly, we perform the BézierCurve data augmentation on source samples (x s i ∈ R H×W ×3 ) before the training stage. Then, the edge detector is exploited to extract the edge maps (e s i ∈ R H×W ) of the augmented samples. Finally, we take the edge maps e s i as input to train the segmentation network ϕ w with parameters w by minimizing cross-entropy loss:EQUATIONWe use the edge detector to compress the image into a single-channel edge map. It effectively filters domain-specific information and trains a model with high generalization performance.The network locates the segmentation object by the gradient change (Roberts, Prewitt, Sobel, and Laplacian) or the anatomy contour (Canny and AutoCanny) of the target area. Evaluation Metrics We take the Dice coefficient (Dice) as our evaluation metric, which measures the overlapping ratio between prediction and ground truth. The higher the Dice value, the better the segmentation performance. 
comparison experiments: 
 We compare our method with SOTA single-source domain generalization methods including IBN-Net (Pan et al., 2018) , SW (Pan et al., 2019) , RobustNet (Choi et al., 2021) , SADN (Zhou et al., 2022) , CSDG (Ouyang et al., 2021) , and CIConv (Lengyel et al., 2021) . For a fair comparison, we employ the same segmentation network to train the CIConv model. Besides, we also provide the results without domain generalization by directly applying the model learned in the source domain to unknown target domains (Lower Bound) and with supervised training on the target domain (Upper Bound). In addition, the comprehensive comparison between CIConv and ours is given in Appendix F.Table 1 and Table 2 report the comparison results on the BraTS'19, Prostate, and MMWHS datasets respectively. Overall, our model outperforms others, especially in the large distribution shift dataset (BraTS'19 and MMWHS). For the results of normalization and whitening-based models (IBN-Net, SW, and RobustNet), which are designed for nature image, their performance is significantly lower than our model in each evaluation dataset. For the results of data augmentation-based methods (SADN and CSDG), their performance is unstable on different datasets. The distribution of grayscale values varies across different datasets and the level of domain shift varies among different SDG segmentation settings. However, the augmented samples fail to cover the unseen target domain distribution on the specific task and lead to terrible generalization performance. In addition, the performance of CIConv is lower than our model on all three datasets. Qualitative examples are shown in Figure 2 . As we can see, our model can produce accurate and sharp predictions at the boundary of anatomies. The enlarged qualitative results refer to Appendix G. To enhance the model's attention at the boundary of targets, previous works (Lengyel et al., 2021; Liu et al., 2021 Liu et al., , 2022;; You et al., 2023) have tried different strategies. Here, we conducted a comprehensive analysis to the impact of image edge on the model generalization ability. We employ the vanilla U-Net (Ronneberger et al., 2015) as the segmentation network which is borrowed from Pytorch-UNet. Other configurations are the same as the main experiment. The visualization of different edge-guided strategies and corresponding explanations are provided in Figure 3 . These edge-guided strategies can be divided into two categories: (i) using the edge map as the supervision signal to increase the model's attention at the boundary of segmentation targets. (ii) concatenating the feature map and edge map to force the model learning domain invariant representation and enhance the generalization ability. Note that we make the same process at the testing stage for the second category experiments (Exp. 1, 2, 3, and 4). Table 3 and Table 4 report the comparison results on BraTS'19, Prostate, and MMWHS datasets respectively. Overall, adopting the edge map as an additional guided signal can improve model generalization performance compared to the Lower Bound. Notably, employing the image edge as input to train the model directly brings tremendous generalization ability gains on the three datasets. We note that (i) for the former, the performance is lower than ours, probably because this category strategy weakens the supervision of the edge information via the segmentation head at the training stage, and (ii) for the latter, the performance is lower than ours, possibly due to the grayscale information making the model overfit on the source domain. En with a single Conv2d segmentation layer. Exp. 6 means employing the image edge as the supervision of feature map X 1De with a single Conv2d segmentation layer. Exp. 7 means employing the image edge as the supervision of feature map X 2De with a single Conv2d segmentation layer. AutoCanny is employed in all experiments. 
conclusion and discussion: 
 In this work, we use the edge of image as input to train a network. It improves the model's generalization performance significantly on unknown target domains. Extensive experiments on three typical medical image segmentation datasets demonstrate our approach achieves superior generalization performance compared to the state-of-the-art SDG methods. However, our model has the following limitations: (i) The optimal edge extractor is different in diverse segmentation scenarios, which brings great challenges to choosing the best one for an unseen dataset. (ii) In low-contrast images (like Ultrasound or CT), the model cannot extract valuable edge information well, which may lead to poor segmentation performance. (iii) When the segmentation target is small (like multiple sclerosis or cochlear), the extracted edge information may be similar to the surrounding noise, which will lead to the wrong segmentation results. In addition, there are limitations in the experimental setup of BraTS'19 because different sequences focus on different structures, which may lead to the tumor is not well visible in on specific modality. The steps of the Canny algorithm (Canny, 1986) include Image Smoothing, Gradient Calculation, Non-maximum Suppression, and Edges Checking.Image Smoothing Gaussian filter is used to smooth images and get rid of the noise which is defined as :G(x, y) = 1 2πσ 2 exp(- x 2 + y 2 2σ 2 ) (6)where σ stands for the size of the Gaussian Kernel, which controls the extent of smoothing the image. This critical parameter needs to be set manually based on experience.Gradient Calculation The traditional Canny algorithm adopts a limited difference of 2 × 2 neighboring area to calculate the magnitude and direction of the image gradient. The operator of the partial derivative of the image in the X and Y directions is defined by:EQUATIONNon-maximum Suppression After acquiring the gradient magnitude image, it's needed to perform non-maximum suppression (NMS) on the image to accurately locate edges. The process of NMS can help guarantee that each edge is one-pixel width.Edges Checking Canny adopts a double-threshold method to select edge points after carrying on non-maximum suppression. The pixels whose gradient magnitude is above the high threshold will be marked as edge points, and those whose gradient magnitude is under the low threshold will be marked as non-edge points, and the rest will be marked as candidate edge points. Those candidate edge points that are connected with edge points will be marked as edge points. This method reduces the influence of noise on the edge of the final edge image. The low and high thresholds need to be set manually based on experience. 
 
