Pulmonary Lobe Segmentation in CT Images using Alpha-Expansion

Nicola Giuliani

, Christian Payer

, Michael Pienn

, Horst Olschewski

and Martin Urschler

2,4

Ludwig Boltzmann Institute for Lung Vascular Research, Graz, Austria

Institute of Computer Graphics and Vision, Graz University of Technology, Graz, Austria

Department of Pulmonology, Medical University of Graz, Graz, Austria

Ludwig Boltzmann Institute for Clinical Forensic Imaging, Graz, Austria

Keywords:

Lung Lobe Segmentation, Discrete Optimization, Graph Cuts, Alpha-Expansion.

Abstract:

Fully-automatic lung lobe segmentation in pathological lungs is still a challenging task. A new approach for

automatic lung lobe segmentation is presented based on airways, vessels, ﬁssures and prior knowledge on

lobar shape. The anatomical information and prior knowledge are combined into an energy equation, which

is minimized via graph cuts to yield an optimal segmentation. The algorithm is quantitatively validated on an

in-house dataset of 25 scans and on the LObe and Lung Analysis 2011 (LOLA11) dataset, which contains a

range of different challenging lungs (total of 55) with respect to lobe segmentation. Both experiments achieved

solid results including a median absolute distance from manually set ﬁssure markers of 1.04mm (interquartile

range: 0.88-1.09mm) on the in-house dataset and a score of 0.866 on the LOLA11 dataset. We conclude that

our proposed method is robust even in case of pathologies.

1 INTRODUCTION

Lung lobe segmentation from thoracic computed to-

mography (CT) images is a promising method to re-

place invasive methods for the quantiﬁcation and lo-

calisation of parenchymal destruction in lung dis-

eases (Bragman et al., 2017). This is of particular

interest in Chronic Obstructive Pulmonary Disease

(COPD) (Tanabe et al., 2012) (Weder et al., 1997).

There, computer-aided diagnosis algorithms can be

used for the detection and grading of emphysematous

changes and the evaluation of ﬁssure integrity. The

former can aid in establishing a patient’s need for lung

volume reduction surgery and the latter can identify

patients who can beneﬁt from valve-based lung vol-

ume reduction (Schuhmann et al., 2015).

The human lung is divided into ﬁve lobes by tree

ﬁssures, invaginations of visceral pleura extending

from the periphery of the lungs to the hilum (Hayashi

et al., 2001). The right lung is separated into three

lobes by two ﬁssures, the oblique and the horizontal

ﬁssure. The left lung is divided into two lobes by the

oblique ﬁssure. Typically the ﬁssures are a double-

layer of visceral pleura devoid of vascular structures

and airways, however, there is a substantial variation

in the general population (Aziz et al., 2004).

In thoracic CT images, the ﬁssures appear as

bright planar structures. However, their thin and vari-

able structure in combination with image noise, blur-

ring due to patient movement, and inhomogeneous

intensity values make them hard to detect with auto-

matic algorithms. Additional challenges are posed by

vessels and bronchi running in close proximity and

by pathological deformations of the ﬁssure by adja-

cent lung tissue. Developmental failure or pathologic

processes may even cause the absence of complete ﬁs-

sures (Hayashi et al., 2001).

This creates a need for computer algorithms capa-

ble of identifying ﬁssures where they are visible on

the thoracic CT images and extrapolate to plausible

lobe boundaries in regions where they are not. Several

approaches have been proposed besides the semiauto-

matic methods (Lassen-Schmidt et al., 2017). Some

methods are based on using information on lobar

shape i.e. learning an atlas and ﬁtting the atlas to

potential incomplete ﬁssures (Zhang et al., 2006).

Whereas others are using anatomical information of

the lung such as the airway and vascular trees to inter-

polate a boundary in regions where no ﬁssures are de-

tected (Van Rikxoort et al., 2010) (Doel et al., 2012).

As (Doel et al., 2015) have pointed out, both

approaches have advantages and disadvantages and

Giuliani, N., Payer, C., Pienn, M., Olschewski, H. and Urschler, M.

Pulmonary Lobe Segmentation in CT Images using Alpha-Expansion.

