GraphMorph: Tubular Structure Extraction by Morphing Predicted Graphs
Authors: Zhao Zhang
Ziwei Zhao
Dong Wang
Liwei Wang
Venue: NeurIPS 2024 poster (2024)
Keywords: Image Segmentation
Tubular Structure Extraction
Branch-level Features
Graph Representation
Primary area: machine_learning_for_healthcare
TL;DR: We propose GraphMorph, which enhances tubular structure extraction by focusing on branch-level features, using a Graph Decoder and Morph Module to achieve topologically accurate predictions, and demonstrating effectiveness across multiple datasets.

Abstract: Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks, such as blood vessel segmentation and road network extraction. Diverging from traditional approaches based on pixel-level classification, our proposed method, named GraphMorph, focuses on branch-level features of tubular structures to achieve more topologically accurate predictions. GraphMorph comprises two main components: a Graph Decoder and a Morph Module. Utilizing multi-scale features extracted from an image patch by the segmentation network, the Graph Decoder facilitates the learning of branch-level features and generates a graph that accurately represents the tubular structure in this patch. The Morph Module processes two primary inputs: the graph and the centerline probability map, provided by the Graph Decoder and the segmentation network, respectively. Employing a novel SkeletonDijkstra algorithm, the Morph Module produces a centerline mask that aligns with the predicted graph. Furthermore, we observe that employing centerline masks predicted by GraphMorph significantly reduces false positives in the segmentation task, which is achieved by a simple yet effective post-processing strategy. The efficacy of our method in the centerline extraction and segmentation tasks has been substantiated through experimental evaluations across various datasets. Source code will be released soon.

GraphMorph: Tubular Structure Extraction by Morphing Predicted Graphs
Zhao Zhang Ziwei Zhao? Dong Wang² Liwei Wang
Center for Data Science, Peking University "Yizhun Medical AI Co., Ltd
SState Key Laboratory of General Artificial Intelligence,
School of Intelligence Science and Technology, Peking University
*Center for Machine Learning Research, Peking University
Pazhou Laboratory (Huangpu), Guangzhou, Guangdong, China
zhangzh@stu, pku. edu. dong. wang@yizhun-aii com
ziwei www.zzaaooiiiuuaaaa aii.ai.ooo com wanglvūpku www.:pppkuuuuuu..o.oo edu.
Abstract
Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks, such as blood vessel segmentation and road network extraction. Diverging from traditional approaches based on pixel-level classification, our pro- posed method, named GraphMorph. focuses on branch-level features of tubular structures to achieve more topologically accurate predictions. GraphMorph com- prises two main components: Graph Decoder and Morph Module. Utilizing multi-scale features extracted from an image patch by the segmentation network, the Graph Decoder facilitates the learning of branch-level features and generates a graph that accurately represents the tubular structure in this patch. The Morph Module processes two primary inputs: the graph and the centerline probability map, provided by the Graph Decoder and the segmentation network, respectively. Employing a novel SkeletonDijkstra algorithm, the Morph Module produces a centerline mask that aligns with the predicted graph. Furthermore, observe that employing centerline masks predicted by GraphMorph significantly reduces false positives in the segmentation task, which is achieved by simple yet effective post- pestt-rocessing strategy. The efficacy of our method in the centerline extraction and segmentation tasks has been substantiated through experimental evaluations across various datasets. Source code will be released soon.
Introduction
Extraction of tubular structures is an essential step in many computer vision tasks [39 13
In medical applications, accurate segmentation retinal vessels can provide crucial insights into various cardiovascular and ophthalmologic diseases (8). In the field of urban planning and geographic information systems, the precise extraction of road networks aids in traffic management, urban devel- opment, and emergency response planning (28). Existing deep learning- based methods model tubular structure extraction as pixel-level classification task [34] or point set prediction task [40], without explicitly predicting the topological structures. To focus more on topology, some advanced methods design novel backbones or modules [36] 23 (33, or introduce new loss functions from the topological perspective [14 37 25 However, they are still limited the framework of pixel-level prediction.
We argue that most pixel-level frameworks have not effectively exploited the nature of tubular structures, which are inherently composed of several branches that are interconnected in complex ways. Specifically, pixel-level loss functions, like softDice Loss (26) and Focal Loss [20). struggle with subtle inaccuracies and are particularly ineffective at addressing complex topological errors.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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(b) Label
(o) DiseL
(d) eiDiceLoss
(c) GraphMorph
Prodiction
(a) Image
Diec, cfDico
82.72, 92.03 4,
84,98, 95.17
87.39, 97.83 0,
97.83
Bu error, x emoo(UX
0,
Graph
Figure 1: Illustrating the impact of topological feature utilization segmentation accuracy. (a) An input neuron image. Column (b) Ground truth with segmented membranes (white) and its centerline (blue lines); the constructed graph (nodes in red, edges in green). Column (c) and (d) Predictions of two methods [66 37] without explicit topological learning, highlighting broken branches (false negatives in yellow), redundant branches (false positives in green), and topological errors (in red). Column (e) Our GraphMorph guarantees topological accuracy by learning explicit branch-level features. Details of skeletonization and graph construction are given in Appendix Evaluation metrics: Dice and clDice (higher is better), So error and x error (lower is better).
Under the pixel-level frameworks, despite attempts to pay more attention to fine branches topological features [14 (33,, they still struggle with fully capturing the complex topological nature of tubular structures. We demonstrate this deficiency by providing example in Figure [ For systematic understanding of the issues of pixel-level frameworks, we summarize them into three categories: (1) Broken branches or false negatives (FNs), (2) Redundant branches or false positives (FPs). (3) Topological errors (TEs). Therefore, understanding tubular structure extraction solely from pixel-level perspective is fundamentally flawed.
37 2 or
Recognizing these limitations, we shift our focus to branch-level features. which are more essential for accurately capturing the nuances of tubular structures. Any complex tubular structure can be broken down into several branches, which distinguishes from non-tubular objects. This perspective inspires to extract tubular structures in two steps: (1) predicting the location of the two endpoints of each branch; (2) finding the optimal path between the two endpoints of each branch. Such solution is intuitively aligned with human perception, and able to offer several advantages. Specifically, the endpoints of branches are accurately predicted the first step, redundant branches (FPs) are then potentially reduced; and the second step ensures that there is path connecting the two endpoints of each branch, so that broken branches (FNs) and TEs are effectively suppressed. Besides, learning branch-level features during training elevates the model's focus on topology, which implicitly improves topological accuracy.
To effectively utilize branch-level features of tubular structures, we propose GraphMorph, pipeline for obtaining topologically accurate centerline masks. GraphMorph consists of Graph Decoder and training-free free Morph Module, which corresponds to the two steps of our solution respectively. The Graph Decoder, given multi-scale features extracted from an image patch by segmentation network, predicts the graph G of the tubular structure. G is defined by node set V= {(ri, v)) 1 which contains the coordinates of all critical points vital for maintaining topology, and an adjacency matrix A E {0, 1) NNN, which encodes the connectivity among nodes. Fach pair of connected nodes in the graph corresponds to two endpoints of branch of the tubular structure, thus the Graph Decoder takes full advantage of branch- features through this graph representation. Technically, the prediction of is addressed as a set prediction problem, solvable by our modified version of Deformable DETR 49). To efficiently obtain the adjacency matrix A, we design lightweight link prediction module that capitalizes on the extracted node features. Concretely, since the number of nodes in each tubular structure may be different, generate linear weights and biases dynamically conditioned on node features, and the adjacency list of each node obtained from its corresponding linear parameters (See Figure Z.
The Morph Module, a core contribution of this work, intended to obtain topologically accurate centerline masks. While studies in the image-to-gree to-grphh task [38 32 also utilize graph representation,

