Original: FuzzyNet: A Fuzzy Attention Module for Polyp Segmentation
Revised: FuzzyNet: A Fuzzy Attention Module for Polyp Segmentation

Original: Anonymous Author(s)

Original: AffiliationAddress email

Original: Abstract
Revised: Abstract

Original: Polyp segmentation is essential for accelerating the diagnosis of colon cancer.
Revised: Polyp segmentation is essential for accelerating the diagnosis of colon cancer.

Original: However, it is challenging because of the diverse color, texture, and varyinglighting effects of the polyps as well as the subtle difference between the polyp andits surrounding area.
Revised: However, it is challenging because of the diverse color, texture, and varying lighting effects of the polyps as well as the subtle difference between the polyp and its surrounding area.

Original: To further increase the performance of polyp segmentation,we propose to focus more on the problematic pixels that are harder to predict.
Revised: To further increase the performance of polyp segmentation, we propose to focus more on the problematic pixels that are harder to predict.

Original: Tothis end, we propose a novel attention module named Fuzzy Attention to focusmore on the difficult pixels.
Revised: To this end, we propose a novel attention module named Fuzzy Attention to focus more on the difficult pixels.

Original: Our attention module generates a high attention scorefor fuzzy pixels usually located near the boundary region.
Revised: Our attention module generates a high attention score for fuzzy pixels usually located near the boundary region.

Original: This module can beembedded in any convolution neural network-based backbone network.
Revised: This module can be embedded in any convolution neural network-based backbone network.

Original: We embedour module with various backbone networks: Res2Net, ConvNext and Pyramid
Revised: We embed our module with various backbone networks: Res2Net, ConvNext and Pyramid

Original: Vision Transformer and evaluate the models on five polyp segmentation datasets:
Revised: Vision Transformer and evaluate the models on five polyp segmentation datasets:

Original: Kvasir[9], CVC-300[22], CVC-ColonDB[21], CVC-ClinicDB[2], and ETIS[20].
Revised: Kvasir [11], CVC-300 [30], CVC-ColonDB [29], CVC-ClinicDB [2], and ETIS [28].

Original: Our attention module with Res2Net as the backbone network outperforms thereverse attention-based PraNet by a significant amount on all datasets.
Revised: Our attention module with Res2Net as the backbone network outperforms the reverse attention-based PraNet by a significant amount on all datasets.

Original: In addition,our module with PVT as the backbone network achieves state-of-the-art accuracyof 0.937, 0.811, and 0.791 on the CVC-ClinicDB, CVC-ColonDB, and ETIS,respectively, outperforming the latest SA-Net, TransFuse and Polyp-PVT.
Revised: In addition, our module with PVT as the backbone network achieves state-of-the-art accuracy of 0.937, 0.811, and 0.791 on the CVC-ClinicDB, CVC-ColonDB, and ETIS, respectively, outperforming the latest SA-Net, TransFuse and Polyp-PVT.

Revised: The source code is available at: https://github.com/krushi1992/FuzzyNet.

Original:  Introduction
Revised:  Introduction

Original: Polyp segmentation is an essential task to accelerate the diagnosis of colorectal cancer[20][15], whichis considered the most prevalent cancer worldwide.
Revised: Polyp segmentation is an essential task to accelerate the diagnosis of colorectal cancer[19][22][28], which is considered the most prevalent cancer worldwide.

Original: If the polyp is detected earlier, the mortality ratecan further be reduced.
Revised: If the polyp is detected earlier, the mortality rate can further be reduced.

Original: Colonoscopy is considered the effective technique for CRC screening, whichdetects the polyps that may cause colon cancer.
Revised: Colonoscopy is considered the effective technique for CRC screening, which detects the polyps that may cause colon cancer.

Original: Detecting polyps is a complicated process becauseof their similar appearance to background pixels.
Revised: Detecting polyps is a complicated process because of their similar appearance to background pixels.

Original: Sometimes, even an experienced clinician findsit very difficult to recognize and thus leads to missing detection of polyps because of their subtledifference.
Revised: Sometimes, even an experienced clinician finds it very difficult to recognize, and thus leads to missing detection of polyps because of their subtle difference [14] [23].

Original: In addition, polyps are widely varied in size, texture, and color.
Revised: In addition, polyps are widely varied in size, texture, and color.

Original: Therefore an accurateand automatic polyp segmentation method is required to detect the cancerous polyp in  early-stage toreduce the mortality rate [11].
Revised: Therefore an accurate and automatic polyp segmentation method is required to detect the cancerous polyp in the early-stage to reduce the mortality rate [13].

Original: Convolution neural networks have achieved tremendous performance gain on various medical imagesegmentation tasks, including the polyp segmentation [19][29][10][1][3].
Revised: Convolution neural networks have achieved tremendous performance gain on various medical image segmentation tasks, including the polyp segmentation [1][3][9][12]

Original: Various methods have beenproposed to tackle the issue of detecting difficult boundary pixels accurately, either by using separateedge supervision [6][16] or attention modules.
Revised: Various methods have been proposed to tackle the issue of detecting difficult boundary pixels accurately, either by using separate edge supervision [6][20] or attention modules.

