An iterative Bayesian approach for nearly automatic liver segmentation: algorithm and validation

Abstract

PurposeWe present a new algorithm for nearly automatic liver segmentation and volume estimation from abdominal Computed Tomography
Angiography (CTA) images and its validation.

Materials and methodsOur hybrid algorithm uses a multiresolution iterative scheme. It starts from a single user-defined pixel seed inside the liver,
and repeatedly applies smoothed Bayesian classification to identify the liver and other organs, followed by adaptive morphological
operations and active contours refinement. We evaluate the algorithm with two retrospective studies on 56 validated CTA images.
The first study compares it to ground-truth manual segmentation and semi-automatic and automatic commercial methods. The second
study uses the public data-set SLIVER07 and its comparison methodology.

ResultsWe achieved for both studies, correlations of 0.98 and 0.99 for liver volume estimation, with mean volume differences of 5.36
and 2.68% with respect to manual ground-truth estimation, and mean volume variability for different initial seeds of 0.54
and 0.004%, respectively. For the second study, our algorithm scored 71.8 and 67.87 for the training and test datasets, which
compares very favorably with other semi-automatic methods.

ConclusionsOur algorithm requires minimal interaction by a non-expert user, is accurate, efficient, and robust to initial seed selection.
It can be effective for hepatic volume estimation and liver modeling in a clinical setup.

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DOI 10.1007/s11548-008-0254-1
ORIGINAL ARTICLE
An iterative Bayesian approach for nearly automatic liver
segmentation: algorithm and validation
M. Freiman · O. Eliassaf · Y. Taieb · L. Joskowicz ·
Y. Azraq · J. Sosna
Received: 7 January 2008 / Accepted: 18 June 2008
© CARS 2008
Abstract
Purpose We present a new algorithm for nearly automatic
liver segmentation and volume estimation from abdominal
Computed Tomography Angiography (CTA) images and its
validation.
Materialsandmethods Ourhybridalgorithmusesamultire-
solution iterative scheme. It starts from a single user-defined
pixel seed inside the liver, and repeatedly applies smoo-
thed Bayesian classification to identify the liver and other
organs, followed by adaptive morphological operations and
active contours refinement. We evaluate the algorithm with
two retrospective studies on 56 validated CTA images. The
first study compares it to ground-truth manual segmentation
andsemi-automaticandautomaticcommercialmethods.The
secondstudyusesthepublicdata-setSLIVER07anditscom-
parison methodology.
Results We achieved for both studies, correlations of 0.98
and 0.99 for liver volume estimation, with mean volume dif-
ferences of 5.36 and 2.68% with respect to manual ground-
truth estimation, and mean volume variability for different
initialseedsof0.54and0.004%,respectively.Forthesecond
study, our algorithm scored 71.8 and 67.87 for the training
and test datasets, which compares very favorably with other
semi-automatic methods.
Conclusions Our algorithm requires minimal interaction by
a non-expert user, is accurate, efficient, and robust to initial
M. Freiman (B ) · O. Eliassaf · Y. Taieb · L. Joskowicz
School of Engineering and Computer Science,
The Hebrew University of Jerusalem,
Givat Ram Campus, Jerusalem 91904, Israel
e-mail: freiman@cs.huji.ac.il
Y. Azraq · J. Sosna
Department of Radiology, School of Medicine,
Hadassah Hebrew University Medical Center, Jerusalem, Israel
seed selection. It can be effective for hepatic volume estima-
tion and liver modeling in a clinical setup.
Keywords
of abdominal organs · Computer-assisted diagnosis
Computed tomography · Segmentation
Introduction
Liver segmentation and volume estimation from abdominal
computed tomography angiography (CTA) images is a key
task in many clinical applications. It includes the assessment
of hepatomegaly and liver cirrhosis, liver regeneration after
hepatectomy, hepatic transplantation planning for size com-
patibility, and monitoring of patients with liver metastases,
where the disease is related to an enlargement of the liver,
among others. To be of practical clinical use, the liver seg-
mentationandlivervolumeestimationmustbeaccurate,fast,
robust,andnearlyautomatic,sothatradiologistscanperform
it without the help of a technician.