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they struggle to directly obtain accurate centerline masks due to the curved nature of tubular objects. In contrast, our Morph Module generates topologically accurate centerline masks via a novel SkeletonDijksttra algorithm. Specifically, a centerline probability map Pm. together with the graph G, output by the segmentation network and the Graph Decoder respectively, serve as the input to the Morph Module. Afterwards, considering the skeleton property of centerlines, our SkeletonDijkstrr algorithm finds the optimal path between each pair of connected nodes. In particular, during path finding from the start point to the end point, we always restrict the path to single pixel width to satisfy the skeleton property of centerlines. Consequently, the topology of the resulting centerline mask is guaranteed by G. leading to reduction in TEs. This method also minimizes the occurrence of broken branches (FNs) and redundant branches (FPs), which is a significant improvement over direct pixel-level operations on Pm. such thresholding.
We conduct the experiments by beginning with the centerline extraction task to verify the effects of the two components of GraphMorph. Experimentally, serveing as an auxiliary training module to learn the graph representation, the Graph Decoder enhances the segmentation network's focus on branch-level features, thus both volumetric metrics and topological metrics are boosted. Furthermore, employing the Morph Module at inference stage considerably improves topological metrics. For the segmentation task, we develop streamlined post-processing strategy to refine segmentation masks via the topologically accurate centerline masks output by the Morph Module, significantly suppressing false positives of segmentation results. To verify the effectiveness of Graph and the post-processing strategy, we conduct extensive experiments across four typical tubular structure extraction datasets. We have applied our methodology on three powerful backbones and achieved consistent improvements in all metrics. Moreover, compared with the state-of-the-ard methods, our approach achieves the best results across all datasets.
In a nutshell, our contributions can be summarized as the following: (1) We introduce GraphMorph, an innovative framework specifically tailored for tubular structure extraction. Based on the proposed Graph Decoder and Morph Module, the branch-level features are fully exploited and the topologically accurate centerline masks are derived naturally. (2) For the segmentation task, an efficient post- processing strategy significantly suppresses false positives via the centerline masks predicted by GraphMorph, ensuring that the segmentation results more closely aligned with the predicted graphs. (3) Experimental results on three medical datasets and one road dataset underscore the effectiveness of our method. For both centerline extraction and segmentation tasks, GraphMorph has achieved remarkable improvements across all metrics, especially in topological metrics.
2 Related Work
Image segmentation of tubular structures. Deep bearning-based methods have achieved impressive results in segmentation tasks 21 34 [5 To further enhance the segmentation performance of tubular
structures, novel network architectures [16,
40 33] and sepology-preserviig 33) have been proposed. For example, in terms of network architec- ture, DSCNet [33] utilizes dynamic snake convolution to capture fine and tortuous local features;
22
36 41
23
45
loss functions [14 29 37 25
PointScatter [40] explores the point set representation of tubular structures and introduces a novel greedy- region-wise bipartite matching algorithm to improve training efficiency. of loss functions, clDice [37] proposes differentiable soft skeletonization method and achieves loss calculation at centerline level, which implicitly helps model focus more on the fine branches; TopoLoss [1] and TCLoss 33 measure the topological similarity of the ground truth and the predic- tion via persistent homology. Despite these advancements, all of the above methods are still confined to the framework of pixel-level classification and can not entirely overcome their inherent limitations.
terms
Our method attempts to morph the predicted graphs of tubular structures to let the network focus more branch-level features, thus ensuring the topological accuracy of predictions.
Image to graph. There are two mainstream subtasks this area: road network graph detection 43 38
12] and scene graph generation [17 19.. These tasks usually entail detecting key components as nodes (i.e., key points in roads, objects scenes) and determining their interrelations as edges (i.e., connectivity in roads, interactions in scenes). Our work differs from these approaches in three ways. Firstly, we use only junctions and endpoints as nodes, which allows for explicit semantic characterization of nodes in our graph representation, unlike road network detection tasks where path points may also be regarded as nodes. Secondly, considering the curved nature of tubular objects, we propose Morph Module to obtain topologically accurate centerline masks, a goal that is not addressed
3

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Segmentation network
Imput image
ROI Align
Probability map
Ground truth
Graph Decoder
Modified Deformable DETR
Kig ou agnalg
Cuardinate Read
Soash Prote
Tranfonnee Fneeder
Transfommer Daceder
Goods
Fand Precl
fcature tokees
Ouguui queics
Filter
Position encoding
Node queries
Adjacency matrioes
Link prediction module
ReigteedBCEB Los
Matched queries
Centitzon MLP
052
6:11
034
Contiioo weight & his
Valuo
Stanedd
Link prediction module
E75
4.30
073
302
022
6:31
8:0
846
Figure 2: Overview of the training process. Given an image, the segmentation network outputs probability map the centerline or segmentation and produces multi-scale feature maps. Then, regions of interest (ROIs) are randomly sampled from the image, and their corresponding features fed into the Graph Decoder, which predicts the nodes within these ROIs using a modified Deformable DETR and outputs the adjacency matrices utilizing the proposed link prediction module.
by these works. Finally, our dynamic link prediction module is time-efficient, compared with elaborate and time-consuming designs in these works, such [rin]-token in RelationFormer (38). For a clear understanding, we experimentally compare the differences between our approach and RelationFormer in Appendix[[ [ These distinctions make model not only time-efficient but also applicable to the task of tubular structure extraction with more complex topology.
3 Method
This section provides a detailed description of the training and inference procedures GraphMorph. illustrates Figuureeillustrates the training process of approach, where the segmentation network and Graph Decoder are included. We detail these two components in Section [3.1 and 3.2 respectively. The training details are given in Section 3.3 Section (.44 introduces the algorithmic flow of the Morph Module, followed by the inference processes for the centerline extraction and segmentation tasks.
3.1 Segmentation Network
The segmentation network processes an input image 7 with shape H x W. It serves purposes: (1) outputting probability map of tubular structures; (2) providing multi-scale features for the Graph Decoder. For training efficiency, we randomly sample R regions of interest (ROIs) with size H H in the feature maps (R 3 in Figure 2 for illustration). The ROI is defined as any region containing centerline points. The adoption of ROIs brings two key benefits: reduces the model's learning complexity due to simpler topological structures within each ROI, and improves training efficiency by decreasing the number feature tokens processed in the transformer. Technically, We adopt ROI Align [10] to extract multi-scale ROI features. Note that the generality of Graph allows it to be adapted to any type of segmentation network. In the experimental part, we validate the enhancement of GraphMorph on variety of segmentation networks.
3.2 Graph Decoder
The Graph Decoder is intended to predict the graph for each ROI. Specifically, the modified De- formable DETR A9 is responsible for detecting the nodes, while the link prediction module handles predicting the connectivity among these nodes. In the following, we will dissect each component to elucidate their roles.

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Modified Deformable DETR. We have made two adjustments to the standard Deformable DETR 49 Firstly, since the targets are nodes with only 2-dimensional coordinates, we replace the original box head with coordinate head that outputs 2-dimensional vectors. Secondly, considering the typically small size of ROIs, we reduce the number of layers in the transformer encoder to three while keep the decoder at six layers. Note that each ROI is treated as an independent sample and different ROIs will not interact with each other in the whole training process. Formally, the process of node prediction can be expressed as follows:
F Transformer
PF)
Q' TransformerDecodeer (F*.Q)
(2)
8" = Sigmoid ClassHeed (Q*)).
0" = Sigmoid (CoordHeadd (Ør)
(3)
where r = 1,,,.... R. F E LX denotes the multi-scale features of the r-th ROI, and Q E kxc is the initial node queries, where L and K are the scale of feature maps and the number of node queries respectively. PE is the multi-scale sinusoidal positional encoding used in [49]. ClassHoad is single linear layer, and CoordHead is a 3-layer multilayer pereeptron (MLP). S" R and 6" E RR xx2 are the classification scores and coordinates of the nodes for the r-th ROI respectively.
Link prediction module. Since the number of nodes for each ROI may be different, we design a dynamic module generating linear weights and biases conditioned on node features to directly predict the adjacency matrix A. For the r-th ROI sample, Q" E RRKx is the output queries of the Transformer decoder. The queries matched with the ground truth nodes (the number is denoted as P,) during the bipartite matching process are preserved, and the rest queries are filtered out. We denote the kept queries as Q" E RR,. As depicted in Figure 2 the matched queries Q" will be fed into two MLPs, The ConditionMI.P generates a (C + 1)-dimensional vector for each matched query, which serves as the weights and biases of the condition linear layer. The ValueMLP maps the queries to a value space. With the values as input, the condition linear layer of the p-th query generates the adjacency list of it. The process can be formulated as follows:
W ConditionMLP((2)) E ERC1 V VaaleeML(Q") E P.
(4)
A = Sigmoid V + (Wplc+1) E
(5)
Ār [(Ar)* (Āz)* (Ax, 7"1 e R.PP.
(6)
where p = 1,,, ..., Pr.. Here, Q7 denotes the p-th item of Q", and C' is its dimension. W refers to the linear parameters conditioned on the p-th matched query. AS represents the predicted adjacency list for the p-th matched query, and the concatenation of all lists forms the final adjacency matrix Á".
3.3 Training Details
Graph construction. To train the Graph Decoder, we represent the ground truth of each ROI as a graph (see Figure 2. The detailed graph construction process can be found in Appendix B
Label assignment based on bipartite matching. Bipartite matching is widely used in solving set prediction problems 12 49 40). As in (4), we first calculate the cost between the predicted and ground truth nodes. The predicted nodes are denoted as 9 = {(5A. 6x) > where we omit the index of the ROI sample for simplicity. Under the general assumption that K is larger than the number of ground truth nodes P,. thus we pad the set of ground truth nodes with Ø (no node) to achieve a size of K. The ground truth set can be denoted as
{(,, e.) })) where is the target class label and v E (0, 1 is the coordinate of the node. For a permutation a E G k. where (o(()) is assigned to y: K), we define the cost between y: and (1) as:
(i (6=11
2, 1,
Cmatch Mo(s)) ) = Aclass
Colass Colas + Accond 1l (art Ccoord Cooondi (V;, (o(1))
(7)
where Aetass and Aecond are hyperparameters. (
(rocat( 1) - Liveal (t): 0),
(i e) is defined as -a . (1 "
log(s) if c 1, and -(1 - a) 8" log(1 8) c
where a and y are hyperparameters. foond is commonly used ej loss. The optimal à is defined as
K
ô arg min
Liaath (vi, (o(s))
(8)
GE
1=1
5