Original: However, the use of edge supervision reduces thegeneralization capability of the model and requires extra boundary annotations, which are expansive.
Revised: However, the use of edge supervision reduces the generalization capability of the model and requires extra boundary annotations, which are expensive.

Original: The attention-based methods used reverse attention [5], focusing on the background region to minethe boundary clues.
Revised: The attention-based methods used reverse attention [5], focusing on the background region to mine the boundary clues.

Original: However, we believe the performance can be further improved if we focus moreon the difficult pixels instead of the background pixel.
Revised: However, we believe the performance can be further improved if we focus more on the difficult pixels instead of the background pixel.

Original: Therefore, in this work, wepropose a novelattention module named Fuzzy attention to encourage the model to focus on the hard boundary pixels.
Revised: Therefore, in this work, we

Original: [Figure]
Revised: [Figure]

Revised: propose a novel attention module named Fuzzy attention to encourage the model to focus on the hard boundary pixels.

Original: The pixels that are not categorized straightforwardly as foreground or background pixels are considered hard pixels.
Revised: The pixels that are not categorized straightforwardly as foreground or background pixels are considered hard pixels.

Original: The smaller the difference between the foreground and background attention score,the higher the complexity.
Revised: The smaller the difference between the foreground and background attention score, the higher the complexity.

Original: Our attention module uses the above observation to calculate the finalattention score, which results in a high score for difficult pixels, usually lying around the boundaryregion, and lower weights for the easy pixels.
Revised: Our attention module uses the above observation to calculate the final attention score, which results in a high score for difficult pixels, usually lying around the boundary region, and lower weights for the easy pixels.

Original: Figure 1 shows an image of the polyp, its groundtruth, and the prediction masks generated by PraNet and our FuzzyNet, respectively.
Revised: Figure 1 shows an image of the polyp, its ground truth, and the prediction masks generated by PraNet and our FuzzyNet, respectively.

Original: It can be seenfrom the original image that the region around the boundary is hard to predict, resulting  an unevenedge, as shown in Figure 1-(c).
Revised: It can be seen from the original image that the region around the boundary is hard to predict, resulting in an uneven edge, as shown in Figure 1-(c).

Original: However, our model predicts the mask closer to the ground truthwith a smooth boundary as shown in Figure 1-(d).
Revised: However, our model predicts the mask closer to the ground truth with a smooth boundary as shown in Figure 1-(d).

Original: Like reverse attention in PraNet [5], we apply thismodule in parallel on the top of the last three levels of the feature map along with deep supervision.
Revised: Like reverse attention in PraNet [5], we apply this module in parallel on the top of the last three levels of the feature map along with deep supervision.

Original: The encoder is considered the backbone network in the segmentation task, which extracts the rowfine level to coarse level features and is further processed by various small architectures modules toenhance the feature representation.
Revised: The encoder is considered the backbone network in the segmentation task, which extracts the row fine level to coarse level features and is further processed by various small architectures modules to enhance the feature representation.

Original: Therefore, to observe the impact of various backbone architecturetypes, we embed our module in three different networks: Res2Net [7], ConvNext [12], and PVT[23], and compare the performance.
Revised: Therefore, to observe the impact of various backbone architecture types, we embed our module in three different networks: Res2Net [8], ConvNext [15], and PVT [31], and compare the performance.

Original: Our result shows that the proposed module with Res2Netas a backbone network significantly outperforms PraNet with the same backbone [5] on variouspolyp segmentation datasets, including Kvasir[9], CVC-ClinicDB[2], CVC-ColonDB [21], CVC-300,and ETIS[20].
Revised: Our result shows that the proposed module with Res2Net as a backbone network significantly outperforms PraNet with the same backbone [5] on various polyp segmentation datasets, including Kvasir[11], CVC-ClinicDB[2], CVC-ColonDB [29], CVC-300, and ETIS[28].

Original: In addition, our attention module with the PVT as a backbone network achievesstate-of-the-art accuracy on CVC-ClinicDB, CVC-ColonDB and ETIS by exceeding the performanceof recently proposed SA-Net, TransFuse, and Polyp-PVT.
Revised: In addition, our attention module with the PVT as a backbone network achieves state-of-the-art accuracy on CVC-ClinicDB, CVC-ColonDB and ETIS by exceeding the performance of recently proposed SA-Net, TransFuse, and Polyp-PVT.

Original: The main contributions of this work are summarized below:
Revised: The main contributions of this work are summarized below:

Original: We propose a novel attention module, named Fuzzy attention, to focus more on the difficult pixels which usually lie near the boundary region.
Revised: We propose a novel attention module, named Fuzzy attention, to focus more on the difficult pixels which usually lie near the boundary region.

Original: It can be embedded in any backbone network in parallel after the last three feature maps.
Revised: It can be embedded in any backbone network in parallel after the last three feature maps.

