Towards Generalizable Retina Vessel Segmentation with Deformable Graph Priors
Authors: Ke Liu
Shangde Gao
Yichao Fu
Shangqi Gao
Venue: NeurIPS 2025 poster ()
Keywords: probabilistic modeling
Primary area: machine_learning_for_sciences

Abstract: Retinal vessel segmentation is critical for medical diagnosis, yet existing models often struggle to generalize across domains due to appearance variability, limited annotations, and complex vascular morphology. We propose GraphSeg, a variational Bayesian framework that integrates anatomical graph priors with structure-aware image decomposition to enhance cross-domain segmentation. GraphSeg factorizes retinal images into structure-preserved and structure-degraded components, enabling domain-invariant representation. A deformable graph prior, derived from a statistical retinal atlas, is incorporated via a differentiable alignment and guided by an unsupervised energy function. Experiments on three public benchmarks (CHASE, DRIVE, HRF) show that GraphSeg consistently outperforms existing methods under domain shifts. These results highlight the importance of jointly modeling anatomical topology and image structure for robust generalizable vessel segmentation.

Towards Generalizable Retina Vessel Segmentation with Deformable Graph Priors
Ke Liu
Shangde Gao
Yichao Fu" Zhejiang University
Shangqi Gao
2 University of Cambridge
[kliu, gaosd, fuyi (uyichao)@zju.. @zju. sg21620cam. ac. uk
Abstract
Retinal vessel segmentation is critical for medical diagnosis, yet existing models often struggle to generalize across domains due to appearance variability, limited an- notations, and complex vascular morphology. We propose GraphSeg, variational Bayesian framework that integrates anatomical graph priors with structure-aware image decomposition enhance cross-domain segmentation. GraphSeg factor- izes retinal images into structure- preeserrep and structure-degraded components, enabling domain-invariant representation. A deformable graph prior, derived from a statistical retinal atlas, is incorporated via a differentiable alignment and guided by unsupervised energy function. Experiments three public benchmarks (CHASE, DRIVE, HRF) show that GraphSeg consistently outperforms existing methods under domain shifts. These results highlight the importance of jointly modeling anatomical topology and image structure for robust generalizable vessel segmentation. Code can be found at wew.ghi..co//Aaa.. haabubb.oomAAAAMOL//aaa.....
Introduction
Retinal vessel segmentation is vital assist in the diagnosis of common retinal discases, such as diabetic retinopathy, age-related macular degeneration, and retinal detachment, which have been recognized as the leading causes of vision impairment and blindness globally by the World Health Organization (WHO) P] However, automatic segmentation is challenging due to high image heterogeneity. Particularly, retinal structures are changing with age, and some structures could be overlapped or occluded due to retinal lesions [ Besides, imaging artifacts widely exist in retinal images due low contrast, eye movement, and noise, increasing the difficulties of distinguishing fine structures like blood capillaries (2
Conventional supervised models have shown promising performance in automatically recognizing vascular structures and segmenting retinal vessels [-5). However, these models expect manual annotation of retinal vessels, which requires expert ophthalmologists and is labor-intensive, especially for blood capillaries [6. Besides, while automatic vessel segmentation models have shown promising performance in recognizing vascular structures, they struggle distinguish fine structures mixed with lesions or imaging artifacts, leading to discontinuous segmentation that breaks vascular structures. Moreover, supervised models tend be over-dependent on training data when annotations are limited, and thus often deliver poor generalizability in unseen scenarios [7]. Furthermore, although large amounts of unannotated images are readily available, models trained solely with supervised losses often fail to generalize to unseen domains, due to their inherent reliance on labeled data.
"Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Recent Bayesian approaches have shown promising generalizability by imposing statistical priors on medical image segmentation 8 9 These methods built probabilistic graphical models describe the statistical correlation among images, noises, and targets. By statistically modeling local neighboring systems of pixels, they showed impressive ability in capturing compact shapes of organs, such as the heart and prostate. However, they overlooked the morphological characteristics of vascular structures such as retinal arteries, veins, and capillaries. Compared with compact shapes, vascular shapes have a higher surface-to-volle ratio, and the local modeling approaches lacked sensitivity in capturing long-range dependencies between pixels along vascular structures. Few works have focused on learning the long-range morphology of vessels by fitting skeleton priors extracted from ground truth [4], but they lack adaptability for unseen domains. Graphs have proven effective for representing non-Euce Non-Euclidean irregular structures. Recent advances in graph shape analysis showed that retinal vessel structures can be effectively represented by principal graph components, independent of a specific image and its annotation [10] [1]. Hence, it is promising to incorporate image-agnostic retinal graph priors into vessel segmentation for better model generalization.
Motivated by the success of Bayesian image segmentation and graph shape analysis, we propose Bayesian retinal vessel segmentation framework for modeling vascular shapes by imposing retinal graph priors. Specifically, we propose probabilistic graphical model by jointly modeling images, vascular shapes, and the retinal graph atlas. To mitigate the spatial misalignment structure between vascular shapes and the retinal graph atlas, we introduce deformable retinal graph prior from the atlas based on the learnable displacement field between vascular shapes of images and graph priors. To drive structural matching between images and priors, we develop statistical model for the vascular shape, aiming to maximize the geometric similarity between vascular shapes and deformable graph priors. Based variational inference, build deep neural networks solve the probabilistic graphical model and achieve promising generalizability in unseen scenarios, demonstrating the effectiveness of incorporating retinal graph priors in vessel segmentation.
As a summary, our main contributions are: (I) We propose a Bayesian retinal vessel segmenta- tion framework for modeling vascular structures, which overcomes the limitations of conventional Bayesian image segmentation models only focusing on compact shapes; (2) We develop deformable retinal graph priors for matching heterogeneous vessel structures in retinal images, and design statistical model for vascular structures to drive the spatial alignment between image vascular struc- tures and deformable graph priors; and (3) We validate the Bayesian retinal vessel segmentation framework on multiple commonly used datasets, and demonstrate its superior generalizability for unseen scenarios.
2 Related Works
2.1 Retinal Vessel Segmentation
Retinal vessel segmentation has emerged critical tool in healthcare, providing non-invasive biomarkers for cardiovascular risk assessment [ 2). Although deep learning methods, including U-Net variants (e.g., ResU-Net [12], FR-Net (5)), and Transformer-based hybrid frameworks [13] 14], with their symmetric encoder-decoder structure and skip connection [3], have significantly improved segmentation accuracy, several persistent challenges hinder clinical adoption. Specifically, discon- nected vessel predictions and spurious bifurcations can compromise the reliability of diagnostic procedures (2). Moreover, the model's 's robustness limited by factors such as performance degrada- tion under low-contrast conditions, the presence of imaging artifacts, and variability across different devices. Existing graph-based methods [13 | offer partial solution to these issues, which are promising for representing non- -on-Euclidean or irregular structures. However, they lack explicit anatomi- cal constraints, resulting in implausible structures during domain shifts. While Generative Adversarial Networks (GANs) [16] enable the segmentation and reconstruction of blood vessel networks with no human input, they introduce instability during the training process, a problem especially prevalent in pathological cases. To address these issues, we propose variational Bayesian framework, integrating deformable graph priors with displacement field, which offers a principled and effective path toward anatomically consistent and generalizable medical image segmentation.

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Landmart
Probabilistic Graphical Model.
(b) Gcometric similarity and dissimilarity
Figure 1: Overall framework. (a) shows the probabilistic graphical model. White circles denote variables, and dashed white circles denote prunable variables. Specifically, X denotes the observed image, A and S are structur-degraded and structure- structure-prsserved components respectively. Z denotes the probability of foreground, and represents deformable graph determined by linear weights w, displacement field 6, and a set of principal graph components B (agnostic to X). (b) shows the geometric similarity between adjacent vascular segments and the dissimilarity between landmarks and its neighbors.
2.2 Image Decomposition
Image decomposition is widely explored, driven by the assumption that underlying data often lies in low-dimensional subspace [17 29, offering strong potential in medical image analysis. Principal component analysis (PCA) demonstrates that the low-rank components of matrices
its basis elements [8]. Babacan et al. [17 introduced variational Bayesian methods for posterior inference, though their practical adoption has been limited by computational complexity. Recently, deep learning- based image decomposition methods have emerged. Deep image prior (DIP) [19] is introduced to capture essential image statistics from a single observation, enhanced DIP for image denoising 20). and RONet for efficient subspace interpretable learning (21). BayeSeg [22 g addresses the challenges of domain generalization for medical image segmentation, which decomposes radiological images into compact shape and appearance variables. The segmentation process is then modeled locally smooth variable dependent only on shape features through variational Bayesian inference framework. These innovations highlight the Bayesian framework's 's unique capacity to integrate statistical prior knowledge for promising generalizability, a pivotal benefit for retinal vessel segmentation.
2.3 Domain Generalization for Medical Image Segmentation
Domain generalization (DG) aims to train models on one or multiple source domains that robustly generalize unseen target domains (7]. Current DG approaches for vessel segmentation broadly di-
vide into three categories: Data-centric augmentation methods enrich training diversity via synthetic domain shifts [33 24 AADG (23 optimizes data augmentation policies through Sinkhorn distance-
based diversity maximization and reinforcement learning to enhance cross-domain generalization. Meta-learning methods optimize for generalization through episodic training 25 26). Liu et al. [25) address both centralized and federated learning scenarios through shape-aware meta-objectives and frequency-spa -ppcne interpolation to enhance model robustness against domain shifts. Domain-invariant representation methods focus domain-agnosti feature extraction 29 A Hessian based vector field 288 is proposed to model vessel structures as domain-invariant features, achieving superior cross-domale generalization in retinal vessel segmentation. Despite the progress, retinal vascular segmentation faces significant domain shifts due to differences in imaging artifacts, and the morphological characteristics of vascular structures, and existing studies remain underexplored. In particular, the lack of transparency in feature invariance of adversarial and meta-learning methods hinders clinical trust. Domain alignment strategies often fail maintain microvascular continuity low contrast variations.
3 Methodology
In this section, we present our method for generalizable retinal vessel segmentation, which integrates the structural graph prior into segmentation networks through variational Bayesian framework. As

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illustrated in Fig. Ta we first introduce the probabilistic graphical model (PGM) that captures the underlying structure of retinal vessels by matching with the deformable graph prior, followed by a detailed description of the variational inference process that enables us to learn the model parameters and perform segmentation. For convenience, we denote the vectorization of by x, consistent with the notation used elsewhere.
3.1 Deformable Graph Prior Guided Decomposition and Segmentation
Image Decomposition. Artifacts in retinal images could lead to unsatisfactory segmentation deviated from vascular structures. Motivated by the success of image decomposition in disentangling shape information, we decompose an image into a structure-pis preuurree component, S. and structure- degraded counterpart, A. as shown in Fig. Ta The former presents the enhanced vascular structure closer to the ground truth, whereas the latter contains noisy structures degraded by vessel-like artifacts that adversely affect segmentation. Concretely, let X E Rhxx denote grayscale image, we decompose
into a structure- pressevve variable $ and a structure-degraded variable A, i.e., X S A. By assuming A follows Gaussian distribution with mean and inverse variance p. the distribution p(X|S, A) can be expressed as, p(X SS A) = [N m, diag(p)-1) To increase the capacity of in modeling artifacts, m assumed be variable follows Gaussian prior II, and p is assumed to be a variable follows a Gamma prior (plop.
(mmp/ (oh) )
Deformable Graph Prior. Conventional Bayesian approaches directly used manual annotations to guide the learning of anatomical structures [8] They presented promising generalizability in cross-domain segmentation, but are limited to compact anatomy with a low surface-tor voluuuee ratio. To encourage models to accurately capture vascular structures, we propose a deformable graph prior to guide image decomposition and vessel segmentation. Specifically, let A {G1, (GI...... Gx)
denote a graph atlas, where graphs {G, J. have different vertex sets {Vn Vn while sharing consistent vascular structure defined by a common edge E, and B (BI ........ Bx) denote K principle graph components of A. Furthermore, let G w B + 6, where the multiplication and addition operations are applied only for the vertex set of B, then the parametric graph G determines a deformable graph prior, as shown in Fig. la Here, prior N( 0, (o"))- and determines a linear combination. 5 follows another Gaussian prior (6 II) and defines displacement field.
R follows Gaussian
Landmark Detection. In general, adjacent vascular segments exhibit high geometric similarity along the direction of vessels. However, this pattern is disrupted when vessels are branching points, which are referred to landmarks, shown Fig. [b] Detecting these landmarks important since they disobey geometric similarity and reversely affect vascular structure matching between the structure-preet preeserved component S and the deformable graph prior G. To detect landmarks, introduce a variable, D, in Fig. which follows a Gamma prior, G ( 78).
Vessel Segmentation. Let Y E R denote a vessel annotation of X, and Z E R denote the probability of vessel segmentation, where p(Z) follows Beta prior, B(zla (.). Then the distribu- tion 22) determines a supervised loss function for segmentation, such as cross-entropy or Dice loss. However, such pixel-wise loss functions struggle to capture vaseular structures effectively, as they overlook long-range dependencies between pixels along the vessels. Motivated by the advantage image decomposi-
of retinal graphs in preserving vaseular structures, develop structure-presery tion and vessel segmentation guided by the deformable graph prior: Concretely, let H(S: ; Z, G, D) denote energy function that quantifies the quality of vascular structure matching between S and (7, G) based on detected landmarks D, then p(S|Z, G, D) xx exp( (SS;; Z, G, D)} determines a deformable graph prior-guided image decomposition and vessel segmentation. Nevertheless, the definition of (S; Z. G, D) is nontrivial and will be detailed in the following section.
3.2 Statistical Modeling of Vascular Structure
Implicit Neural Representation. The first challenge of defining H(S: Z, G, D) lies in measuring the structural similarity between S and G. However, S is pixel-wise, while the vertex set of G is low-dimensional and sparse, making it difficult to directly define the structural similarity between and G. To tackle the difficulty, we used implicit neural representation to map G to the same space as S. Concretely, let fc(+) denote a graph neural network parameterized by ( to predict the Gaussian parameters of each vertex, then sample Gaussian cloud from fc (G) by Gaussian splatting,