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This optimal assignment can be efficiently obtained by Hungarian algorithm [8]
Loss functions. To train the Graph Decoder, the overall loss function is comprised of three compo- nents: pixel-wise loss Pisel between the probability map and the ground truth binary mask (in this work, we use softDice [26] and cIDice (37)), Hungarian bipartite matching loss Litungarian between the predicted and ground truth nodes, weighted-BCU loss Lddjacency between the predicted and ground truth adjacency matrices of the matched queries. For image with It ROI samples, the last two loss functions are defined as:
Huunariin (y) 13)
Σ
Aelass Lincal (8/ca))88)))))) (8)(0)) 4i + Acoord { (oh0)) u;))
(9)
R
P.
P.
P.
Pr
0.5
0.5 Nneg
Lddjaconcy (y, 1)
=
A log Ai,) +
[11
Ary) log(1 - Ab (10)
pos
{
j=1
$#1 1=1
where pos is the total number of positive locations in ground truth {A-)==1 12 number of negative locations. Thus, the overall loss function is Luaat Lrisel LHungurian Adjacency
and Nnce is the total Jr=1
3.4 Morph Module and Inference
The Morph Module is used to get topologically accurate centerline masks, by morphing the predicted graphs from the Graph Decoder. In this subsection, first introduce the Morph Module, followed by the inference processes for the centerline extraction and segmentation tasks.
Morph Module. We present the algorithmic flow in Algorithm [ In particular, G {V, E} the graph of an image patch (same size as an ROI sample), and Pm is the probability map of centerlines obtained from the segmentation network. We iterate over each edge and use our proposed SkeletonDijkssraa algorithm to find the optimal path with minimum cost. The union of these paths forms the final centerline mask.
Skeleton Dijkstra modified from Dijkstra algorithm 7 We have made two key adaptations for centerline extraction: (1) To restrict the path to single pixel width, ensuring the property of the skeleton, we mandate that all path points, except for the start and end points, satisfy N (where N is the number of centerline points in its eight neighbours, see Appendix B). (2) To suppress potential false-posine poss-posiivee edges from the Graph Decoder, we exclude the paths with an average cost exceeding a threshold pthresh- These refinements optimize the algorithm to yield topologically accurate centerline masks. The detailed algorithmic flow of SkeletonDijkstte can be seen Algorithm Zjn Appendix D
Algorithm 1 Morph Module
Input: Node V, Edge E, Probability map P... Output: Centerline mask M
Initialize M zero matrix with the same size Pm
Initialize C.. where Cm [i]]]]]]] = - Pm][i]] for each element
for all edges (u, v) in do
path + SkeletonDijkstra(u, v. Cm. Pthrresh)
for all points p in path do
Set M [p.x]] [p.y] =
end for end for return .
Inference centerline extraction. As depicted in Figure 3 the centerline extraction process begins with generating centerline probability map via the segmentation network. Then, sliding window inference is employed across the entire image in Graph Decoder to obtain graphs for all split patches. Finally, the Morph Module produces the centerline mask for each patch, and the combination of these masks forms the complete centerline mask of the entire image.
Inference of segmentation. Since the segmentation probability map S., can not be used directly by the Morph Module, we first threshold S,, to obtain segmentation mask S and skeletonize into centerline mask p The distance from each pixel to the nearest centerline point in P is calculated

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Segmentation netwerk
Thresheld
Ingut image
Multi-scale features
Centectine probability
Threshold-only result (for comparison)
Gruph Marple
Gruph Decoder
Morph Module
Ground truth
G Predicted graphs
M
Final prediction
Figure 3: Inference process of centerline extraction. First, the segmentation network generates centerline probability map Pm along with multi-scale image features. Subsequently, the Graph Decoder utilizes the image features to predict graphs G via sliding window inference. Finally, the Morph Module employs Pmm. to find the optimal path between each pair of connected nodes in G, resulting in final centerline mask. This approach achieves higher topological accuracy compared to direct thresholding of Pm-
and normalized create distance map D. Then the centerline probability map Pm is obatined by Pm. = Sm x (1 D). Employing the Morph Module on P.. yields a topologically precise mask M To suppress false positives in 5%, (especially isolated regions), post-processing strategy is initiated from Mo = M @ Sm This strategy involves iteratively expanding Mo within the boundaries of St until stabilization. The stabilized mask MT is then taken the final output. This approach, as confirmed by experiments, effectively diminishes false positives and enhances topological accuracy. The meettomee soft skeletonization method (from S. to Pm)) and post- proccssons strategy introduce minimal time cost and are straightforward to implement, with detailes in Appendix [E.] and Appendix E.2
Experiments
4.1 Experimental Setup
Datasets. We evaluate GraphMorph three medical datasets and road dataset. DRIVE 39 and STARE [13] are retinal vessel datasets commonly used in medical image segmentation. ISBI12
contains 30 Electron Microscopy images segment membranes. The Massachusetts Roads (Mass- Road) dataset contains 1171 aerial images for road network extraction. We use the data splits for DRIVE and STARE provided in MMSegmentation 66. For ISBI12, following previous works (35] we split it into 15 images for training and 15 for testing. For MassRoad, we follow [40] to construct the training set, and the total 63 images of the official validation and
are used for testing.
Baselines. We adopt affluent baselines for comparison, including UNet 34], ResUNet [47), CS-
Net (30]. DC-UNet (22), TrensUNet [4, DSCNet (33] and PointScatter [40] Partieularly.
LinkNet34 3 and D-Linknet34 48 as baselines for the MassRoad dataset. In addition, we compare
with TopoLoss [44 which is topology based loss function.
Metries. For the centerline extraction task, we use Dice [50), Accuracy (ACC) and AUC as volumetric metrics. For robust evaluation, we give tolerance of a 5- 5-pixel region around the ground truth centerline mask following [9] We compute topological metrics following [40]. including the mean absolute errors of So. 81 and the Euler characteristie. To compare fairly, skeletonize the prediction before evaluation. For the segmentation task, we adopt Dice, clDice 37 and ACC as volumetric metrics and the same topological metrics the centerline extraction task. Moreover, ARI (Adjusted Rand Index) 15 and VOI (Variation of Information)
24 are used to evaluate clustering similarity.
Implementation Details. For three medical datasets, we use randomly cropped 384 x 384 images for training. The size of ROI samples is 32 and the stride of sliding window used inference process is 30. For MassRoad dataset, the cropped size is 768 x 768, H = 48 and the stride is 45. For all experiments, we use 64 ROI samples per image (R 64) to train the Graph Decoder, and the number of node queries in the modified Deformable DETR is set to 100 (K 100). According to previous

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experiences [3], the default hyperparameters used in loss functions are as follows: Adtass = 0.2, Assord = 0.5, a 0.6, 7 = 2. We use a 0.75 for MassRoad due to the sparse nature of the road networks. For all types of segmentation networks, we use multi-scale features ranging from the lowest resolution to the xx downsampling of the original image as input of the Graph Decoder. More implementation details are introduced in Appendix A.
Table I: Centerline extraction performance on four public datasets based on UNet.
Donrect
Mathoal
Velumetrio mntrics (?)
Tepalogical metrics (4)
Dice
AUC
ACC
Sg crner
D, crce
3 eeeor
softiiie 20
0.7253 0.0127
01933 a 0L0099
0.9708 = 0.0015
2.109 2 0.112
1,590 0.107
2.537 0.139
DRIVE
SonE 25
PonneScattze (0)
Griph Decoder
0,7506 0.01277
0.2381
0.0113
0.800
0.9851
+: 1.000
0
0.9755
0,9783 0.0912
2 0.0055
3.259 2 20.15
1.552 2 0.064
2,080 00110
3,500 2
1
saftxor
+ Griph Decoder+ + Morph Modale
0.3496 0:01
0.9766 e 0.0012
0.588 a 0.038
1,074
0.973
0.893 0.061
sofe 20
0.5428 0.0104
0.893
0000063
0.977 = 00,003
4.045 2 0.
2.113
0.205
1
Diee (6) Groh Trooder
Pointscatter 20
0.6565 0.0089
0.5486 000095
09101
0.9240
+000057
0.0061
0.942 0.0002
0.0913 0,9747
4 0.177
6,308 a 0.277
3.156
2.793 0:010
0.1224
6.548
oi 26 + Cluph Deonder + Morph Modele
0.6687 0.0092
0.9742 0.0014
0.665 a 0.049
0.858 0.859
Dift Un
1:7119 0:0991
0.9200
0.0333
0.989
0.0012
1.874
1,200 0.113
2.063
STARE
annDxee (26 Clugh Dexoder
Peintscatior 20
0.7298 0J8428
0:7234 0.0414
0.9494
(L3506 0J0200
0.0179
0.9866
0,98%
0.0012
0.149 2,060
1.467
1 0:04
1,365
0.116
2.213
1:654 0:119
sonDiie 25 + Grugh Desoder + Morph Modale
0.7291 0.0387
0.9899 a 0.0011
0,482 = 0.042
0J977
1.633
softDice
0.6339
019718
000047
0,9922
0.0909
L 0,116
0.0087
1,968 0.097
MassRoad
sofDice 26 Grugh Deodeer
Peintsctterr [00
0.6405 00.014
0.6289
=0.0175
819694
(19731 BJINA5
0L0142
0.1009 0.9941
0,9942
3.333 a 0.134
8 0.0K5
1.729 01088
0.006
2.229 0.100
3,429 0.144)
sonDioe
a Grugh Decoder e Morgh Module
0.6385 0.0016
0,9942 0.0009
0,620 = 9.021
0.003
1.123 0.075
4.2
Main Results
We first verify the effectiveness of GraphMorph on the centerline extraction task. Then, considerable experiments are conducted on the more common segmentation task, demonstrating the powerful topological modelling capability of GraphMorph.
Centerline Extraction. In our experiments with UNet and softDice loss on four public datasets, detailed in Table T the inclusion of the Graph Decoder during training enables the network to learn branch-level features, leading to enhanced performance in both volumetric and topological metrics. During inference, the utilization of Morph Module results in a slight decrease in volumetric metrics; however, there is notable enhancement in topological metrics, confirming that our network has effectively captured branch-level features of tubular structures. Overall, the combined use of the Graph Decoder and Morph Module showcases the ability to refine the segmentation network's performance, particularly in preserving the crucial topological characteristics. Our methods also beat previous SOTA Pointscatter [40] by a large margin..
Table 2: Segmentation performance based on different segmentation networks.
Datsor
Hackbwne
Mahvol
Volumetri metkss (f)
Distibbtioon
Tepologioll metrics
Dian
ziDio
ACC
ARK
VOLU
R. cemee
UNe 54
Uithice-Ours
sofiDiic 25
0.8188
0 0.0600
0.535
0.0023
0.26720001
0.346 0002
0.002
1 10.000
1003
DRIVE
Red
Exl
sofiltie: 25
08865
0.2233 1 0,809
0.094
05183
0.2233
0UI172
0.9541
03555
B.022
0.777 8 0U011
0.231
10011
01336
1001
0.723
1 1.96
à RU44
0986 A 0J01
10591000
0L993 0J63
1.5001000
softDice 26
0,909=00012 000123
0.503 0.0:85
0.9520 0.0027
0.761
0.350
1211 20.073
L015
1.00
UNe 3
sofiDiee SeftDiceoOurs
26
222066
=00092
0.295
0.9419 2 0,086
0.0088
0.9166
0,211
2 0.087
0.0050
2.05
2
0.785
0.745
0.000
0.039
(.361 1 100034
0.569 1.945
0.520 0003
0665
2.736
0.455
15R112
sontiie Kg
01366
0.900 0J006
0 0,0055
00017
2017
01573 +0045
01700
CS Ne M
sofiDie 26 SeftiicerOuus
03163 =0611
0.0115
0.991
0.9499 000051
a 0.0022
0.9144
0.243 2 0,066
0.0075
2.63
0.754 0.49
0.723 20145
0:45 20,000
0.342
100034
0.515 0.16
20043
2
NG
SeftDcceOuurs
0
0.766
STARF
INd
sonDice X6
08151 2: 8.8513
+.7962=00022
01343
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0.761 0185
0.77910053
U.253 01136
1
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1
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SeftDicerOurs
1b
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0122420062
UNo 4
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NG
0.0199
00018
0.8816 00151
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0.9700 + (10016
0,773 = B.005
0.754:00016
01237
133700003 0.03
0.386 : 00016
0.879
0 11166
0.754
4177
MasiRoud
RoUNN::
sottiie [% SeftDiceeUurs
01563
09973
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a
C5.Ns.
SeftDicer Ours
sofillic [b
0,770 0.0147
0.4119
(17715 0.0K3
0.876 00163
0877 D.005
0,979 = R,005
I1245: (181
2.741
(1240 0012
01340
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[1437
0.773
0.75 1 gins
0:254 I1P
Segmentation. In the initial phase of our segmentation experiments, we assessed the effectiveness of our method across different segmentation networks and datasets. As detailed in Table enhancements were evident in various metrics for all dataset and network combinations. The improvements in
8