Nearly automatic liver segmentation, which is essential
for hepatic volumetry, is known to be a very challenging task
due to the ambiguity of liver boundaries, the complexity of
the liver surface, and the presence of surrounding organs.
Many previous works propose automatic or semi-automatic
methods for liver segmentation. These methods can be clas-
sified into four main categories: (1) atlas-guided methods
[1–3]; (2) region growing methods [4,5]; (3) deformable
models and level sets based methods [6,7], and; (4) clas-
sification based methods [8,9]. In many cases, the methods
produce inaccurate segmentations, as they do not make full
use of the intensity and geometric information present in the
original images.
To circumvent this problem, a hybrid two-phase approach
consisting of a preliminary segmentation (usually atlas- or
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intensity-based) followed by a deformable model refinement
was proposed [10,11]. This approach works well when the
preliminary segmentation is close to the final one, since if it
is off (e.g., due to a local minima), it is very unlikely that the
refinement step will manage to significantly improve it.
Metaxas et al. [12] propose a hybrid iterative scheme for
generalobjectsegmentation.Inthisscheme,theresultsofone
method are used by the second one repeatedly until conver-
gence.Specifically,thismethodcomputesfirstaMarkovran-
dom field from manually selected initial pixel seeds inside
eachorgan,andthenusesitastheinitialmeshfordeformable
model based segmentation. The process is repeated with the
resulting contour until convergence. The advantage of this
methodisthatwhileeachiterationproducesonlysmallmodi-
fications, the accumulated modification can be significant.
However, the computation of 3D Markov Random Fields is
computationally expensive, so the implementation uses 2D
fields instead, with the consequent sacrifice in accuracy.
The disadvantages of the semi-automatic methods [4–
7,12] are that most of them require significant user inter-
action, such as the selection of multiple pixel seeds, or the
manualdrawingofinitialcontours.Thisinitializationistime-
consuming and user-dependent, which significantly affects
the robustness of the methods. Because of the liver boun-
dary ambiguity, expert radiological knowledge, which is not
always available, is often required to obtain a proper initiali-
zation. Automatic methods [1–3] do not require user initia-
lization but depend on good prior shape models, which are
sensitive to shape variations between healthy and sick livers,
different patient ages, and image scanning protocols.
In this paper, we present a hybrid, nearly automatic liver
segmentation algorithm that uses an iterative classification
scheme. The algorithm repeatedly applies multiresolution
smoothed Bayesian classification followed by adaptive mor-
phological operations and active contours refinement. The
smoothed Bayesian classification uses patient-specific ‘soft’
thresholdingcoupledwithneighborhoodinformationinstead
ofasimplebinarythreshold[10,11]foramoreaccurateclas-
sification.Adjacentorgansandtissuesareexplicitlyremoved
during the classification step using an intensity distribution
model developed for this purpose. The resulting segmenta-
tion is refined with an active contours step.
To evaluate and validate our algorithm accuracy and
robustness, we performed two retrospective studies on vali-
dated clinical datasets totaling 56 CTA images. In the first
study, which consists of 26 CTA scans, we compared the
results of our algorithm to those of a ground-truth manual
segmentation and semi-automatic and automatic commer-
cial methods. The evaluation includes both the volume and
surface measurements. In the second study, we used the SLI-
VER07 (Segmentation of the Liver Competition 2007) data-
set, a publicly available database of 30 CTA images [18].
We compared the results to their ground-truth segmentation
and other published methods. In both the studies, the propo-
sed algorithm achieved a high score among semi-automatic
methods with much less user interaction and lower variabi-
lity.
Method
Our algorithm consists of three main steps: (1) intensity-
based classification; (2) adaptive morphological adjustment,
and; (3) geodesic active contours refinement. After each ite-
ration, the internal parameters of the classification step are
updated before its application. This coupling is designed
to overcome a biased classification due to ambiguous liver
boundaries and biased pixel seed selection. To speed up the
segmentationandmakeitmorerobustandaccurate,thealgo-
rithmusesamultiresolutionapproach.Startingfromthecoar-
sestleveloftheimagepyramid,thealgorithmiteratesoneach
level until convergence, and then switches to the next, more
refined level. The final step is performed at full resolution
on the original image. Table 1 outlines the procedure. We
describe each step in detail next.
