TopNet: Topology Preserving Metric Learning
for Vessel Tree Reconstruction and Labelling

arXiv:submit/3375250 [cs.CV] 18 Sep 2020

Deepak Keshwani1 , Yoshiro Kitamura1 , Satoshi Ihara1 , Satoshi Iizuka2 , andEdgar Simo-Serra3
1

Imaging technology center, Fujifilm corporation, Japan
Center for Artificial Intelligence Research, University of Tsukuba, Japan3
Department of Computer science and engineering, Waseda university, Japan
deepak.keshwani@fujifilm.com
2

Abstract. Reconstructing Portal Vein and Hepatic Vein trees from contrast enhanced abdominal CT scans is a prerequisite for preoperative
liver surgery simulation. Existing deep learning based methods treat vascular tree reconstruction as a semantic segmentation problem. However,vessels such as hepatic and portal vein look very similar locally andneed to be traced to their source for robust label assignment. Therefore,
semantic segmentation by looking at local 3D patch results in noisy misclassifications. To tackle this, we propose a novel multi-task deep learning
architecture for vessel tree reconstruction. The network architecture simultaneously solves the task of detecting voxels on vascular centerlines(i.e. nodes) and estimates connectivity between center-voxels (edges) inthe tree structure to be reconstructed. Further, we propose a novel connectivity metric which considers both inter-class distance and intra-class
topological distance between center-voxel pairs. Vascular trees are reconstructed starting from the vessel source using the learned connectivity
metric using the shortest path tree algorithm. A thorough evaluation
on public IRCAD dataset shows that the proposed method considerably
outperforms existing semantic segmentation based methods. To the bestof our knowledge, this is the first deep learning based approach whichlearns multi-label tree structure connectivity from images.
Keywords: Deep Learning · Vessel Tree Reconstruction · Vessel Segmentation · Liver Vessel · Centerline Detection · Computed Tomography.

1

Introduction

Primary liver cancer is the third most common cause of cancer mortality [2].
Liver resection is currently the most prevalent treatment method with 5-year
survival rates of up to 40% [11]. To perform a safe liver resection, preoperative
surgical simulations have been found to be very useful [19,17]. In these simulations, a 3D model of the liver which shows the anatomical structures of portal
and hepatic veins together with tumour location is reconstructed. Using vascular
reconstructions, blood flow patterns around the tumour is analysed to compute

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Raw CT image

Semantic segmentation results

TopNet results

Fig. 1. Portal and hepatic vein structures obtained with semantic segmentation andproposed TopNet. The red rectangles indicate vessel misclassifications.

the resection region. The analysis of blood flow requires not just segmentationof vascular structures but their representation as a tree structure.
Rule based methods for hepatic and portal vein reconstruction have beenstudied and a comprehensive literature survey can be found in [6]. Most popular rule based methods are based on global optimization techniques like graphcuts [20,1]. Graph cut based techniques use a handcrafted energy term between
vascular nodes. A downside of such methods is that they work well only in conditions for which the rules were handcrafted. For instance when both portal
and hepatic veins are high in contrast [20]. Recently, deep learning-based semantic segmentation methods have been proposed for liver vessel recognition
tasks [9,13,14]. In these methods, semantic segmentation is used to classify avoxel by extracting information from a local 3D patch (also known as the networks receptive field) centered around it. However, since portal and hepatic veins
look very similar locally, these methods result in noisy vessel misclassifications
as shown in Figure 1. Such noisy misclassifications magnify the tree reconstruction error. Additionally, within semantic segmentation literature, simultaneous
segmentation of portal and hepatic vein from CT volumes has not been tackled. Either only hepatic [13,14] or only portal vein [9] segmentation has beentargeted.
In this work, we propose TopNet, a deep metric learning method for vasculartree reconstruction. The main idea is to learn the connectivity metric between
vascular voxel pairs rather than to assign absolute labels. Conceptually, TopNet
is a two stage network. The first stage computes center-voxels along the centerlines of all the vessels. The second stage learns the connectivity metric between
center-voxel pairs in the form of topological distance between the voxels along
the vascular tree. To generate a global tree, center-voxels are connected consecutively starting from the vessel source using the learned topology metric. We
summarize the main contributions of this work as follows:
1. Proposed a novel multi task architecture designed for tree reconstruction,
which detects nodes (voxels on vascular center lines) and estimates edges(connectivity between center-voxels) in the tree to be reconstructed.
2. Proposed a novel topology metric which learns both inter-class distance andintra-class topological distance between vascular voxel pairs in multiple trees.

