Abstract—The mapping and labeling of the major intra-

hepatic blood vessels may facilitate planning liver interventions

and surgery. However, the automatic labeling of liver veins is

challenging due to imperfect segmentations caused by partial

volume effects and image resolution that result in undesirable

false connections between hepatic and portal veins. In this

paper, we propose a novel method to model the continuity of

consecutive venous branches in a probabilistic manner. Then

the model is automatically labeled via inference. The method

incorporates low-level metrics for neighboring nodes and

mid-level metrics for neighboring branches. Making use of these

metrics, the automatic labeling becomes a probabilistic tracing

procedure starting from each end nodes of the vessel skeleton.

The method has only one free parameter whose value is not

critical to labeling results. Experiments using data from healthy

and pathological patients were performed and the results

illustrate an accuracy of 0.97±0.08.

I. INTRODUCTION

IVER venous trees, including the portal and hepatic veins,

are critical vascular structures important for

computer-aided diagnosis, surgical planning and image-

guided interventions, and can determine surgical resection

cutting planes or convective heat loss during thermal ablation

[1]. Several works [2-6] were presented for liver vessel

segmentation in contrast- enhanced or multiphase CT images.

However, only several methods [6-10] proposed to label

segmented vessels as the left, middle and right hepatic, and

left and right portal veins. In clinical practice, these five

vessel trees serve as important anatomical boundaries for the

Couinaud liver segments and critical landmarks for liver

surgery and intervention planning [11].

Among the proposed labeling methods, Homann et al. [7]

Manuscript received October 7, 2013.

X. Kang, Q. Zhao, K. Sharma, R. Shekhar and M.G. Linguraru are with

the Sheikh Zayed Institute for Pediatric Surgical Innovation, Children’s National Medical Center, DC 20010, USA (phone: 202-476-5596; e-mail:

{xkang, qzhao, kvsharma, rshekhar, mlingura}@cnmc.org).

K. Sharma is with the Department of Diagnostic and Interventional Radiology, Children’s National Medical Center, DC, 20010, USA

R. Shekhar and M.G. Linguraru are with the Departments of Radiology

and Pediatrics, School of Medicine and Health Sciences, George Washington University, Washington, DC, 20037, USA

B.J. Wood is with the Radiology and Imaging Sciences, Clinical Center,

National Institutes of Health, Betehsda, MD 20892, USA (e-mail: bwood@cc.nih.gov).

separated the hepatic and portal venous systems in a semi-

automatic manner, using a graph-based technique. However,

this method did not separately label the left, middle and right

hepatic veins. Soler et al. [8] proposed a fully automated

method that identified the portal vein alone. Selle et al. [9]

proposed a similar semi-automated method for vessel

identification that also only identified the portal vein. Finally,

the method in [14] struggled in the presence of pathology and

image variability.

Anatomically, the portal and hepatic veins are functionally

separated and do not directly communicate. However, due to

noise, imaging resolution, partial volume effect and vessel

course, touching vessels are almost unavoidably found in CT

images and therefore the resulting vessel segmentations. This

is especially true in single-phase contrast-enhanced CT

images.

To solve the touching vessels, Soler et al. [8] used the fact

that the portal venous system contains no loops. However,

this concept becomes invalid when dealing with the entire

hepatic venous system because the portal and hepatic vein

branches may form complex false loops when they touch, as

shown in Fig. 1. In [8], this type of artificial connection was

removed by checking if the angle between two branches of a

bifurcation exceeds a fixed threshold of 135°. However, this

is not applicable for large complex loops and for trification or

n-fication nodes, which we often see in our study (Fig 1c).

AUTOMATIC LABELING OF LIVER VEINS IN CT BY

PROBABILISTIC BACKWARD TRACING

Xin Kang, Qian Zhao, Karun Sharma, Raj Shekhar, Bradford J. Wood and Marius George Linguraru

L

Fig. 1. Challenges in automatic liver vessel labeling caused by touching but not communicating vessels: a) large and b) complex false

loops formed by portal and hepatic vein branches, and c) trifurcations

on the vessel skeleton.