Original: We investigate the impact of various types of backbone networks: Res2net [7], ConvNext[12],and PVT[23], along with our attention module through extensive experiments.3.
Revised: We investigate the impact of various types of backbone networks: Res2net [8], ConvNext[15], and PVT[31], along with our attention module through extensive experiments.

Original: Extensive experimental results show that our Fuzzy attention module outperforms the reverse attention-based model, PraNet [5], by a significant margin with the same Res2Net backbone on the polyp segmentation datasets: Kvasir, CVC-ColonDB [21], CVC-ClinicDB[2], CVC300[22].
Revised: Extensive experimental results show that our Fuzzy attention module outperforms the reverse attention-based model, PraNet [5], by a significant margin with the same Res2Net backbone on the polyp segmentation datasets: Kvasir, CVC-ColonDB [29], CVC-ClinicDB[2], CVC300[30].

Original: With PVT [23] as a backbone network, we achieve state-of-the-art accuracy on the CVC-ClinicDB, CVC-ColonDB and ETIS datasets.
Revised: With PVT [31] as a backbone network, we achieve state-of-the-art accuracy on the CVC-ClinicDB, CVC-ColonDB, and ETIS datasets.

Original:  Related Work
Revised:  Related Work

Original: Various approaches have been proposed to segment the polyp in colonoscopic images using eitherhandcrafted features or deep features extracted bythe deep learning networks.
Revised: Various approaches have been proposed to segment the polyp in colonoscopic images using either handcrafted features or deep features extracted by deep learning networks.

Original: All approaches can bebroadly divided into two categories:
Revised: All approaches can be broadly divided into two categories:

Original: Classical computer vision approaches: Early polyp segmentation approaches use low-level handcrafted features, including texture[14] and geometric features.
Revised: Classical computer vision approaches: Early polyp segmentation approaches use low-level handcrafted features, including texture[18] and geometric features.

Original: [13] used a simple linear iterativeclustering superpixel to segment the polyp.
Revised: [17] used a simple linear iterative clustering superpixel to segment the polyp.

Original: As mentioned above, all the method has a high falsedetection rate because of the high similarity between polyps and the surrounding area.
Revised: As mentioned above, all the method has a high false detection rate because of the high similarity between polyps and the surrounding area.

Original: Deep learning based approaches: There have been various deep learning-based approaches proposedfor the polyp segmentation task.

Original: It started with the [1], which first uses a convolutional network for

Original: FA FA
Revised: FA FA

Original: FA +
Revised: FA +

Original: S 𝑓 !
Revised: S 𝑓 !

Original: 𝑓 " 𝑓 # 𝑓 $ 𝑆 % 𝑆 # 𝑆 $ 𝑆 & 𝑅 # 𝑅 $ 𝑅 &
Revised: 𝑓 " 𝑓 # 𝑓 $ 𝑆 % 𝑆 # 𝑆 $ 𝑆 & 𝑅 # 𝑅 $ 𝑅 &

Original: Input
Revised: Input

Original: Prediction 𝑓 & 352 x 352 x352 x+ +
Revised: Prediction 𝑓 & 352 x 352 x352 x+ +

Original: FA -Fuzzy Attention Module -Partial Decoder + -Element-wise Addition
Revised: FA -Fuzzy Attention Module -Partial Decoder + -Element-wise Addition

Original: S -Sigmoid Activation  the polyp segmentation and outperforms the traditional methods.
Revised: S -Sigmoid Activation Deep learning based approaches: There have been various deep learning-based approaches proposed for the polyp segmentation task. It started with the study [1], which first employs a convolutional network for the polyp segmentation and outperforms the traditional methods.

Original: The U-shaped encoder and decoderarchitectures: U-Net [19], U-Net++ [29], ResUNet++ [10], ACS-Net [27] and Enhanced U-Net [17]started dominating the segmentation field because of their tremendous performance gain.
Revised: The U-shaped encoder and decoder architectures: U-Net [25], U-Net++ [37], ResUNet++ [12], ACS-Net [35] and Enhanced U-Net [22] started dominating the segmentation field because of their tremendous performance gain.

Original: To alleviate the issues of complex boundary regions, SFA [6] and PSI [16] include an extra edgesupervision branch.
Revised: To alleviate the issues of complex boundary regions, SFA [6] and PSI [20] include an extra edge supervision branch.

Original: However, it requires extra boundary annotation and has an overfitting problem.
Revised: However, it requires extra boundary annotation and has an overfitting problem.

Original: PraNet [5] introduces the reverse attention mechanism to mine the boundary region gradually byfocusing more on background pixels.
Revised: PraNet [5] introduces the reverse attention mechanism to mine the boundary region gradually by focusing more on background pixels.

Original: In contrast, to reverse attention, our module focuses more onthe complex pixels usually lying around the boundary region.
Revised: In contrast, to reverse attention, our module focuses more on the complex pixels usually lying around the boundary region.