DOI: 10.5220/0006624103870394

In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - Volume 4: VISAPP, pages

387-394

ISBN: 978-989-758-290-5

387

the presented methods face problems with pathologi-

cal lungs, which makes pulmonary lobe segmentation

still a challenging task and an active area of research.

In this work, we propose a method that allows to

use both anatomical structures as well as prior knowl-

edge on the shape of lobes. To that end we combine

information from anatomical lung structures such as

the airways, vessels and ﬁssures with prior knowl-

edge on the appearance of the lobes in form of the

Potts model into an energy equation. Furthermore,

the ﬁssure segmentation step of (Lassen et al., 2013)

is improved by extending it to a multiscale approach.

This leads to an increase of detected ﬁssures, which

is especially of importance in cases where they are

pathologically thick. Minimizing this energy equation

via α−expansion is consequently yielding an optimal

lung lobe segmentation.

Up to our knowledge, we are the ﬁrst to incorpo-

rate anatomical structures into a multi-label graph cut

segmentation for lung lobe segmentation and show

promising results following this approach.

2 METHODS

We present a method for pulmonary lobe segmen-

tation based on minimizing an energy equation via

graph cuts. The aim of our study was to develop

the aforementioned energy equation, which takes

anatomical structures and prior knowledge about the

shape of lung lobes into account. Figure 1 shows

an overview of the algorithm. First the airway tree

and the lungs are segmented. After separating the

lungs into left and right lung, a segmentation of the

vessel trees is performed for each side. The ﬁssures

are segmented in the next step by considering the

vessel trees. In the ﬁnal step of the algorithm all

lung structures are combined in an energy equation,

which is then minimized using the α-expansion algo-

rithm (Boykov et al., 2001). The result is a 3D volume

where each voxel is assigned to one of ﬁve labels cor-

responding to the lobes.

2.1 Computing Lung Structures

In this section the computation of the airway, lung,

vessel and ﬁssure segmentation is described.

2.1.1 Airways

The airway segmentation is a combination of two al-

gorithms. Using the ﬁrst approach, initially a point

inside the trachea is detected by scanning for a dark

circle in the top-most slices. Starting from this point,

an iterative 3D-region growing algorithm is applied

to segment the airways (Helmberger et al., 2014).

The second airway segmentation is obtained by using

the PartialLungLabelMapImageFilter from the Chest

Imaging Platform (San Jose Estepar et al., 2015). As

each algorithm has its own strengths and performs

better in different cases they are combined to obtain

more stable results.

After obtaining an airway segmentation the

branches of the airway are labelled corresponding to

the lung lobes. In order to achieve this, the seg-

mentation ﬁrst has to be skeletonized. Based on the

anatomical structure of the airway tree it is now pos-

sible to label the branches. This is done similar to

the method presented in (Gu et al., 2012). First an

undirected acyclic graph is extracted from the airway

skeleton. Starting from a root vertex at the trachea the

next branching point is found by looking for a vertex

with three neighbors. Having found the carina it is

now possible to separate the airway into left and right

lung. The left lung can easily be divided into upper

and lower lobe by ﬁnding the next branching point

and comparing the coordinates of the branches’ end

points. In the right lung the same approach is used for

three lobes.

2.1.2 Lungs

Similar to the airway segmentation, the lung seg-

mentation is a combination of two algorithms. First

the lung is segmented following a grey-level thresh-

olding (Otsu, 1979) approach with subsequent mor-

phological closing operations. In cases where this

approach fails the PartialLungLabelMapImageFilter

from the Chest Imaging Platform (San Jose Estepar

et al., 2015) is used.

With the help of the labelled airway segmentation,

the lung can now be separated into left and right lung.

2.1.3 Vessels

The algorithm by (Payer et al., 2016) is used for

the vessel segmentation. It is ﬁrst enhancing vascu-

lar structures with a multiscale tubularity ﬁlter (Law

and Chung, 2008). Vessel paths are generated by

identifying regularly spaced local maxima in the ves-

sel enhanced images, which are connected to four-

dimensional tubular paths (Benmansour et al., 2013).