 Appendix: We have manually designed the corresponding Cany detector parameters for each domain of each dataset. For all scenarios, the size of the Gaussian kernel 3 × 3. The configuration of the double-threshold is provided in Table 5 . We realized that for the same case, the edge or gradient map in each domain is different by the same edge detector. Therefore, we use data augmentation to simulate the data distribution of unknown target domain before edge extraction to enrich the gradient information of edgeguided training. The visualization of the BézierCurve augmented image and corresponding edge and gradient map is shown in Figure 7 . Edge Detector Different edge detectors will extract distinct image edges or gradients for the same image, which affects the training process and testing performance. Accordingly, we conducted comprehensive comparison experiments on classical edge detectors, including Canny (Canny, 1986) , AutoCanny (Rong et al., 2014) , Roberts (Roberts, 1963) , Prewitt (Prewitt et al., 1970) , Sobel (Kittler, 1983), and Laplacian (LeCun et al., 1998) .BézierCurve Augmentation For edge-guided models, data augmentation is supposed to simulate the edge or gradient information of the unseen target samples to train a model with great generalization ability. To this end, we also explore the above edge-guided models on the BézierCurve (Zhou et al., 2019) augmented samples, which is a simple idea to generate different styles by adjusting the gray value distribution of images. Table 6 and Table 7 show the results. As we can see, taking the edge as input promotes the generalization ability of the model remarkably and the BézierCurve can further improve its performance. We note that different edge extractors are sensitive to specific types of edges like edge orientation, noise environment, and edge structure. In different segmentation scenarios, the texture, intensity, and noise of medical images are diverse. This leads to the discrepancy between the valuable edge extraction and the irrelevant noise filtering by different edge extractors, which makes the optimal edge detector on each domain different. This will bring great challenges to choosing the best one for an unseen dataset.  


Decision: The paper  proposes a new domain generalization/adaptation technique for medical image segmentation. 

The original reviews appreciated the work, but raised concerns of clarity and claims and experimental setup, However, after a productive rebuttal and discussion period, The authors were able to adapt the work and improve the experimental presentation, and the reviewers all agree that the paper should be accepted.

Congratulations to the authors and I appreciate the thorough review and discussion from the reviews!

Reviews: review: paper_summary: paper_summary: The authors proposed a method for single-source domain generalization. Rather than directly using the images as inputs, the authors proposed to use the edge maps as the network input. The results show that training solely on the edge maps could outperform the competing methods that are trained on images.
main_review: main_review: The proposed method seems to be interesting and it should be worthy to be exposed to the community for discussions. 
Before accepting this paper, I would highly recommend the authors move the Table 3 and 4 to appendix, and move the impact of fusion strategies to the main paper.
strength_weakness: strength_weakness: The results of Table 3 and Table 4 are not informative. The ablation studies are showing that with Bezier curve (intensity flipping) augmentation the results can be improved. This is expected as random contrast adjustment has been one of the most important augmentation techniques for quite a while. The Bezier curve augmentation may be simply replaced by gamma adjustment, as long as the augmentation can help flip the intensity profiles. Instead, I believe the experiments in the appendix about fusion strategies should be moved to the main content. This is because the authors are claiming that using edge map directly as input, rather than late fusion or edge + image, is a better strategy. This is one of the major findings of this paper and thus I would recommend to move these experiments to the main paper.
questions: questions: N/A
paper_summary: paper_summary: In this work, the authors tackle the issue of building a segmentation model that, having trained on a single source domain, can generalize well to different kinds of domain shift which would be plausible at test time. The methodology they offer is to pre-process input images with edge detection mechanisms, with the hope that although the image content can change between different domains the edges are consistent features that will transfer better. The authors also discuss how one could benefit from special data augmentation using Bezier curves. Finally, they evaluate all of their claims across three different medical image segmentation datasets, and compare against state of the art SDG models.
main_review: main_review: The authors improved the rigor of their experimental description, including additional information regarding statistical significance, and justified the choices they made. Thus, I believe this paper should be included in the conference as it is a simple method that demonstrates strong results for the proposed task.
strength_weakness: strength_weakness: - It's unclear that the premise of "train once, adapt anywhere" is useful in practice, and if it is, then the datasets chosen are all datasets which have an ample amount of public availability that could be used simultaneously as leverage to train models. I think that the results would be more compelling if the chosen tasks required such an extreme environment as SDG.
- The role of data augmentation/Bezier curves in this paper is confusing. From my perspective, they should be complementary methods to the Edge detectors chosen. Additionally, it's unclear if the other SDG methods were provided the same level of data augmentation (excluding the note on CIConv*). The data augmentation is not mentioned in the contributions but is a large part of the paper.
- All reported dice numbers are lacking variance statistics to quantify how close the reported results are. This is problematic because the authors claim in the contributions that their method achieves superior generalization performance in comparison to baselines, but visually from Figure 2, CSDG, CIConv, and the proposed method all look very similar, and the performance in the table is also very similar.
- One of the contributions listed is explaining that multiple attempts were made of integrating the edge information into the network; however, this result is buried in the appendix and it is unclear why it is a main contribution.
- The writing is not very polished and has both typos and confusing wording.
questions: questions: Here are a series of questions I had throughout the paper:
- Why pre-make the dataset corresponding to the Bezier curves and not do that on the fly?
- How does EGSDG perform without data augmentation? It seems unfair to compare the traditional SDG methods with EGSDG which was able to train with additional data aug.
- How does EGSDG perform with other kinds of data augmentations that are listed in Table 2?
paper_summary: paper_summary: The author present a single-source domain generalization method by using the edge map as the invariant feature for different target distributions. This work includes comprehensive experiments conducted on BraTS, prostate and MMWHS datasets indicating that the proposed method exhibit superior performance comparing with commonly used DG approaches.
main_review: main_review: The response given by the author coincide with the general intuition. Although the limitations of the proposed method are obvious, they are clearly stated and still worth discussion for future improvement. Thus, I would keep the score as weak accept.
strength_weakness: strength_weakness: 1. Utilizing the edge information is well-explored in many studys and thus lack of novelty. For example:
> * [Domain generalization for robust MS lesion segmentation](https://www.spiedigitallibrary.org/conference-proceedings-of-spie/12464/124640Z/Domain-generalization-for-robust-MS-lesion-segmentation/10.1117/12.2654373.short)
> * [Transfer Learning with Edge Attention for Prostate MRI Segmentation](https://arxiv.org/pdf/1912.09847.pdf)
> * [Edge U-Net: Brain tumor segmentation using MRI based on deep U-Net model with boundary information](https://www.sciencedirect.com/science/article/pii/S0957417422018516?casa_token=_wEAByImOTkAAAAA:153Iz_CWZKYQrE2WNLIcGReUeXgaqrFACshLAS9ZDIpPAKyvQt_mLRJ8EgSpSffOgURuB8vs9g)