Original: ACS-Net [27] also introduces theattention mechanism to focus more on the hard pixels, however, it employs a predefined pixel scoreto classify the pixel as hard or easy.
Revised: ACS-Net [35] also introduces the attention mechanism to focus more on the hard pixels, however, it employs a predefined pixel score to classify the pixel as hard or easy.

Original: Other attention-based models, SA-Net [24] and Enhanced U-Net [17] use different attention mechanisms to give more attention to the foreground region and adaptively select the features.
Revised: Other attention-based models, SA-Net [32] and Enhanced U-Net [22] use different attention mechanisms to give more attention to the foreground region and adaptively select the features.

Original: TranFuse[28] and Polyp-PVT [4] use the latest vision transformer for the polyp segmentation task and achievean excellent result.
Revised: TranFuse [36] and Polyp-PVT [4] use the latest vision transformer for the polyp segmentation task and achieve an excellent result.

Revised: The attention mechanism has also been successfully applied in many other applications [7][16][26][27].

Original: In one of our experiments, we also embedded our attention module inPyramid
Revised: In one of our experiments, we also embedded our attention module in

Original:  Vision Transformer and established state-of-the-art accuracy on various datasets.
Revised: Pyramid Vision Transformer and established state-of-the-art accuracy on various datasets [21].

Original:  Method
Revised:  Method

Original: The overview of our proposed network is shown in Figure 2.
Revised: The overview of our proposed network is shown in Figure 2.

Original: We follow the architecture used in the
Revised: We follow the architecture used in the

Original: PraNet [5] and replace the reverse attention module in PraNet with our proposed Fuzzy attentionmodule.
Revised: PraNet [5] and replace the reverse attention module in PraNet with our proposed Fuzzy attention module.

Original: Specifically, our model takes the RGB image as an input and passes it through the backbonenetwork, followed by the partial decoder, which employs multi-resolution feature maps to generatethe initial global semantic map.
Revised: Specifically, our model takes the RGB image as an input and passes it through the backbone network, followed by the partial decoder, which employs multi-resolution feature maps to generate the initial global semantic map.

Original: This global map is then passed through a series of fuzzy attentionmodules, which gradually mine the boundary cues.
Revised: This global map is then passed through a series of fuzzy attention modules, which gradually mine the boundary cues.

Original: We apply deep supervision after each attentionmodule and the initial global map.
Revised: We apply deep supervision after each attention module and the initial global map.

Original: The map generated by the last attention layer is considered thefinal prediction map.
Revised: The map generated by the last attention layer is considered the final prediction map.

Original: The detailed explanation of each element of the architecture is elaborated below.
Revised: A detailed explanation of each element of the architecture is elaborated below.

Original: X

Original: [Figure]
Revised: [Figure]

Original: 𝑅 !

Original: 3.1 Backbone Network
Revised: 3.1 Backbone Network

Original: [Figure]

Original: In the segmentation task, the encoder is considered as the backbone network, which generates theessential row multi-resolution features from fine level to abstract { f i , i = 1 , ... 5 } .
Revised: In the segmentation task, the encoder is considered as the backbone network, which generates the essential row multi-resolution features from fine level to abstract { f i , i = 1 , ... 5 } .

Original: It is consideredthe heart of the segmentation model because the model performance heavily relies on the featuresgenerated by it.
Revised: It is considered the heart of the segmentation model because the model performance heavily relies on the features generated by it.

Original: Therefore, to observe the impact of various types of backbone networks (eitherconvolution-based or transformer-based), we use three different networks in our experiments: Res2Net[7], ConvNext [12], and PVT [23].
Revised: Therefore, to observe the impact of various types of backbone networks (either convolution-based or transformer-based), we use three different networks in our experiments: Res2Net [8], ConvNext [15], and PVT [31].

Original: 3.2 Partial Decoder
Revised: 3.2 Partial Decoder

Original: [Figure] As mentioned in the previous section, the encoder generates five levels of multi-resolution featuremaps f i , i = 1 , ... 5 .
Revised: As mentioned in the previous section, the encoder generates five levels of multi-resolution feature maps f i , i = 1 , ... 5 .

Original: These feature maps are further divided into two types: low level { f i , i = 1 , 2 }and high level { f i , i = 3 , 4 , 5 } .
Revised: These feature maps are further divided into two types: low level { f i , i = 1 , 2 } and high level { f i , i = 3 , 4 , 5 } .

Original: As observed in [26], low-level features increase the computation costby a large amount and have less contribution towards increasing the performance.
Revised: As observed in [34], low-level features increase the computation cost by a large amount and have less contribution towards increasing the performance.

Original: Therefore, weemploy the parallel partial decoder proposed in [26], which aggregates only the high-level features togenerate the global initial semantic map, and it is further refined in attention modules.
Revised: Therefore, we employ the parallel partial decoder proposed in [34], which aggregates only the high-level features to generate the global initial semantic map, and it is further refined in attention modules.