In the resulting local maxima graph a path for each

edge between its two end points is extracted that min-

imizes the geodesic distance. The tubular paths are

then ﬁltered and grouped together to distinct vascular

subtrees. As we are not interested in knowing which

vessel is an artery or vein, the algorithm is stopped at

this point.

VISAPP 2018 - International Conference on Computer Vision Theory and Applications

388

Airways

Lungs

Vessels Fissures

Approx. Lobes

Optimal Lobes

( f

)

p,q

( f

, f

)

min(E( f ))

Figure 1: Overview of the segmentation pipeline. The airways, lungs, vessels and ﬁssures are computed subsequently. The

airway segmentation is used to obtain an approximate lung lobe segmentation. All lung structures and the approximate seg-

mentation are then combined in an energy equation, which, leads to the optimal 3D lung lobe segmentation after minimization.

2.1.4 Fissures

Pulmonary ﬁssures appear as sheet-like structures in

CT scans. Based on an eigenvalue analysis of the

Hessian matrix H, voxels that are part of a sheet-

like structure are enhanced. The eigenvalues of the

Hessian matrix are deﬁned as |λ

| ≤ |λ

In (Lassen et al., 2013) the authors proposed a ﬁs-

sure similarity measure S

Fissure

, which combines two

features F

Structure

and F

Sheet

Fissure

= F

Structure

· F

Sheet

(1)

Structure

= θ(−λ

−(λ

−α)

(2)

Sheet

= e

−λ

(3)

Structure

is used for ﬁnding structure in the image.

The parameters α and β in (2) are set to 50 and 35 re-

spectively. As ﬁssures appear as bright structures on

a dark background the Heavyside function θ ensures

that voxels with an eigenvalue of λ

≥ 0 are not con-

sidered as ﬁssures. F

Sheet

is used to capture sheet-like

structures. Vessels have larger λ

values than ﬁssures

and are thus suppressed by this term. The parameter

γ is set to 25. The values for the presented parameters

were chosen according to the empirical analysis pre-

sented in (Lassen et al., 2013).

A mask of potential ﬁssure voxels M

is constructed

by computing S

Fissure

for every voxel in the image and

by only keeping those voxels that satisfy S

Fissure

0.1. M

is then ﬁltered by a 3D-vector-based con-

nected component analysis with a 6-neighborhood. In

case of a sheet the eigenvector corresponding to λ

points perpendicular to the direction of the structure.

This property is used to measure the similarity of ad-

jacent voxels by calculating the inner product of the

normalized eigenvectors of neighboring voxels. Two

neighboring voxels are considered as connected, if the

aforementioned inner product is larger or equal than

0.98. All components that are smaller than a thresh-

old are then rejected.

For the computation of H the differentiation is deﬁned

as a convolution with derivatives of Gaussians (Frangi

et al., 1998). In (Lassen et al., 2013) the computa-

tion was done with σ = 1.0mm. In cases of patho-

logical lungs it often occurs that ﬁssures are signiﬁ-

cantly larger than in healthy lungs. Empirical analy-

sis showed that H computed with σ = 1.0 was often

too low to capture thick ﬁssures. As our energy equa-

tion in (4) is fairly robust against false positives con-

cerning ﬁssures, we favoured computing the ﬁssure

segmentation on multiple scales for σ in the range

of [0.5 − 2.0]. This range has empirically shown to

detect ﬁssures to a great extent on a variety of CT

datasets. These results on multiple scales are then

combined into a single image F

. The drawback

of increasing σ to large values up to 2.0mm can lead

to a lot of vessels being falsely detected as ﬁssures.

To circumvent this problem, the previously computed

vessel segmentation is dilated and subtracted from the

multiscale ﬁssure segmentation F

. Figure 2 on the

Pulmonary Lobe Segmentation in CT Images using Alpha-Expansion

389

Figure 2: Left: Example for a ﬁssure segmentation result

of a right lung with pathological thick ﬁssures. While the

ﬁssures are almost fully segmented, the result also contains

falsely detected structures. Right: A reference standard, in

which the ﬁssures are fully segmented.

left shows a multiscale ﬁssure segmentation result of

a right lung with pathological thick ﬁssures.

2.2 Segmentation

The actual segmentation of the lung into its lobes

is achieved by computing an approximate solution,

which is then reﬁned by minimizing an energy equa-

tion that contains information on the lung structures

computed in section 2.1.