2. The qualitative results in Figure. 2 are very hard to see. Visually, it seems like CSDG and CIConv have similar output with the proposed method.
questions: questions: 1. In the ablation study, the experiment indicate that the selection of edge detector can result in at most 7% of difference in the outcome. It seems that Sobel work well on some of the modalities while AutoCanny does well on others. How to determine which one to use given an unseen domain?

2. The experiment are conducted to segment large targets in general. Therefore, although there is not pre-processing step (e.g., anisotropic diffusion) taken to smooth the image, the noisy edge map doesn't seem to be a problem. But what if the target is small, for example, multiple sclerosis (MS) and cochlear?
paper_summary: paper_summary: The authors propose a single-source domain generalization method for medical image segmentation. 

Surprisingly simple, it applies edge detection and augmentations to the single source domain and trains a regular segmentation network on the masks.
main_review: main_review: I thank the communication from the authors.
The authors are responsive and address most of my concerns, including the confusion about the original title, an issue in the BraTS experimental setup, and the limitations of this work. 

I raised my score from borderline to borderline accept, and then to weak accept.
strength_weakness: strength_weakness: Although the presented methodology is interesting in the context of single-source DG, there are a few key concerns: 

x. **Experimental setting for brain tumor segmentation is incorrect**. 

Generalizing T2 to other modalities is not a good setting because different tumor structures are annotated from different modalities. For example, the segmentation labels one could see from FLAIR and T2 are different. 

x. **Limited comparison on public datasets.** 

While one of the datasets used for evaluation is not well curated, the authors didn't compare their method with others on other 'standard' datasets like, abdominal CT-MRI, and Cardiac bSSFP-LGE in Ouyang et al's work (the CSDG method). 

More comparisons would probably highlight the advantages and disadvantages of the proposed method. It would be interesting to discuss about it. 

x. **Limited discussion about the proposed method.** 

While edge detection shows promising results, some discussions are needed regarding the limitations. 

For example, it might be degraded when the texture information (instead of shape or edge) is dominant or when the contour is not clearly visible, for example, ultrasound or CT images.

x. **The title is very confusing.** 

'Adapt' in the title might give the reader an impression that they are doing 'domain adaptation'. In reality, the authors are just doing domain generalization. 

I suggest the authors change the title, like just 'Edge-Guided Single-source Domain Generalization for Medical Image Segmentation'.
questions: questions: Please see the weakness part. 

The setting for the brain tumor is wrong. 

Please check the CSDG paper for detailed datasets used for comparisons. 

For the other points, please check the weakness part.

Comments: title: Thanks for the response to my questions
Thank you to the authors.
thank you Jun
thank you
Further clarification on questions.
further clarification
there is no adaptation in domain generalization. please use 'deploy'.
The brain tumor segmentation setting is **incorrect**. Please double check.
comment: Thanks a lot again.
- We clarified the limitations of our model in the discussion section.
- The ensemble strategy is a good idea and we will further explore it in future work.
1.I think it is fine to have certain limitations for a specific method and I do recommend to clearly state the limitations to the input image in the conclusion.
2.Maybe using some kinds of ensemble to multiple edge maps acquired by different edge detectors can provide a better outcome.
Thanks a lot again. We revised the paper based on the useful suggestions.
Thank you for the thorough addition of 95% confidence intervals. I think that these show that EGSDG w/ Aug indeed shows a thorough improvement over baselines (and thus should be included in the paper), and thus I am changing my score to accept.
Thank you for being responsive and updating the manuscript. 
My concerns are all addressed. 
The score is further updated.
Thank you for the detailed clarification.