Original: 3.3 Fuzzy Attention Module
Revised: 3.3 Fuzzy Attention Module

Original: The human’s natural tendency is to roughly locate the object and then gradually mine the complex region by concentrating more on that area.
Revised: The human’s natural tendency is to roughly locate the object and then gradually mine the complex region by concentrating more on that area.

Original: We apply a similar approach for medical image segmentationto clearly distinguish the background area and foreground objects (polyp or skin lesion) by focusingmore on the hard pixels using the Fuzzy attention module.
Revised: We apply a similar approach for medical image segmentation to clearly distinguish the background area and foreground objects (polyp or skin lesion) by focusing more on the hard pixels using the Fuzzy attention module.

Original: We apply this module parallelly on thehigh-level feature maps { f i , i = 3 , 4 , 5 } which produce the resultant feature map { R i , i = 3 , 4 , 5 } ,where R 3 is used to generate the final prediction map.
Revised: We apply this module parallelly on the high-level feature maps { f i , i = 3 , 4 , 5 } which produce the resultant feature map { R i , i = 3 , 4 , 5 } , where R 3 is used to generate the final prediction map.

Original: The block diagram of the fuzzy attentionmodule isas shown in Figure[-
-]
Revised: The block diagram of the fuzzy attention module is shown in Figure[-
-]

Original: Specifically, the resultant feature maps are calculated as:
Revised: Specifically, the resultant feature maps are calculated as:

Original: [Equation]
Revised: [Equation]

Original: The attention maps A i have high scores for difficult pixels and low scores for easy pixels.
Revised: The attention maps A i have high scores for difficult pixels and low scores for easy pixels.

Original: It ismathematically formulated as:
Revised: It is mathematically formulated as:

Original: [Equation]
Revised: [Equation]

Original: where.
Revised: where.

Original: A fi represents the forward attention map, with a high score for the foreground object anda low score for the background area, and A ri indicates the reverse attention map, which has a high score for the background pixels and low score for the foreground pixels.
Revised: A fi represents the forward attention map, with a high score for the foreground object and a low score for the background area, and A ri indicates the reverse attention map, which has a high score for the background pixels and low score for the foreground pixels.

Original: The attention maps can bemathematically formulated as:
Revised: The attention maps can be mathematically formulated as:

Original: [Equation] [Equation]
Revised: [Equation] [Equation]

Original: where Up indicates the upsampling operation, σ ( . ) represents the sigmoid activation, and S i is theglobal map from the previous layer.
Revised: where Up indicates the upsampling operation, σ ( . ) represents the sigmoid activation, and S i is the global map from the previous layer.

Original: Pixel’s difficulty can be associated with the absolute differencebetween the forward and reverse attention score; the lower the absolute difference, the higher thedifficulty.
Revised: Pixel’s difficulty can be associated with the absolute difference between the forward and reverse attention score; the lower the absolute difference, the higher the difficulty.

Original: To focus more on the complex pixels, we further subtract the absolute difference from 1followed by sigmoid activation as shown in equation 2.
Revised: To focus more on the complex pixels, we further subtract the absolute difference fromfollowed by sigmoid activation as shown in equation 2.

Original: 3.4 Loss Function
Revised: 3.4 Loss Function

Original: We use the combination of weighted IoU loss L wIOU and weighted cross-entropy loss L wBCE as ourmain loss function [18][25].
Revised: We use the combination of weighted IoU loss L wIOU and weighted cross-entropy loss L wBCE as our main loss function [24][33].

Original: We apply deep supervision after each resultant map generated by theattention module along with the initial global map.
Revised: We apply deep supervision after each resultant map generated by the attention module along with the initial global map.

Original: The total loss can be formulated as:
Revised: The total loss can be formulated as:

Original: [Equation]
Revised: [Equation]

Original: where S g is the global map and S 3 , S 4 , and S 5 are the output maps generated by the attention module.
Revised: where S g is the global map and S 3 , S 4 , and S 5 are the output maps generated by the attention module.

Original:  Experiments4.1 Datasets
Revised:  Experiments 4.1 Datasets

Original: We conducted experiments on five publicly available polyp segmentation datasets: ETIS, CVCClinicDB, CVC-ColonDB, CVC-300, and KVasir.
Revised: We conducted experiments on five publicly available polyp segmentation datasets: ETIS, CVCClinicDB, CVC-ColonDB, CVC-300, and KVasir.

Original: ETIS is an old dataset with 196 polyp images andits ground truth mask.
Revised: ETIS is an old dataset with 196 polyp images and its ground truth mask.

Original: CVC-ClinicDB and CVC-300 comprise 612 and 300 images from 29 and 13colonoscopy video sequences, respectively.
Revised: CVC-ClinicDB and CVC-300 comprise 612 and 300 images from 29 and 13 colonoscopy video sequences, respectively.

Original: CVC-ColonDB is a small-scale dataset containing 380images fromthe 15 short colonoscopy sequences.
Revised: CVC-ColonDB is a small-scale dataset containing 380 images from 15 short colonoscopy sequences.