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Decorpooline
Delomtbble graph prike
Pres O
G
Mans Cri
OrgiAlle
Eri
DOS tJ
Psi 0g
Miuatar yroums
O- a- B
Oss
Coppasin
Spoiil olgroen
Segpoendios
Cland farm Sckdkes
1 n. Extting (1- Eoer feal
if's
74
15 min(U.11 Mid Eul Aud
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Figure 2: Network Architecture of GraphSeg. GraphSeg consists of three modules: image decompo- sition (green), vessel segmentation (blue) and deformable graph prior (yellow). During the training stage, the deformable graph prior guides both the decomposition and segmentation processes, In the inference stage, only decomposition and segmentation modules are used.
which not only has the same dimension as S, but also is differentiable. For convenience, the resulting Gaussian cloud is notated s (G). Details are in Appendix A.2.5
Vascular Structure Matching. Retinal vessels present geometric similarity between adjacent vascular segments but dissimilarity between landmarks and their neighbors, shown in Fig. [b] Motivated by this, we unfold S E kxxx to Sunfold E R using sliding window of size where each k x & matrix represents local patch located at the central pixel. Similarly, we can unfold hw- denote the grid points corresponding to the Gaussian cloud 5 as Sh unnfold Let {w: (xz, U/) Ti=0
S, then these points can be partitioned into two groups based on whether they belong to the vertex set of deformable graph G. Concretely, IG (ildeg(v.) 0} denote the indices of nodes with non-zero degree and [ ((,))) denotes the indices of u 's neighbors. Based on all-to-all cosine similarity defined
by C' = Simeos (Snffold, S fold) E 2g huw the dissimilarity from G-to-neighbor can be defined as:
Hazneighhor (S: D)
Σ Σ exp( c...
sEle jEIN(v;)
Here, 2j RJ 1 denotes the i-th pixel with a big probability belongs to vascular foreground. This loss forces learn similar adjacent vascular segments while detect dissimilar landmarks. Similarly, the similarity from G-to- --to-background can be defined as,
hu
HGzbackproundd (S; 2,
Σ jEtG
Σ (1-2)) exp(ds c.j)-
(2)
2=0
Here, (1 (1-2) 24) == 1 denotes the i-th pixel with big probability belongs to vasculr background.
This enforces our model to distinguish between vascular structure and non-vascular background. By combining both, we define energy function by.
H(S: Z, G, D) = HG2neighher (S; Z, D) + Hozbackgrouna( Z. D).
(3)
This aims to keep adjacent local shapes (if not landmarks) similar possible while distinguishing unconnected local shapes. Finally, we have,
p,(S)Z,G, D) exp(- 7, G, D)),
which informs a structure-preserve image decomposition and vessel segmentation, guided by the deformable graph prior.
3.3 Deep Variational Inference
Maximum a posteriori. Let = {s, m. p, 2, d, 6, w) denote the set of variables that need to be inferred, we aim to maximize Pç (V (x) x p(x )pC (V), which however is intractable due to unknown
5

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parameters Ç. To tackle the difficulty, we adopt variational distribution qo (V) to approximate (()xx) and maximize an evidence lower bound (ELBO) as follows,
In (V
C(S, 0; == (X0())
(5)
To V (V)
Since PV( pxx V ( v the above equation be converted to, L(S, 0; x) = Eg (o [In [(x (V())l())))lxx(())
(6)
The first term induces a reconstruction loss,
E [In (s)mm.)))) [Ins(x|s, m, m)]]-
(7)
KL Divergence. Based on the PGM in Fig. the prior p(V) can be expressed as,
Pc (v) (s, m, p; d, w) P. d, 6, w) wyy
(8)
Next, we factorize the variational distribution ( (V/ x) as two distributions corresponding to the set of image-related variables, {s, m. m. and the
cructure-related variables, {z, d, ó, w).
[x)) (s, 0, 2, d. 6, w x) (s, m. g)x))o d, 6, w/s).
(9)
The distribution of the image-related variables can be further factorized as,
qo m, p\x) go () ()) m) m.
(10)
Similarly, the distribution the structure-related variables can be further factorized as, (z(2, d, 8, w w|s) qo (w]s))[(w]ss))) de (ö|s, d, w)ge (z|s, d, w). Based on the above factorization, the second KL divergence term in Eq. (6) can be unfolded as,
(11)
KT,(go (V ()xx))p<(())) = (z [o m, m, ( d, 5, d, w)p(m))(p))
+ (x/(x,)) (g d, 6, w ((ss)lp())p(d))p)))))p
(12)
Closed-form Solutions. Since p follows a Gamma prior, its variational distribution also follows Gamma distribution, i.e., qo(p)x, m, s) G(plop 7p). By minimizing the KL divergence over qe (p|x, x, m, s), we have the following closed-formed solution,
1
Φp. 6
2 Tp =
2 (z; - m.)²
(13)
Similarly, the variational distribution of d follows Gamma distribution, i.e., qo (dls) G(dloa na)- Its distributional parameters can be explicitly computed by,
02 Na. -{ n8 + max (0, Hz, EjETwO,, Cij - (1 11x E Cag) if Ig otherwise
78 m (1 -22 Ejelc Ca.5}
(14)
Here, max min is used to ensure a feasible Gamma distribution, and 8,, mi, رi,j denotes obtained samples by Markov Chain Monte Carlo (MCMC) sampling.
Learnable Variational Posteriors. Given (p|x, m, s) ((poo 7p) and go (d|s) G(d 7a). the variational distributions of other variables can be learned by minimizing.
L(C, 0, d) (V1x)) |- In [) + (go ()))p((())))
C0; p) L. (0) + (0, d) + C.) + +w)
(15)
image-related
structure-related
Please refer to Appendix
A.2 for the detailed formulation of this section.
Network Architecture. We implement the variational inference framework with deep neural net- works, as shown in Fig. 2 GraphSeg consists of three modules: image decomposition, deformable graph prior, and vessel segmentation. For the decomposition module, we employ two separate residual networks (30), denoted as /A and fs, to infer the structure-degraded component m and the structure- preserved representation of the input image x. Both m and modeled as samples drawn from

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Gaussian distributions, enabling a probabilistic interpretation of the decomposed features. For the deformable graph prior module, we first utilize convolutional neural network fw infer the latent principal component coefficients w from the input vascular structure representation s. The misaligned graph template is then reconstructed as w B, and refined by a graph neural network (GNN) sa to predict a displacement field 8 ~ N (Hs, ag). This results in deformable graph topology G. For the segmentation module, a second graph neural network fc is used to predict the local scale parameters of each node G, producing the final graph-based vascular structure 5 through Gaussian splatting. This result is correlated with the decomposed structure S for downstream segmentation. A third U-Net decoder is used to infer the final segmentation map z, which is modeled as a sample from a Beta distribution, (zz Se). After that, the unsupervised energy loss, Lg (0, S: d), is computed based on the consistency among the predicted segmentation z, the graph-based structure S the decomposed structure S, and the landmark d. as formulated in Eq. (3) where d is obtained through closed form as Eq. (14). Finally, we combine the Dice loss with the unsupervised loss in Eq. (T3 by L(S, x. p. d) Diice (0; y) for training neural networks.
4
Experiments
To assess the performance and generalization capability of GraphSeg, we train it on single dataset and evaluate it across all other datasets to measure its generalization effectiveness.
4.1 Setup
Datasets and Metrics. We employ four widely recognized datasets: CHASE 31, HRF 32, DRIVE [33. and STARE [34]. For evaluation, we mainly employ the Accuracy (Acc), F1, Soft Dice, Sensitivity, and Specificity evaluate the segmentation performance. Acc, FI, and Soft Dice are used to measure the overall segmentation performance, while Sensitivity and Specificity are used to measure the performance of vascular foreground and non-vascular background, respectively.
Compared Approaches. We mainly compare GraphSeg with the following representative methods: (1) previous ofatc-of-the-art vessel segmentation models. including FR-Net [5] and FSG-Net [II];
(2) widely adopted architectures for medical image segmentation, such as U-Net 35), AttUNet 36
AGNet (37. ConyUNeXt (38) DCSAU-Net [39]. R2UNet 40), and SAUNet 41 (3) strong and generalizable baseline, BayeSeg [ and (4) Skelcon 4 which attempts introduce the skeleton structural prior into retinal vessel segmentation. To ensure a fair comparison in generalization ability, both U-Net and BayeSeg are re-implemented with the same segmentation backbone used in GraphSeg to eliminate architecture-induce
bias. The graph construction follows Bal et al. [42). Graph Atlas is obtained by performing their code on the training set of CHASE, More implementation details can be found in the Appendix B
4.2 Experimental Results
We first compare GraphSeg with state-of-the-ar methods in terms of accuracy, sensitivity, specificity, Fl score, and Soft Dice. To evaluate cross-domain generalization, the models trained on one dataset and tested on the others. Finally, we conduct an ablation study to quantify the contribution of each component within GraphSeg.
4.2.1 Comparison with Previous Models
To evaluate the effectiveness of GraphSeg on retinal vessel segmentation, we first compare our Graph- Seg with previous models by training and testing on the same dataset. As shown in Table [ under the same segmentation backbone, both BayeSeg and GraphSeg outperform U-Net across all datasets, highlighting the effectiveness of the variational decomposition in improving vascular segmentation. Furthermore, GraphSeg consistently surpasses BayeSeg, especially on structure-sensitive metrics such as Soft Dice and F1 score, demonstrating the additional benefit of incorporating a graph-based structural prior. Compared with other state-of-the-as methods (e.g., FR-Net, FSG-Net, Skelton), GraphSeg achieves competitive or superior results, confirming that our framework is comparable to specialized architectures while offering stronger anatomical consistency and generalization potential. Without loss of generality, any other models, including the FR-Net and FSG-Net, can be integrated into GraphSeg framework for graph prior injection.
7

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Table 1: Performance comparison of different methods across CHASE, DRIVE, and HRF datasets. The best results per dataset are in bold. Note that U-Net, BayeSeg, and GraphSeg used the same segmentation backbone.
Dataset
Method
Accuracy
Soft Dice
F1
Sensitivity
Specificity
Skelton
95.61
80.71
78.95
78.17
97.94
FR-Net
97.26
80.10 10
79.10
84.74
97.65
FSG-Net
97.52
81.34
81.02
86.00
98.26
CHASE
U-Net
95.17
79.74
78.39
81.97
96.79
BayeSeg
95.45
80.48
79.62
82.93
96.99
GraphSeg
96.54
82.91
81.82
87.84
97.40
Skelton
94.61
81.50
80.39
83.23
98.59
FR-Net
97.01
83.91
82.99
83.86
98.15
FSG-Net
97.04
84.19
83.23
84.21
98.30
DRIVE
U-Net
90.89
61.09
61.09
48.55
98.51
BayeSeg
94.48
79.08
78.56
77.60
97.06
GraphSeg
96.13
85.23
84.82
83.02
98.15
Skelton
95.90
79.87
78.59
78.53
98.86
FR-Net
97.01
81.92
80.70
81.67
98.42
FSG-Net
97.10
82.51
81.57
83.61
98.99
HRF
U-Net 89.79
71.37
67.76
78.15
91.74
BayeSeg
95.35
81.77
81.05
75.44
98.42
GraphSeg
95.88
84.29
83.89
81.58
98.07
4.2.2 Cross-domain Generalization
Cross-dataset Generalizability. To assess the generalizability of GraphSeg, perform cross- dataset evaluations by training the model on the CHASE dataset and testing it on three unseen datasets: DRIVE, HRF and STARE. As shown in Table we compare against ten strong baselines. To ensure a fair comparison, U-Net, BayeSeg, and GraphSeg are trained with the same data augmentation and implemented with the from training protocols or model capacity. In particular, U-Net is trained and tested on each dataset independently, serving an in-domain reference. BayeSeg and GraphSeg are trained on CHASE and evaluated on all test sets to assess their cross-domain performance.
segmentation backbone, eliminating potential confounding factors
Across domains, BayeSeg and GraphSeg consistently outperform others in Soft Dice, demonstrating the advantage of image decomposition in improving robustness under distribution shift. Notably, GraphSeg outperforms the second best by 7.43 in Soft Dice and 6.46 in Fl Score the HRF dataset, where the background more complex and noisy, highlighting the importance of incorporating graph structure prior cross-domain generalization. Compared with the in-domain results in Table [ although BayeSeg and GraphSeg present significant performance drops due the low-resolution nature of DRIVE, which raises difficulties in decomposing vascular structures, GraphSeg still performs much better on DRIVE, demonstrating the effectiveness statistical modeling of vsacular structures.
Generalizability on Cross-dataset Graph Prior. also use the graph prior from the CHASE to train GraphSeg the DRIVE dataset, shown in Table The results are summarized as follows: (1) GraphSeg (trained) outperforms U-Net (trained) due the graph prior extracted from one dataset can be transferred to the other dataset. (2) GraphSeg outperforms U-Net (trained) on most metrics, which confirms the generalizability of GraphSeg and demonstrates the robustness of our framework with respect to graph priors.
graph prior, which demonstrates that
4.3 Ablation Study
To evaluate the impact of the graph prior and the image decomposition module, we conduct an ablation study by training the models on the CHASE dataset and testing them on the DRIVE dataset. Both the two modules contribute positively to the generalization performance shown in Table 4