- The results of baseline methods with data augmentation are as follows (there are augmentation operations in RobustNet and CSDG): 
## BraTS
|Methods|T1|T1ce|Flair|Average|
|-|-|-|-|-|
|IBN-Net_BasicAug|13.53|20.58|68.92|34.34|
|SW_BasicAug|15.34|23.99|68.43|35.92|
|IBN-Net_BezierCurve|48.35|44.80|64.28|52.48|
|SW_BezierCurve|42.95|42.09|57.20|47.41|


## Prostate
|Methods|SiteA|SiteC|SiteD|SiteF|SiteE|Average|
|-|-|-|-|-|-|-|
|IBN-Net_BasicAug|73.39|57.37|69.65|60.14|75.27|67.16|
|SW_BasicAug|71.67|60.39|70.88|55.67|73.00|66.32|
|IBN-Net_BezierCurve|68.57|44.05|65.70|68.16|74.12|64.12|
|SW_BezierCurve|71.49|57.71|74.02|62.47|73.93|67.92|

## MWHS
|Methods|AA|LAC|LVC|MYO|Average|
|-|-|-|-|-|-|
|IBN-Net_BasicAug|66.22|69.55|71.19|56.99|65.99|
|SW_BasicAug|61.48|72.71|70.20|54.40|64.70|
|IBN-Net_BezierCurve|61.41|59.19|69.37|50.19|60.04|
|SW_BezierCurve|50.46|54.61|61.03|46.34|53.11|

- The comparison results with 95% confidence intervals are as follows (we admit that there are discriminatory limitations of the selected samples for different methods in the qualitative results)：
## BraTS
|Methods|T1|T1ce|Flair|Average|
|-|-|-|-|-|
|UpperBound|74.42(72.85,75.98)|71.64(69.90,73.37)|82.75(81.57,83.92)|76.27|
|LowerBound|13.82(12.92,14.71)|11.58(10.44,12.71)|66.61(64.86,68.35)|30.67|
|IBN-Net|34.37(33.61,35.12)|48.27(47.60,48.93)|42.33(41.46,43.19)|41.66|
|SW|31.83(30.43,32.32)|40.48(39.37,41.58)|34.95(33.83,36.06)|35.75|
|RobustNet|8.59(7.70,9.47)|10.14(8.89,11.38)|68.29(66.62,69.95)|29.01|
|CSDG|46.76(44.77,48.74)|44.99(42.91,47.06)|60.20(58.38,62.01)|50.65|
|CIConv|15.36(14.35,16.36)|20.83(19.62,22.03)|76.07(74.44,77.69)|37.42|
|CIConv*|53.82(51.82,55.81)|52.69(50.24,54.45)|74.05(72.28,75.81)|60.19|
|EGSDGw/oAug.|51.38(49.36,53.39)|50.35(48.29,52.40)|71.63(69.95,73.30)|57.79|
|EGSDGw/Aug.|62.59(60.76,64.41)|54.68(52.67,56.68)|77.07(75.46,78.67)|**64.78**|

## Prostate
|Methods|SiteA|SiteC|SiteD|SiteF|SiteE|Average|
|-|-|-|-|-|-|-|
|UpperBound|89.13(87.64,90.61)|89.96(88.88,91.03)|89.31(86.76,91.85)|87.76(82.30,93.21)|89.34(86.17,92.50)|89.10|
|LowerBound|63.62(58.90,68.33)|19.42(12.88,25.95)|81.06(72.72,89.39)|83.89(75.32,92.45)|71.17(58.06,84.27)|63.83|
|IBN-Net|67.36(62.33,72.38)|46.79(41.14,52.43)|65.09(58.10,72.07)|71.45(65.72,77.17)|76.88(66.40,87.35)|65.51|
|SW|70.83(66.29,75.36)|51.71(46.57,56.84)|70.89(62.90,78.87)|51.96(44.44,59.47)|68.97(61.41,76.52)|62.87|
|RobustNet|73.27(68.90,77.63)|55.04(48.67,61.40)|77.41(68.58,86.23)|54.79(46.67,62.90)|70.21(61.16,79.25)|66.14|
|CSDG|69.75(65.55,73.94)|61.47(58.24,64.69)|74.27(67.70,80.83)|76.31(71.18,81.43)|70.54(64.77,76.30)|70.47|
|CIConv|73.48(68.46,78.49)|63.51(57.15,68.86)|80.8(71.64,89.95)|62.15(52.49,71.80)|74.93(65.89,83.96)|70.97|
|CIConv*|76.41(72.54,80.27)|59.74(55.23,65.84)|76.63(65.72,87.53)|78.10(69.89,86.30)|77.17(66.53,87.80)|73.61|
|EGSDGw/oAug.|72.70(67.63,77.76)|59.54(54.23,65.84)|83.00(76.70,89.29)|70.36(63.31,77.40)|81.11(71.91,90.30)|73.34|
|EGSDGw/Aug.|78.51(73.70,83.31)|64.16(58.77,69.54)|82.95(76.22,89.679)|77.34(71.28,83.40)|78.20(70.81,85.58)|**76.23**|