TopNet3

3. Verified that the proposed method achieves higher accuracy than existing
methods with a large margin for portal and hepatic vein reconstruction.

2

Related work

TopNet uses deep metric learning to connect detected center-voxels. In this regard, our approach is closer to deep metric learning approaches for image instance segmentation tasks [4,15,5,18]. These methods map pixels from image
space to features space such that pixels belonging to the same instance are close
to each other and separated by a margin if they belong to different instances.
The methods differ in how they measure similarity in the feature space. Amongthe similarity metrics, cosine similarity has been used extensively [15,18]. Another way in which these methods differ is the way pixels are clustered in thelearned feature space to generate instances. In this work, the task is not just instance segmentation (vessel segmentation) but to learn connectivity within the
instance (vessel trees). For this purpose, we propose a novel deep metric learning
approach.

3

TopNet

The proposed TopNet is a multi-task 3D Fully Convolutional Neural Network(3D-FCN). All the tasks share a common base encoder and task specific decoders
as shown in Figure 2. The proposed architecture is similar to 3D-UNet [3], withthe difference that our approach has three decoders for three different tasks
instead of one. Such Multi-task architectures with shared encoder and task specific decoders have also been proposed earlier [12]. For detailed architecture,please refer to the supplementary material. The first task is extraction of all
the vessels from the image. The second task is assigning a centerness score to
all the voxels within the vessel mask such that the centermost voxel is assigned
a minimum value. Using this centerness score, center-voxels are computed using non-maximum suppression. The final task is learning connectivity between
center-voxels, which is proportional to topological distance between the centervoxels. Figure 2 shows the conceptual representation of topological distance withsolid red lines. The network is trained by minimizing the sum of loss terms fromeach of the three tasks. The formulation of loss for each task is described in thefollowing sections.
3.1

Vessel Extraction Decoder

The task of separating all the vessels from the background is formulated as asemantic segmentation problem. The loss function used for this task is the diceloss function which has shown to improve the accuracy in segmentation tasks
with severe class imbalance [16]. We compute vessel extraction loss Vloss as

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Vessel Extraction
decoder

Centerness
decoder

Topological distancedecoder

Base encoder

Fig. 2. TopNet methodology with base encoder and three task specific decoders.

PN0
i=1 vi v i
PN 0 ,
i=1 vi +i=1 v i2

Vloss = 1 − PN

(1)where the sums run over the N voxels, of the ground truth binary vessel volume
vi ∈ V , and predicted vessel volume v 0 i ∈ V 0 .
3.2

Centerness Decoder

The task of generating a centerness score map is formulated as a regression
problem. The ground truth centerness score map is the distance transform ofbinary volume mi ∈ M representing the vessel center voxels. We consider thecenterness score map only within the ground truth binary vessel volume V . The
voxels outside the vessel region are masked out when computing the training loss.
The training loss for the regression task is formulated as weighted smoothL1 loss
between the ground truth centerness score Si and predicted centerness score Si0summed over the voxels belonging to vessel mask V . We use smoothL1 function
as defined in [8] and the weight is inverse square of true centerness score i.e. Si2 .
Mathematically, the centerness loss Closs is given as
1
Closs = PN

X 1
(smoothL1 ( Si − Si0 )).
Si2i=1 vi i|vi =1(2)

Weighting the loss function is essential because the loss would otherwise behighly biased towards the voxels away from the center. During the inference, thecenterness score is masked using the predicted vessel mask. The vessel centerpoints are extracted by first thresholding the centerness score map followed byapplying non-maximum suppression (NMS) on negative centerness score map.
In this work, we use a threshold of 1.5 and NMS window of 5 × 5 × 5.
3.3

Topology distance Decoder

Topological distance decoder outputs an 8-dimensional feature vector for eachvoxel in CT volume. The network is trained to map vessel center-voxels into theTopNet5feature space such that the L2 norm between two center-voxels in the feature
space is proportional to the topological distance between along the vascular trees.
For voxel pairs belonging to different vascular trees, the L2 norm is greater thana set margin. The pairwise loss between the two voxels i and j with associatedvessel labels li and lj is defined as(smoothL1 (k xi − xj k −αDij ) ∀i, j | li = lj , i 6= j,
T op(xi , xj ) =γ ∗ max(0, [K− k xi − xj k])otherwise.