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Table 2: Cross-dataset evaluation: Models trained CHASE and evaluated other datasets. U-Net is trained and tested on each dataset as strong baseline.
Dataset
Model
Ace
Soft Dice
F1
Sensitivity
Specificity
U-Net
95.17
79.74
78.39
81.97
96.79
FSGNet
97.52
81.34
81.02
86.00
98.26
FRNet
97.26
80.10
79.10
84.74
97.65
AtUUNet
97.54
66.02
77.06
78.92
98.56
AGNet
97.44
76.25
77.58
85.14
98.13
CHASE (train)
ConyUNeXt
97.21
72.40
73.93
75.97
98.39
DCSAU-net
97.17
74.33
74.68
79.87
98.12
R2UNet
96.96
67.99
71.73
74.60
98.20
SAUNet
97.47
76.17
77.23
82.02
98.33
BayeSeg
95.45
80.48
79.62
82.93
96.99
GraphSeg
96.54
82.91
81.82
87.84
97.40
U-Net (trained)
90.89
61.09
61.09
48.55
98.51
FSGNet
95.62
57.51
57.56
44.39
99.46
FRNet
96.65
71.33
73.57
67.53
98.85
AttUNet
95.07
45.27
50.22
38.75
99.30
AGNet
96.25
69.46
70.59
55.21
98.59
DRIVE
ConvUNeXt
97.07
61.91
63.77
74.35
97.92
DCSAU-net
95.30
62.30
62.56
56.82
98.19
R2UNet
95.01
63.86
67.02
70.14
96.60
SAUNet
96.46
69.78
70.67
61.92
99.06
BayeSeg
92.34
71.68
70.71
61.85
97.87
GraphSeg
93.56
77.16
76.01
68.09
98.19
U-Net (trained)
89.79
71.37
67.76
78.15
91.74
FSGNet
95.90
68.26
68.56
71.50
98.28
FRNct
97.00
64.99
67.56
69.78
97.28
AtUNet
97.37
54.20
65.29
66.41
97.94
AGNet
96.70
63.03
64.54
66.69
97.10
HRF
ConyUNeXt
96.52
59.74
60.04
63.58
99.07
DCSAU-net
96.63
61.70
62.09
68.56
97.30
R2UNet
94.21
49.07
52.03
88.87
94.40
SAUNet
97.15
65.87
67.17
83.92
97.65
BayeSeg
92.05
70.73
70.13
67.71
96.13
GraphSeg
93.38
78.16
76.59
78.90
96.88
U-Net (trained)
90.98
60.81
59.66
55.71
95.95
FSGNet
96.15
54.08
54.23
45.43
99.33
FRNet 93.04
64.91
67.07
62.39
98.96
AttUNet
95.71
37.91
41.97
34.39
99.54
AGNet 96.52
67.49
68.82
66.74
98.47
STARE
ConvUNeX:
95.97
52.65
53.30
46.89
98.96
DCSAU-net
94.77
47.59
47.83
45.65
97.75
R2UNet
95.53
49.90
50.86
50.63
98.22
SAUNet
96.87
61.50
62.23
56.44
99.29
BayeSeg
92.85
67.82
66.82
59.78
97.65
GraphSeg
93.65
72.76
71.43
68.72
97.69
Introducing the decomposition module alone brings consistent improvements across metries, particularly in sensitivity and Dice score, indicating enhanced structural representation. When the graph prior additionally incorporated, the model achieves the best performance, demonstrating the complementary role of topological constraints in further improving generalization to unseen data.

---

Table Evaluation of model generalizability on the cross-dataset graph prior
Dataset
Model
Acc
Soft Dice
Fl
Sensitivity
Specificity
GraphSeg (trained)
96. 13
85.23
84.82
83.02
98.15
DRIVE (train)
U-Net (trained)
90.89
61.09
61.09
48.55
98.51
GraphSeg
95.02
82.56
79.37
89.70
95.69
CHASE
U-Net (trained)
95.17
79.74
78.39
81.97
96.79
GraphSeg (trained)
96.54
82.91
81.82
87.84
97.40
GraphSeg
93.91
78.20
77.25
78.40
96.34
HRF
U-Net(trained)
89.79
71.37
67.76
78.15
91.74
(raihSeggtrained) 95.88
84.29
83.89
81.58
98.07
Table 4: Ablation on the effect of graph prior and image decomposition to generalizability.
Decomposition Graph prior
Accuracy
Soft Dice
F1
Sensitivity
Specificity
90.75
66.56
64.07
55.04
97.19
92.34
71.68
70.71
61.85
97.87
93.56
77.16
76.01
68.09
98.19
Discussion
Why does GraphSeg work? The success of GraphSeg can be attributed to its unique integration of graph structure prior and image decomposition, which is modeled with energy function as Eq. The graph structure prior effectively captures the anatomical coherence of vascular trees, allowing the model to leverage both local connectivity and global shape constraints. This enables GraphSeg to achieve high-quality segmentation even challenging scenarios, like complex noisy backgrounds. The image decomposition module further enhances this by disentangling the structure- preserved component from artifacts, leading to improved segmentation accuracy. Moreover, the introduction of an unsupervised energy function in Eq. (3) enables natural extension of GraphSeg to semi-supervised learning settings, which are both practical and significant in real-world medical applications. We leave this direction promising future work.
How does GraphSeg generalize? The generalizability of GraphSeg stems from two key factors: (1) the use of graph structure prior that captures the underlying anatomy of retinal vessels, allowing the model learn robust representations that are less sensitive domain shifts; (2) the incorporation of variational Bayesian framework that enables the model adaptively learn stochastic intermediate samples from variational distributions, enhancing its ability to generalize to unseen domains. This combination allows GraphSeg maintain high performance across different datasets.
6 Conclusion
In this work, proposed GraphSeg, variational Bayesian segmentation framework that integrates a deformable graph prior to anatomically consistent retinal vessel segmentation. By jointly modeling image decomposition and graph-aligned structural inference, GraphSeg captures both local connectiv- ity and global vascular topology. Extensive experiments across CHASE, DRIVE, HRF, and STARE datasets demonstrate state-of-the-ard accuracy and strong cross-domain generalization. our method consistently outperforms prior work in structure-sensitive metrics such as Soft Dice and F1, especially in challenging domains like HRF. Ablation studies further confirm the complemen- tary roles of the graph prior and image decomposition. Overall, GraphSeg provides principled and generalizable approach for structure-ane aware medical image segmentation. Limitation: While GraphSeg demonstrates strong performance and cross- cross-domain generalization, its current formulation requires pre-processing step to extract skeletons and construct graphs from segmentation masks. This dependency may introduce slight variations due to heuristic rules (e.g., junction merging, branch pruning), and future work could explore end-to-end learnable graph extraction to reduce reliance on hand-crafted morphological pipelines.
particular,
10

---

Acknowledgments and Disclosure of Funding
This work was supported by the National Natural Science Foundation of China (61971 142,, 142, 62111530195 and 6201 1540404), the development fund for Shanghai talents (2020015), and the Shanghai Municipal Education Commission-Artinn Intelligence Initiative to Promote Research Paradigm Reform and Empower Disciplinary Advancement Plan (grant no. 24KXZNA13).
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14

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A Method Details
A.1 Graph Construction and Shape PCA
The graph construction and shape PCA are conducted on the training set of CHASE dataset in this work. Given the segmentation masks, we construct graph-based representation our graph structural prior. Following Bal et al. [4] and Luo et al. [43, The process involves the following steps: (I) Skeletonization: We apply morphological thinning to obtain I-pixel-wide vessel skeleton, which preserves the topological structure while discarding width information. (2) Graph Construc- tion: Nodes are extracted by identifying endpoints and bifurcations on the skeleton based on pixel connectivity. Edges are defined as pixel chains connecting node pairs, resulting in an undirected graph represented by an adjacency matrix. (3) Graph Refinement: To address artifacts such as node fragmentation and false intersections, we apply topological corrections by merging closely located nodes and pruning spurious connections based on angular continuity. (4) Graph Registration: Each graph is aligned to a common mean template using factorized graph matching [44). Both node similarity (Euclidean distance) and edge similarity (shape distance computed via Square Root Velocity Functions, SRVFs 45) are considered. (5) Shooting Vector Computation: The deformation from the mean graph G₁, to each registered graph Gž is encoded as a shooting vector 8Vg- G - (6) Feature Vector Construction: We concatenate the shooting vector and node coordinate differences into a digh-dimensional vector stt to capture both topological and geometric variability. (7) Principal Component Analysis. PCA is applied to the set [s= The resulting PCA coefficients characterize structural variation and are used in GraphSeg.
]= to obtain compact shape representation.
A.2 Deep Variational Inference Details
A.2.1 Derivation of Variational Inference
Let V = {s, m, p. d. 8, w) denote the set of variables that need to be inferred, aim to maximize ( x) x p(x W))((V) V). We adopt a variational distribution go (
(V [x) to approximate (V)x). As
result, this can be optimized by maximizing an evidence lower bound (ELBO) as follows,
Pc (V x) [(S xxx) = (v/p) In
(16)
4a V xx)
Since (V, = p(x ( ) the above equation can be converted to L(S, x) (x [In p(x KT (V (V)x))l)))))
(17)
where the first term induces reconstruction loss:
Ex-ge [In p [)) E (x.mm.)))))) [[x|s, m, p)]
(18)
Based on the PGM as shown in Fig. la the prior p(v) can be expressed as:
Pe (v) = (s, m, P. 6, w) = p, d, 8, w wipmmm/po(llppeehppppppppppppppp
(19)
Variational Distributions. The variational distribution go (V) x)) can be factorized as two distributions corresponding to the set of image-related variables, (s, m, p}. and the set structure-related variables, {z, d, d, w).
go [1/) = (s, m, p, z, d, w w/x) = qo (s, m, pl d, 6, w/s).
(20)
The distribution of the image-related variables can be further factorized by,
( m, p\x) (m (s)x m () s).
(21)
That is we first estimate the mean m of a and then infer the vascular shape, s, from x, m, and finally infer the inverse variance p from x, m, s. Similarly, the distribution of the structure-related variables can be further factorized by,
go (2, d, 6, w/s) = go (d|s (z, ö, w|s
(22)
= go go) w|s, d)go(z|s,
(23)
go (dls) (wls, d d) d, (2), d, w).
(24)
15

---

That is we detect landmarks, d, from the vascular shape estimate the linear weights w which determines vascular template w" B, infer displacement field between the vascular shape and template, and predict the segmentation z from the shape, landmark, and estimated graph w B + 8.
Based the above factorizations, the second KI. divergence term in can be unfolded as,
KL (M (V())llp<(V) (.)( [g m, plx) w w)p(m))(e)) [L d, 6, w/s) (ws))ppe)))((d)))))mm)))))
(25)
+ E (six,m)
(26)
A.2.2
Closed-form Solution of
Given other variables, go go(o|x x, m, = ps 7p) can be inferred by minimizing,
C(op: 7pp) =E |- (x m, p)] (g0 m, s)[lp(p)]] C
(27)
= (pp/..mm.ss))) (B px m, p)] Cl
[In ( m, s)] Eg (plx.m.s) [mn)(p)
(28)
(29)
The minimum is achieved when
In qo (p) x, m, = In ppp) + (o( [inp(x|s, m. p)] +
(30)
hww-1
110p - 1) p: -6pn)
(31)
1=
[In Pi (xx - (0-mm))2pp +C
(32)
hww-1
1 IIn pi - (7% + lz - 8 ppl +
[(6 p 2
(33)
Here, we use Markov Chain Monte Carlo (MCMC) sampling in (3) to approximate the expectation in 33 Since (p(p), m. s) ppl Tp). we finally have
1 pp. 08 +
Tp. 2/
2 (x:
8:
-m;)?.
(34)
2
A.2.3 Closed-form Solution of
Given other variables, go (dlss = G(dl n1) can be inferred by minimizing,
L(da, 7a) = E In c, 6, w)] + [K (dls) + C
(35)
= (dlss)s) In [c[ss] (d|s) [Inp(d) + (vra [impe(s d, (w)
+C]
(36)
The minimum achieved when In (dlss) In p(d) + (
w)] C
(37)
hw-1
Inp(d)) + Σ Σ
Pa. expt -., +
Σ
(1 - -a.) exp(d 2 + C
iElo JEIN(VE)
jela i=0
(38)
hw
=
[109 - 1) In - -dd4
(39)
kw-1 (1 (22) exp(d; (r C, (40)
Ma, expl -d, Eng) + velo jEIN(wE)
jEla
1=0
where Ms. 022 (a,,, 3.). and we approximate the expectation the right-hand of 37 by the MCMC sampling in (38). Furthermore, since exx + Az + O(22), we have exp( Eig R3
16

---

1 - di Caty and exp(d; C.,t 2 1 + d, Et.. As result, we can convert the above formula to.
(ngo(d|s))
Σ
[0] - 1) - -(1a + Ma; EjETNON Cnd - (1 - -2s)) Ejero ais) di
(41)
iEla
+
Σ
(00g 1) d, - (7å (1 -M2) Ejeto Ass d.) +C.
(42)
Thus, the parameters of qo (d|s) G(dloa na) can be explicitly expressed as,
7a
+ max Ma, EjETwOn GiS (1 M2.) Ejero and if la otherwise
04. = 0g. 7d
min (1 M2,)) Ejele Cz.}
(43)
Here, max min is used to ensure a feasible Gamma distribution.
A.2.4
Unsupervised Loss Details
In Eq. 15 the unsupervised loss consists of image-related parts and structure-related parts. To be specific, we describe the terms as follows:
(0;xx,)) Fyp( [-1np(x|ss m, p)]
(44)
[- Inx m,
(45)
hw-1
Eyo (mlx))))a)
Pallor - (0 -mm) +C
(46)
1=0
|0
mll milasagima) + C,
(47)
where Up:
dp. Tpc
denotes the mean of pt- Suppose yo(m) NM diag(o?))) then
f. (
Eg (m/xx) [KI ( (m|xx [p(m))]
(48)
Egg (m//x) [ln go (m|x)) + E (m |- Imp(m)]
(49)
2 on fmlm
p 112 マ 11 1, 1z In, +C
(50)
Suppose (s)x), m) = (sss diag(o?)), then
(o (: d) (.w() ( m) (slz, d. 8, w))]
(51)
(s)xx,m [ln (s)xx, m)] + E Eg (s x, 62.d), |- In (s w]]
d, hw-1
(52)
hw--1
Σ Σ
Uz. -M. +
Σ Σ (1 (1-M2.) Mz.) Ma, (Cr,) )
In o + C,
icla jEIN(e.)
jelc
(53)
where, Ma, (t) = (1 - (for t < Ya,)) denotes the moment-generrating function of d,. In practical implementation, we need to clip &. and ensure it satisfy -%d, +e S Cis S nd, E. Suppose (z|s, d, 5, w) = B(zla,, 32). then
(0)
(x)s..... [K (z|s, 8, w) w))))(
(54)
go (x)( [In
d, 8, w)] (
(55)
hw-1
T((z)) + (az, - a,) + (3z. - 33)((()))
(56)
I(az, + +B,))
hw-1
[[o2 0 + 380 az., - B2,)bbaz., + Bzi) +C.
(57)
17