978-1-4673-1961-4/14/$31.00 ©2014 IEEE 1115

However, a fixed threshold value may not be robust in cases

where the vessel anatomy is affected by pathology.

In this paper, we propose a novel method to accomplish the

automatic labeling of the five major intra-hepatic veins:

left/middle/right hepatic veins and left/right portal veins. Our

approach models the a priori knowledge on vessel trees using

probability functions. The local and segment direction

continuity are modeled using von Mises-Fisher distribution.

The diameter change in two consecutive vein segments was

modeled using logistic function. Then, a probabilistic tracing

is designed to achieve the automatic labeling based on these

models. Our method was evaluated using clinical data.

II. METHODS

A. Vessel Segmentation and Skeleton Extraction

The starting of our method is the segmented liver, which

can be obtained using a method such as in [15]. Then the

hepatic and portal veins are segmented automatically from

contrast-enhanced CT images. The vessel enhancement filter

proposed by Sato et al. [4] is first applied. Then, the kernel

graph-cut method [12] is used to extract the veins from the

enhanced vessel, providing good robustness and avoiding

user-specified parameters. The segmentation is converted to a

surface mesh from which a vessel skeleton is extracted by

Laplacian-based contraction [13]. A skeleton node is further

classified as an end node or a branching node. The node

diameters were calculated using the distance transform on the

segmentation result. Finally, an undirected graph

representation was built from the skeleton. The automatic

vessel labeling is carried out on the undirected graph.

B. Probability Metrics

Our method models two types of a-priori knowledge on the

vessel structure to guide the labeling. One is the fact that a

branch should have a good directional continuity with its

parent branch. The other is that a branch is expected to have a

smaller diameter than its parent branch.

The continuity in vessel direction is model as orientation

consistency using von Mises-Fisher (vMF) distribution [13]

po(v1,v2 ) =k

2p ek - e-k( )exp kv1

Tv2( ) (1)

where k > 0 is the concentration parameter and v1,2 are unit

vectors representing the directions. This metric is superior to

the cosine function as 1) vMF is a probability function while

cosine is not, 2) vMF is defined on a sphere in 3D while the

support of cosine is [-π/2, π/2], and 3) vMF in directional

statistics is an analogue of the normal distribution.

The preference in diameter change is modeled as diameter

consistency using a logistic function

pd (d1,d2 ) =1

1+ e- d2-d1( )

, (2)

where d1 and d2 are the mean diameter of child and parent

branches or segments. This metric has two advantages. First,

pd can be considered as a probability. Second, it follows the

intuitive judgment of a human observer. When two segments

have the same diameter (i.e., d2 = d1), pd = 0.5. That is, it is

hard to judge if the second segment is preferred as a parent

segment only using diameter. But when d2 > d1, pd increases,

reflecting the fact that the parent segment is expected to have

a larger diameter. Similarly, when d2 < d1, pd < 0.5.

C. Probabilistic Backward Tracing

Intuitively, one may start labeling from the root node of

hepatic and portal veins. However, doing this in automatic

labeling has potential drawbacks when reaching a branching

node, there may not be enough information available to

determine how many child branches the current segment has,

especially when portal and hepatic veins intersect. In the

proposed method, the labeling starts from the end nodes. In

this case, we use the fact that any segment has one and only

one parent segment. Thus, when reaching a branching node,

the problem is to determine which segment connected to the

branching node should be the parent segment.

To determine the parent segment, we define the segment

continuity of the current segment Sc and the candidate parent

segment Scp as a joint probability

C Sc,Scp( ) = po vc{L},vcp{L}( )´ po vc{S},vcp

{S}( )´ pd dc,dcp( ), (3)

where v{L}

and v{S}

represent the local tangent direction at the

branching node and segmental direction. The local direction

is calculated using the finite difference of the neighboring

nodes of the branching node. The segmental direction is

calculated as a geodesic distance weighted direction

v{S} = vi di( )iÎS

å , (4)

where vi is the local direction of the i-th node on the segment

S and di is the geodesic distance from the i-th node to the

current branching node. v{S}

depicts the overall direction of S

by considering directions of all fragments of the segment.