---

Table 3: Comparison with SOTA methods on the segmentation task. Best results are in bold;
second- besst are underlined. Our approach secures all leading scores and most secondary peaks.
Datacd
Badlsce
Moleo
Wiaremtic (orricit)
Tepulegiol (eriiv(()
ACC
2i coee
UNe UNn
naiis 1005
08128 6 m100
0.955 + D0331
0.567 +0.01
0 -2000
191 101-0000
1 0015
1.907 6
cilice 22
08850
1075
08500 +5 0165
c D0371
0765 -1:05
0 337 -000
0 0990--0000 0176
1:181 + +0171
Polmocter LB
nares 100
C 00370
0758 +1:005
140-01800 118
-20 -010
DRIVE
DSCSa 13
sofiibec
[11111 201003
08107 22
00002 g 00032
0053 103352
0.52 0.01
1257 2005
1,500 x 00857
sofiBber
08855 20.0044
20.082
00338 4 00323
0.58 0.080
0 1344 00000
205200000
1154-25 206-20082
1,20 x (URR2
20.000
05006500006
00502
127=0000
UNa
03278
UNei
0.8168 20,007
25507.9.000
00030 g 00321
0.67 0
0.55 0.00
g 8/M
0357 8 6/355
UNe
wnttis 12
8 00000
09995-6 -07755
Co + D033
DA51 600
0 0.000
0 500 0066
0
0.738 + 0055
<ifice
n8107 -1:000
09001-01100
COICT+ B0W
BASC 11200
8 113 m18
961 0085
15112
DSCNa (3
USe
Tepodano
sofiliee
08104 20000
08151 20:067
0.554 20.07c
20.075
C010 2 00034
C0107 a 00355
059, 0
0699 10005
0257 2003
0.733 0.00
0 0556 m61
0 0450 (4
0142 00152
0567 20145
6,581 x 0U444
(,99) a 0044)
Taa
sollliee
00:06-20:000
0.009000007 20.005
Goler 00335
0238
0754-0067
0666.2000
0.76 20167
0:71
2014
UNa
00000
10007 20/009
00011 00357
0345=000
0.561 0.301=0:00
x 0011
UNai
IC333 201666
2 60955
0.35320054
0,22 x 1:949
UNai
setikee HB
2 00034
0
0309 20172
USai
Prinocalis
08171 20.005
03555 20.051
E0043 00341
0595 0335
0255 02231
2015
0 0544 0000
0781 2009
1091 x C0095
STARE
DOCNa 13
UNg
Tepouaoo [+]
solliies
0L115 20.440
0564 20:066
0500 20189
50000 00045
0201 20:4
0226
0 000h 20106
0
166
2 20
2000
029 x 10050
DC-UNd 19
vollisae
0.3956 2.0647
0530
20.03
C0728 a 00352
0.555 0355
0255 0024
0 0354 0254:0001
0721 25
0075 x 0082
UNc
05310200044
D 18872
02713 20735
0 20146
01I5 20000
5/01 5
USe
00005
05147290054
0.14--0.022
UNa
Hg
IJ506 21.0146
USei
<lDix 22
037788
20.043
05773 20.05
C0PT5 2 00337
0:577 2 00555
0.244 0.03
0512 0012
0,06 2019
6002 a 6096
UNe
Paisocuati 48
0L785 20.042
08730 20
CUPT8 B00335
0:48 00005
012220003
0 0600-2112
2000
5000 x 00114
Tepedaso
05758
05755 20.0
CUP81 00035
01507
02:5
0 043020018
LinkNed4
sollDbe
0.7752 20.051
20.002
60775 00335
0:344 0.53
0.34 0053
0 0.69:20002
0.775 33176
6.771 a 6/772
DaLasketth 55
sollBwee
0.755 20.014
08763 000
60P75 00035
0244 0003
0 500 20102
2.265
0.777 x (U072
USa
03316200011
0
0.81
0.3531 00,013
0.201-0000
volumetric and distribution metrics underscore our method's effectiveness in the precision and reliability in segmenting and clustering accuracy. Most notably, the substantial advancements in topological metrics, particularly in the 30 error, highlight our method's 's proficiency in capturing the intricate branch-level features of tubular structures.
Moreover, the comprehensive comparisons presented in Table across various datasets underscore the superiority of our method over current ofate-of-the-art techniques. The results unequivocally illustrate that our approach excels in all evaluated metrics, outstripping other methodologies. The crux of this advancement lies in the exploitation of branch-level features. Compared to our approach, traditional pixel-level classification strategies, whether employing grid representations like softDice [26] or clDice (37) point representations akin to Pointscatter [40], inherently lack in capturing the essential branch-level features. Innovatively, Our method incorporates the graph representation to capture explicit branch-level features, and morphs the predicted graphs to topologically accurate centerline masks, which are subsequently utilized for post proccssoc....g.. The excellent performance of various metrics, especially topological metrics, proves the validity of our approach.
4.3 Ablation Study
Size of ROI (H). See 4 the experimental results on the DRIVE dataset suggest that default ROI size of H = 32 provides a favorable balance across the evaluation metrics. Specifically, when H is reduced, an increase in 30 error is observed, indicating diminished topological accuracy. Conversely, increasing H does not offer substantial metric improvements and leads to higher computational demands. Hence, H 32 is adopted the default ROI size for all three medical datasets. Similarly, the default ROI size for the MassRoad dataset has been determined to be H- = 48.
Threshold in the Morph Module (Pthresh). We conduct experiments the centerline extraction task. A smaller value of Ptbresh denotes a more stringent selection criterion, with Pthresh = 1.0 indicating that all paths are considered without any selection filter. As detailed in Table S the best results were achieved at Pthresh = 0.5, which is adopted as the default setting across all experiments.
Post-processiin processicn on the Segmentation Task. As shown in Table incorporating post pposesrocessing has led to slight improvement volumetric metrics and a significant elevation in topological metrics. Notably, the substantial enhancement in the 30 metric primarily results from the successful suppression of false positives, which aligns with our initial hypothesis. For a qualitative demonstration, we direct the reader to the visual comparisons presented in the Appendix G.2
9