---

Here, r(-) and (-) denote Gamma and Digamma functions, respectively. Suppose (o w)
(8 diag( ) then
(x(0) = E (d)s,,d
[g d, w)llp()))
(58)
= E yo (.)a.d..w))
[In (6 d, w)] I8 (. (-1p((())
(59)
1
2 o8 Holl
[ of) (1. +
+C..
(60)
2
Finally, suppose go s. d) -N(ww ding(o (2)) then
(0) = En (wis,d) [g ( (w/s, d)]lp(w))]
(61)
= Eg (w)s.d) [In (W/sws d)) + E (w|s,d) [- Inp(w))
(62)
1 o Mew 1l2 + 1
1o (1, +
(63)
A.2.5 Gaussian Splatting for Implicit Neural Representation
In this work, we sample 20 points on each edge and denote the entire graph with these points (including the sampled points and the nodes) as new nodes (v) and their connections new edges
(e). Then we input the new graph G(V, E) into a Graph Neural Network to predict the parameters for Gaussian splatting, including the (a, 6, and s), where the feature of each node its coordinates
46 Note that the symbol definition is only used in this section for implicit neural representation explanation.
For the Gaussian splatting process, given a set of input nodes [v: where each node associated with Gaussian parameters (a;, 02; 8,), the splatted field value spatial location R2 is defined as:
N Σ
(u)
8: ((
v., E;)
where (uu Vi, E,) denotes 2D anisotropic Gaussian:
(a) v.)
((u v., E.)
2x E,
1/2
exp
The covariance matrix Σ, is constructed from the scale or and orientation 0; as:
Σ; = R(O.) o
coo 0 sin 0 sin Og
R(O.) with R(O,)
cos 0
where e < of a small constant to ensure anisotropy.
For each pixel in the image grid, calculate the splatted field SG
A.2.6 Hyper- paramees
For Gaussian distributions ( ow) and N ((14s, a5). we set the prior distribution to be (o 1). For (mm, Jm). set the prior distribution to be (0, 0.5) for the first 200 epochs for easier extraction of shape component, and then set it to be A ((, 1) for better decomposition of images. For the Gamma distributions,
set the prior distribution of G( Tip be G(2. 10 6) and G( 7a) to be ((2, 10-4). ). For the Beta distribution, The sliding window size for unfolding is & = For all losses used, we summed all items and divided them by hw.
set the prior distribution of B(a,, 82) to be B(2, 2).
B Experimental Details
B.1 Evaluation Metrics
The evaluation metries used in this paper are defined as follows:
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Table Cross-datase evaluation: GraphSeg and BayeSeg are trained on CHASE and evaluated on CHASE, DRIVE, and HRF. U-Net is trained and tested on each dataset as strong baseline. Numbers in parentheses indicate the performance drop relative to the results in Table T
Note that the same
segmentation backbone was used for fair comparisons.
Test Set
Method
Accuracy
Soft Dice
F1
Sensitivity
Specificity
U-Net (train)
95.17
79.74
78.39
81.97
96.79
CHASE
BayeSeg (train)
95.45
80.48
79.62
82,93
96.99
GraphSeg (train)
96.54
82.91
81.82
87.84
97.40
U-Net (train)
90.89
61.09
61.09
48.55
98.51
DRIVE
BayeSeg
92.34 (22.14))
71.68 (U7.40)
70.71 (L7.85)
61.85 (115.75)
97.87 (J0.81)
GraphSeg
93.56 (12.57)
77.16 (U8.07)
76.01 (18.81)
68.09 (114.93)
98.19 (J0.04)
U-Net (train)
89.79
71.37
67.76
78.15
91.74
HRF
BayeSeg
92.05 (L3.30) 30)
70.73 (.04)
70.13 (U10.92)
67.71 (J7.73)
96.13 (J2.29)
GraphSeg
93.38 (12.50)
78.16 (16.13)
76.59 (L7.30)
78.90 (12.68)
96.88 (11.19)
TP-TN Accuracy TPTTN FPIEN
2TP F1 2/T++P++FN
SoftDiee 2E, tiditt E E.
TP Sensitivity TP+FN-
TN Specificity = TN+FP.
where TP, TN, FP, and FN denote true positive, true negative, false positive, and false negative pixels, respectively. y and denote the ground truth and prediction.
B.2 Implementation details
We implement our method using PyTorch and train it on cluster with NVIDIA A800 GPU. The batch size is set to 4, and the learning rate is set to 0.001. We use the Adam optimizer with a weight decay of 1e-5. The model trained for 500 epochs, and we use early stopping based on the validation loss. The input images are resized to 256x256 pixels, and data augmentation techniques such as random rotation, and flipping are applied during training. For the image decomposition, we adopted the two ResNets with ten layers, and for the segmentation network, we used the efficient U-Net [35] For the matching process, we use two two-layer graph convolutional networks (GCN) 47 with 64 channels and three-layer convolutional network (CNN). We follow the training, validation and test data splitting in [II].
B.3 Dataset Details
We employ four widely recognized datasets: CHASE 31, HRF 32 DRIVE 33 and STARE 34
CHASE contains 28 color retina images with size of 999 960 pixels. The HRF dataset consists of 45 color retina images with a size of 3504x2336 pixels. The DRIVE dataset contains 40 color retina images with size of 565 pixels. The STARE dataset consists of 20 color retina images with size of 700x605 pixels. In this work, we use the training set one dataset and the test set of the other datasets evaluate the generalization performance of method. We also resize the images to the resolution of 256 x 256 pixels for training and testing.
C Additional Results
C.1
Cross-domain Performance Drop
We also provide the cross-dataset relative performance drops of SOTA methods in table. 5 The noticeable performance drops demonstrates that there still considerable room for improving the generalizability of current segmentation models.
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Table 6: Computational cost comparison.
Model
Parameters (M)
GFLOPs
Inference Time (8)
Memory (MB)
FSGNet
18.32
89,59
6.23
925.42
FRNet
7.38
55.19
4.67
374.65
AtUUNet
34.88
66.54
2.08
269.88 80
AGNet
9.33
16.73
5.99
330.72
ConvUNeXt
3,51
7.18
2.82
160.07
DCSAU-net
2.60
6.72
6,45
180.37
R2UNet
39.09
152.71
3.20
323.44
SAUNet
0.48
2.33
1.59
37.66
BayeSeg
19.32
88.82
7.95
144.50
GraphSeg
19.32
88.82
7.78
145.95
C.2 Computational Complexity
We provide the computational cost comparison as follows. The computational costs are comparable for GraphSeg other methods. In the inference stage, only need run the Decomposition (green Figure 2) and Segmentation (blue in Figure 2 parts. Therefore, the computational costs are comparable. Besides, without the deformable graph prior, GraphSeg is downgraded BayeSeg, thus the computational costs are almost the same for GraphSeg and BayeSeg for inference. We trained GraphSeg for 2.8 hours GTX 4090. Since each method different training settings, is directly comparable. Therefore, we focus on inference metrics, which are more relevant for practice as shown in Table. 6
C.3 Results on Different Resolutions
Table 7: Comparison of GraphSeg performance with different image resolutions (128 128 vs.
256 256 nodes) various datasets.
Dataset
Resolution
Acc
Soft Dice
Sens
Spec
128
95.79
83.00
81.52
87.35
97.19
CHASE
256
96.54
82.91
81.82
87.84
97.40
128
95.19
84.00
83.50
80.45
97.88
DRIVE
256
96.13
85.23
84.82
83.02
98.15
128
95,42
83.74
82.90
80.12
98.02
HRF
256
95.88
84.29
83.89
81.58
98.07
We compare GraphSeg performance using two different image resolutions: 128x 128 and 256 256. As shown in Table 7 increasing the image resolution generally improves segmentation quality across all datasets. In particular, the 256x pixel setting leads to consistent gains in accuracy and structure-sensinee the most, with Dice increasing from 84.00 85,23 and F1 from 83.50 to 84.82. This suggests that higher-resolution images provide finer structural representation, enabling better modeling of small vessels and complex bifurcations. While the improvements are modest on CHASE, they remain stable, indicating the robustness of GraphSeg to image resolution.
metrics such as Dice and F1 on DRIVE and HRF. Notably. DRIVE benefits
C.4
Visual Results
C.4.1
Segmentation Results
We also present cross-domain visual results segmentation to further demonstrate the generalization ability of GraphSeg. As shown in the visualizations, despite the significant structural variations across different datasets, GraphSeg consistently produces accurate and coherent vessel segmentation, highlighting its strong generalizability.
20

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Data
CHASE
DRIVE
HRF
Image
Model trained on CHASE
Model trained on DRIVE
Model trained HRF
Gold Standard
Cross-domain segmentation results from GraphSeg. Each column shows one dataset, while each row compares predictions from models trained on different domains.
Figure 3:
C.4.2 Decomposition Results
We further provide three groups of visual decomposition results in Fig. to illustrate the effectiveness of our graph prior and image decomposition framework. To assess the gross-domain generalizability of GraphSeg, we additionally present cross cross-dataset visualizations in Fig. Fig. As shown in these figures, input images are consistently decomposed into structure-preservedd component (s) and structure-degraeed component (m.) The segmentation is performed solely on the structure-preserved component 8, which maintains consistent style across different domains. This domain-invarian representation largely explains the strong generalization capability of GraphSeg.
21

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Image
Figure 4: Visualization of image decomposition on CHASE dataset. Each row shows the input, structure-degren degraded component (m), structure structure-preservee preserved component (s), and learned mask (2).
Image
m
Figure 5: Cross dataset visualization of image decomposition on HRF dataset. GraphSeg trained on CHASE dataset and tested on the other dataset. Each row shows the input, structure-degraded component (m.) structure-preserved component (s), and learned mask (z).
C.4.3 Sampled Vascular Structure for Training
We also provide illustrative examples in Fig. 7 to further explain the generalizability of GraphSeg. The sampled mructure-preserver components (8) during training often contain substantial noise due to MCMC, which implicitly serves as form of data augmentation. A model that can accurately segment
22