Original: Kvasir dataset is relatively new, with 1000 polypimages.
Revised: Kvasir dataset is relatively new, with 1000 polyp images.

Original: We compare our FuzzyNet with state-of-the-art models:
Revised: We compare our FuzzyNet with state-of-the-art models:

Original: PraNet, Enhanced U-Net, ACSNet,
Revised: PraNet, Enhanced U-Net, ACSNet,

Original: MSEG[8], SA-Net, TransFuse, and Polyp-PVT, along with the previous approaches U-Net, U-Net++,and ResU-net++.
Revised: MSEG[10], SA-Net, TransFuse, and Polyp-PVT, along with the previous approaches U-Net, U-Net++, and ResU-Net++.

Original: 4.2 Evaluation Metrics
Revised: 4.2 Evaluation Metrics

Original: We utilize the Dice coefficient and Intersection over Union (IOU) as our evaluation metrics which aredefined below:
Revised: We utilize the Dice coefficient and Intersection over Union (IOU) as our evaluation metrics which are defined below:

Original: Dice coefficient: It is defined as:
Revised: Dice coefficient: It is defined as:

Original: [Equation]
Revised: [Equation]

Original: where A denotes the predicted set of pixels and B is the ground truth of the image.
Revised: where A denotes the predicted set of pixels and B is the ground truth of the image.

Original: Intersection over union (IoU): It is another standard metric to evaluate the performance of thesegmentation task.
Revised: Intersection over union (IoU): It is another standard metric to evaluate the performance of the segmentation task.

Original: It is defined as:
Revised: It is defined as:

Original: [Equation]
Revised: [Equation]

Original: where A denotes the predicted set of pixels and B is the corresponding ground truth of the set ofpixels.
Revised: where A denotes the predicted set of pixels and B is the corresponding ground truth of the set of pixels.

Original: 4.3 Implementation Details
Revised: 4.3 Implementation Details

Original: In our experiments, we follow the same training settings used in PraNet for the Res2Net backboneand Polyp-PVT for ConvNext and PVT backbone.
Revised: In our experiments, we follow the same training settings used in PraNet for the Res2Net backbone and Polyp-PVT for ConvNext and PVT backbone.

Original: All the models are trained on a V100 GPU, with[Table] shows that our model outperforms the by a significant margin on batch-size 16 and Adam optimizer with an initial learning rate of 0.0001.
Revised: All the models are trained on a V100 GPU, with batch-size 16 and Adam optimizer with an initial learning rate of 0.0001.

Original: We employ multi-scaletraining for all the backbone networks instead of data augmentation techniques by following the
Revised: We employ multi-scale training for all the backbone networks instead of data augmentation techniques by following the

Original: PraNet and PVT.
Revised: PraNet and PVT.

Original: We employ the backbone networks Res2Net, ConvNext, and Pyramid Vision
Revised: We employ the backbone networks Res2Net, ConvNext, and Pyramid Vision

Original: Transformer, initialize the weights with pretrained weights trained on ImageNet-1K and train themfrom scratch. 
Revised: Transformer, initialize the weights with pretrained weights trained on ImageNet-1K and train them from scratch. [Table]

Original: 4.4 Learning Ability
Revised: 4.4 Learning Ability

Original: Setting : We evaluate the learning ability of our model on the dataset ClinicDB and Kvasir-Seg.
Revised: Setting : We evaluate the learning ability of our model on the dataset ClinicDB and Kvasir-Seg.

Original: Clinic-DB consists of 612 images extracted from 31 colonoscopy videos, whereas Kvasir-Seg consistsof a total of 1000 polyp images.
Revised: Clinic-DB consists of 612 images extracted from 31 colonoscopy videos, whereas Kvasir-Seg consists of a total of 1000 polyp images.

Original: We follow the same setting as PraNet and Polyp-PVT, which include900 and 548 images from ClinicDB and Kvasir-Seg datasets as the train set, and the remaining 64and 100 images are used as the test set.
Revised: We follow the same setting as PraNet and Polyp-PVT, which include 900 and 548 images from ClinicDB and Kvasir-Seg datasets as the train set, and the remainingand 100 images are used as the test set.

Original: Results: Table 1 shows the result on Kvasir and CVC-ClinicDb datasets.
Revised: Results: Table 1 shows the result on Kvasir and CVC-ClinicDb datasets.

Original: Our FuzzyNet model with
Revised: Our FuzzyNet model with

Original: Res2Net as a backbone network achieves 2% higher mean dice than PraNet on CVC-ClinicDB andachieves comparable results on the Kvasir dataset which demonstrates the better learning ability ofour model.
Revised: Res2Net as a backbone network achieves 2% higher mean dice than PraNet on CVC-ClinicDB and achieves comparable results on the Kvasir dataset which demonstrates the better learning ability of our model.