---

Table 4: Effect of ROI size H on two tasks.
Table 5: Effect of Pthresh-
Sepmentation
Conterline Extraction
Dataset
p. I_thresh
Dice
ACC
Ag
81
Daraset
H
Dioc
elDice
Ai
0.25
70.90
97.67
0.815
1.528
1.121
82.61
0.763
74.36
0,771
DRIVE
0.5
14.97
91.36
0.555
1.074
0.893
32
82.44
$2.78
0.692
74.97
0.555
1.0
74.80
97.68
0.604
1,270
1.069
48
82.43
82.78
0.676
74.90
0.492
64
82.44
82.63
0.666
74.72
0,540
Table 6: Effect of post-processing.
16
78.16
87.66
0.457
61.36
2,268
Datascl
Methol
Dasc
elDix:
0 cmoe
MassRoad
32
78.33
87.90
0.414
62.90
0.944
DRIVE
w.s Phod-roasssing
R2,44
82.41
52.66
$2.78
0.932
0,692
0.982
0.932
0.951
1.199
78.53
64
78.35
57.93
0.396
63.27
0.539
Macotood
w.t. Phedepoarssing
78.45
8,68
0.757
4.4 Qualitative Results
We qualitatively analyze the role of GraphMorph in reducing FNs, FPs, and TEs the segmentation and centerline extraction tasks, as detailed in Figure 4 The results show that our method can effectively reduce the three types of errors in both tasks. This is due to the utilization of branch-level features during training and the effective design of inference process. Furthermore, we visualize the graphs predicted by the Graph Decoder well the role of the Morph Module in suppressing various errors in Appendix G.1
Segmentation
Centerline Extraction
Image
Label
softDice
elDice
GraphMorph
Label
sofiDice
GraphMorph
Figure 4: Visual comparison for our GraphMorph with other methods (zoom for details). Areas indicated by yellow arrows show false negatives (FNs), areas pointed by green arrows demonstrate false positives (FPs), and regions highlighted by red arrows are topological errors (TEs) identifiable in other methods but are accurately resolved by our approach.
Conclusion
This paper introduces GraphMorph, framework that diverges from traditional pixcl-level prediction methods in tubular structure extraction. By integrating two core components, the Graph Decoder and the Morph Module, GraphMorph adaptly captures and leverages branch-level features. Equipped with our proposed link predcition module and DicketonDijkstra algorithm, the training and inference processes of the network are efficiently carried out. For the segmentation task, it further employs straightforward yet effective post-processing strategy that substantially reduces false positives in the predictions. Extensive evaluations across various datasets for medical image segmentation and road network extraction have demonstrated the superiority of GraphMorph over existing methods, particularly in terms of topological metrics. This breakthrough not only boosts precision in application- specific tasks but also sets robust foundation for future research in tubular structure extraction.
10

---

Acknowledgements
This work supported by National Science and Technology Major Project (2022ZD011900) and National Science Foundation of China (NSFC62276005).
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14

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Appendix
A Implementation Details
In this section, we provide more implementation details of GraphMorph.
For fair comparison to previous works like PointScatter [0], we use ADAM optimizer with initial learning rate 1e-3 and cosine learning rate schedule with warm-up strategy to train the network. The weight decay is set to be le-4 uniformly. We train the network for 3K iterations for the three medical image datasets, and 10K for MassRoad. We use batchsize=4 for all datasets. We implement GraphMorph based on PyTorch [31] and Detectron2 [42]
Our SkeletonDijkstre algorithm is designed to run solely on CPU due to its computational nature. We use Pthresh 0.5 across all experiments. To enhance performance and efficiency, we have imple- mented this algorithm in C++. For detailed understanding of the algorithm, refer to the pseudo-code provided in Appendix
B Graph Construction
The process of constructing graph be briefly summarized in three steps follows: (1) Generate the centerline mask of the tubular structure using skeletonization algorithm [46]; (2) Analyze each centerline point P by counting the centerline points among its eight neighbors (denoted N, not including P). Define as a junction N 2 3 and as an endpoint if path points and are considered nodes. Junctions and endpoints form the node set V of the graph G. (3) If there is a pathway consisting of only path points between two nodes, then there is an edge between them. All edges form the edge set E. We use publicly accessible implementations of skeletonization and graph construction!
1. Points with N
However, the resultant graph may contain elements such loops (closed paths where node connects back to itself) and multiple edges (more than one edge connecting the same pair of nodes). Addressing both these elements is crucial; otherwise, reconstructing such structures during the inference process would be challenging. As depicted in Figure 5, to manage these complexities, we introduce new nodes in the following manner:
Loops: insert new nodes at selected points within the loop to break the cycle.
2. Multiple edges: After resolving loops, we then add nodes along edges where multiple connections exist between the same pair of nodes.
These modifications ensure that the graph structure simplified and ready for more effective processing during inference.
Millie
(a)
Figure 5: (a) Stages of graph construction from the binary mask of road network. The first stage demonstrates skeletonization process to a centerline mask. In the second image, we highlight the endpoints in orange and junctions in purple. Adjacent junctions are merged and considered single junction. Subsequent stages illustrate resolving Loops and reducing Multiple edges. (b) Example of calculating N.
sskinag.mmmphooegy..lelmmiigg hutps//githubb.om//naagg
15

---

Table Comparison of [rln]-token and our dynamic module on the DRIVE and STARE datasets. The "Time" metric represents the cumulative time required to process all sliding windows in the link prediction phase for a single 384 384 image patch during inference.
Node Detection (t)
Edge Detection
Volumetric metrics
Topological metrics (1)
Dataset
Method
Timels
AP@0.5
AR
AP620.
AR600.5
Dice
ACC
Ao ermor
( emoor
eerror
DRIVE
token
0.2823
52.40
58,20
23.33
37.78
74.95
97.76
0.548
1.026
0.866
Dynamic
0.1582
52.30
58.11
23.25
37.89
74.97
97.76
0.555
1,074
0.893
[=leettoken 0.1385
54.95
61.44
27.84
43.73
73.99
98,92
0.483
0.731
0.663
STARE
Dynamic
55.06
61.90
0.482
0.799
C Link Prediction Module
To validate the effectiveness of our dynamic link prediction module, we compare it with the approach used in RelationFormer [38).
RelationFormer learns additional [rin]-token during the training of DETR encode the relation- ships between node queries. the inference stage, to predict the connection between two nodes, the method concatenates the features of the two nodes with the [rin]-token into single vector. This vector is then processed by a three-layer MLP to predict the probability connection between the nodes. Let us assume that there are P matched queries, denoted as Q" E RPxC' In RelationFormer, the connection probability for each node pair is computed individually, resulting computational complexity of O(p² x ). In contrast, our dynamic module achieves a complexity of O(P x C?) 6). reducing the computational burden.
(Equation
Table presents a comparison between the [#ln]-token and our dynamic module on the task of centerline extraction. The metries "Node Detection" and "Edge Detection" reproduced from RelationFormer, which measure the accuracy of the nodes and edges extracted by the Graph De- coder. Other metrics assess the accuracy of the centerline masks output by the Morph Module. All experiments are based on UNet. The results demonstrate that both methods achieve comparable performance. However, our method significantly reduces the computational complexity, thereby shortening the inference time. This enhancement makes our approach more suitable for applications requiring fast processing speeds without sacrificing performance.
D SkeletonDijkstra Algorithm
The pseudo-code of our Skeleton SkeketonDijkssraa algorithm is given in Algorithm 2 which finds the optimal path satisfying the skeleton nature for two points.
E Details of Processing in Segmentation
E.1 Soft Skeletonization
See soft skcleton function in Listing I In the segmentation task, the segmentation network outputs the segmentation probability Sm, which we need to soft skeletonized into the centerline probability Pm, for input into the Morph Module.
E.2 Post-processing to Suppress False Postives
See dilate_with seath_see__imis limit function in Listing In the segmentation task, after obtaining topologi- cally accurate centerline masks by the Morph Module, false positives be greatly suppressed with this post-processing strategy.
F Computational Resources
Hardware Configuration. Experiments were conducted using NVIDIA GeForce RTX 3090 with 24 GB GPU memory. The CPU used was an Intel(R) Xeon(R) CPU E5-2680 v4 @ 2.40GHz, which features 28 cores.
Analysis of training process. Training on the DRIVE dataset with UNet backbone and batch size of 4 using "SoftDicc+Ours" method requires approximately 11.8 GB of GPU memory, compared
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Algorithm 2 SkeletonDijkstra Algorithm
Input:
Start point 8, End point e, Cost map C, Path threshold Pthresh Minimum
Output:
path from s under threshold Pthresh Initialize priority queue Q with (0, [s])
Initialize visited set Vis while not Q empty do (cost, path) - Q-pop()
curr f- last element of path Add curr Vis if curr then
uvg f cost/ length(path)
if avg > Pthresh then
return Ø
end if
return path
end if'
for each n in neighbors of curr do if in Vis then
continue
end if
neis meis_in-_pllh + count of nts neighbors in palh
if neis_in_pallh < then
path <- path concatenated with [v]]
cost cost C'n.xxI[nn)
(.ouss((cost,pptt path))
end if end for end while
to 5.4 GB of "SoftDice". More comparison between these two methods are show in Table The increase in parameters and FLOPs in our approach primarily stems from the integration of the Graph Decoder featuring a DETR module. This component crucial for predicting accurate topological structures of the graphs. Advancements in transformer architectures that reduce computational overhead could potentially enhance the efficiency of our model during training.
Inference time analysis. The inference times for each model component are summarized in Table 9 The data presented in the table was obtained by processing 384 384 image patch from the DRIVE dataset. ROI size is H = 32, with a sliding window stride of 30. As shown in the table, significant time concentrated on the Morph Module. The primary time expenditure currently arises from processing the patches sequentially in our sliding window strategy. However, as each patch operates independently, there is significant potential enhance efficiency by parallelizing the computations of all patches. Recognizing this opportunity, we plan to focus future work on optimizing the Morph Module by implementing parallel processing techniques to accelerate inference.
Table 8: Comparison of required resources during training.
Method
Params
FLOPs
Time per iteration (s)
GPU Memory
Softiie
39M
187G
0.203
5.4 GB 11.8 GB
softDice+Ours
48M
268G
0.589
Table 9: Inference timing for each Module.
Module
Device
Time
Segmentation network
GPU
0.0101
Deformable DETR
GPU
0.1194
Link prediction module
GPU
0.0379
Morph Module
CPU
0.2933
(Segmentation) Post- processing
CPU
0.0279
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Listing Python codes of the soft skeletonization operation and post-processing strategy during the inference process of the segmentation task.
import numpy np import ev2
from ekimage morphology import skeletonize
from scipy adinage import distance_tranaforn.
(et.eekeletoaeeeg.pro up. adarray):
centerline probabiliit dap from segmentation probability map- seg_prob: segnentation probabslity ostpst froe the segrentation Network.
10
seg_mask seg_prob 0.5
12
ske skeletoniza
13
distmap dietance_tranefore ("ake.aste astype (np. bool_))
14
distmap ap.clip(distmap, 0, 64) / 64
15
cline_prob seg-prob (1 distmap)
16
return eline_prob
17
18
def dilate_vith_ (eline_clleeealll seg_mask, kermel_aize-3)
19
suppress faise postives. cline_mask: centerline mask output from the Norph module.
process
segmentation
21
22
seg. mask: segnentation sask thresholded from the segmentation probadility map.
23
kernei,size: kernel size the dilation operation.
24
kernel op. ((kernel_pa) kernel_size), up.ti)))) res (p-nioinu seg_naak) True: dilatad_clina_ma pask er2.dilate (rea, kernel, iterations=1)
26
28
29
dilated_res dilated_
res
30
dilated_res wtt.eeeppp.miiiiii.... mp.minimum (dilattddddlltreeee...ee sog_nask)
31
dilated_cline_mat ros dilated_ros
ap.array_ aqual (dilated_cline__. break
res):
33
res silatee_cline_aee reture cliaaedd_clin_nna.
35
G More Visualization Results
G.1 Visualization of Predicted Graphs
We visualize the graphs predicted by the Graph Decoder within the context of the centerline extraction task and analyze the role of the Morph Module. As shown in Figure the first four rows illustrate the Graph Decoder's robust capability to predict graphs. By comparing the final predicted results obtained through the Morph Module (last column) with those obtained by thresholding Pm. at 0.5 (fourth column), mitigated. However, the Morph Module also has limitations. Notably, the setting of Pitesh might lead to overlooking some true- true-positive edges due to inaccuracies Pm. which is illustrating in the last two rows in Figure 6 This highlights areas for future improvement.
evident that issues such as redundant and broken branches are effectively
G.2 Visualization of Effect of Post-processing on the Segmentation Task
Figure showwcsess the impact of post-processing in mitigating false positives within segmentation tasks, procedure fully elaborated in Appendix E.2 This figure clearly reveals the elimination of isolated regions, originally predicted by the segmentation networks, across all datasets. Notably, the excision of such regions-ofter minute in scale-exerts nominal effect volumetric metrics while markedly bolstering topological metrics. This enhancement in the integrity of topological metrics through post- post-processing substantiated by the data in Table
H Limitations
Despite the advancements offered by GraphMorph, the method exhibits certain limitations. First, the reliance on post-processing for the segmentation task indicates a potential underutilization of branch-level features. Although false postives are significantly suppressed, segmentation results not always topologically aligned with predicted graphs, suggesting room for improvement in
18