Then, at a branching point, the segment continuities of all

candidate parent segments are calculated using (3) and the

candidate segment with the best continuity is chosen as the

parent segment; that is,

Sp = argmaxScp C Sc,Scp( ). (5)

The probabilistic tracing runs as follows 1) Start from an

end node. 2) Trace from the start node on the skeleton until a

branching node is reached. 3) Find out all the other segments

connected to the branching node as candidates. 4) Determine

the parent segment using (5). 5) Take the start node of the

parent segment as the new start node. And (6) go to 2) unless

a root branching node is reached.

D. Root Branching Nodes Identification

In the backward tracing, root branching nodes of hepatic

and portal veins are required. A root branching node is the

branching node where the hepatic or portal veins start to

separate. A root node is the end node where the hepatic or

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portal vein enters the liver. These nodes can be identified

automatically by using the knowledge on their anatomical

location in the liver coordinate system.

First, the liver coordinate system is calculated using the

principle component analysis on the liver mask (Fig. 2) and

the liver size is computed from bounding box. Then, vessel

skeleton is transformed to the liver coordinate. According to

the liver anatomy, the root node of the portal vein is in the

middle third of the back of the liver, in the liver coordinate

system. The root node of the hepatic vein is in the middle

third of the upper back of the liver. When multiple nodes were

found, the one with the largest diameter and is closest to the

liver surface was chosen. The root branching node was

identified as the branching node closest to the root node.

E. Automatic Labeling

After tracing is performed for all end nodes, we obtain a set

of paths, each starting from an end node. The automatic

labeling is then achieved in the following three stages.

Identification: A path is labeled as “hepatic” if it ends at

the hepatic root branching node, or is labeled as “portal” if it

ends at the portal root branching node. Otherwise, the path is

labeled as “unknown” if it ends at another end node.

Merging: The “unknown” paths are merged into either

“hepatic” or “portal” if possible. First, the intersections of an

“unknown” path with the known paths are identified. Then, if

all intersections belong to a certain class (e.g., “portal”), the

“unknown” path is labeled as that class. If intersections

belong to two classes, the “unknown” path is labeled as the

class that has more intersection nodes. Otherwise, it remains

labeled as “unknown.”

Separation: The three hepatic veins and two portal veins

are further labeled according to their anatomical relationship

to the root branching nodes. For the portal vein, we first get

the two neighboring nodes of the portal root branching node

in the liver coordinate, one on the left and the other on the

right. Then, all “portal” paths pass the left node are labeled as

“left portal” and all “portal” paths that pass the right node are

labeled as “right portal.” Similarly, the “right hepatic”,

“middle hepatic” and “left hepatic” are assigned to the

according “hepatic” paths.

III. EXPERIMENTS AND RESULTS

Experiments were performed using contrast-enhanced CT

images of 20 cases (3 pathological and 17 normal), aquired at

the portal venous enhancement phase at a fixed delay using

the Isovue-300 contrast agent. These images were collected

with LightSpeed Ultra and QX/I, Brilliance 64 and mx8000

IDT 16, and Definition scanners. Slice thickness ranged from

0.7 mm to 1.5 mm and slice resolution from 0.5 mm to 0.8

mm. Due to the noise and partial volume effect, touching

vessels were seen in these images.

Fig. 2 shows a typical result of our automatic labeling after

performing the identification and merging stages. The

close-up shows two branching nodes where a portal vein

touches two hepatic veins. Using the proposed method, these

veins were labeled correctly by taking advantages of the

probabilistic backward tracing. Fig. 3 shows the result after

the separation stage, in which the labels were mapped to the

segmented vessel surface for a better visualization. Despite

three branching nodes where the portal and the hepatic veins

touched, the proposed method labeled those veins correctly.