Original: Our model with ConvNext as a backbone network outperforms the ACSNet, PraNet,
Revised: Our model with ConvNext as a backbone network outperforms the ACSNet, PraNet,

Original: EU-Net, and SA-Net on the Clinic-DB dataset by 3.4%, 2.3%, 2%, and 0.6%, respectively, in termsof mean-dice.
Revised: EU-Net, and SA-Net on the Clinic-DB dataset by 3.4%, 2.3%, 2%, and 0.6%, respectively, in terms of mean-dice.

Original: In addition, it also achieves 0.9%, 0.9%, and 0.03% higher mean dice than the ACSNet,
Revised: In addition, it also achieves 0.9%, 0.9%, and 0.03% higher mean dice than the ACSNet,

Original: PraNet, and SANet, respectively, on the Kvasir dataset.
Revised: PraNet, and SANet, respectively, on the Kvasir dataset.

Original: With Pyramid Vision Transformer as abackbone network, we achieve the state-of-the-art accuracy 0.937 on the CVC-ClinicDB dataset andcomparable mean dice on the Kvasir dataset as Polyp-PVT.
Revised: With Pyramid Vision Transformer as a backbone network, we achieve the state-of-the-art accuracy 0.937 on the CVC-ClinicDB dataset and comparable mean dice on the Kvasir dataset as Polyp-PVT.

Original: 4.5 Generalization Ability
Revised: 4.5 Generalization Ability

Original: Setting: To evaluate the generalization ability of the model, we use three unseen datasets: ETIS,
Revised: Setting: To evaluate the generalization ability of the model, we use three unseen datasets: ETIS,

Original: ColonDB, and CVC-300.
Revised: ColonDB, and CVC-300.

Original: The ETIS, ColonDB, and CVC-300 datasets consist of a total of 190, 380,and 60 images, respectively.
Revised: The ETIS, ColonDB, and CVC-300 datasets consist of a total of 190, 380, and 60 images, respectively.

Original: The images of these datasets belong to different medical centers, whichmeans that the training and testing sets are different and the model has not seen the test images beforeduring training.
Revised: The images of these datasets belong to different medical centers, which means that the training and testing sets are different and the model has not seen the test images before during training.

Original: Results:
Revised: Results:

Original: The result is shown in the table 2.
Revised: The result is shown in the table 2.

Original: It can be seen from the result that our model has a bettergeneralization performance compared to state-of-the-art models.
Revised: It can be seen from the result that our model has a better generalization performance compared to state-of-the-art models.

Original: On ColonDB and ETIS, we achievedthe highest performance by outperforming the Polyp-PVT.
Revised: On ColonDB and ETIS, we achieved the highest performance by outperforming the Polyp-PVT.

Original: On CVC-300, our model achieves comparable performance as Polyp-PVT.
Revised: On CVC-300, our model achieves comparable performance to Polyp-PVT.

Original: In addition, our model with Res2Net as a backbone outperforms
Revised: In addition, our model with Res2Net as a backbone outperforms

Original: PraNet by 3.1%, 2.7%, and 10% on CVC-300, CVC-ColonDB, and ETIS respectively in terms ofmean dice, which demonstrates that Fuzzy Attention module has an outstanding generalization abilitycompared with the Reverse Attention module in PraNet.
Revised: PraNet by 3.1%, 2.7%, and 10% on CVC-300, CVC-ColonDB, and ETIS respectively in terms of mean dice, which demonstrates that Fuzzy Attention module has an outstanding generalization ability compared with the Reverse Attention module in PraNet.

Original: With PVT as a backbone network, our model 
Revised: With PVT as a backbone network, our model outperforms the latest SANet and TransFuse by 5.8% and 6.7% on CVC-ColonDB, 4.2% and 5.5% on ETIS respectively. It also achieves 1.1% higher mean dice than SA-Net and comparable mean dice as TransFuse on CVC-300.

Original: [Table]
Revised: [Table]

Revised: -300 dataset.

Revised: The reported result is the average of three experiments.

Original: [Table]
Revised: [Table]

Original: outperforms the latest SANet and TransFuse by 5.8% and 6.7% on CVC-ColonDB, 4.2% and 5.5%on ETIS respectively.

Original: It also achieves 1.1% higher mean dice than SA-Net and comparable meandice as TransFuse on CVC-300.

Original: 4.6 Effectiveness of Fuzzy Attention
Revised: 4.6 Effectiveness of Fuzzy Attention

Original: The effectiveness of the Fuzzy attention module can be verified by comparing the result of our modelwith the Res2Net backbone with PraNet.
Revised: The effectiveness of the Fuzzy attention module can be verified by comparing the result of our model with the Res2Net backbone with PraNet.

Original: For a fair comparison, apart from the type of attentionmodule, we utilize a similar backbone, hyperparameters, augmentation, and regularization techniqueas used in PraNet.
Revised: For a fair comparison, apart from the type of attention module, we utilize a similar backbone, hyperparameters, augmentation, and regularization technique as used in PraNet.