## MMWHS
|Methods|AA|LAC|LVC|MYO|Average|AA|LAC|LVC|MYO|Average|
|-|-|-|-|-|-|-|-|-|-|-|
|UpperBound|89.74(87.49,91.98)|84.99(82.91,87.06)|87.44(85.35,89.52)|83.34(81.78,84.89)|86.38|80.76(79.66,81.85)|82.29(81.26,83.11)|92.38(91.34,93.41)|78.23(77.48,78.97)|83.42|
|LowerBound|32.18(31.82,32.53)|35.92(35.07,36.76)|19.53(18.95,20.10)|9.42(9.20,9.63)|24.26|18.44(18.19,18.68)|8.84(8.04,9.63)|38.72(38.65,38.78)|9.65(9.49,9.80)|18.91|
|IBN-Net|59.04(56.36,61.71)|67.63(65.23,70.02)|67.34(65.04,69.63)|45.49(43.03,47.94)|59.88|31.23(30.34,32.11)|42.36(41.73,42.98)|59.91(58.78,61.03)|34.63(33.62,35.63)|42.03|
|SW|52.94(50.29,55.58)|69.52(67.03,72.00)|64.28(61.96,66.59)|44.64(42.20,47.07)|57.84|38.95(37.85,40.04)|47.62(46.84,48.39)|62.82(61.65,63.98)|33.30(32.29,34.30)|45.67|
|RobustNet|68.07(65.66,70.47)|74.68(72.07,77.28)|62.56(60.25,64.86)|46.09(43.48,48.69)|62.85|52.27(51.35,53.18)|60.08(59.04,61.11)|67.26(65.95,68.56)|32.97(31.91,34.02)|53.14|
|CSDG|66.91(64.39,69.42)|68.06(65.75,70.36)|64.43(61.95,66.90)|52.24(50.23,54.24)|62.91|37.10(36.07,38.12)|51.76(50.43,53.08)|70.64(69.25,72.02)|41.38(40.18,42.57)|50.22|
|CIConv|67.42(65.13,69.70)|70.83(68.48,73.17)|65.19(62.80,67.57)|42.77(41.07,44.46)|61.55|45.40(44.34,46.45)|45.38(44.10,46.65)|57.08(55.74,58.41)|32.44(31.65,33.22)|45.08|
|CIConv*|78.38(75.63,81.12)|75.67(73.57,77.76)|69.33(67.09,71.56)|55.92(53.86,57.97)|69.83|45.75(44.40,47.09)|50.64(49.45,51.82)|71.93(70.56,73.29)|35.33(34.45,36.20)|50.91|
|EGSDGw/oAug.|73.67(71.01,76.32)|72.45(69.87,75.02)|57.31(54.73,59.88)|57.42(55.22,59.61)|65.21|54.11(53.04,55.17)|53.41(52.28,54.53)|62.74(61.32,64.15)|32.86(31.74,33.97)|50.78|
|EGSDGw/Aug.|73.45(70.66,76.23)|78.48(75.95,81.00)|71.94(69.36,74.51)|60.13(57.86,62.39)|**71.00**|55.14(54.16,56.11)|57.34(55.97,58.70)|72.50(71.19,73.80)|45.84(44.81,46.86)|**57.71**|
We revised the paper based on the useful suggestions with the following modifications:
- We took the "Train Once, Deploy Anywhere" as the title.
- We moved Table 3 and Table 4 to the appendix and placed the impact of fusion strategies in the main content.
- We discussed the limitations of our model and admitted the experimental limitations of BraTS in the discussion section.
- We clarified the performance difference of different fusion strategies and edge detectors.

Thanks a lot again.
Thank you. Please update the PDF accordingly if it is still possible.
I raised my score to borderline accept.
Thank you to the authors for the response, here are a few things I still am wondering.

1. For data augmentation, what I was more interested in knowing was how the proposed baselines methods, not the proposed methods, did under the different data augmentation regimes because it seems like when CIConv was given the bezier curves dataset that it became the best performer. I would like to know if applying even the basic kinds of augs during the training process of the other methods gave similar boosts.

2. The variance numbers leave me very confused as to the statistical significance of the improvement over other baselines methods. I think it would be better to show 95% confidence intervals of the statistics and (if possible) to run paired-t tests across the results to a) know when things are actually significant and b) to co-bold things that perform the same. 

For the time being I will maintain my score of borderline, but I am open to increasing it if the proposed results end up in fact being statistically significant.
Thank you for the detailed and constructive comments. We admit that there are limitations in the experimental setup of BraTS. Except for the BraTS experiments, we believe that we made a comprehensive analysis to the impact of image edge on the model generalization ability and found that employing the image edge as input to train the model directly brings tremendous generalization performance gains. Extensive experiments on the MMWHS and Prostate datasets demonstrate our method achieves superior generalization performance.
For BraTS, if you generalize the model trained on 'TMC' (which is the center ID from the example you show) to other center IDs, such as 'Washington', then I am fine with this setup. 
What you propose, i.e., training on T2 with a merged tumor map, and generalizing to FLAIR and T1-, does not make sense to me **without defining what you wish to generalize**. 

Maybe I could explain what is a good generalization setup from my understanding: 

1. acquisition shift: prostate, one site --> other sites (what you presented). This is a common setup. I fully agree with this. 

2. cross-modality: cardiac CT --> MRI. This also makes sense, because one could see the same anatomy in two modalities. 