(3)Here, k xi − xj k is the L2 norm between the feature representations of the twovoxels, Dij is the topological distance between the voxels along the vascular tree.
α and γ are constants whose values are explained subsequently. To compute thetopological loss, all such center voxel pairs which are in the local neighborhoodof each other are considered. The total loss then becomes
Tloss =1 X
n

X

T op (xi , xj ) .

(4)

i|mi =1 j∈NiHere, Ni is the set of voxels in the local neighborhood of voxel i and n is thetotal number of such voxel pairs for which the loss is computed. In this work,
we use all voxel pairs which lie inside a 3D sphere of radius 15 voxels in theimage space. Thus, the topological distance is normalized from 0 to 1 using the
proportionality factor α = 1/15. This roughly means that the voxels belonging
to the same vascular tree will follow 0 ≤k xi − xj k≤ 1 and if they belong todifferent vascular trees, then k xi − xj k≥ 3. To balance out the two loss terms,
we use γ = 1/3.

3.4

Vascular tree reconstruction

Vascular tree is constructed by aggregating the center-voxels starting from thevessel sources using the topological distance metric learned by the TopNet. We
train a separate network which outputs the location of portal and hepatic veinsources (see supplementary material). Typical portal (pink disc) and hepaticvein (blue disc) sources are shown in Figure 1. For computed vessel sources,
the vascular trees are constructed using Dijkstras multi-source shortest pathtree algorithm. To that end, the undirected graph is formulated as follows. The
vertices of the graph are center-voxels. The weighted edges of the graph are givenby the set (wij/α)2 wij ≤2 . Here, wij =k xi − xj k, i | mi = 1 and j | mj = 1
represents two center-voxels in a local neighborhood defined by a 3D sphereof radius 15. The term (wij/α)2 is essentially the square of topological distance
between the two center-voxels i and j. All the pairs for which wij≥2 are notconsidered as feasible edges, since such edges most likely belong to different
vascular trees.

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Table 1. Characteristics of INTERNAL and public dataset IRCAD.
DatasetTraining

Test

Contrast phase

Slice Thickness

INTERNAL
IRCAD [10]115 CT volumes
None

20 CT volumes
20 CT volumes

Late portal
Late portal

0.5 ∼ 1.0 mm
1.0 ∼ 4.0 mm

4Experiments

We divide the experiments into comparison and ablation studies. The comparisonof TopNet is made against single task 3D-UNet [3] with the dice loss function [16]baseline. This is a standard and competitive baseline for 3D image segmentation
and an upgrade over existing 2D-FCN based existing liver vessel segmentation
methods [9,13,14]. In the ablation study, we investigate the performance withdifferent learning metrics (dice loss based classification, cosine, and topology)
using the same multi-task architecture. For the Multi-task dice loss based classification approach, the last two layers of topology distance decoder are replaced
to output a two-channel probability map for each hepatic and portal vein. Here,
we use a 2 class dice loss summed over all the center-voxels. Multi-task cosine
metric learning method uses the exact same architecture as TopNet but uses cosine metric following from similar works [15,18]. The network uses cosine metricloss between voxel pairs i and j associated with feature vectors xi and xj andvessel labels li and lj is defined as(
1 − 0.5(1 + Sij ) ∀i, j | li = lj , i 6= j,
L (xi , xj ) =(5)
0.5(1 + Sij )otherwise.
kxT x kwhere, Sij = kxiikkxjj k is the cosine similarity metric. To reconstruct vasculartree using the learned metric as mentioned in section 3.4, the weighted edges of
the graph are given by the set {Eij (1 − Sij )}Sij ≥0 Here, Eij is the Euclidean
distance between the center-voxels.
4.1