2.2.1 Approximate Lobe Segmentation

An approximate lung lobe segmentation S

can be

obtained with the help of the airway tree. This is

achieved by taking the lobe based airway segmenta-

tion and computing a distance map on it. Voxels are

then assigned labels I

according to their nearest air-

way branch. This approach is leading to solutions in

good approximation, as the airway branches are typ-

ically centered in the lobes. Figure 3 on the right

shows an approximate lobe segmentation of a right

lung as overlay to the original CT image. On the left

in ﬁgure 3 the corresponding airway segmentation can

be seen.

2.2.2 Energy Equation

The anatomical structures that are described in sec-

tion 2.1 are combined in an energy equation of the

form:

E( f ) =

∑

p,q∈N

p,q

( f

, f

) +

∑

p∈P

( f

) (4)

In (4) the binary term V

p,q

is deﬁning the energy that

is added to the system by two neighboring voxels

p and q with labels f

and f

. It is therefore often

referred to as interaction term. The unary term D

Figure 3: Left: Airway segmentation of a right lung; Right:

CT image (sagittal slice) of the same lung with the approx-

imate lobe labelling shown as overlay; the voxels are as-

signed labels corresponding to their nearest airway branch.

deﬁnes the energy for assigning a single voxel p the

value f

The minimization of (4) is consequently leading

to an optimal lobe segmentation. Boykov et al.

showed that the problem of minimizing energy

equations of the form presented in (4) is often

very difﬁcult and ﬁnding the optimal solution is

NP-hard (Boykov et al., 2001). In the same work an

algorithm (α − expansion) for ﬁnding a local mini-

mum within a known factor to the global minimum

is presented. The α-expansion algorithm is based

on the computation of graph cuts. The cut separates

or segments the vertices of the graph into a set of α

and α vertices. The graph is constructed in a way

that α can only expand. By iterating over all labels

and setting α to the current label it is possible to ﬁnd

solutions for images with multiple labels. The cost

of the graph cut represents the energy of the system.

Thus, only the solutions that undercut the current

lowest solution are kept in the iteration process. If

the algorithm converges, it is stopped.

The energy equation we propose for the lobe

segmentation using the anatomical structures of sec-

tion 2.1 is given by (4) where the binary term V

p,q

shown in (5) and the unary term D

in (6).

p,q

( f

, f

) = k

· P(a, b) (5)

( f

) = 0 if f

= I

= 1.0 ·k

· k

if f

6= I

(6)

The unary term D

is set to 0 if the value f

voxel p equals the value I

in the approximate lobe

segmentation S

. Doing so the system is constrained

to stay relatively close to S

. The anatomical

information retrieved from the lung structures are

VISAPP 2018 - International Conference on Computer Vision Theory and Applications

390

Figure 4: Left: Vasculature of a right lung. The lobe bound-

aries can be guessed from regions devoid of vessels. Right:

An inverted distance map computed on the vasculature.

Dark regions denote regions with high ﬁssure probability.

The real boundary is displayed as overlay.

incorporated into the unary term by the parameters

, k

and k

if f

6= I

The ﬁssures are integrated by the parameter k

, which

equals to 0 if p ∈ F and otherwise to 1. This implies

that voxels that are part of ﬁssures are equally likely

assigned to each label.

is a parameter to include information retrieved

from the lung vessels. A distance map is computed

based on the vessels. This distance map is inverted

and scaled to a range of [0, 1]. Voxels with a large

distance to the vessels have values close to 0, while

voxels part of the vessels have values of 1. Figure 4

on the left shows a vessel tree of a right lung. The

corresponding distance map is visualised on the right.

The true boundary is shown as an overlay on the

distance map.

The airway tree is considered by the third parameter

) in (6). Two considerations regarding the airways

are made. First we assume that the accuracy of

the approximate lobe segmentation S

is higher in

regions that are in close proximity to the airways.

With increasing distance to the airways the certainty

for the correctness of the label for a given voxel

decreases. This property is represented by the param-

eter k

. The second consideration about the airways

is done regarding the relative distance between the

two nearest airway branches to the current voxel. If

a voxel is close to one branch and relatively far away

from the second nearest branch, then the certainty

that this voxel is assigned the right label is increased.