However, generalization from T2 to T1-c is different from 2. **There is a label shift in between**. **The shared label map is annotated based on multiple modalities,** i.e., you might not be able to see and segment the merged tumor mask in T1-c because different modalities capture different structures.
"Train Once, Deploy Anywhere" is a good choice. Thanks again.
Sorry, we had a misunderstanding with the comment. For BraTS, the mask of each case is shared with four sequences. That is, the masks are the same for different sequences. The file directory of one case in BraTS is as follows:
``` bash
BraTS19_TMC_30014_1/
├── BraTS19_TMC_30014_1_flair.nii.gz
├── BraTS19_TMC_30014_1_seg.nii.gz
├── BraTS19_TMC_30014_1_t1ce.nii.gz
├── BraTS19_TMC_30014_1_t1.nii.gz
└── BraTS19_TMC_30014_1_t2.nii.gz
```
The experimental setup of BraTS is consistent with SADN.


- The three sub-structures were merged into one label for segmentation.

- The texture and intensity of brain tumors are diverse in different sequences. Therefore, we believe it is a domain generalization problem.
I would agree if you say 'deploy anywhere'. There is no adaptation in domain generalization. 
It is just **technically** confusing if you agree.
Let me explain what might be wrong in a detailed fashion. 
There are three sub-structures in BraTS ("enhancing tumor" (ET), the "tumor core" (TC), and the "whole tumor" (WT) ). 

**First, it is not clear which structure to segment**. Were the three sub-structures merged into one label? or individual labels were segmented? No information is given in the main text and the appendix G. 

**Second, in BraTS, different modalities see different structures.** For cardiac CT --> MRI, it is fine because the structures are visible and have the same semantic meaning in both modalities. However, in the BraTS case, I would not expect a segmentation method that segments a whole tumor in a T2 scan can segment the whole tumor in T1-c, just because it is not well visible. I would not expect it will segment the enhancing tumor in T1-c either because addressing label shift is not the scope of domain generalization.
Thanks for your useful comments sincerely.
- Yes, we were aware of this issue and made special preprocessing on the BraTS dataset, which has been explained in Appendix G. Concretely, we shuffle all the volumes and divide them into four equal parts for each sequence firstly to prevent the ground truth leakage because the mask of each case is shared with four sequences in BraTS. In the final version, we will place this important information on the main content.

- We consider that the cross-modality and cross-sequence experiment settings have covered the above two situations. In addition, our experimental setup is consistent with existing SDG methods (BraTS[1], Prostate[2], MMWHS[1]). 
> [1] Zhou Z, Qi L, Yang X, et al. Generalizable cross-modality medical image segmentation via style augmentation and dual normalization[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022: 20856-20865.
> [2] Ouyang C, Chen C, Li S, et al. Causality-inspired single-source domain generalization for medical image segmentation[J]. IEEE Transactions on Medical Imaging, 2022, 42(4): 1095-1106.

- Yes, the model has the following limitations:
    1. The optimal edge extractor is diverse in different segmentation scenarios, which brings great challenges to choosing the best one for an unseen dataset.
    2. In low-contrast images (like Ultrasound or CT), the model cannot extract valuable edge information well, which may lead to poor segmentation performance.
    3. When the segmentation target is small (like multiple sclerosis or cochlear), the extracted edge information may be similar to the surrounding noise, which may lead to the wrong segmentation of the target and noise.

- Yes, we have the same consideration when choosing the title. We note that, in essence, both Domain Generalization and Domain Adaptation are doing the "Adapt" operation, so we choose "Train Once, Adapt Anywhere".

- For more fair comparisons, the results of the Edge-guided model without BézierCurve augmentation are as follows:
|Methods|T1|T1ce|Flair|Average|
|-|-|-|-|-|
|UpperBound|74.42|71.64|82.75|76.27|
|LowerBound|13.82|11.58|66.61|30.67|
|IBN-Net|34.37|48.27|42.33|41.66|
|SW|31.83|40.48|34.95|35.75|
|RobustNet|8.59|10.14|68.29|29.01|
|SADN|49.36|38.09|75.87|54.44|
|CSDG|46.76|44.99|60.20|50.65|
|CIConv|15.36|20.83|*76.07*|37.42|
|CIConv*|*53.82*|*52.69*|74.05|*60.19*|
|EGSDG w/o Aug.|51.38|50.35|71.63|57.79|
|EGSDG w/ Aug.|**62.59**|**54.68**|**77.07**|**64.78**|

|Methods|SiteA|SiteC|SiteD|SiteF|SiteE|Average|
|-|-|-|-|-|-|-|
|UpperBound|89.13|89.96|89.31|87.76|89.34|89.10|
|LowerBound|63.62|19.42|81.06|83.89|71.17|63.83|
|IBN-Net|67.36|46.79|65.09|71.45|76.88|65.51|
|SW|70.83|51.71|70.89|51.96|68.97|62.87|
|Robust|73.27|55.04|77.41|54.79|70.21|66.14|
|SADN|62.57|41.46|49.14|60.63|68.85|56.63|
|CSDG|69.75|61.47|74.27|76.31|70.54|70.47|
|CIConv|73.48|*63.51*|80.80|62.15|74.93|70.97|
|CIConv*|*76.41*|59.74|76.63|**78.10**|77.17|*73.61*|
|EGSDG w/o Aug.|72.7|59.54|**83.00**|70.36|**81.11**|73.34|
|EGSDG w/ Aug.|**78.51**|**64.16**|*82.95*|*77.34*|*78.20*|**76.23**|