Dataset and preprocessing

We used an internal dataset for training and both the internal as well as public
IRCAD dataset for evaluation [10]. The characteristics of both the datasets isshown in Table 1. For training, the CT values were normalized from 0 to 1, voxel
spacing in all three dimensions was normalized to 0.7mm. We also crop the CT
volume using the liver region before setting it as input to the network.
4.2

Evaluation metrics and results

We evaluate the results of portal and hepatic vein reconstruction by comparing
respective ground truth and predicted centerlines. When comparing the centerlines, an exact overlap is not possible. For this, we introduce a variable tolerance

TopNetRaw image

Ground truth

3D-FCNClassification

Cosine7

TopNetFig. 3. Comparison between 3D-UNet and proposed TopNet for hepatic and portal
vein extraction. Hepatic vein is shown in green while portal vein is shown in blue. Red
boxes show regions of interest for comparing misclassifications.

term δ which is equal to the radius defined at a ground truth centerpoint following from [7]. Based on this, an illustration of True Positives (TP), False
Positives (FP), False Negatives (FN), and True Negatives (TN) of portal vesselclass is shown in the supplementary material. Using these metrics, we computethe dice coefficient, sensitivity and specificity for hepatic and portal centerlines.
Predicted centerpoints for which there are no associated ground truth centerpoints within the tolerance are ignored while computing the metrics. Usually,
these points would be counted as false positives but we ignore them because in
the IRCAD dataset, small vessels are often unlabelled.
The proposed TopNet considerably outperforms the baseline i.e. single task
3D-UNet method with over 7-8% improvement in all metrics as shown in Table 2. When Multi-task dice loss classification is compared to single-task 3DUNet which also uses the dice loss, a performance improvement of 3-4% is seen.
By this, we can say that multi-stage vessel segmentation works better thansingle-stage method. Within the Multi-task network architecture, TopNet gives
the best results. We observe that if not for topology metric learning, the problem
of abrupt change in vessel labels along the vascular tree (large and medium redboxes) persists as shown in Figure 3. Such misclassifications also occur whenportal and hepatic veins cross each other in close vicinity (small red boxes insecond and third row). We reason that such misclassifications arise because conventional margin based techniques like semantic segmentation or even cosine
metric learning classify or seperate the center-voxels based on frequently seen
vessel patterns in different liver regions within the training dataset. If unique
vessel patterns are observed in test data, the classification fails. With Topology
metric learning on the other hand, we explicitly constrain the network to learn

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D. Keshwani et al.

Cosine metric (result, metric field)

Ground Truth

Topology metric (result, metric field)

Fig. 4. Comparison between Topology and cosine metric learning. Hepatic vein isshown in green while portal vein is shown in blue. Boxes show regions of interestfor comparing misclassifications.
Table 2. Comparison between TopNet and existing methods.
MethodVesselIRCAD

INTERNAL

Dice Specificity Sensitivity Dice Specificity Sensitivity
Single Task
3D-UNetPortal 0.84
[3]
Hepatic 0.84

0.85
0.82

0.82
0.85

0.88
0.86

0.86
0.87

0.87
0.86

Multi Task
Classification Portal 0.87
Hepatic 0.86
Cosine metric Portal 0.85
Hepatic 0.80
TopNetPortal 0.91
Hepatic 0.92

0.85
0.88
0.85
0.82
0.96
0.91

0.88
0.85
0.81
0.86
0.91
0.96

0.92
0.91
0.88
0.85
0.95
0.94

0.93
0.90
0.84
0.90
0.96
0.94

0.90
0.93
0.9
0.84
0.94
0.96

to trace the vessels. To verify this direction of reasoning, we show the similarity
metric field from a reference center-voxel to it’s neighborhood voxels in a misclassified region in Figure 3. It can be seen that the Topology metric shows a smoothtransitioning of the similarity field as compared to cosine metric which shows anabrupt change. Since the cosine metric learning method does not learn absolutelabels, such misclassifications propagate as shown with the yellow box in Figure
4. This explains why the cosine metric learning works poorly as compared to themulti-task classification approach as shown in Table 2.