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Image
Figure 6: Cross dataset visualization of image decomposition on DRIVE dataset. GraphSeg is trained on CHASE dataset and tested on the other dataset. Each row shows the input, structure-degraded component (m), structure- structure-preserved component (s), and learned mask (2).
the target structures from such noisy backgrounds demonstrates strong robustness and generalization capability.
Figure 7: Sampled used for training.
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Reviews:
[{"review_id": "jUyn9iUDfK", "reviewer": "Reviewer_Qe69", "summary": "The paper presents a learning-based Bayesian retinal vessel segmentation method to address classical Bayesian image segmentation models focusing on compact shapes. By proposing a deformable retinal graph prior, the proposed method can match heterogeneous vascular structures and achieve spatial alignment between the vessel branches and deformable graph priors. The Proposed method has been demonstrated on three retinal vessel datasets. While the results of the comparison study for each dataset show comparable performance between the proposed method and the baseline models, the generalization test results of the proposed method show superior performance over the baseline models.", "questions": "Please refer to the above weaknesses.\n\n- It is uncertain whether the proposed method shows state-of-the-art performance when comparing the model to recent vessel segmentation methods.\n- Please provide the computational cost comparison.\n- Please perform a statistical test to see whether the performance of the proposed method is statistically different from the baseline models.", "limitations": "yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "### Strengths\n- The proposed method handles one of the challenging problems of vessel segmentation in matching heterogeneous vessel structures.\n- The proposed deformable graph prior effectively guides the image decomposition and the vessel segmentation through a variational Bayesian framework.\n- The proposed method shows high generalizability performance when evaluating the model on different datasets from the training dataset.\n\n### Weaknesses\n- While there are many learning-based vessel segmentation methods that have been presented [1, 2, 3] recently and showed high generalization performance, the paper compares the proposed method to only three methods. \n- The proposed method requires a higher computational cost to perform vascular structure matching in the inference stage, compared to the methods that only use neural networks.\n- The performance improvement of the proposed method in the generalizability study is quite marginal.\n\n[1] Li, Yang, et al. \"Diffusion probabilistic learning with gate-fusion transformer and edge-frequency attention for retinal vessel segmentation.\" IEEE Transactions on Instrumentation and Measurement (2024).\n\n[2] Kim, Boah, et al. \"C-DARL: Contrastive diffusion adversarial representation learning for label-free blood vessel segmentation.\" Medical Image Analysis 91 (2024): 103022.\n\n[3] Liu, Jianhua, et al. \"HRD-Net: High resolution segmentation network with adaptive learning ability of retinal vessel features.\" Computers in Biology and Medicine 173 (2024): 108295.", "was_revised": true, "final_justification": "After reviewing the authors' rebuttal and the other reviewers' comments, I've increased my rating. The authors have addressed most of my concerns. The proposed method has been compared with recent self-supervised-learning-based methods and still showed superior performance to the existing methods. While the proposed method takes slightly longer time than the baseline models in the inference stage, the proposed method shows statistically higher performance, which would be helpful in vessel segmentation in real clinical practice.", "rebuttal": "Thank you for your comments! All your concerns have been carefully addressed as below. The manuscript will be carefully revised accordingly. We sincerely hope our responses fully address your questions.\n\n>> Q1. It is uncertain whether the proposed method shows state-of-the-art performance when comparing the model to recent vessel segmentation methods.\n\nA1. Thanks for your suggestion. Following your suggestion, we compare GraphSeg with additional seven methods, including AttUNet [6], AGNet [7], ConvUNeXt [2], DCSAU-Net [3], R2UNet [4], SAUNet [8], and CDARL [9]. FRSGNet[1] is current SOTA for retinal vessel segmentation. We tried to compare with the suggested methods. However, the code for HRD-Net is not available, and the code for DPL-GTF-EFA cannot be executed properly. Finally, we provide two experimental results of CDARL. One was tested using the official checkpoint, the other was reproduced on CHASE.\n\nGraphSeg outperforms other methods in model generalization studies (on DRIVE and HRF), especially for F1 and Soft Dice. *For other methods, since the F1 scores and soft Dice scores are significantly lower on DRIVE and HRF, the acc, sensitivity and specificity are not very meaningful due to the significant class imbalance between the foreground (vessels) and background.*\n\n\n- CHASE (train)\n\n| Model         | Acc   | Soft Dice | F1    | Sensitivity | Specificity |\n|---------------|-------|-----------|-------|-------------|-------------|\n| FSGNet        | 97.52 | 81.34     | 81.02 | 86.00       | 98.26       |\n| FRNet         | 97.26 | 80.10     | 79.10 | 84.74       | 97.65       |\n| AttUNet       | 97.54 | 66.02     | 77.06 | 78.92       | 98.56       |\n| AGNet         | 97.44 | 76.25     | 77.58 | 85.14       | 98.13       |\n| ConvUNeXt     | 97.21 | 72.40     | 73.93 | 75.97       | 98.39       |\n| DCSAU-net    | 97.17 | 74.33     | 74.68 | 79.87       | 98.12       |\n| R2UNet        | 96.96 | 67.99     | 71.73 | 74.60       | 98.20       |\n| SAUNet        | 97.47 | 76.17     | 77.23 | 82.02       | 98.33       |\n| CDARL (official) | 78.53 | 11.54   | 0.52  | 0.84        | 83.60       |\n| CDARL (Reproduce) | 83.18 | 16.97 | 15.69 | 26.05       | 86.93       |\n| BayeSeg       | 95.45 | 80.48     | 79.62 | 82.93       | 96.99       |\n| GraphSeg      | 96.54|82.91|81.82|87.84|97.40|\n\n- DRIVE\n\n| Model         | Acc   | Soft Dice | F1    | Sensitivity | Specificity |\n|---------------|-------|-----------|-------|-------------|-------------|\n| FSGNet        | 95.62 | 57.51     | 57.56 | 44.39       | 99.46       |\n| FRNet         | 96.65 | 71.33     | 73.57 | 67.53       | 98.85       |\n| AttUNet       | 95.07 | 45.27     | 50.22 | 38.75       | 99.30       |\n| AGNet         | 96.25 | 69.46     | 70.59 | 65.21       | 98.59       |\n| ConvUNeXt     | 97.07 | 61.91     | 63.77 | 74.35       | 97.92       |\n| DCSAU-net    | 95.30 | 62.30     | 62.56 | 56.82       | 98.19       |\n| R2UNet        | 95.01 | 63.86     | 67.02 | 70.14       | 96.60       |\n| SAUNet        | 96.46 | 69.78     | 70.67 | 61.92       | 99.06       |\n| BayeSeg       | 92.34 | 71.68     | 70.71 | 61.85       | 97.87       |\n| GraphSeg      | 93.56 | 77.16     | 76.01 | 68.09       | 98.19       |\n\n- HRF\n\n| Model         | Acc   | Soft Dice | F1    | Sensitivity | Specificity |\n|---------------|-------|-----------|-------|-------------|-------------|\n| FSGNet        | 95.90 | 68.26     | 68.56 | 71.50       | 98.28       |\n| FRNet         | 97.00 | 64.99     | 67.56 | 69.78       | 97.28       |\n| AttUNet       | 97.37 | 54.20     | 65.29 | 66.41       | 97.94       |\n| AGNet         | 96.70 | 63.03     | 64.54 | 66.69       | 97.10       |\n| ConvUNeXt     | 95.62 | 59.74     | 60.60 | 49.56       | 99.07       |\n| DCSAU-net    | 96.63 | 61.70     | 62.09 | 68.66       | 97.30       |\n| R2UNet        | 94.21 | 49.07     | 52.03 | 88.87       | 94.40       |\n| SAUNet        | 97.15 | 65.87     | 67.17 | 83.92       | 97.65       |\n| BayeSeg       | 92.05 | 70.73     | 70.13 | 67.71       | 96.13       |\n| GraphSeg      | 93.38|78.16|76.59|78.90|96.88|\n\n[1] [ArXiv’25] FSG-Net: Full-scale Representation Guided Network for Retinal Vessel Segmentation\n\n[2] [Knowledge-based systems’22] ConvUNeXt: An efficient convolution neural network for medical image segmentation\n\n[3] [Computers in Biology and Medicine’23] DCSAU-Net: A deeper and more compact split-attention U-Net for medical image segmentation\n\n[4] [Journal of Computational Analysis & Applications’24] Recurrent residual convolutional neural network based on u-net (r2u-net) for medical image segmentation\n\n[5] [Biomedical Optics Express’24] FRD-Net: a full-resolution dilated convolution network for retinal vessel segmentation \n\n[6] [Medical Imaging with Deep Learning’18] Attention u-net: Learning where to look for the pancreas\n\n[7] [ISAIMS’20] AGNet：Retinal Blood Vessel Segmentation via Attention Gate Network\n\n[8] [MICCAI’20] Saunet: Shape attentive u-net for interpretable medical image segmentation\n\n[9] [MedIA'24] C-DARL: Contrastive diffusion adversarial representation learning for label-free blood vessel segmentation\n\n \n>> Q2. … requires a higher computational cost to perform vascular structure matching in the inference stage… Please provide the computational cost comparison.\n\nA2. Thanks for your suggestion, we provide the computational cost comparison as follows. The computational costs are comparable for GraphSeg to other methods. In the inference stage, we only need to run the Decomposition (green in Figure 2) and Segmentation (blue in Figure 2) parts. Therefore, the computational costs are comparable. Besides, without the Deformable graph prior, GraphSeg is downgraded to BayeSeg, thus the computational costs are almost the same for GraphSeg and BayeSeg for inference. We trained GraphSeg for 2.8 hours on GTX 4090. Since each method uses different training settings, it is not directly comparable. Therefore, we focus on inference metrics which are more relevant for practice.\n\n| Model       | Parameters | GFLOPs | Inference Time (s) | Memory (MB) |\n|-------------|------------|--------|--------------------|-------------|\n| FSGNet      | 18.32 M    | 89.59  | 6.23               | 925.42      |\n| FRNet       | 7.38 M     | 55.19  | 4.67               | 374.65      |\n| ATTUNet     | 34.88 M    | 66.54  | 2.08               | 269.80      |\n| AGNet       | 9.33 M     | 16.73  | 5.99               | 330.72      |\n| ConvUNeXt   | 3.51 M     | 7.18   | 2.82               | 160.07      |\n| DCSAU-net  | 2.60 M     | 6.72   | 6.45               | 180.37      |\n| R2UNet      | 39.09 M    | 152.71 | 3.20               | 323.44      |\n| SAUNet      | 0.48 M     | 2.33   | 1.59               | 37.66       |\n| BayeSeg     | 19.32 M    | 88.82  | 7.95               | 144.50      |\n| GraphSeg    | 19.32 M    | 88.82  | 7.78               | 145.95      |\n\n>> Q3. The performance improvement of the proposed method in the generalizability study is quite marginal. Please perform a statistical test to see whether the performance of the proposed method is statistically different from the baseline models.\n\nA3. Thanks for your comment. Following your suggestions, we perform a statistical test between GraphSeg and BayeSeg as follows. GraphSeg outperforms BayeSeg significantly, as shown in the table. For other methods, their F1 scores and soft Dice scores in the model generalization studies are lower than that of BayeSeg, and thus they also have significant difference with GraphSeg in generalizability. \n\n- CHASE DB\n\n| Metric      | t-test   | Wilcoxon | Significant (p < 0.05) |\n|-------------|----------|----------|------------------------|\n| Accuracy    | 0        | 0.00012  | TRUE                   |\n| Soft Dice   | 0.00001  | 0.00024  | TRUE                   |\n| F1          | 0        | 0.00012  | TRUE                   |\n| Sensitivity | 0.00078  | 0.00037  | TRUE                   |\n| Specificity | 0.00022  | 0.00061  | TRUE                   |\n\n- DRIVE\n\n| Metric      | t-test   | Wilcoxon | Significant (p < 0.05) |\n|-------------|----------|----------|------------------------|\n| Accuracy    | 0.00004  | 0.00021  | TRUE                   |\n| Soft Dice   | 0.00483  | 0.00639  | TRUE                   |\n| F1          | 0.00013  | 0.00059  | TRUE                   |\n| Sensitivity | 0.00554  | 0.00422  | TRUE                   |\n| Specificity | 0.00016  | 0.00059  | TRUE                   |\n\n- HRF\n\n| Metric      | t-test   | Wilcoxon | Significant (p < 0.05) |\n|-------------|----------|----------|------------------------|\n| Accuracy    | 0.00018  | 0.00002  | TRUE                   |\n| Soft Dice   | 0.00004  | 0        | TRUE                   |\n| F1          | 0        | 0        | TRUE                   |\n| Sensitivity | 0        | 0        | TRUE                   |\n| Specificity | 0.00502  | 0.00248  | TRUE                   |"}, {"review_id": "F4ktecLKv4", "reviewer": "Reviewer_TdpE", "summary": "This paper proposes GraphSeg, a method that addresses cross-domain generalization in retinal vessel segmentation by combining deformable graph priors with structure-aware image decomposition. Experiments on three public datasets (CHASE, DRIVE, HRF) demonstrate consistent improvements over existing methods under domain shift, validating the importance of jointly modeling anatomical topology and image structure.", "questions": "1. The paper lacks a comprehensive analysis of the computational overhead introduced by the variational Bayesian framework and deformable graph alignment.\n2. How sensitive is the method to the quality and representativeness of the statistical retinal atlas used for graph prior construction?\n3. The paper appears to lack a comprehensive comparison with recent end-to-end deep learning approaches for vessel segmentation (e.g., U-Net variants, Transformer-based methods, recent CNN architectures).", "limitations": "The authors acknowledge the dependency on preprocessing steps for skeleton extraction and graph construction, which represents a major technical limitation. However, the paper also lacks computational complexity discussion, comparison with state-of-the-art end-to-end methods, and failure case analysis specific to the proposed approach.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\n1. The integration of deformable graph priors into a Bayesian segmentation framework represents a significant methodological advancement beyond conventional shape-based priors, specifically addressing the complex vascular morphology challenges.