|Methods|AA|LAC|LVC|MYO|Average|AA|LAC|LVC|MYO|Average|
|-|-|-|-|-|-|-|-|-|-|-|
|UpperBound|89.74|84.99|87.44|83.34|86.38|80.76|82.29|92.38|78.23|83.42|
|LowerBound|32.18|35.92|19.53|9.42|24.26|18.44|8.84|38.72|9.65|18.91|
|IBN-Net|59.04|67.63|67.34|45.49|59.88|31.23|42.36|59.91|34.63|42.03|
|SW|52.94|69.52|64.28|44.64|57.84|38.95|47.62|62.82|33.30|45.67|
|Robust|68.07|74.68|62.56|46.09|62.85|52.27|60.08|67.26|32.97|*53.14*|
|SADN(released)|51.42|50.20|52.86|52.31|51.70|33.38|31.65|33.29|30.45|32.19|
|CSDG|66.91|68.06|64.43|52.24|62.91|37.10|51.76|70.64|*41.38*|50.22|
|CIConv|67.42|70.83|65.19|42.77|61.55|45.40|45.38|57.08|32.44|45.08|
|CIConv*|**78.38**|*75.67*|*69.33*|55.92|*69.83*|45.75|50.64|*71.93*|35.33|50.91|
|EGSDG w/ Aug.|*73.67*|72.45|57.31|*57.42*|65.21|*54.11*|53.41|62.74|32.86|50.78|
|EGSDG w/o Aug.|73.45|**78.48**|**71.94**|**60.13**|**71.00** |**55.14**|*57.34*|**72.50**|**45.84**|**57.71**|
Thanks for your useful comments sincerely.
- Yes, there are indeed many works related to Edge-guided models. For SDG, we note that (i) the medical image segmentation applications where generalization errors often come from imprecise predictions at the ambiguous boundary of anatomies and (ii) the edge of the image is domain-invariant, which can reduce the domain shift between the source and target domain in all network layers. Based on the above motivations, we made a comprehensive analysis to the impact of image edge on the model generalization ability and found that employing the image edge as input to train the model directly brings tremendous generalization performance gains. To the best of our knowledge, we make a first attempt to employ the edge of images as input to train the network. Additionally. due to length limitations, we combined the two images, and the enlarged qualitative result will be added to the Appendix.

- Different edge extractors are sensitive to specific types of edges like edge orientation, noise environment, and edge structure. In different segmentation scenarios, the texture, intensity, and noise of medical images are diverse. This leads to the discrepancy between the valuable edge extraction and the irrelevant noise filtering by different edge extractors, which makes the optimal edge detector on each domain different. The main limitation of our model: On different data sets, the optimal edge detection algorithm is different, which will bring great challenges to choosing the best one for an unseen dataset. We will consider employing the deep learning-based edge detector in an end-to-end fashion in future work.

- Yes, the model has the following limitations:
    1. The optimal edge extractor is diverse in different segmentation scenarios, which brings great challenges to choosing the best one for an unseen dataset.
    2. In low-contrast images, the model cannot extract valuable edge information well, which may lead to poor segmentation performance.
    3. When the segmentation target is small, the extracted edge information may be similar to the surrounding noise, which may lead to the wrong segmentation of the target and noise.
Thanks for your useful comments sincerely.
- For medical image segmentation, unsupervised domain adaptation models require retraining when receiving samples from a new data distribution, and multi-source domain generalization methods might be infeasible when there is only a single source domain. These will pose formidable obstacles to model deployment. To this end, we take the "Train Once, Adapt Anywhere" as our objective and consider a challenging but practical problem: Single-source Domain Generalization. In addition, our experimental setup is consistent with existing SDG methods (BraTS[1], Prostate[2], MMWHS[1]). 
> [1] Zhou Z, Qi L, Yang X, et al. Generalizable cross-modality medical image segmentation via style augmentation and dual normalization[C]//CVPR. 2022:20856-20865.
> [2] Ouyang C, Chen C, Li S, et al. Causality-inspired single-source domain generalization for medical image segmentation[J]. TMI, 2022, 42(4):1095-1106.

- Sorry, we didn't have a reasonable design for the data augmentation experiment. Different augmentation methods should be compared based on the Edge-guided model. The results of Edge-guided models with BézierCurve and RandConv are reported in Table 3, 4, and 9. For Edge-guided models with BasicAug and Cutout augmentation, we found that they were unable to improve the generalization ability after training the model several times (Due to character limitations, the experimental results are not provided). For BézierCurve augmentation, it can indeed be performed on the fly. However, conducting it in the preprocessing stage can effectively reduce the model training time.

- The comparison results with variance are as follows:
|Methods|T1|T1ce|Flair|Average|
|-|-|-|-|-|
|UpperBound|74.42(24.89)|71.64(27.47)|82.75(20.39)|76.27|
|LowerBound|13.82(14.28)|11.58(17.97)|66.61(30.21)|30.67|
|IBN-Net|34.37(12.08)|48.27(10.59)|42.33(14.90)|41.66|
|SW|31.83(15.08)|40.48(17.49)|34.95(19.32)|35.75|
|RobustNet|8.59(14.10)|10.14(19.81)|68.29(28.76)|29.01|
|SADN|49.36|38.09|75.87|54.44|
|CSDG|46.76(31.58)|44.99(32.93)|60.20(31.33)|50.65|
|CIConv|15.36(15.92)|20.83(19.11)|76.07(28.09)|37.42|
|CIConv*|53.82(31.75)|52.69(33.42)|74.05(30.53)|60.19|
|EGSDG w/o Aug.|51.38(32.11)|50.35(32.53)|71.63(29.04)|57.79|
|EGSDG w/ Aug.|62.59(29.00)|54.68(31.75)|77.07(27.81)|**64.78**|