However, if a voxel lies almost inbetween two

branches the certainty is decreased. This property

is represented by the parameter k

. The two pa-

rameters for the airways are combined to k

= k

·k

P(a, b) in the binary term in (5) refers to the Potts

model (Wu, 1982). P(a, b) = k

if a 6= b and 0 oth-

erwise. By using the Potts model in the binary term

the system is pushed towards solutions with closed

structures and smooth boundaries. To favour segmen-

tations with boundaries on the ﬁssures we include a

factor k

. This factor is always 1 except for voxels

that are part of the ﬁssures, in which case k

= 0.

Therefore, boundaries on the ﬁssures are more likely

to occur as they do not increase the energy. In regions

where no ﬁssures are detected by the ﬁssure segmen-

tation algorithm presented in section 2.1.4, the Potts

model leads to smooth interpolations of the indistinct

boundaries between the lung lobes.

3 EXPERIMENTS AND RESULTS

Two different experiments using two distinct datasets

were conducted.

3.1 Experiment 1

The ﬁrst experiment was realised using a dataset of 25

CT images. Two independent and unbiased individu-

als who had been adequately trained and not been part

of the development of the algorithm, manually placed

approximately 500 markers along the ﬁssures. Dis-

tinct markers were set for each ﬁssure making an in-

dividual evaluation for the left oblique, right oblique

and right horizontal ﬁssure possible. Distances be-

tween the manually placed markers on the ﬁssures and

the closest lobe boundary in the segmentation were

determined as measure of segmentation accuracy. The

distances were measured as positive and negative de-

pending on the relative position of the markers and

the boundary resulting from the automatic lobe seg-

mentation. Regarding the left lung this led to positive

distances for markers that are part of the lower lobe in

the automatic segmentation and negative results for

markers that are part of the upper lobe. Consider-

ing the right lung negative values were either used for

markers of the horizontal ﬁssure that were not part of

the middle lobe in the segmentation or markers of the

oblique ﬁssure that were not part of the lower lobe.

Two out of a total of 25 CT images had been ex-

cluded because of undeﬁned ﬁssures in the image and

failing bronchus labelling, respectively. In two further

scans, no markers had been set for the right horizontal

ﬁssure as it was not visible in the CT scans.

Using this evaluation protocol the median distance

was 0.00mm (interquartile range: -0.86-0.00mm).

The right and left oblique ﬁssures median distances

were 0.00mm (0.00-0.80mm) and 0.00mm (-0.86-

0.00mm), respectively. The median distance for the

right horizontal ﬁssure was 0.00mm (-1.05-0.00mm).

Pulmonary Lobe Segmentation in CT Images using Alpha-Expansion

391

The results for each individual case are visualised in

ﬁgure 5.

Using the same evaluation protocol with absolute

distances, the median distance was 1.04mm (0.88-

1.09mm). The right and left oblique ﬁssures median

distances were 0.95mm (0.87-1.06mm) and 0.93mm

(0.87-1.05mm), respectively. The median distance

for the right horizontal ﬁssure was 1.06mm (1.03-

1.09mm).

In ﬁgure 6 on the left, a lung lobe segmentation re-

sult for a left lung can be seen. On the right of ﬁgure 6

the result for the corresponding right lung is shown.

3.2 Experiment 2

Experiment 2 was conducted on the LObe and Lung

Analysis challenge (LOLA11) data set, which con-

tains 55 CT images from different clinically common

scanners and protocols. It includes many cases with

severe pathologies, which makes a segmentation chal-

lenging for automatic algorithms. In cases where the

airway segmentation failed or produced results con-

taining missing airway branches with respect to the

lobes, a manual correction had been performed. A

quantitative (see table 1) as well as a qualitative eval-

uation, by visual inspection, of the segmentation re-

sults on the LOLA11 dataset shows promising results

even on pathological lungs.

Figure 7 shows the results for the left and right lung of

case 42. Even though the left lung contains focal re-

gions of emphysema, the result shows a very precise

segmentation. The result for the right lung shows a

good segmentation even in regions where the oblique

ﬁssure is incomplete.