\n2. The method demonstrates superior performance on unseen scenarios across multiple datasets, addressing a critical limitation in medical image analysis where domain adaptation is essential for clinical deployment.\n\nWeakness:\n1. The method requires preprocessing steps to extract vessel skeletons from segmentation masks and construct graph representations. This introduces potential variability due to heuristic morphological operations (e.g., junction merging, branch pruning) and limits the end-to-end learning capability of the framework.\n2. The combination of variational Bayesian inference with deformable graph alignment may introduce significant computational overhead compared to standard CNN-based approaches. The paper lacks a discussion of runtime complexity and scalability to higher image resolutions.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive comments and kind support! All your concerns have been carefully addressed as below. The manuscript will be carefully revised accordingly. We sincerely hope our responses fully address your questions.\n\n>> Q1. The paper lacks a comprehensive analysis of the computational overhead introduced by the variational Bayesian framework and deformable graph alignment.\n\nA1. Thanks for your suggestion, we provide the computational cost comparison as follows. The computational costs are comparable for GraphSeg to other methods. In the inference stage, we only need to run the Decomposition (green in Figure 2) and Segmentation (blue in Figure 2) parts. Therefore, the computational costs are comparable. Besides, without the Deformable graph prior, GraphSeg is downgraded to BayeSeg, thus the computational costs are almost the same for GraphSeg and BayeSeg for inference. We trained GraphSeg for 2.8 hours on GTX 4090. Since each method uses different training settings, it is not directly comparable. Therefore, we focus on inference metrics, which are more relevant for practice.\n \n| Model| Parameters | GFLOPs | Inference Time (s) | Memory (MB) |\n|-------------|------------|--------|--------------------|-------------|\n| FSGNet      | 18.32 M    | 89.59  | 6.23 | 925.42      |\n| FRNet| 7.38 M     | 55.19  | 4.67 | 374.65      |\n| ATTUNet     | 34.88 M    | 66.54  | 2.08 | 269.80      |\n| AGNet| 9.33 M     | 16.73  | 5.99 | 330.72      |\n| ConvUNeXt   | 3.51 M     | 7.18   | 2.82 | 160.07      |\n| DCSAU-net  | 2.60 M     | 6.72   | 6.45 | 180.37      |\n| R2UNet      | 39.09 M    | 152.71 | 3.20 | 323.44      |\n| SAUNet      | 0.48 M     | 2.33   | 1.59 | 37.66|\n| BayeSeg     | 19.32 M    | 88.82  | 7.95 | 144.50      |\n| GraphSeg    | 19.32 M    | 88.82  | 7.78 | 145.95      |\n\n\n>> Q2. How sensitive is the method to the quality and representativeness of the statistical retinal atlas used for graph prior construction?\n\nA2. Thanks for your insightful question. In this work, the deformable graph prior provides a guidance for the Decomposition part to extract the graph-like structures for subsequent segmentation. As shown in Figure 4-6, the vascular shape $s$ extracted from the Decomposition is graph-like and the other parts, like color and shadow, are decomposed into the $m$. This is the source of our GraphSeg’s generalizability.\n\nThe graph construction follows [1]. Graph Atlas is obtained by performing their code on the training set of CHASE. Following your suggestion, we also use the graph prior from the CHASE to train GraphSeg on the DRIVE dataset. The results are shown as follows: (1) GraphSeg(trained) outperforms UNet(trained) due to the graph prior, **which demonstrates that the graph prior extracted from one dataset can be transferred to the other dataset**. (2) GraphSeg outperforms UNet(trained) on most metrics, which confirms the generalizability of GraphSeg and demonstrates the robustness of our framework with respect to graph priors. \n\n\n- DRIVE (train)\n\n|Model|Acc|SoftDice|F1|Sensitivity|Specificity|\n|---|---|---|---|---|---|\n|GraphSeg(trained)|96.13|85.23|84.82|83.02|98.15|\n|Unet(trained)|90.89|61.09|61.09|48.55|98.51|\n\n- CHASE\n\n|Model|Acc|SoftDice|F1|Sensitivity|Specificity|\n|---|---|---|---|---|---|\n|GraphSeg|95.02|82.56|79.37|89.70|95.69|\n|Unet(trained)|95.17|79.74|78.39|81.97|96.79|\n|GraphSeg(trained)|96.54|82.91|81.82|87.84|97.40|\n\n- HRF\n\n|Model|Acc|SoftDice|F1|Sensitivity|Specificity|\n|---|----|---|---|----|---|\n|GraphSeg|93.91|78.20|77.25|78.40|96.34|\n|Unet(trained)|89.79|71.37|67.76|78.15|91.74|\n|GraphSeg(trained)|95.88|84.29|83.89|81.58|98.07|\n\n[1] PAMI’24. Statistical analysis of complex shape graphs.\n\n>>Q3. The paper appears to lack a comprehensive comparison with recent end-to-end deep learning approaches for vessel segmentation (e.g., U-Net variants, Transformer-based methods, recent CNN architectures).\n\nA3. Thanks for your suggestion. Following your suggestion, we compare GraphSeg with seven additional methods, including AttUNet [6], AGNet [7], ConvUNeXt [2], DCSAU-Net [3], R2UNet [4], SAUNet [8], and CDARL [9]. FRSGNet[1] is the current SOTA for retinal vessel segmentation.\n\nGraphSeg outperforms other methods in model generalization studies (on DRIVE and HRF), especially for F1 and Soft Dice. *For other methods, since the F1 scores and soft Dice scores are significantly lower on DRIVE and HRF, the acc, sensitivity, and specificity are not very meaningful due to the significant class imbalance between the foreground (vessels) and background*.\n\n\n\n- CHASE (train)\n\n| Model         | Acc   | Soft Dice | F1    | Sensitivity | Specificity |\n|---------------|-------|-----------|-------|-------------|-------------|\n| FSGNet        | 97.52 | 81.34     | 81.02 | 86.00       | 98.26       |\n| FRNet         | 97.26 | 80.10     | 79.10 | 84.74       | 97.65       |\n| AttUNet       | 97.54 | 66.02     | 77.06 | 78.92       | 98.56       |\n| AGNet         | 97.44 | 76.25     | 77.58 | 85.14       | 98.13       |\n| ConvUNeXt     | 97.21 | 72.40     | 73.93 | 75.97       | 98.39       |\n| DCSAU-net    | 97.17 | 74.33     | 74.68 | 79.87       | 98.12       |\n| R2UNet        | 96.96 | 67.99     | 71.73 | 74.60       | 98.20       |\n| SAUNet        | 97.47 | 76.17     | 77.23 | 82.02       | 98.33       |\n| CDARL (official) | 78.53 | 11.54   | 0.52  | 0.84        | 83.60       |\n| CDARL (Reproduce) | 83.18 | 16.97 | 15.69 | 26.05       | 86.93       |\n| BayeSeg       | 95.45 | 80.48     | 79.62 | 82.93       | 96.99       |\n| GraphSeg      | 96.54|82.91|81.82|87.84|97.40|\n\n- DRIVE\n\n| Model         | Acc   | Soft Dice | F1    | Sensitivity | Specificity |\n|---------------|-------|-----------|-------|-------------|-------------|\n| FSGNet        | 95.62 | 57.51     | 57.56 | 44.39       | 99.46       |\n| FRNet         | 96.65 | 71.33     | 73.57 | 67.53       | 98.85       |\n| AttUNet       | 95.07 | 45.27     | 50.22 | 38.75       | 99.30       |\n| AGNet         | 96.25 | 69.46     | 70.59 | 65.21       | 98.59       |\n| ConvUNeXt     | 97.07 | 61.91     | 63.77 | 74.35       | 97.92       |\n| DCSAU-net    | 95.30 | 62.30     | 62.56 | 56.82       | 98.19       |\n| R2UNet        | 95.01 | 63.86     | 67.02 | 70.14       | 96.60       |\n| SAUNet        | 96.46 | 69.78     | 70.67 | 61.92       | 99.06       |\n| BayeSeg       | 92.34 | 71.68     | 70.71 | 61.85       | 97.87       |\n| GraphSeg      | 93.56 | 77.16     | 76.01 | 68.09       | 98.19       |\n\n- HRF\n\n| Model         | Acc   | Soft Dice | F1    | Sensitivity | Specificity |\n|---------------|-------|-----------|-------|-------------|-------------|\n| FSGNet        | 95.90 | 68.26     | 68.56 | 71.50       | 98.28       |\n| FRNet         | 97.00 | 64.99     | 67.56 | 69.78       | 97.28       |\n| AttUNet       | 97.37 | 54.20     | 65.29 | 66.41       | 97.94       |\n| AGNet         | 96.70 | 63.03     | 64.54 | 66.69       | 97.10       |\n| ConvUNeXt     | 95.62 | 59.74     | 60.60 | 49.56       | 99.07       |\n| DCSAU-net    | 96.63 | 61.70     | 62.09 | 68.66       | 97.30       |\n| R2UNet        | 94.21 | 49.07     | 52.03 | 88.87       | 94.40       |\n| SAUNet        | 97.15 | 65.87     | 67.17 | 83.92       | 97.65       |\n| BayeSeg       | 92.05 | 70.73     | 70.13 | 67.71       | 96.13       |\n| GraphSeg      |93.38|78.16|76.59|78.90|96.88|\n\n[1] [ArXiv’25] FSG-Net: Full-scale Representation Guided Network for Retinal Vessel Segmentation\n\n[2] [Knowledge-based systems’22] ConvUNeXt: An efficient convolution neural network for medical image segmentation\n\n[3] [Computers in Biology and Medicine’23] DCSAU-Net: A deeper and more compact split-attention U-Net for medical image segmentation\n\n[4] [Journal of Computational Analysis & Applications’24] Recurrent residual convolutional neural network based on u-net (r2u-net) for medical image segmentation\n\n[5] [Biomedical Optics Express’24] FRD-Net: a full-resolution dilated convolution network for retinal vessel segmentation \n\n[6] [Medical Imaging with Deep Learning’18] Attention u-net: Learning where to look for the pancreas\n\n[7] [ISAIMS’20] AGNet：Retinal Blood Vessel Segmentation via Attention Gate Network\n\n[8] [MICCAI’20] Saunet: Shape attentive u-net for interpretable medical image segmentation\n\n[9] [MedIA'24] C-DARL: Contrastive diffusion adversarial representation learning for label-free blood vessel segmentation"}, {"review_id": "FEVnJvBkIz", "reviewer": "Reviewer_pSst", "summary": "The paper introduces a novel method for segmenting vascular structures in color fundus photographs.  The main novelty of the method is to use a deformable graph prior for the vascular network within a Bayesian segmentation framework.  Results show modest improvements against a reasonable set of baselines on several data sets from different sources.  However, the strongest result is in showing greater improvements against baselines in cross-data-set tasks, i.e. training on one and testing on the other.  This suggests greater robustness and generalizability of the proposed approach.", "questions": "Does the presence of pathology affect performance?  An algorithm that works on normal cases (the majority) but fails in the presence of pathology has little clinical utility.", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\nThis is an important problem with clear clinical utility.  \n\nThe methods appear sound and well thought out.\n\nThe experiments and clear and the results nicely demonstrate potential benefit.\n\nWeaknesses\n\nDoes not distinguish veins and arteries unlike other recent work of Zhou et al (in particular https://www.sciencedirect.com/science/article/abs/pii/S1361841524000239 but also https://tvst.arvojournals.org/article.aspx?articleid=2783477), which should be considered in the related work and discussion.  \n\nDoes not consider the effect of pathology in the experimental evaluation.", "was_revised": true, "final_justification": "No update.", "rebuttal": "Thank you for your constructive comments and kind support! All your concerns have been carefully addressed as below. The manuscript will be carefully revised accordingly. We sincerely hope our responses fully address your questions.\n\n>> W1. Does not distinguish veins and arteries\n\nA1. We acknowledge the importance of distinguishing between veins and arteries in retinal vessel segmentation, especially for clinical applications. While our approach focuses on general vascular segmentation, we recognize that specialized methods differentiating veins from arteries, such as those proposed by Zhou et al., may offer additional clinical value. We appreciate the reviewer pointing out this gap, and we will include a discussion on this in the revised manuscript, highlighting the potential for extending our method to vein/artery differentiation. We will also reference Zhou et al.’s work in the related work section to clarify how their method differs from ours and discuss the trade-offs between our generalizable approach and more specialized methods.\n\n>> W2&Q3. Does not consider the effect of pathology in the experimental evaluation. Does the presence of pathology affect performance? An algorithm that works on normal cases (the majority) but fails in the presence of pathology has little clinical utility.\n\nA2. Thank you for your insightful comment. **The HRF dataset includes both healthy and pathological images (e.g., diabetic retinopathy)**, and the DRIVE and CHASE datasets predominantly contain healthy images, with only minor pathological cases. GraphSeg performs well across all three datasets, particularly with respect to generalizability. Although our current experiments focus on generalization across different retinal datasets, we agree that pathology could significantly impact segmentation performance."}, {"review_id": "fugoGtLC2C", "reviewer": "Reviewer_EXz9", "summary": "The authors propose GraphSeg, a variation of Bayesian framework.\nThey introduce a deformable graph prior module in training this network and design a statistical model to align the vasculature and deformable graph.\nTheir deisgn demonstrates superior performance comparing to SOTA while remaining good generalizability.", "questions": "1. Graph Atlas is mentioned four times in the paper. Could you please clarify how the retinal vascular graph atlas is initially obtained?\n2. In the cross-dataset evaluation, it is unclear whether pre-processing and decomposition were applied consistently across all compared methods, or only to the proposed approach. Could you provide a cross-dataset comparison regarding pre-processing? Pre-processing can significantly affect the assessment of generalization ability, and its impact should be clearly demonstrated. \n3. The datasets used in the paper are relatively small and dated (a total of 28+40+45=113 images from 2004, 2013, and 2013). To better validate the performance and robustness of the proposed model, it would be important to include more recent and larger-scale datasets.\n4. In Table 3, sensitivity increases significantly with the addition of more components. Could you explain the reason behind this?\n\nI will raise Originality if 4 and 3 are accomodated; will raise Quality if 1,2,3 are solved.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Clarity: The writing is clear and easy to follow.\n2. Significance: \n - Strong segmentation performance on classic benchmarks.