|Methods|SiteA|SiteC|SiteD|SiteF|SiteE|Average|
|-|-|-|-|-|-|-|
|UpperBound|89.13(6.88)|89.96(4.66)|89.31(6.36)|87.76(17.60)|89.34(8.07)|89.10|
|LowerBound|63.62(21.93)|19.42(28.28)|81.06(20.83)|83.89(27.65)|71.17(33.43)|63.83|
|IBN-Net|67.36(23.35)|46.79(24.42)|65.09(17.47)|71.45(18.47)|76.88(26.72)|65.51|
|SW|70.83(21.06)|51.71(22.23)|70.89(19.95)|51.96(24.25)|68.97(19.27)|62.87|
|RobustNet|73.27(20.27)|55.04(27.54)|77.41(22.07)|54.79(26.18)|70.21(23.07)|66.14|
|CSDG|69.75(19.50)|61.47(13.95)|74.27(16.42)|76.31(16.54)|70.54(14.71)|70.47|
|CIConv|73.48(23.32)|63.51(23.18)|80.8(22.88)|62.15(31.14)|74.93(23.04)|70.97|
|CIConv*|76.41(17.98)|59.74(19.52)|76.63(27.26)|78.10(26.48)|77.17(27.14)|73.61|
|EGSDG w/o Aug.|72.70(23.52)|59.54(27.28)|83.00(15.74)|70.36(22.73)|81.11(23.45)|73.34|
|EGSDG w/ Aug.|78.51(22.34)|64.16(23.31)|82.95(16.82)|77.34(19.55)|78.20(18.83)|**76.23**|

|Methods|AA|LAC|LVC|MYO|Average|AA|LAC|LVC|MYO|Average|
|-|-|-|-|-|-|-|-|-|-|-|
|UpperBound|89.74(25.06)|84.99(23.12)|87.44(23.29)|83.34(17.38)|86.38|80.76(21.71)|82.29(18.40)|92.38(20.53)|78.23(14.73)|83.42|
|LowerBound|32.18(3.94)|35.92(9.48)|19.53(6.42)|9.42(2.43)|24.26|18.44(4.91)|8.84(15.87)|38.72(1.32)|9.65(3.10)|18.91|
|IBN-Net|59.04(29.82)|67.63(26.67)|67.34(26.56)|45.49(27.35)|59.88|31.23(17.55)|42.36(12.36)|59.91(22.43)|34.63(19.99)|42.03|
|SW|52.94(29.46)|69.52(27.70)|64.28(25.81)|44.64(27.16)|57.84|38.95(21.79)|47.62(15.42)|62.82(23.13)|33.30(19.98)|45.67|
|RobustNet|68.07(26.80)|74.68(29.06)|62.56(25.75)|46.09(29.11)|62.85|52.27(18.19)|60.08(20.63)|67.26(25.93)|32.97(20.99)|53.14|
|SADN|51.42|50.20|52.86|52.31|51.70|33.38|31.65|33.29|30.45|32.19|
|CSDG|66.91(28.00)|68.06(25.69)|64.43(27.66)|52.24(22.37)|62.91|37.10(20.33)|51.76(26.41)|70.64(27.48)|41.38(23.83)|50.22|
|CIConv|67.42(25.52)|70.83(26.11)|65.19(26.55)|42.77(18.94)|61.55|45.40(21.03)|45.38(25.41)|57.08(26.53)|32.44(15.54)|45.08|
|CIConv*|78.38(30.61)|75.67(23.37)|69.33(24.96)|55.92(22.92)|69.83|45.75(26.85)|50.64(23.59)|71.93(27.17)|35.33(17.33)|50.91|
|EGSDGw/oAug.|73.67(29.63)|72.45(28.74)|57.31(28.52)|57.42(24.43)|65.21|54.11(21.11)|53.41(22.31)|62.74(28.22)|32.86(22.27)|50.78|
|EGSDGw/Aug.|73.45(31.06)|78.48(28.14)|71.94(28.76)|60.13(25.28)|**71.00**|55.14(19.36)|57.34(27.14)|72.50(25.87)|45.84(20.36)|**57.71**|

- Sorry, we didn't well organize the paper. As the main contribution of this work, the analysis of edge fusion strategies should be discussed in the body. In the final version, we moved Table 3 and Table 4 to the appendix and placed the impact of fusion strategies in the main content. In addition, we will double-check the wording of the entire article.
Thanks for your useful comments sincerely.
- Yes. For the BraTS dataset, we note that the tumor is brighter in the T2 sequence and darker in the T1 sequence. Therefore, the intensity flipping augmentation can significantly improve the generalization performance. However, taking only intensity flipping may hurt the model's segmentation accuracy on other datasets, like the cross-center Prostate dataset.

- Sorry, we didn't well organize the paper. As the main contribution of this work, the analysis of edge fusion strategies should be discussed in the body. In the final version, we moved Table 3 and Table 4 to the appendix and placed the impact of fusion strategies in the main content.

- These edge-guided strategies can be divided into two categories: 
    1. using the edge map as an additional supervision signal to increase the model’s attention at the boundary of segmentation targets. The performance is lower than ours, probably because this category strategy weakens the supervision of the edge information via the segmentation head at the training stage.
    2. concatenating the image or its features with the edge map to force the model learning domain invariant representation and enhance the generalization ability. The performance is lower than ours, possibly due to the grayscale information making the model overfit on the source domain.