On the right in ﬁgure 8 the segmentation result for

the right lung of case 13 is visualised. It shows the

slice of the same right lung shown in ﬁgure 3. Start-

ing from the initial segmentation in ﬁgure 3 the ﬁnal

result follows perfectly the ﬁssures. On the left in ﬁg-

ure 8 the result for the left lung of case 1 is shown.

Two different challenging cases regarding the lobe

segmentation are shown in ﬁgure 9. On the left, the

left lung of case 6 is shown. The lung shows an exam-

ple for lung ﬁbrosis together with regions of emphy-

sema and a bulla. Due to these severe pathologies, the

upper lobe is uncommonly small. In conjunction with

a poor airway segmentation this leads to an approxi-

mate lobe segmentation that is far away from the opti-

mal, thus resulting in a weak segmentation of the pul-

monary lobes. On the right the result for the right lung

of case 54 is shown. While the segmentation is very

precise with respect to the right oblique ﬁssure, the

segmentation of the middle lobe is not correct. This

can be explained by a weak approximate segmenta-

Table 1: Results of lobe segmentation for the 55 scans in

the LOLA11 challenge.

LU LL RU RM RL

mean 0.929 0.884 0.873 0.714 0.928

SD 0.118 0.231 0.169 0.322 0.104

min 0.272 0 0 0 0.341

Q1 0.922 0.919 0.853 0.575 0.909

median 0.971 0.965 0.938 0.863 0.973

Q3 0.991 0.983 0.977 0.941 0.983

max 0.997 0.993 0.996 0.994 0.995

score: 0.866

tion, which was derived from an already weak airway

segmentation.

With a score of 0.866, our algorithm performs in the

range of the other state-of-the-art methods. Merely

the interactive approaches show distinctly better re-

sults (LOLA11, 2017). Detailed comparisons to other

methods are difﬁcult to perform, as labelled datasets

for lobe segmentation are not publicly available.

4 CONCLUSION AND FUTURE

WORK

In this paper, we have proposed a new algorithm

for fully automatic lung lobe segmentation using α-

expansion. This approach allows to combine anatom-

ical structures, derived from the original CT image,

as well as prior knowledge on the shape of lung lobes

into an energy equation. The Potts model is used as

prior knowledge, which is leading to smooth lobar

surfaces. An initial approximation to the lung lobe

segmentation, close to the actual segmentation, is ﬁrst

derived by computing a distance map on the labelled

airway segmentation. The multiscale ﬁssure segmen-

tation approach is drastically improving the amount of

detected ﬁssures while simultaneously increasing the

amount of spuriously detected structures. False posi-

tives in the ﬁssure segmentation are however no issue

regarding the ﬁnal lobe segmentation as the system

stays close to the initial approximation. Thus ﬁnding

a good approximation is important to achieve good

results, which is evident from the observation that a

poor segmentation is almost always attributable to a

weak approximate lobe segmentation.

While limitations in our method are seen in the

airway and lung segmentation steps, which consist

of the combination of two algorithms to yield robust

results, the approach of minimizing the devised

energy equation has shown good results for lobe

segmentation in our experiments.

VISAPP 2018 - International Conference on Computer Vision Theory and Applications

392

Figure 5: Distances of the individual markers from the nearest automatically detected ﬁssure for each patient in experiment 1.

Figure 6: Example for a segmentation result of a left lung

(left) and a right lung (right) a patient from experiment 1.

Figure 7: Segmentation results for LOLA11 case 42. Note

the invisible ﬁssure (arrow).

With this work we established a general method

with modular components as suggested in (Doel et al.,

2015). Future work will consist of gradually improv-

ing the individual modules for lung, vessel, ﬁssure

and especially airway segmentation.

ACKNOWLEDGEMENTS

The assistance of Grazyna Kwapiszewska is highly

appreciated.

Figure 8: Left: Segmentation result for the left lung of

LOLA11 case 1. Right: Segmentation result for the right

lung of LOLA11 case 13.

Figure 9: Left: Segmentation result for the left lung of

LOLA11 case 6. Right: Segmentation result for the right

lung of LOLA11 case 54.

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