\n - Generalization is a practical challenge in medical imaging. The authors explore the potential of Bayesian frameworks to address this issue.\n3. Originality: \nThe use of retinal priors, such as landmark detection, reflects a solid integration with real-world clinical scenarios. I personally appreciate this practical approach.\n\nWeaknesses:\n1. Quality:  \n - The experiments may not fully support the claimed superiority of the method. There is a lack of repeated trials to assess consistency and robustness.\n - Scale of Data: The dataset used is relatively small, which may limit the generalizability of the findings.\n - The cross-dataset generalization experiments are limited and not comprehensive enough to confirm the method’s robustness.\n\n2. Originality: The limitation in experiments makes it difficult to judge the reliability and practical value of the method. Since the paper use many exisiting ideas without novel changes such as landmark detection, Bayesian modeling, or image decomposition, the paper should at least provide strong experimental evidence (not just in discussion) to show the advantage of combining these ideas (why not the others) or highlight some design principles of the framework. These may help the paper demonstarate the uniqueness of their pipeline.", "was_revised": true, "final_justification": "Thank you for your reply! I recognize the authors fully address my concerns on Originality and partially address my concerns on Quality. I will raise my score.\nMy remaining concern is that the preprocessing may inadvertently align the data distribution in a way that favors the proposed model, potentially leading to an overestimation of its generalization ability, and that the dataset aspect (inclusion of more datasets and having a detailed introduction on the dataset usage) may affect reproducibility and the assessment of generalization in broader scenarios.\nThis is the evaluation concern that draws the Borderline accept.", "rebuttal": "Thank you for your comments! All your concerns have been carefully addressed as below. The manuscript will be carefully revised accordingly. We sincerely hope our responses fully address your questions.\n\n>> W1.1 The experiments may not fully support the claimed superiority of the method. There is a lack of repeated trials to assess consistency and robustness.\n\nA1.1. Thanks for your comment. The improvement of GraphSeg in generalizability study is significant. We also perform a statistical test as follows. GraphSeg outperforms BayeSeg significantly as shown in the table\n\n- CHASE DB\n\n| Metric| t-test   | Wilcoxon | Significant (p < 0.05) |\n|-----|----------|----------|------------------------|\n| Accuracy    | 0  | 0.00012  | TRUE |\n| Soft Dice   | 0.00001  | 0.00024  | TRUE |\n| F1    | 0  | 0.00012  | TRUE |\n| Sensitivity | 0.00078  | 0.00037  | TRUE |\n| Specificity | 0.00022  | 0.00061  | TRUE |\n\n- DRIVE\n\n| Metric| t-test   | Wilcoxon | Significant (p < 0.05) |\n|-------------|----------|----------|------------------------|\n| Accuracy    | 0.00004  | 0.00021  | TRUE |\n| Soft Dice   | 0.00483  | 0.00639  | TRUE |\n| F1    | 0.00013  | 0.00059  | TRUE |\n| Sensitivity | 0.00554  | 0.00422  | TRUE |\n| Specificity | 0.00016  | 0.00059  | TRUE |\n\n- HRF\n\n| Metric| t-test   | Wilcoxon | Significant (p < 0.05) |\n|-------------|----------|----------|------------------------|\n| Accuracy    | 0.00018  | 0.00002  | TRUE |\n| Soft Dice   | 0.00004  | 0  | TRUE |\n| F1    | 0  | 0  | TRUE |\n| Sensitivity | 0  | 0  | TRUE |\n| Specificity | 0.00502  | 0.00248  | TRUE |\n \n\n\n>> W.1.2 Scale of Data: The dataset used is relatively small, which may limit the generalizability of the findings. The cross-dataset generalization experiments are limited and not comprehensive enough to confirm the method’s robustness.\n\nA1.2. Thank you for your comment. The three datasets used in this work (DRIVE, HRF, and CHASE) are widely recognized as standard benchmarks for retinal vessel segmentation [1]. To further evaluate the generalizability of GraphSeg, we have also conducted experiments on the STARE dataset and compared with seven additional methods, including AttUNet [6], AGNet [7], ConvUNeXt [2], DCSAU-Net [3], R2UNet [4], SAUNet [8], and CDARL [9]. All models were trained on the CHASE dataset, and evaluated by ACC, Soft Dice, F1 score, Sensitivity, and Specificity. **Note that Soft Dice, F1 score, Sensitivity are more appropriate** to evaluate vessel segmentation performance *due to the significant class imbalance between the foreground (vessels) and background*. From the test results on STARE one can see that GraphSeg outperforms other methods in soft Dice, F1 score, and Sensitivity, further confirming the superior generalizability of GraphSeg. \n\n- CHASE (train)\n\n| Model   | Acc    | Soft Dice | F1    | Sensitivity | Specificity |\n|----------------|--------|-----------|-------|-------------|-------------|\n| FSGNet  | 97.52  | 81.34     | 81.02 | 86.00| 98.26|\n| FRNet   | 97.26  | 80.10     | 79.10 | 84.74| 97.65|\n| AttUNet | 97.54  | 66.02     | 77.06 | 78.92| 98.56|\n| AGNet   | 97.44  | 76.25     | 77.58 | 85.14| 98.13|\n| ConvUNeXt      | 97.21  | 72.40     | 73.93 | 75.97| 98.39|\n| DCSAU-net     | 97.17  | 74.33     | 74.68 | 79.87| 98.12|\n| R2UNet  | 96.96  | 67.99     | 71.73 | 74.60| 98.20|\n| SAUNet  | 97.47  | 76.17     | 77.23 | 82.02| 98.33|\n| CDARL (official) | 78.53 | 11.54    | 0.52  | 0.84 | 83.60|\n| CDARL (Reproduce) | 83.18 | 16.97  | 15.69 | 26.05| 86.93|\n| BayeSeg | 95.45  | 80.48     | 79.62 | 82.93| 96.99|\n| GraphSeg| 96.54|82.91|81.82|87.84|97.40|\n\n- DRIVE\n\n| Model   | Acc    | Soft Dice | F1    | Sensitivity | Specificity |\n|----------------|--------|-----------|-------|-------------|-------------|\n| FSGNet  | 95.62  | 57.51     | 57.56 | 44.39| 99.46|\n| FRNet   | 96.65  | 71.33     | 73.57 | 67.53| 98.85|\n| AttUNet | 95.07  | 45.27     | 50.22 | 38.75| 99.30|\n| AGNet   | 96.25  | 69.46     | 70.59 | 65.21| 98.59|\n| ConvUNeXt      | 97.07  | 61.91     | 63.77 | 74.35| 97.92|\n| DCSAU-net     | 95.30  | 62.30     | 62.56 | 56.82| 98.19|\n| R2UNet  | 95.01  | 63.86     | 67.02 | 70.14| 96.60|\n| SAUNet  | 96.46  | 69.78     | 70.67 | 61.92| 99.06|\n| BayeSeg | 92.34  | 71.68     | 70.71 | 61.85| 97.87|\n| GraphSeg| 93.56  | 77.16     | 76.01 | 68.09| 98.19|\n\n- HRF\n\n| Model   | Acc    | Soft Dice | F1    | Sensitivity | Specificity |\n|----------------|--------|-----------|-------|-------------|-------------|\n| FSGNet  | 95.90  | 68.26     | 68.56 | 71.50| 98.28|\n| FRNet   | 97.00  | 64.99     | 67.56 | 69.78| 97.28|\n| AttUNet | 97.37  | 54.20     | 65.29 | 66.41| 97.94|\n| AGNet   | 96.70  | 63.03     | 64.54 | 66.69| 97.10|\n| ConvUNeXt      | 95.62  | 59.74     | 60.60 | 49.56| 99.07|\n| DCSAU-net     | 96.63  | 61.70     | 62.09 | 68.66| 97.30|\n| R2UNet  | 94.21  | 49.07     | 52.03 | 88.87| 94.40|\n| SAUNet  | 97.15  | 65.87     | 67.17 | 83.92| 97.65|\n| BayeSeg | 92.05  | 70.73     | 70.13 | 67.71| 96.13|\n| GraphSeg| 93.38|78.16|76.59|78.90|96.88|\n\n- STARE\n\n| Model   | Acc    | Soft Dice | F1    | Sensitivity | Specificity |\n|----------------|--------|-----------|-------|-------------|-------------|\n| FSGNet  | 96.15  | 54.08     | 54.23 | 45.43| 99.33|\n| FRNet   | 93.04  | 64.91     | 67.07 | 62.39| 98.96|\n| AttUNet | 95.71  | 37.91     | 41.97 | 34.39| 99.54|\n| AGNet   | 96.52  | 67.49     | 68.82 | 66.74| 98.47|\n| ConvUNeXt      | 95.97  | 52.65     | 53.30 | 46.89| 98.96|\n| DCSAU-net     | 94.77  | 47.59     | 47.83 | 45.65| 97.75|\n| R2UNet  | 95.53  | 49.90     | 50.86 | 50.63| 98.22|\n| SAUNet  | 96.87  | 61.50     | 62.23 | 56.44| 99.29|\n| BayeSeg | 92.85  | 67.82     | 66.82 | 59.78| 97.65|\n| GraphSeg| 93.65  | 72.76     | 71.43 | 68.72| 97.69|\n\n[1] [ArXiv’25] FSG-Net: Full-scale Representation Guided Network for Retinal Vessel Segmentation\n\n[2] [Knowledge-based systems’22] ConvUNeXt: An efficient convolution neural network for medical image segmentation\n\n[3] [Computers in Biology and Medicine’23] DCSAU-Net: A deeper and more compact split-attention U-Net for medical image segmentation\n\n[4] [Journal of Computational Analysis & Applications’24] Recurrent residual convolutional neural network based on u-net (r2u-net) for medical image segmentation\n\n[5] [Biomedical Optics Express’24] FRD-Net: a full-resolution dilated convolution network for retinal vessel segmentation \n\n[6] [Medical Imaging with Deep Learning’18] Attention u-net: Learning where to look for the pancreas\n\n[7] [ISAIMS’20] AGNet：Retinal Blood Vessel Segmentation via Attention Gate Network\n\n[8] [MICCAI’20] Saunet: Shape attentive u-net for interpretable medical image segmentation\n\n[9] [MedIA'24] C-DARL: Contrastive diffusion adversarial representation learning for label-free blood vessel segmentation\n\n>> W2. Originality… The limitation in experiments makes it difficult to judge the reliability and practical value of the method…\n\nA2. Thanks for your concern. We provide additional results as shown in the table above. Experiments show the superiority of our GraphSeg. We would like to clarify the originality of our contributions. Specifically, our work introduces: (1) a novel Bayesian retinal vessel segmentation framework that goes beyond traditional methods focusing on compact shapes; (2) the development of deformable retinal graph priors for aligning heterogeneous vascular structures in retinal images, along with a statistical model to drive the alignment between image vascular structures and these graph priors; and (3) extensive validation of our framework across multiple widely used datasets, demonstrating its superior generalizability in unseen scenarios.\n\n>> Q3. Could you please clarify how the retinal vascular graph atlas is initially obtained?\n\nA3. Thanks for your concern. We strictly follow [1] to construct the graph Atlas as we described in Appendix.A.1\n\n[1] PAMI’24. Statistical analysis of complex shape graphs.\n\n>>Q4. …whether pre-processing and decomposition were applied consistently across all compared methods… \n\nA4. Thank you for your valuable comment. In our cross-dataset evaluation, we ensured consistency in the pre-processing steps across all compared methods to provide a fair comparison. Specifically, the same pre-processing pipeline (including image resizing, normalization, and augmentation) was applied uniformly to all methods, including the proposed GraphSeg approach.\n\nFor the decomposition step, which is specific to GraphSeg and BayeSeg, we only applied it to these two methods and not to the baseline approaches. We will clarify this point in the revised manuscript and emphasize that while pre-processing was consistent, the combination of decomposition and deformable graph priors were unique to GraphSeg. It’s worth to mention that the decomposition and deformable graph priors in GraphSeg are trained end-to-end instead of stage-by-stage.\n\n>> Q5. … To better validate the performance and robustness of the proposed model, it would be important to include more recent and larger-scale datasets…. \n\nA5. Please refer to A1.2.\n\n>> Q6. In Table 3, sensitivity increases significantly with the addition of more components. Could you explain the reason behind this?\n\nA6. Thank you for your insightful question. The significant increase in sensitivity observed with the addition of more components in Table 3 is attributed to the model’s ability to capture finer details of the vascular structures, particularly in challenging cases where small or faint vessel segments are present.\n\nAs more components are introduced, the model becomes better at distinguishing between foreground vascular structures and the background, improving its sensitivity to vessels that might otherwise be overlooked. This is especially beneficial in scenarios with complex or noisy images, where the model needs to identify subtle vascular features."}, {"review_id": "uxdjUsf3BB", "reviewer": "Reviewer_D8Hv", "summary": "The paper proposes GraphSeg, a novel variational Bayesian framework for retinal vessel segmentation that addresses the challenge of cross-domain generalization. GraphSeg builds upon Bayesian approaches such as BayeSeg and Indeed, and additionally integrates deformable graph priors derived from a statistical retinal atlas, enabling domain-invariant representations. A probabilistic graphical model (PGM) is introduced to jointly model images, vascular shapes, and graph priors, with a differentiable alignment mechanism guided by an unsupervised energy function. The framework leverages implicit neural representations and Gaussian splatting to align graph priors with image structures. Experiments on three public datasets—CHASE, DRIVE, and HRF—demonstrate GraphSeg’s superior performance, particularly in cross-domain settings, outperforming methods like the supervised trained U-Net, BayeSeg, and FSG-Net.", "questions": "1. Is GraphSeg the first method to use a retinal atlas or Bayesian framework for retinal vessel segmentation, or are there prior works that have explored similar anatomical priors? If so, how does GraphSeg differ from these approaches?\n2. Given that the retinal atlas is derived from the CHASE dataset, how consistent is its distribution with those of other datasets like DRIVE and HRF, which may differ in imaging perspectives or conditions? Does the constructed retinal atlas generalize well across diverse datasets?\n3. How does GraphSeg compare to FSG-Net, U-Net, and BayeSeg in terms of model parameters, computational cost (e.g., FLOPs), and training/testing speed? A quantitative comparison would help assess the practical deployability of GraphSeg.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. Well-Motivated Research Problem. Retinal vessel segmentation is critical for diagnosing retinal diseases, but it faces challenges due to limited annotated data and significant domain variability across multi-center datasets. The paper effectively motivates the use of graph priors, specifically a statistical retinal atlas, to enhance cross-domain generalization. \n2. Innovative Framework. The integration of a statistical retinal atlas as a deformable graph prior is a novel contribution. The use of retinal atlas derived from the CHASE dataset, combined with a variational Bayesian framework, introduces a fresh perspective to vessel segmentation. The ablation study in Table 3 convincingly demonstrates the effectiveness of the graph prior in improving generalization, with notable improvements in Soft Dice when trained on CHASE and tested on DRIVE.