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Image Patch
Centerline GT
Probability(PPn)
Thresholded
Predicted Graph
GraphMorph
DRIVE
STARE
ISB112
MassRoad
DRIVE
ISBI12
Figure 6: Visualization of intermediate results in the centerline extraction task. The results in the fourth column are obtained by thresholding P.. at 0.5. Comparisons across the first four rows illustrate that GrrphMorph achieves improved results through morphing predicted graphs. The last two rows demonstrate how the settings of Pthresh in the Morph Module may lead to concessions to Pm, resulting in false negatives.
segmentation performance. Additionally, the necessity to train on relatively small ROIs, due to the complex nature of tubular structures, requires sliding window technique during inference. This technique may not fully capture comprehensive branch-level details and the global context of the entire tubular structure. Based on the limitations, future developments will aim to refine segmentation algorithms utilize predicted graphs directly, thereby reducing dependency on post-processing. Concurrently, efforts will also focus the capability of processing larger fields of view in single analysis, thus preserving global context and enhancing feature consistency across the entire structure.
I Additional Experiments on 3D Dataset
The application of GraphMorph to 3D medical datasets can be initially explored for its clinical significance. Thus, have extended GraphMorph the pulmonary arterial vascular segmentation dataset from the PARSE challenge, which includes 100 annotated 3D CT scans. These
the 3D UNet architecture and tested it on
divided in 7:1:2 ratio for training, validation, and testing.
The preliminary results, as detailed in Table TO, show that our method consistently outperforms existing basclines across all metries, mirroring the success observed with 2D data. This alignment
19

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Image
Label
W.o. Post
GraphMorph
DRIVE
STARE
ISBI12
MassRoad
Figure 7: Visualization of the effect of the post post-processing in the segmentation task across four datasets. Columns represent, from left to right: original images, ground truth segmentation labels, thresholded output from the segmentation network (w.o. Post), and results with post-processing. Green arrows highlight areas where false positives have been successfully suppressed.
Label
SoftDice
GraphMorph
Figure 8: Visual comparison for our GraphMorph with baseline on the segmentation task. Areas indicated by yellow arrows show false negatives (FNs) and areas pointed by green arrows demonstrate false positives (FPs) appear in baseline but are accurately predicted by our approach.
20

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between 2D and 3D results not only underlines the effectiveness of our method but also its adaptability 3D vessel segmentation task, which indicates the potential of Graph in clinical diagnosis. Moreover, Figure demonstrates that Gorphhorph effectively suppresses false positives (FPs) and false negatives (FNs) fine structures. Further attempts on 3D datasets will be made to validate its effectiveness.
Table 10: Segmentation performance of GraphMorph on PARSE dataset.
Volumetric metrics (T)
Distribation metries
Ropological metrics (L)
Backbone
Method
ARK()
UNet
Sife
0.7968 0.0166 0,8350 + 0,0122
0.9878 0.0121
0.779 + 0.017
0.154 0.019
1.087 0.078
1.130 + 0.082
SottDice=Ours
0.8196 0.0138
0.8730 0.0111
0.9901 0.0015
0.805 & 0.014
0.115 0.015
0.536 0.839
0.602 a 0.045
J Broader Impacts
In this work, we present Morph,,rph, a framework aimed at improving the extraction of tubular structures in medical image analysis, such as blood vessels and other elongated anatomical features. Fine-scale structures often consist of interconnected branches forming cohesive networks critical to physiological functions. By enhancing topological accuracy, GraphMorph provides more coherent and precise representations of these structures. These improved predictions with better topology in medical diagnostic scenarios related to tubular structures may assist clinical diagnosis. While our results are promising, they are based on publicly available datasets that may not fully capture the complexity and variability of real- world clinical data; therefore, further validation datasets necessary to confirm its applicability in clinical settings. At the present stage, we do not foresee any potential negative societal impacts arising from our work. Our goal is contribute useful tool for the medical imaging community, supporting efforts to improve segmentation accuracy and ultimately aiding in better healthcare outcomes.
more 3D
21