Intensity-based classification
Intensity model generation
The first step of the algorithm is the construction of an inten-
sity model that differentiates between the liver and other
organsandtissues,whichareinterpretedasbackground.The
main challenges are to handle the ambiguous boundary bet-
ween the liver and other organs, such as the kidney, and to
properly identify the background organs. To overcome these
difficulties, we propose to use a five-class model for voxel
classification according to their gray level value.
The first class represents the liver. The remaining four
classes represent other organs and tissues whose gray level
Table 1 Outline of the liver segmentation algorithm
Input: voxel seed inside the liver, selected manually.
1. Intensity-based classification
1. Intensity model generation
2. Voxel classification with smoothed MAP rule
2. Adaptive morphological operations
1. Largest connected component selection
2. Hole filling
3. Morphological opening
3. Geodesic active contours refinement
1. Energy image generation
2. Active contours refinement
Repeat 1–3 until convergence.
Output: Liver contour segmentation and voxel classification.
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values are above or below the liver class. We model each
class with a normal distribution defined by its intensity mean
and variance values. In the first iteration, the mean and the
variance of a rectangular neighborhood around the user-
selected pixel seed inside the liver are computed and taken
as the initial parameter values of the liver class.
In subsequent iterations, the segmented region from the
previous iteration is used to compute the mean and variance
values of the liver class. The remaining four classes model
organs near and far (above/below) the liver in the intensity
domain. The mean value of each class is computed with res-
pect to the liver class mean value. Formally, the liver class
Xliveris defined as:
Xliver∼ N(µliver,σ2
The other four classes Xiare modeled as:
liver)
(1)
Xi∼ N(µi,σ2
for each i ∈ {near-low, near-high, far-low, far-high}. The
means of these classes are defined as:
i)
(2)
µnear−high= µliver+ (knear× σliver)
µnear−low= µliver− (knear× σliver)
µfar−high= µliver+ (kfar× σliver)
µfar−low= µliver− (kfar× σliver)
where the factors knear and kfar are determined from
Chebyshev’s inequality:
(3)
Pr(|Xi− µliver|) ≥ kσliver) ≤
1
k2
(4)
This inequality ensures that at least (1 −
the values are within k standard deviations from the mean
value. This ensures that each voxel from the ambiguous liver
boundary has a high probability of being in both the liver
and near classes. Its final classification will then depend on
its neighboring voxels. Initially, we set σi = σliverfor all
classes.
The values of the parameters knearand kfarare set experi-
mentally by searching the two-dimensional parameter space
in the appropriate parameter intervals. Each vector of the
parameter values is ranked by comparing the segmentation
resultsusingtheseparametervaluesonthetrainingdatasetsto
their ground truth segmentation. Figure 1 shows an example
plot of the liver distributions and its two nearby classes.
1
k2) × 100% of
Voxel classification
Thesecondstepistheuniqueclassificationofeachvoxel.The
classification relies on the voxels intensity values and their
neighboring voxels. Neighborhood information is important
since voxel intensity values are correlated. Our classification
follows the three-step method by Teo et al. [13] (Table 2).
Fig. 1 The estimated Gaussian distributions of the liver and its two
nearbyclassesascomputedbyourmethod.Thehorizontalaxisaregray
level Hounsfield units, while the vertical axis are class probabilities
Table 2 Voxel classification with a smoothed MAP rule
Input: An intensity model described with classes
1. Generate for each class a membership map from the volume
based on the class intensity model
2. Smooth the membership maps using an anisotropic diffusion
process
3. Computethesegmentationlabelmapwiththemaximumpos-
terior (MAP) rule
Output: Segmentation label map
In the first step, we compute the probability C(j,i)of a
voxel Vjwith intensity value vjto belong to class ci, where
i∈{liver, near-low, near-high, far-low, far-high}usingBayes
rule:
Pr(vj|ci) ∝ Pr(ci|vj)Pr(ci)
where Pr(ci|vj) is obtained from the intensity model gene-
rated in the previous step, and Pr(ci) is assumed to be from
a uniform distribution. The resulting five maps quantify the
membership probability of each voxel to each class.