5

Conclusion

We proposed a deep metric learning method which learns multi-label tree structure connectivity from images. We converted a hard problem of assigning absolute labels to vessels to a simpler one. Topological metric learning is simpler
because it just learns local connectivity and does not require global image context. For global connectivity, we use the shortest path tree algorithm which uses
the learned metric to connect vascular voxels. The results show that using topological metric learning, the issue of noisy misclassifications is resolved. We believethat the approach is general enough to be applicable to vessel segmentation tasks

TopNet9in other organs. This is because the network is constrained to learn connectivity
rather than other absolute labels. There are a few downsides to this approach
as well. First, the method has multiple manually fine tuned parameters involved
both in detecting the center-voxels and creating vascular trees using the learned
topology metric. Second, the shortest path tree algorithm which is used to create
global connectivity is sensitive to misdetection of vascular center voxels. Due tothis, in the future it would be interesting to explore a method which can embed
tree generation algorithms like the shortest path into the training process.

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Acknowledgements
This research was done in cooperation with the Hepato-Biliary-Pancreatic Surgery
Division, the University of Tokyo Hospital. We would like to thank Prof. Kiyoshi
Hasegawa, Dr. Junichi Kaneko, Dr. Ryugen Takahashi, and Dr. Yusuke Kazami
for their valuable advice and curating a liver vessel dataset

Topological
EuclideanarXiv:submit/3375250 [cs.CV] 18 Sep 2020

Image space

Feature space
SOFTMAX

ReLU

Conv 1x1x1, 2

Conv 1x1x1, 1

Conv block, 8Conv block, 8Conv block, 8

Max Pool 23

Deconv Block

Conv block, 16

Deconv Block
Conv block, 16

Conv block, 16

Max Pool 23

Deconv Block

Deconv Block

Conv block, 32

Conv block, 32

Conv block, 32

Max Pool 23

Deconv Block

Deconv Block

Conv block, 64

Conv block, 64

Conv block, 64

Conv 1x1x1, 8
Conv block, 8Deconv Block
Conv block, 16
Deconv Block
Conv block, 32
Deconv Block
Conv block, 64

Max Pool 23

Deconv Block

Deconv Block

Deconv Block

Conv block, 128

Conv 1x1x1, 64

Conv 1x1x1, 64

Conv 1x1x1, 64

Conv block, 256

Conv block, 256

Conv block, 256

Vessel extraction
decoder

Centerness
decoder

Toplogical distancedecoderBaseencoder

Figure 1: TopNet Architecture: The Conv block in each encoder and decoder
denotes two sets of Conv[3 × 3 × 3] → BatchN orm → ReLU operations. The
Deconv blocks are transposed convolutional operators with filter size 4 × 4 ×
4. Skip connections are used between the encoder and all three task specificdecoders and the features are concatenated.

image
Conv block, 8
Max Pool 23
Conv block, 16
Max Pool 23
Conv block, 32
Max Pool 23
Conv block, 64
Max Pool 23
Conv block, 128

SOFTMAX
Conv 1x1x1, 3
Conv block, 8Deconv Block
Conv block, 16
Deconv Block
Conv block, 32
Deconv Block
Conv block, 64
Deconv Block
Conv 1x1x1, 64

Figure 2: VesselSource detector. Left: Network architecture which outputs a 3channel probability map for background region, portal vein source and hepaticvein source points respectively, Right: detected portal vein (pink) and hepaticvein (blue) sources.

1

TN

FP

𝛿

FN

TP

true portal centerline
predicted portal centerline

ignoredtrue hepatic centerline
predicted hepatic centerline

Figure 3: An illustrations of terms used in the evaluation metrics.

Raw image

Ground truth

Comparison

TopNetFigure 4: Comparison of TopNet with different approaches on IRCAD datset.
Red boxes show regions of interest. First two rows: Single-task 3D-FCN Vs
TopNet. Third now: Multi-task Cosine metric Vs TopNet. Fourth row: Multitask classification Vs TopNet.

2