The segmentation and labeling results were evaluated by

an experienced interventional radiologist. The number of vein

branches per case varied between 57 and 129. For

segmentation, on average 95% of veins up to the 4-th order

branches were correctly segmented. Missed veins were

generally small peripheral branches (< 2 mm). In one case

with very low contrast, three branches of approximately 3

mm were not segmented. For labeling, a labeled branch was

Fig. 2. A typical automatic labeling result after the identification and

merging stages. The segmented vessels are shown as transparent meshes. The hepatic and portal veins are depicted by blue and red lines,

respectively. The three arrows show the liver coordinate system. The

close-up shows two branching nodes where a portal vein touches with

two hepatic veins. The proposed method labeled them correctly.

Fig. 3. The automatic labeling result after the separation stage. For a

better visualization, the labels were mapped to the segmented vessel surface. The left, middle and right hepatic veins are in cyan, purple and

blue, respectively. The left and right portal veins are in yellow and

green, respectively. The hepatic and portal roots are shown in brown.

There are three branching nodes (highlighted by the orange circles)

where the portal veins touch the hepatic veins. The proposed method

produced correct result at these nodes.

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assessed as correct or incorrect. The labeling accuracy was

calculated by dividing the number of correct labeled branch

by the number of all segmented branches. The mean and

standard deviation of the labeling accuracy was 0.97±0.08. In

addition, the proposed method produced similar results for

pathological and normal cases.

Fig. 4 shows results of a pathological case and the only one

failure case in the experiment. In the pathological case,

although the veins were significantly different from a normal

case and deformed due to the presence of a big tumor, our

method produced correct result. In the failure case, the veins

were closer to each other, possibly compressed by adjacent

anatomy. Additional to that, the partial volume effect led to

false branching nodes from touching veins, forming several

consecutive false cycles. These introduced challenges in the

tracing and merging stages. Consequently, a sub-branch of

the right hepatic vein was mislabeled as a sub-branch of the

right portal vein, leading to a low accuracy of 0.661. To deal

with these consecutive touching nodes, a robust checking

stage may be needed to further analyze the result after the

merging stage, taking the labeled network as a whole and

incorporating some learning strategy. Manual verification

could also correct or reject.

In our method, the value of the free parameter k in (1) is

not critical since at each branching node, a parent segment is

chosen as the candidate segment with the highest continuity

in terms of the local and segmental directions and diameter

preference. The comparison between the candidate segments

will be the same as long as the value of k is fixed. We used

k = 2.4 as po = 0.5 when the angle between v1 and v2 is π/2.

IV. CONCLUSION

A novel automatic labeling method of the major intra-

hepatic veins in contrast-enhanced CT is proposed and

demonstrated. The technique models the continuity of vessel

branches using probability functions and uses the continuity

measure to label the entire hepatic vessels as left, middle and

right hepatic veins, and left and right portal veins. The

labeling is a procedure of probabilistic inference and thus is

robust to the challenging condition wherein segmented

hepatic and portal veins form artificial branching nodes and

complex loops, which may induce a failure mode. This can

potentially facilitate CAD, liver surgery and planning, and

image-guided interventions by providing detail information

on the liver vascular structure.

The proposed method uses a low-level and a middle level

metrics. One future work is to develop high-level metrics to

measure plausibility of the individual tracing path and the

labeled network. Evaluation using more clinical patient CTs

is another future work, as well as integration into the

workflow for partial liver segment resection surgery or

interventional image guided procedures.

ACKNOWLEDGMENT

This project was supported in part by a philanthropic gift

from the Government of Abu Dhabi to Children’s National

Medical Center and the Intramural Research Program of the

National Institutes of Health, Clinical Center.

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Fig. 4. The automatic labeling results of a pathological case (left) and the

only one failure case (right) in the experiment. See text for explanations.

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