Next, we incorporate the neighborhood information to
the classification process by smoothing the probability maps
C(j,i)for each class i separately using the anisotropic diffu-
sion equation proposed by Perona and Malik [14]:
(5)
∂I
∂t
= ∇ · a∇I, with a = e−|∇I|2
b2
(6)
where ∇I is the image gradient, and a is the conductivity
coefficient of the local image edges smoothing, which inver-
sely depends on the image gradient magnitude and scaling
factor b that helps to differentiate between noise and real
image gradients. The anisotropic smoothing process flattens
smallpeeksinthemembershipprobabilitymaps,mostlikely
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Fig. 2 Illustration of the segmentation steps: a Smoothed Bayesian
classification. b Largest connected component selection. c Application
of morphological operators. d Active contours refinement
misclassification, while preserving sharp edges between dif-
ferent objects.
Finally, we apply the maximum posterior (MAP) rule:
C(j,final)= argmax
ci
Pr(vj|ci)
(7)
The rule sets the final membership of each voxel to the class
with the highest probability. The binary segmentation image
is generated by selecting only the voxels that belong to the
liver class. Figure 2a shows an example of a classified slice.
Adaptive morphological adjustment
The third step is the identification of the liver region. The
previous classification yields most of the liver region, addi-
tionaldisconnectedregionsoutsidetheliver,andholesinside
the liver. Regions outside the liver correspond to anatomical
structures with intensity values similar to that of the liver,
such as the kidney and the spleen. Holes correspond to small
tumors and artery and portal veins inside the liver whose
intensityvaluesaredistinctlydifferentfromtheliverintensity
valuesduetotheuseoftheimagingcontrastagent.Toobtain
thecorrectliversegmentation,thedisconnectedregionsmust
be eliminated, and the holes inside the liver must be filled.
This is done with a set of adaptive morphological operators.
We first remove the disconnected regions outside the liver
by identifying the largest connected component in the labe-
led image, as illustrated in Fig. 2b. Next, we use a closing
morphological operator tofillholes insidetheliver,followed
by an opening operator to separate the liver from surroun-
ding organs such as the kidney, the spleen, and the heart. The
operators radiuses are adaptively computed from the liver
volume estimation Vliverobtained from the previous classifi-
cation step with:
Ropen= Vliver∗ C
Rclose= Ropen∗ R
where C and R are predefined radius constants computed by
searchingthetwo-dimensionalparameterspaceintheappro-
priate parameter intervals. The adaptive parameter adjust-
ment of the morphological operators allows the accurate
and automatic application of the morphological operators
to achieve the required liver segmentation. The result of this
step is an updated labeled map of the liver, as illustrated in
Fig. 2c.
(8)
Geodesic active contours refinement
The classification and the morphological adjustment may
miss parts of the liver volume. In addition, the liver boun-
daries may be inaccurate in several regions. To correct this,
we repeatedly apply a fine-tuning active contours segmenta-
tion [15]:
F = αgI + βcgI+ γ(∇gI· N)
where gI is the speed function derived from the gradient
magnitude of the input image I, c is the mean curvature of
the contour, N is the normal of the voxel, and α, β, and γ are
weights that modulate the relative contributions of the three
components of F. This equation is solved using the level-set
method, where the deformed contour is represented as the
zeroth level set of the function φ:
(9)
∂
∂tφ(x,t) = F∇φ
(10)
definedateveryvoxelintheinputimage,wherex isthevoxel
coordinate and t is the time point.
Since the active contours method is well suited for struc-
turesboundedbystrongimageintensityedges,weemphasize
theliverboundariesbyapplyingawindowingfunctiontothe
original image:
⎧
⎪⎪⎪⎪⎩
where I?is the new image, I is the original image, and µliver
and σliverare the liver class parameters as computed in the
intensity model step. Figure 2d illustrates the result of this
step.