\n3 . Comprehensive Methodology. GraphSeg combines multiple advanced techniques, including Bayesian modeling, graph construction with shape PCA, graph neural networks, and Gaussian splatting for implicit neural representation. The method's design is thorough, with a clear probabilistic graphical model (Fig. 1) and a detailed network architecture (Fig. 2). The use of an unsupervised energy function to guide structural alignment is particularly noteworthy, enabling the model to capture long-range vascular dependencies effectively.\n\nWeaknesses\n1. Insufficient Experimental Validation. \na) Preprocessing Dependency: the paper acknowledges the dependency on pre-processing for skeleton extraction and graph construction, which involve heuristic rules for junction merging and branch pruning. However, the extent of manual intervention in these steps is not clearly quantified, which could potentially lead to unfair comparisons with other methods. The authors should clarify the degree of human involvement and the robustness of these heuristics.\nb) Limited Cross-Dataset Evaluation: while GraphSeg emphasizes strong cross-domain generalization, the evaluation is limited to three datasets (CHASE, DRIVE, HRF). To substantiate the claim of robust generalization, additional datasets such as STARE, DRHAGIS, LES-AV, and RETA should be included in Table 2 to cover a broader range of imaging conditions and vascular morphologies. \nc) Limited Comparison Methods: The cross-dataset evaluation in Table 2 includes only U-Net and BayeSeg as comparison methods. More comparison methods are needed for Cross-dataset evaluation.\n2. Unclear Presentation. \na) Vascular Structure Matching: The explanation of the vascular structure matching in Section 3.2 is not sufficiently clear. Specifically, the variable d in Equation (1) lacks a clear definition of its meaning and value range. \nb) Comparison with BayeSeg: A more detailed comparison highlighting the technical distinctions and advantages would strengthen the contribution’s novelty. \nc) Lack of Code Availability: Providing an anonymized code repository, including preprocessing steps, at submission would enhance trust in the results.", "was_revised": true, "final_justification": "After carefully considering the rebuttal and the discussion, I maintain a positive assessment of this work, for the following reasons:\n1) The authors’ rebuttal provides additional experimental evidence that supports the effectiveness of the proposed method.\n2) The use of a deformable statistical graph prior introduces a novel and original approach to addressing domain shift in retinal vessel segmentation. \n3) One limitation is the reliance on preprocessing steps to extract vessel skeletons and construct graph representations. These steps may introduce variability and reduce the robustness and reproducibility of the overall pipeline.", "rebuttal": "Thank you for your constructive comments and kind support! All your concerns have been carefully addressed as below. The manuscript will be revised accordingly. We sincerely hope our responses fully address your questions.\n>> W1(a) Preprocessing Dependency: … the extent of manual intervention in these steps is not clearly quantified…\n\nA1(a): The graph atlas construction is only performed once on the CHASE training set before training. To evaluate the robustness, we use the graph prior from the CHASE to train GraphSeg on the DRIVE dataset. The results show: 1) GraphSeg(trained) outperforms UNet(trained) due to the graph prior, which demonstrates that the graph prior extracted from one dataset can be transferred to the other dataset. 2) GraphSeg outperforms UNet(trained) on most metrics, which confirms the generalizability of GraphSeg and demonstrates the robustness of GraphSeg to graph priors\n\n|Model|Acc|SoftDice|F1|Sen|Speci|\n|--|--|--|--|--|--|\n| ||**DRIVE(TRAIN)**| | | |\n|GraphSeg(trained)|96.13|85.23|84.82|83.02|98.15|\n|Unet(trained)|90.89|61.09|61.09|48.55|98.51|\n| | |**CHASE**| | | |\n|GraphSeg|95.02|82.56|79.37|89.70|95.69|\n|Unet(trained)|95.17|79.74|78.39|81.97|96.79|\n|GraphSeg(trained)|96.54|82.91|81.82|87.84|97.40|\n| | |**HRF**| | | |\n|GraphSeg|93.91|78.20|77.25|78.40|96.34|\n|Unet(trained)|89.79|71.37|67.76|78.15|91.74|\n|GraphSeg(trained)|95.88|84.29|83.89|81.58|98.07|\n>> W1(bc) Cross-Dataset Evaluation. … additional datasets and Comparison Methods…\n\nA1(bc): We provide additional results by including more datasets and additional seven methods, i.e., AttUNet[3], AGNet[4], ConvUNeXt[5], DCSAU-Net[6], R2UNet[7], SAUNet[8], CDARL[9]. FRSGNet[1] is current SOTA for retinal vessel segmentation\n\nGraphSeg outperforms other methods in generalization studies (on DRIVE and HRF), especially for F1 and Soft Dice. For other methods, since the F1 scores and soft **Dice scores are significantly lower, the acc, sensitivity and specificity are not very meaningful due to the significant class imbalance between the foreground (vessels) and background**\n\nThe test results on the new STARE dataset show that GraphSeg outperforms other methods in soft Dice, F1, and Sensitivity, further confirming the superior generalizability of GraphSeg\n\n[1][ArXiv’25] Full-scale Representation Guided Network for Retinal Vessel Segmentation\n\n[2][BOE’24] a full-resolution dilated convolution network for retinal vessel segmentation\n\n[3][MIDL’18] Learning where to look for the pancreas\n\n[4][ISAIMS’20] Retinal Blood Vessel Segmentation via Attention Gate Network\n\n[5][KBS’22] An efficient convolution neural network for medical image segmentation\n\n[6][CBM’23] A deeper and more compact split-attention U-Net for medical image segmentation\n\n[7][JCAA’24] Recurrent residual convolutional neural network based on u-net (r2u-net) for medical image segmentation\n\n[8][MICCAI’20] Shape attentive u-net for interpretable medical image segmentation\n\n[9][MIA’24] Contrastive diffusion adversarial representation learning for label-free blood vessel segmentation\n\n|Model|Acc|SoftDice|F1|Sens|Speci|\n|--|--|--|--|--|--|\n| | |**CHASE(TRAIN)**| | | |\n|[1]|97.52|81.34|81.02|86.00|98.26|\n|[2]|97.26|80.10|79.10|84.74|97.65|\n|[3]|97.54|66.02|77.06|78.92|98.56|\n|[4]|97.44|76.25|77.58|85.14|98.13|\n|[5]|97.21|72.40|73.93|75.97|98.39|\n|[6]|97.17|74.33|74.68|79.87|98.12|\n|[7]|96.96|67.99|71.73|74.60|98.20|\n|[8]|97.47|76.17|77.23|82.02|98.33|\n|[9] (official)|78.53|11.54|0.52|0.84|83.60|\n|[9] (Reproduce)|83.18|16.97|15.69|26.05|86.93|\n|BayeSeg|95.45|80.48|79.62|82.93|96.99|\n|GraphSeg|96.54|82.91|81.82|87.84|97.40|\n| | |**DRIVE**| | | |\n|[1]|95.62|57.51|57.56|44.39|99.46|\n|[2]|96.65|71.33|73.57|67.53|98.85|\n|[3]|95.07|45.27|50.22|38.75|99.30|\n|[4]|96.25|69.46|70.59|65.21|98.59|\n|[5]|97.07|61.91|63.77|74.35|97.92|\n|[6]|95.30|62.30|62.56|56.82|98.19|\n|[7]|95.01|63.86|67.02|70.14|96.60|\n|[8]|96.46|69.78|70.67|61.92|99.06|\n|BayeSeg|92.34|71.68|70.71|61.85|97.87|\n|GraphSeg|93.56|77.16|76.01|68.09|98.19|\n| | |**HRF**| | | |\n|[1]|95.90|68.26|68.56|71.50|98.28|\n|[2]|97.00|64.99|67.56|69.78|97.28|\n|[3]|97.37|54.20|65.29|66.41|97.94|\n|[4]|96.70|63.03|64.54|66.69|97.10|\n|[5]|95.62|59.74|60.60|49.56|99.07|\n|[6]|96.63|61.70|62.09|68.66|97.30|\n|[7]|94.21|49.07|52.03|88.87|94.40|\n|[8]|97.15|65.87|67.17|83.92|97.65|\n|BayeSeg|92.05|70.73|70.13|67.71|96.13|\n|GraphSeg|93.38|78.16|76.59|78.90|96.88|\n|||**STARE**||||\n|[1]|96.15|54.08|54.23|45.43|99.33|\n|[2]|93.04|64.91|67.07|62.39|98.96|\n|[3]|95.71|37.91|41.97|34.39|99.54|\n|[4]|96.52|67.49|68.82|66.74|98.47|\n|[5]|95.97|52.65|53.30|46.89|98.96|\n|[6]|94.77|47.59|47.83|45.65|97.75|\n|[7]|95.53|49.90|50.86|50.63|98.22|\n|[8]|96.87|61.50|62.23|56.44|99.29|\n|BayeSeg|92.85|67.82|66.82|59.78|97.65|\n|GraphSeg|93.65|72.76|71.43|68.72|97.69|\n>> W2(a) Definition of the variable $d$ in Eq (1).\n\nA2(a): The variable $d$ represents the landmark detection variable that identifies the points where vascular structures exhibit significant geometric dissimilarity. These are typically the branching points or bifurcations of blood vessels, which is firstly introduced in line 153\n\nThe variable $d$ follows a Gamma prior distribution, and its value is defined within the context of the model’s optimization to help guide the detection of landmarks by enforcing structural constraints during the vascular structure matching\n>> W2(b) Comparison with BayeSeg: A more detailed comparison would strengthen the contribution’s novelty\n\nA2(b): The key technical differences between GraphSeg and BayeSeg as follows:\n- Graph-based Prior: Comparing to BayeSeg, GraphSeg introduces a deformable retinal graph prior that allows for better modeling of vascular structures with topological flexibility. The deformable graph prior, adapting to different vascular morphologies, is a key distinction that enhances the robustness and generalizability of GraphSeg across domains, as demonstrated in the ablation study\n- Anatomical Consistency: BayeSeg focuses on shape-based decomposition without explicit structural alignment to a prior, while GraphSeg integrates anatomical constraints through the deformable graph prior, leading to better vessel structure continuity\n- Domain Generalization: By jointly modeling anatomical topology and image structure, GraphSeg performs better in unseen domains, as evidenced by experiments on multiple retinal datasets\n\nNotably, the deformable graph priors are derived from a shared retinal atlas, enabling the modeling of dependencies between vascular structures across different retinal images. This fundamentally distinguishes GraphSeg from conventional models (e.g., BayeSeg), which operate independently on each image under the i.i.d. assumption, thus neglecting cross-sample anatomical dependencies.\n>> W2(c) Lack of Code Availability.\n\nA2(c): We are committed to making the entire code publicly available upon acceptance of the paper. The pre-processing strictly follows [1] by performing their code on the CHASE dataset.\n\n[1] PAMI’24. Statistical analysis of complex shape graphs.\n>> Q3. Is GraphSeg the first method to use a retinal atlas or Bayesian framework for retinal vessel segmentation? how does GraphSeg differ from others?\n\nA3. To our knowledge, GraphSeg is the first method to combine a deformable graph prior with a Bayesian framework for retinal vessel segmentation. While prior works have explored Bayesian frameworks and anatomical priors separately, GraphSeg introduces a novel approach by using deformable retinal graph priors that adapt to various vascular structures across datasets. This is a unique contribution that distinguishes GraphSeg from previous methods.\n\nPrevious works like BayeSeg have employed Bayesian frameworks for segmentation but only focused on compact anatomies such as heart and prostate. Similarly, graph-based approaches have been used in CT vessel segmentation [1], but they tried to construct image-specific graphs from the first-stage segmentations to further refine segmentations by graph convolutional networks, which is different with our image-agnostic deformable graph priors constructed from retinal Atlas for informing vessel topology.\n\n[1] Graph Convolution Based Cross-Network Multi-Scale Feature Fusion for Deep Vessel Segmentation\n>> Q4. ...how consistent is the distribution of the constructed retinal atlas... the generalization of the constructed retinal atlas...\n\nA4. The distribution of vessel graphs are different as shown in Figure 3 in appendix. However, since our graphs are deformable with $\\delta$ for capturing displacement, the graph atlas extracted from CHASE can be transferred to other datasets. To evaluate the generalizability, we use the graph prior from the CHASE to train GraphSeg on the DRIVE dataset. The results and explanation are shown in the response A1(a) to W1(a). The results show that the graph prior extracted from one dataset can actually be used for the other dataset.\n>> Q5. ...computational complexity...\n\nA5. We provide the computational cost comparison as follows. The computational costs are comparable for GraphSeg to other methods. In the inference stage, we only need to run the Decomposition (green in Figure 2) and Segmentation (blue in Figure 2) parts. Therefore, the computational costs are comparable. Besides, without the Deformable graph prior, GraphSeg is downgraded to BayeSeg, thus the computational costs are almost the same for GraphSeg and BayeSeg for inference. We trained GraphSeg for 2.8 hours on GTX 4090. Since each method uses different training settings, it is not directly comparable. Therefore, we focus on inference metrics which are more relevant for practice.\n\n|Model|Param(M)|GFLOPs|InferTime(s)|Mem(MB)|\n|--|--|--|--|--|\n|[1]|18.32|89.59|6.23|925.42|\n|[2]|7.38|55.19|4.67|374.65|\n|[3]|34.88|66.54|2.08|269.80|\n|[4]|9.33|16.73|5.99|330.72|\n|[5]|3.51|7.18|2.82|160.07|\n|[6]|2.60|6.72|6.45|180.37|\n|[7]|39.09|152.71|3.20|323.44|\n|[8]|0.48|2.33|1.59|37.66|\n|BayeSeg|19.32|88.82|7.95|144.50|\n|GraphSeg|19.32|88.82|7.78|145.95|"}]

Author rebuttal:

Meta-review: This paper presents an interesting formulation for retinal vessel segmentation, which integrates anatomical graph priors to enhance cross-dataset performance. During the review process, reviewers pointed to the lack of sufficient methods compared in the empirical validation, questioned the computational overhead introduced by the proposed approach, as well as the limited size of the employed datasets. After discussions, the authors successfully addressed most of these comments, which led to all the reviewers recommending the acceptance of this work, particularly due to its potential impact in cross-dataset settings. After reading all the comments, I believe that this work could be accepted, as it brings an interesting probabilistic segmentation method tailored to the retinal vessel segmentation task, and thus interesting for the medical community (or other domains whose images share structural similarities with vessels). Having said this, I also believe that additional datasets (e.g., AV-WIDE, IOSTAR, or UoA-DR, for example) could have been used to strengthen the empirical validation, as they are used in relevant papers and offer distinct challenges to the datasets employed (for example multi-centric and multi-devices images).
Decision: Accept (poster)