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Reviews:
[{"review_id": "xiC8kktXz9", "reviewer": "Reviewer_Ysem", "summary": "This paper presented a method called GraphMorph, for tubular structure extraction to achieve more topologically accurate predictions. GraphMorph consists of a Graph Decoder and a Morph Module: 1) the Graph Decoder generates/decodes/learns a graph structure from the ouput of segmentation network and segmentation image features;  2) then the Morph Module processes the graph provided by the Graph Decoder and the centerline probability map given from the segmentation network by employing a novel SkeletonDijkstra algorithm, to output the final centerline mask. Various popular datasets are used for empirical validation.", "questions": "1, The SkeletonDijkstra Algorithm is proposed by authors alone, any reference?\n2, My main questions are more related to the overall technical contributions to this line of work: a) The datasets are pretty small and have been extensively tested in the past. There is an over-fitting concern on these small and widely used datasets, in analogy to the \"peek too much\" bias. b) all examples are primarily 2D patches. From the qualitative examples shown in the paper, they looks more like \"toy examples\". Does the methods work on full 3D CT scans, like extracting lung airway trees? c) The numerical improvements reported in the paper, overall are marginal. \n\n3, Authors makes claims as follows: \"Broader Impacts: The GraphMorph framework significantly enhances medical diagnostics by improving the accuracy of tubular structure extraction, such as blood vessels, which is crucial in AI-assisted medical image analysis. These advancements can lead to more precise diagnostics, potentially reducing unnecessary medical procedures and costs. Furthermore, if the capability for real-time analysis is further enhanced, it could significantly impact emergency medical responses by accelerating decision-making and improving patient outcomes. Ultimately, our research not only advances technical knowledge in medical image analysis, but also holds potential for significant positive impacts in healthcare efficiency and patient care.\"  \n\nThese claims are significantly over-claimed. The examples shown here are very much toy examples on small image patches. In real world healthcare diagnosis, robust 3D tubular structures like vessels for heart and lung, or airway trees need to be precisely extracted at certian depth from 3D CT scans. Topology constrained tubular structures are parsed from medical image analysis literature (there are many previous work on vessel extraction, and lung airway extraction). The method proposed here does not seem to work directly in such real applications. So authors need to be very careful about making such claims.  \n\n4, The results here are far from clinically useful. on smaller datasets for evaluation, error bars or std should also be reported.", "limitations": "as weakness", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1, The paper is well written with good clarity.\n2, The method proposed overall is unsuprising but logical (but definately not a breakthrough).", "weaknesses": "My main questions are more related to the overall technical contributions to this line of work: a) The datasets are pretty small and have been extensively tested in the past. There is an over-fitting concern on these small and widely used datasets, in analogy to the \"peek too much\" bias. b) all examples are primarily 2D patches. From the qualitative examples shown in the paper, they looks more like \"toy examples\". Does the methods work on full 3D CT scans, like extracting lung airway trees? c) The numerical improvements reported in the paper, overall are marginal. \n\nAuthors makes claims as follows: \"Broader Impacts: The GraphMorph framework significantly enhances medical diagnostics by improving the accuracy of tubular structure extraction, such as blood vessels, which is crucial in AI-assisted medical image analysis. These advancements can lead to more precise diagnostics, potentially reducing unnecessary medical procedures and costs. Furthermore, if the capability for real-time analysis is further enhanced, it could significantly impact emergency medical responses by accelerating decision-making and improving patient outcomes. Ultimately, our research not only advances technical knowledge in medical image analysis, but also holds potential for significant positive impacts in healthcare efficiency and patient care.\"  \n\nThese claims are significantly over-claimed. The examples shown here are very much toy examples on small image patches. In real world healthcare diagnosis, robust 3D tubular structures like vessels for heart and lung, or airway trees need to be precisely extracted at certian depth from 3D CT scans. Topology constrained tubular structures are parsed from medical image analysis literature (there are many previous work on vessel extraction, and lung airway extraction). The method proposed here does not seem to work directly in such real applications. So authors need to be very careful about making such claims.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive feedback! We will respond to your concerns below.\n\n**Q1:** The SkeletonDijkstra Algorithm is proposed by authors alone, any reference?\n\n**A1:** The SkeletonDijkstra algorithm proposed by our paper represents an innovative adaptation of the classic Dijkstra's algorithm, specifically tailored to the unique challenges of tracing centerlines in tubular structures. This adaptation was necessary to handle the specific topology and morphology of tubular structures that are not addressed by traditional shortest path algorithms. While we have no external references for this particular adaptation, our extensive experiments in the paper confirm its efficacy and accuracy.\n\n**Q2:** The datasets are pretty small and have been extensively tested in the past. \n\n**A2:** Thanks for the comments. In medical imaging, especially for tubular structure analysis, large-scale public datasets are scarce due to privacy concerns and data collection complexities. The datasets we selected, while smaller relative to those used in broader computer vision tasks, are established benchmarks within the medical imaging community. Despite their frequent use in previous studies, these datasets still present unresolved challenges [1] [2], especially related to topological errors that happen regularly, which is derived from under-utilisation of branch-level features of tubular structures. Our approach mitigates this problem through the efficient exploitation of branch-level features.\n\nTo demonstrate the broader applicability of our approach, we have conducted experiments on the Massachusetts Roads dataset with 1171 aerial images in the paper. Moreover, we provided further validations with 3D CT scans in our rebuttal pdf. These results not only demonstrate the method's effectiveness but also its potential in more clinically relevant, real-world settings.\n\n**Q3:** All examples are primarily 2D patches. The effectiveness of the method on 3D data needs to be validated.\n\n**A3:** We recognize the need to validate our method, GraphMorph, on 3D datasets for its clinical relevance. Thus, we have extended GraphMorph to use the 3D UNet architecture and tested it on the pulmonary arterial vascular segmentation dataset from the PARSE challenge [3], which includes 100 annotated 3D CT scans. These cases were divided in a 7:1:2 ratio for training, validation, and testing.\n\nThe preliminary results, as detailed in Table 2 of our rebuttal pdf, show that our method consistently outperforms existing baselines across all metrics, mirroring the success we observed with 2D data. This alignment between 2D and 3D results not only underlines the effectiveness of our method but also its adaptability to 3D vessel segmentation task. We plan to apply our method to more diverse 3D medical datasets to further validate the effetiveness of our method.\n\n**Q4:** The numerical improvements reported in the paper, overall are marginal.\n\n**A4:** Thanks for the comments. Our method, GraphMorph, is specifically designed to enhance the accuracy of topological features in tubular structure extraction, which is a critical aspect often overlooked in most traditional pixel-level frameworks. The focus of our method on topological accuracy is reflected in the significant improvements in topological metrics, such as the reduction of $\\beta_0$ error by 25% to 45% as reported in Table 2 of our paper.\n\nWhile the improvements in volumetric metrics like Dice and clDice are relatively modest (approximately 1%), the advancements in topological integrity are significant. Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks. The greatly reduced topology errors are derived from our direct exploitation of branch-level features. This can also be illustrated by our experiments on the 3D pulmonary artery dataset PARSE.\n\n**Q5:** On smaller datasets for evaluation, error bars or std should also be reported.\n\n**A5:** Thanks for the suggestion. We have provided error bars in our rebuttal pdf (detailed in Table 1). As can be seen from the results, most improvements of our method over baselines are significant. We will definitely include error bars for all experimental results in the revised version of the paper.\n\n**Q6:** \"Ultimately, our research not only advances technical knowledge in medical image analysis, but also holds potential for significant positive impacts in healthcare efficiency and patient care.\" These claims are significantly over-claimed.\n\n**A6:** We appreciate your feedback on our claims regarding the broader impacts of GraphMorph. Our results on 2D datasets demonstrate the clinical potential of our method for 2D tubular structure extraction. However, we acknowledge that its performance in complex 3D vascular tasks was not fully explored in the initial submission. In our rebuttal pdf, we have included preliminary results from applying GraphMorph to 3D pulmonary artery segmentation, where we observed obvious improvements.\n\nMoving forward, we plan to extend our evaluations to more diverse 3D datasets to further validate and demonstrate the clinical applicability of our method. We will also ensure that our claims will be carefully measured to reflect the current state and future potential of our research accurately in the revised version.\n\nReferences:\n\n[1] Hu, Xiaoling, et al. \"Topology-preserving deep image segmentation.\" Advances in neural information processing systems 32 (2019).\n\n[2] Dong Wang, et al. \"Pointscatter: Point set representation for tubular structure extraction.\" European Conference on Computer Vision, pages 366–383. Springer, 2022.\n\n[3] Luo, et al. \"Efficient automatic segmentation for multi-level pulmonary arteries: The PARSE challenge.\" arXiv preprint arXiv:2304.03708, 2023.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tlZdM1x5jN", "reviewer": "Reviewer_CJeh", "summary": "This paper proposes a method to extract tubular structures from images. Specifically, the authors have integrated graph extraction into the segmentation architecture. They have proposed a link prediction part to predict graph connectivity in tandem with the segmentation network. They combined the predicted graph into a segmentation branch via a morphing module during inference.", "questions": "1. See weaknesses\n2. I was wondering whether the morph module could also be used during training to correct some segmentation errors.", "limitations": "Limitations have been discussed well.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The method is well-motivated, and the paper is well-written.\n2. The link prediction idea is technically sound for computationally efficient connectivity prediction.\n3. The morph module, which integrates the predicted graph in the segmentation, is novel. It seems effective, as demonstrated in Table 1 and Figure 6.\n4. The proposed method seems to improve segmentation results across different metrics over multiple datasets.", "weaknesses": "1. Is the threshold in the SkeletonDijkstra algorithm dataset-dependent?\n2. Is the segmentation network trained simultaneously with the graph decoder or one before the other?\n3. Are there any metrics computed on the extracted centerlines?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your detailed feedback! Please see our answers for your questions below.\n\n**Q1:** Is the threshold in the SkeletonDijkstra algorithm dataset-dependent?\n\n**A1:** $p_{thresh}$ is a hyper-parameter which is dataset-independent. It is set to 0.5 as the default setting across all experiments. We will add this setting to the \"Implementation Details\" in the revised version.\n\n**Q2:** Is the segmentation network trained simultaneously with the graph decoder or one before the other? \n\n**A2:** The segmentation network and the graph decoder are trained simultaneously to optimize both components effectively and enhance overall training efficiency. This joint training approach allows the segmentation network to leverage the branch-level features provided by the graph decoder, leading to more coherent and accurate predictions of tubular structures.\n\n**Q3:** Are there any metrics computed on the extracted centerlines?\n\n**A3:** In addressing the metrics for evaluating the quality of extracted centerlines, Table 1 in our main paper presents a detailed breakdown of the metrics. These metrics are calculated by comparing the centerline masks predicted by our model with the ground truth masks, detailed below:\n\n1. **Volumetric Scores:** The first three columns of Table 1 focus on volumetric scores which assess different aspects of quality of extracted centerlines:\n   - *Dice* evaluates the overlap between the predicted centerline and the ground truth. A higher Dice score indicates better alignment between the predicted centerline and its corresponding label.\n\n   - *AUC* and *ACC* provide a comprehensive evaluation of the model’s ability to classify pixels correctly, indicating the model's performance in distinguishing between the centerline of tubular structures and the background.\n\n2. **Topological Metrics:** The last three columns of Table 1 introduce topological metrics, which indicate accurate representation of topology:\n   - *$\\beta_0$ error* measures the error in the number of connected components of the extracted centerline. Predicted broken or redundant vessels will cause this metric to rise.\n   - *$\\beta_1$ error* assesses the accuracy in the number of loops or cycles within the centerline, which is effective for evaluating complex vascular topology.\n   - *Euler characteristic error ($\\chi$​ error)* combines the first two topological aspects, providing a holistic view of the topological accuracy.\n\nMetrics like Dice, ACC, $\\beta_0$ error, $\\beta_1$ error, and $\\chi$ error are also utilized in Table 2 and Table 3 of our main paper, which evaluate the performance of our model on the segmentation task. By using share metrics across different contexts, we establish a consistent framework for evaluating our approach against both tasks.\n\n**Q4:** I was wondering whether the morph module could also be used during training to correct some segmentation errors.\n\n**A4:** Currently, the morph module is designed to operate during the inference phase and does not propagate gradients, which precludes its direct use in training the segmentation network. However, the patterns of connectivity it identifies have significant potential to refine the training process.\n\nRecognizing this potential, the possibility of modifying the morph module to enhance error correction during training is promising. One feasible approach could involve developing a differentiable version of the morph module that can be integrated into the back propagation process. Another one is to enhance the training process by assigning increased weights to path points identified by the morph module as crucial for connectivity. Such developments could enhance the robustness and accuracy of segmentation networks, and we plan to pursue this direction in our future work.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "g9pa4ptWy7", "reviewer": "Reviewer_4DfY", "summary": "In this work, the authors tackle curvilinear image segmentation. In particular, they move away from pixel-level prediction which has limitations when predicting thin structures. They propose GraphMorph which predicts location of endpoints of each branch and finds the optimal path between them. In this way, they are able to improve upon both False Positive and False Negative errors. Their method can be applied to any segmentation backbone.", "questions": "See weaknesses section", "limitations": "The authors have adequately mentioned the limitations of their method, specifically the small ROI which can miss spatial context necessary for good performance.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Their method is able to handle both FP and FN errors. Otherwise, most existing methods in literature tend to tackle only FN errors.\n-  The authors compare against adequate baselines and have improvements over them.", "weaknesses": "- For the performance mentioned in the tables, the authors should provide standard deviation to understand whether their method is statistically significant or not. The authors should conduct t-test [1] to confirm this.\n- The authors should provide the computational complexity of their method with respect to the baselines. The complexity should be about the training and inference time of their method. I suspect the algorithm is slow due to iterating over each edge.\n\n**References**\n\n[1] Student, 1908. The probable error of a mean. Biometrika, pp.1–25.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive feedback! We will answer your questions below.\n\n**Q1:** For the performance mentioned in the tables, the authors should provide standard deviation to understand whether their method is statistically significant or not. The authors should conduct t-test to confirm this.\n\n**A1:** Thanks for your suggestion. We have provided error bars in our rebuttal pdf (detailed in Table 1). As can be seen from the results, most improvements of our method over baselines are significant. We will definitely include error bars for all experimental results in the revised version of the paper.\n\nRegarding the t-test, we demonstrate the comparison of segmentation performance on the PARSE and ISBI12 datasets based on UNet, and the results are shown in the following table. PARSE is a 3D pulmonary artery dataset, and we show the results of GraphMorph's experiments on it in the rebuttal pdf.\n\n| Dataset | Metric          | t-Statistic | p-Value |\n| ------- | --------------- | ----------- | ------- |\n| PARSE   | Dice            | 2.0749      | 0.0386  |\n|         | clDice          | 3.9496      | <0.0001 |\n|         | $\\beta_0$ error | -12.3858    | <0.0001 |\n|         | $\\beta_1$ error | -4.1148     | <0.0001 |\n|         | $\\chi$ error    | -11.1030    | <0.0001 |\n| ISBI12  | Dice            | 2.6297      | 0.0137  |\n|         | clDice          | 2.9060      | 0.0071  |\n|         | $\\beta_0$ error | -7.1229     | <0.0001 |\n|         | $\\beta_1$ error | -2.9271     | 0.0035  |\n|         | $\\chi$ error    | -7.4095     | <0.0001 |\n\nThe statistical results from our t-tests clearly demonstrate that GraphMorph significantly improves segmentation performance on both 2D and 3D datasets, as evidenced by the significant p-values across all metrics for the PARSE and ISBI12 datasets. Notably, while improvements in volumetric scores such as Dice and clDice are significant, the most striking results are observed in the topological metrics ($\\beta_0$ error, $\\beta_1$ error, and $\\chi$ error), where our method consistently demonstrates substantial enhancements. These results underline the capability of GraphMorph to effectively leverage branch-level features to optimize the extraction of tubular structures' topology. \n\n**Q2:** The authors should provide the computational complexity of their method with respect to the baselines. The complexity should be about the training and inference time of their method. I suspect the algorithm is slow due to iterating over each edge.\n\n**A2:** We appreciate the request for detailed computational complexity comparisons. Below is a table that outlines the resource utilization during the training process on the DRIVE dataset with a UNet backbone.\n\n| Method        | Params | FLOPs | Time per iteration/s | GPU Memory |\n| ------------- | ------ | ----- | -------------------- | ---------- |\n| SoftDice      | 39M    | 187G  | 0.203                | 5.4 GB     |\n| softDice+Ours | 48M    | 268G  | 0.589                | 11.8 GB    |\n\nThe increase in parameters and FLOPs in our approach primarily stems from the integration of the Graph Decoder featuring a DETR module. This component is crucial for predicting accurate topological structures of the graphs. Advancements in transformer architectures that reduce computational overhead could potentially enhance the efficiency of our model during training. Implementations such as Lite-DETR [1], noted for their efficiency in handling transformers, could serve as alternatives to the current DETR module, potentially reducing training time and computational resource usage.\n\nAs detailed in Appendix F, the inference time analysis has been conducted in Table 5. The results show that the Morph Module is the most time-consuming part during inference process. However, the iterative execution over each edge using the SkeletonDijkstra algorithm is not the primary contributor to this time consumption. This is because the algorithm operates on much smaller patches. For example, a $384 \\times 384$ image is divided into numerous $32 \\times 32$ patches. Due to the limited size, running SkeletonDijkstra on one patch is highly efficient (about 0.01s per patch). The primary time expenditure currently arises from processing these patches sequentially. However, as each patch operates independently, there is significant potential to enhance efficiency by parallelizing the computations of all patches. Recognizing this opportunity, we plan to focus future work on optimizing the Morph Module by implementing parallel processing techniques to accelerate inference. Additionally, your question has inspired us to explore the parallelization of edge operations within each patch, which may further reduce time cost. We intend to detail these improvements in revised version of our paper and believe this will substantially elevate the operational efficiency of our model.\n\nReferences:\n\n[1] Li, Feng, et al. \"Lite detr: An interleaved multi-scale encoder for efficient detr.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2023.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PxD8m5XHEp", "reviewer": "Reviewer_S6G1", "summary": "The paper presents a technique (called GraphMorph) for extracting tubular patterns as found for instance in retinal images (veins) and aerial images (roads). \nThe proposed pipeline is made of several modules: a segmentation network providing centerline probability and features, \na graph decoder for detecting nodes and connectivity and a morph module to get centerline masks.\nExperimental results demonstrate the efficiency of the proposed pipeline against state of the art methods on several benchmarks.", "questions": "are experiments  for setting $p_{thresh}$ (lines 560-563 )   done on test sets?", "limitations": "Limitations are addressed in the paper (e.g. in appendix I line 586, and in appendix H line 576-578).", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is well written  and clear.\nExperimental results against SOTA are convincing.", "weaknesses": "Some hyperparameters (e.g thresholds) have to be set.\nThe methodology is not always clear to set these parameters e.g.  \nare experiments  for setting $p_{thresh}$ (lines 560-563 )   done on test sets?\n\nminor remarks:\n- Fig 2 \"Modified Deformbale DETR\" -> Deformable\n\n- Figure 3 caption: \"Inferece\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive suggestions! We will correct the typo error you raised in the revised version. Please find our reply to your questions below.\n\n**Q1:** Some hyperparameters (e.g thresholds) have to be set. The methodology is not always clear to set these parameters. e.g. are experiments for setting $p_{thresh}$ (lines 560-563 ) done on test sets?\n\n**A1:** Thanks for the suggestions. Parameters like $\\lambda_{\\text{class}}=0.2$, $\\lambda_{\\text{coord}}=0.5$, $\\alpha=0.6$, and $\\gamma=2$ in the loss function (lines 462) are adopted from established settings in previous works, such as Deformable DETR[1]. We adapted $\\alpha=0.75$ specifically for the MassRoad dataset to better handle the sparse nature of road networks. Parameters like learning rate and weight decay were set in line with those used in Pointscatter[2] to ensure a fair comparison. For $p_{thresh}$, we empirically set it to 0.5 for all experiments on the four used datasets. In Table 9 of Appendix, we compared it to other thresholds on the test set of DRIVE dataset and found the values close to 0.5 yielded better results.\n\nReferences:\n\n[1] Xizhou Zhu, et al. \"Deformable detr: Deformable transformers for end-to-end object detection.\" arXiv preprint arXiv:2010.04159, 2020.\n\n[2] Dong Wang, et al. \"Pointscatter: Point set representation for tubular structure extraction.\" European Conference on Computer Vision, pages 366–383. Springer, 2022.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
Dear Reviewers and ACs,