I
?(x) =
⎪⎪⎪⎪⎨
µliver+ σliver
I(x)
if I(x) > µliver+ σliver,
if µliver− σliver≤ I(x)
or I(x) ≤ µliver+ σliver,
if I(x) < µliver− σliver.µliver− σliver
(11)
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Algorithm iterations
The intensity based classification, morphological operators,
and active contours steps are repeatedly applied to the image
until no further change occurs (Table 1). The iterations are
necessary for fine-tuning the intensity model to improve the
classificationandminimizetheimportanceoftheinitialvoxel
seed selection. The intensity based classification updates the
classes model by computing the mean and variance of the
liverclassfromthecurrentliverregionandupdatingtheother
four classes by computing their mean and variance para-
meters with Eq. 3. The morphological operations are then
applied on the resulting classes to find the new liver region.
Theactivecontoursrefinementimprovestheliverboundaries
fitting.
(a)
(b)
Fig. 3 Updates during the iterative scheme. a Intensity model (mean
and standard deviation of liver). The horizontal axis represents the
number of iterations; the vertical axis represents the mean (point)
and variance (interval) of the liver class in Hounsfield units (HU).
b Estimated liver volume (in ml) during the iterations
The algorithm starts on a coarse level of the image
pyramid. The switching criterion between pyramid levels is
convergence at a given resolution level. Starting from the
coarsest level of the pyramid, the algorithm iterates on each
level until convergence, and then switches to the next more
refined level on the pyramid. The final step is performed on
the original image, at full resolution.
Figure 3 illustrates the importance of the iterations in the
fine-tuning of the liver intensity model and in the corres-
ponding liver volume estimation. Figure 3a shows the liver
class parameters according to the algorithm iterations. In the
firstiteration,theparameterswerecomputedaccordingtothe
manually selected pixel seed. In the remaining iterations,
the mean and variance of the liver class were updated accor-
dingtothesegmentedliverregion.Notethesignificantchange
in the estimated variance during the iterations. Figure 3b
shows the changes in the estimated liver volume during the
iterative process. Note how the estimated liver volume
converges to its final estimation in several iterations.
Experimental validation
To evaluate our algorithm, we implemented it with ITK soft-
ware library [16] and with the smoothed Bayesian classifi-
cation module from [17]. We conducted two retrospective
studies on two validated clinical datasets totaling 56 CTA
scans. Figure 4 illustrates the result of our algorithm on one
of the datasets.
Parameter setup
The algorithm internal parameter values were empirically
set after exploration on 10 CTA test images as follows. The
classification parameters in Eq. 3 were set to knear = 2.2
and kfar= 4. These parameter values guarantee by Cheby-
shev’s inequality Eq. 4 that at least 80% of the liver voxels
are classified as liver, and at least 70% of the voxels that
belong to the near classes will be classified as near, even if
the normal distribution of the liver intensities assumption is
notcorrect.ThemorphologicaloperationparametersinEq.8
were set to C = 4 and R = 1.2. Note that the values are in
millimeters, not voxels, to properly model the anisotropic
nature of the data. Each pair of parameters was determined
after about 20 runs on the test CTA images. Each pair of
parametervalueswasrankedbycomparingthesegmentation
results using the predetermined parameter values on the trai-
ning dataset to their ground truth segmentation. The values
of the highest ranking pair were then selected. The parame-
ters of the geodesic active contours (Eq. 9) module were set
as follows: the propagation parameter was set to α = −1,
the curvature scaling term and the advection term were set
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Fig. 4 Example of a segmented liver. The red contour is our segmen-
tationresult,andthebluecontour istheground-truthsegmentation.For
3D movies that illustrate the algorithm results, please refer to: http://
www.cs.huji.ac.il/~freiman/LiverSeg
both to c = γ = 0.33. The number of iterations of the active
contours step was set to 7 for each iteration of the algorithm.
Weusedathree-levelmultiresolutionpyramidprecompu-
tedfromtheoriginalCTAimages.Theanisotropicsmoothing
parameters of the classification probability maps in Eq. 6
weresettob = 1fortheconductancetermandtot = 0.0625
for the time-step. The smoothing process performs two ite-
rations at the coarsest level of the image pyramid and four
iterations in the two subsequent levels.