Original: It can be seen from the table our model outperforms PraNet on the CVC-ClinicDBdataset by 2% and achieves a comparable result on the Kvasir dataset.
Revised: It can be seen from the table our model outperforms PraNet on the CVC-ClinicDB dataset by 2% and achieves a comparable result on the Kvasir dataset.

Original: It improves the result on unseendataset by a significant margin of 2.7%, 10%, and 1.9% on CVC-ColonDB, ETIS, and CVC-300respectively.
Revised: It improves the result on unseen datasets by a significant margin of 2.7%, 10%, and 1.9% on CVC-ColonDB, ETIS, and CVC-300 respectively.

Original: The overall result of all datasets along with GFlops and the total number of parametersare listed in Table 3.
Revised: The overall result of all datasets along with GFlops and the total number of parameters are listed in Table 3.

Original: We can observe a significant performance gain of 0.9% and 5% on the averageof seen and unseen datasets respectively.
Revised: We can observe a significant performance gain of 0.9% and 5% on the average of seen and unseen datasets respectively.

Original: The outstanding results on the unseen dataset prove thegeneralization capability of the proposed fuzzy attention, which is significantly higher than reverseattention.
Revised: The outstanding results on the unseen dataset prove the generalization capability of the proposed fuzzy attention, which is significantly higher than reverse attention.

Original: Furthermore, fuzzy attention does not add an extra number of parameters and the computation cost.
Revised: Furthermore, fuzzy attention does not add an extra number of parameters and the computation cost.

Original: With the same amount of parameters and GFlops: 32M and 13.11 GMac respectively, we achieve asignificant performance gain compared to reverse attention-based PraNet.
Revised: With the same amount of parameters and GFlops: 32M and 13.11 GMac respectively, we achieve a significant performance gain compared to reverse attention-based PraNet.

Original: In addition, we visualize the segmentation mask generated by our model and PraNet.
Revised: In addition, we visualize the segmentation mask generated by our model and PraNet.

Original: It can beseen from the result shown in Figure 4 that our model correctly classifies the fuzzy pixels near theboundary compared to PraNet model.
Revised: It can be seen from the result shown in Figure 4 that our model correctly classifies the fuzzy pixels near the boundary compared to PraNet model.

Original: For most of the images, PraNet seems to be misclassifiedbackground pixels as foreground pixels because of the high focus on the background pixels inreverse attention.
Revised: For most of the images, PraNet seems to be misclassified background pixels as foreground pixels because of the high focus on the background pixels in reverse attention.

Original: In contrast to PraNet, the resultant mask generated by our model has well-definedboundaries, and the results are closer to the ground truth.
Revised: In contrast to PraNet, the resultant mask generated by our model has well-defined boundaries, and the results are closer to the ground truth.

Original: In addition, our model’s performance isconsistent irrespective of the lighting and reflection condition in the image.Furthermore, we also Original GT
Revised: In addition, our model’s performance is consistent irrespective of the lighting and reflection condition in the image.

Original: PraNet Polyp-PVT SANet Ours visualize the segmentation mask generated by Polyp-PVT and SA-Net.
Revised: Furthermore, we also visualize the segmentation mask generated by Polyp-PVT and SA-Net.

Original: It can be seen from the figurethat our resultant mask has fewer false positive pixels and a smooth boundary than all other methods. 
Revised: It can be seen from the figure that our resultant mask has fewer false positive pixels and a smooth boundary than all other methods. [Figure]

Original:  Conclusion
Revised:  Conclusion

Original: This paper has presented a novel attention mechanism to encourage the network to focus moreon the fuzzy region, which usually lies around the boundary.
Revised: This paper has presented a novel attention mechanism to encourage the network to focus more on the fuzzy region, which usually lies around the boundary.

Original: We embed our attention modulewith various backbone networks: Res2Net, ConvNext, and Pyramid Vision Transformer (PVT) forpolyp segmentation.
Revised: We embed our attention module with various backbone networks: Res2Net, ConvNext, and Pyramid Vision Transformer (PVT) for polyp segmentation.

Original: Our result shows that the fuzzy attention module significantly outperforms
Revised: Our result shows that the fuzzy attention module significantly outperforms

Original: PraNet, which employs the reverse attention mechanism on all polyp segmentation datasets.
Revised: PraNet, which employs the reverse attention mechanism on all polyp segmentation datasets.

Original: With the
Revised: With the

Original: PVT as the backbone network, our model achieves state-of-the-art accuracy on the CVC-ClinicDB,
Revised: PVT as the backbone network, our model achieves state-of-the-art accuracy on the CVC-ClinicDB,

Original: CVC-ColonDB, and ETIS dataset for polyp segmentation.
Revised: CVC-ColonDB, and ETIS dataset for polyp segmentation.

Revised: Acknowledgement

Revised: This work was partly supported in part by the Natural Sciences and Engineering Research Council of

Revised: Canada (NSERC) under grant nos.

Revised: RGPIN-2021-04244 and ALLRP 576612-22, and the National

Revised: Institutes of Health (NIH) under grant no. 1R03CA253212-01.