We were encouraged to receive the following positive comments from reviewers: "The method is well-motivated"(CJeh), "The paper is well written with good clarity"(Ysem), "Their method is able to handle both FP and FN errors."(4DfY), "Experimental results against SOTA are convincing."(S6G1). Your comments are very valuable in improving our paper.

Reviewers Ysem and 4DfY both suggested adding error bars to the experimental results. We have updated Table 2 of the main paper and put it in the rebuttal pdf (detailed in Table 1). As can be seen from the results, most improvements of our method over baseline is significant. We will ensure that error bars for all experiments are provided in the revised version of the paper.

Below, we address specific concerns raised by individual reviewers in detail.

Meta-review: The reviewers appreciate the authors' contribution to tubular segmentation, which is a challenging problem -- here, the authors combine the task of pixel classification with the tasks of identifying underlying graph structure and centerlines, with the goal of producing more topologically faithful segmentations. This problem is difficult yet important, and the authors' contributions are interesting; I therefore recommend acceptance.

In their final version, the authors should take good care to incoroporate the reviewers' comments in to their paper. *Particularly important* is the comments from reviewer Ysem, who points out that the authors are drawing far too strong conclusions about their paper. I agree with the reviewer, and the authors should modify their statements for the cameraready.
Decision: Accept (poster)