First study
The first study compares our algorithm to ground-truth
manual segmentation and to semi-automatic and automatic
commercial methods.
The study dataset consists of 26 CT scans from 26 adult
patients(averageage54years;range32–78).Thescanswere
acquired in a 16-channel detector scanner (Brilliance 16,
Philips Medical Systems, Groningen, The Netherlands) with
2mmslicethicknessand1mmincrement(200–250mAs,120
kVp). The clinical findings of these scans included 13 heal-
thy livers, 3 livers with cirrhosis, 4 with metastases, and 6
withprimarylivertumors.Thedatasetwasusedinaprevious
study by Sosna et al. [9].
We compared the results of our method to those obtai-
ned from a manual tracing of the liver contour in each slice
performed by a dedicated technologist on a Vitrea 2 works-
tation (Vital Images, Plymouth, MN, USA), which serves as
the ground-truth. In addition, we compared our method to a
prototype automatic segmentation tooland asemi-automatic
paint-brush tool in a Philips EBW 3.0 workstation, (Philips
Medical Systems, Groningen, The Netherlands). The results
of these methods were reported by Sosna et al. [9].
The liver scans were segmented with each method. The
livervolumeestimateswerethencomputeddirectlyfromthe
resulting segmentation. The liver volumes were compared to
the ground-truth using linear regression analysis. User inter-
action and computation times were also recorded. In addi-
tion, we evaluated the robustness of our algorithm and the
commercial automatic method (2) by comparing the volume
differences of three runs with different initialization seeds.
Since we did not have access to the manual segmentation,
we could not compare our segmentation to the gold standard
using other measures, as we did in the second study.
Themeanlivervolumecomputedfromthemanualtracing
was 1,657 mL (milliliters), with a range of 1,050–2,647 mL.
The mean liver volume computed with our method (1) was
1,648 mL (range 981–2744 mL), with the commercial auto-
matic method (2) 1479 mL (range 926–2,417 mL) and with
the commercial semi-automatic method (3) 1,619 mL (range
1,018–2,541 mL). Our method estimated the liver volume
much better than the commercial automatic algorithm.
Table 3 summarizes the other measurement results. The
mean absolute difference between the estimated liver vol-
umes between manual tracing and our method was 5.36%
(std=3.48%)ofthelivervolume,withthecommercialauto-
matic method it was 10.55% (std 5.98%), and with commer-
cial semi-automatic method it was 2.65% (std = 1.45%).
These results indicate that our algorithm estimated the liver
volume more accurately than the commercial automatic
method. The calculated correlation coefficient for liver vol-
ume between the manual tracing and our method measu-
rements was 0.98, which is better than the correlation of
the other methods. The correlation between the commer-
cial automatic method and the ground-truth was 0.97, and
Table 3 First study experimental results summary for 26 CTA scans
Method Volume diff. % Corr. coeff. Variations %
1. Ours
2. Commercial
automatic
3. Commercial
semi-automatic
5.36 (3.48)
10.55 (5.98)
0.98
0.97
0.54 (0.76)
2.09 (2.85)
2.65 (1.48)0.99–
The first column indicates the method used. The second column shows
theestimatedvolumedifference(meanandstandarddeviationinparen-
thesis). The third column shows the correlation coefficient with the
ground-truth manual tracing segmentation. The last column shows the
mean(std)volumeestimationvariationsforthedifferentseedselections
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between the commercial semi-automatic method and the
ground-truthwas0.99.Themeanvolumedifferencebetween
initializationswithdifferentpixelseedswithourmethodwas
0.54%(std=0.76%)and2.09%(std=2.85%)withthecom-
mercialautomaticmethod,whichindicatesthatouralgorithm
is highly robust to seed selection.
The mean segmentation time of the manual tracing was
7:24min,mostofitwasusertime.Ourmethodrequiredafew
seconds of user time for pixel seed selection and a mean of
23:22 min for processing on a standard PC. The commercial
automatic method running time was 0:37 min on dedicated
workstation, which is not directly comparable to our method
running time. The commercial semi-automatic method total
segmentation time was 5:14 min. Most of it was user time
due to its interactive method.
Second study
For the second study, we used the SLIVER07 (Segmenta-
tion of the Liver Competition 2007) [18] publicly available
database and comparison methodology. We compared the
resultstotheirground-truthsegmentationandotheravailable
methods.
The dataset consists of 30 CTA images with ground-truth
manual segmentations validated by two experts. The data-
set consists of two parts. The first 20 scans were used as
a training set and include the ground-truth segmentations.
The remaining 10CTA scans wereused as testsets,and their
ground-truthsegmentationsarenotaccessible.Fivemeasures
were computed: (1) volumetric overlap error; (2) absolute
volume difference; (3) average symmetric surface distance;
(4) root mean squares (RMS) symmetric surface distance,
and;5)maximum symmetricsurfacedistance.Themeasures
and aggregate grade were computed on the test set by the
database providers as described in [18].
Table4summarizestheresultsofourmethod.Theaverage
values for the test and training sets were as follows: (1) volu-
metric overlap error 8.55 and 7.81%; (2) absolute volume
difference 2.78 and 2.63%; (3) average symmetric surface
distance 1.46 and 1.28 mm; (4) root mean squares (RMS)
symmetricsurfacedistance2.94and2.55mm,and;(5)maxi-
Table4 Secondstudyexperimentalresultssummaryfor30CTAscans
from the SLIVER07 datasets
Dataset Volume diff. %Corr. coeffVariations %
1. Training
2. Test
2.63 (1.64)
2.78 (2.14)
0.99
–
0.004 (0.005)
–
The first column indicates the dataset. The second column shows the
estimated mean (std) volume difference. The third column shows the
correlationwiththeground-truthmanualtracingsegmentation.Thelast
column shows the mean (std) volume estimation variations for the dif-
ferent seed selections
mum symmetric surface distance 26.72 and 22.77 mm. The
correlation between our volume estimation and the ground
truthonthetrainingsetwas0.99.Notethatsincetheground-
truth is not available for the test set, we could not compute
the correlation value for it. Note also that this detailed quan-
titative evaluation was not possible for the first database, as
no ground-truth segmentations were available to us.
We also evaluated the robustness of our method by repea-
tedly selecting different initial seeds and comparing the
results. We chose three different seeds initializations on the
training dataset of 20 CTA images. The absolute volume dif-
ference was 0.004%, which is negligible.
The results suggest that our method is both accurate and
robust to pixel seed selection. Our method achieved a total
score of 71.8 on the training set and of 67.87 on the test set
as computed in [18]. It is ranked forth of the semi-automatic
method. However, all other semi-automatic methods require
significantly more user interaction and therefore, are more
time-consumingandlessrobusttodifferentuserinteractions.
Conclusions
We have presented a new algorithm for the nearly automatic
liver segmentation and volume estimation from abdominal
CTA images. The hybrid algorithm uses a multiresolution
iterative scheme that comprises a smoothed Bayesian clas-
sification coupled with set of adaptive morphological opera-
tions and active contours refinement.
The main advantages of our method are that it requires
minimal user interaction for initialization—a single pixel
seed inside the liver—does not require any adjustment of the
internal parameters, is robust, and can be performed by non-
experts. The multiresolution iterative approach allows the
robustsegmentationoftheentireliversurfacewithoutexten-
sive shape prior information and/or significant user interac-
tion to overcome local minima.
Our experimental results show that our algorithm is effec-
tiveandreliablewhencomparedtotheground-truthandother
commercial methods. Our algorithm achieves a more accu-
rate and robust volume estimation than the commercial auto-
matic method when compared to the manual segmentation.
Although our segmentation results are not better than those
of the commercial interactive tool, our method requires only
one pixel seed selection which can be done by a non-expert
user in few seconds, while the commercial interactive tool
requires more than 5 min of expert user time for the segmen-
tation. Our method can thus be effective for hepatic volume
estimation and liver modeling in a clinical setup.
In the future, we plan to extend our method to entire liver
analysis, including tumors and vessels segmentation inside
the liver, and to apply our algorithm to other medical image
segmentation tasks, such as kidney and spleen.
123

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