Automatic cardiac ventricle segmentation in MR images: a validation study.

Abstract

Segmenting the cardiac ventricles in magnetic resonance (MR) images is required for cardiac function assessment. Numerous segmentation methods have been developed and applied to MR ventriculography. Quantitative validation of these segmentation methods with ground truth is needed prior to clinical use, but requires manual delineation of hundreds of images. We applied a well-established method to this problem and rigorously validated the results.
An automatic method based on active contours without edges was used for left and the right ventricle cavity segmentation. A large database of 1,920 MR images obtained from 59 patients who gave informed consent was evaluated. Two standard metrics were used for quantitative error measurement.
Segmentation results are comparable to previously reported values in the literature. Since different points in the cardiac cycle and different slice levels were used in this study, a detailed error analysis is possible. Better performance was obtained at end diastole than at end systole, and on mid-ventricular slices than apical slices. Localization of segmentation errors were highlighted through a study of their spatial distribution.
Ventricular segmentation based on region-driven active contours provided satisfactory results in MRI, without the use of a priori knowledge. The study of error distribution allows identification of potential improvements in algorithm performance.

Full text

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Int J CARS manuscript No.
(will be inserted by the editor)
Automatic cardiac ventricle segmentation in MR images:
a validation study
Damien Grosgeorge · Caroline Petitjean ·
J´ erˆ ome Caudron · Jeannette Fares ·
Jean-Nicolas Dacher
Received: date / Accepted: date
Abstract Purpose Segmenting the cardiac ventricles in magnetic resonance (MR) im-
ages is required for cardiac function assessment. Numerous segmentation methods have
been developed and applied to MR ventriculography. Quantitative validation of these
segmentation methods with ground truth is needed prior to clinical use, but requires
manual delineation of hundreds of images. We applied a well-established method to
this problem and rigorously validated the results.
Methods An automatic method based on active contours without edges was used for
left and the right ventricle cavity segmentation. A large database of 1920 MR images
obtained from 59 patients who gave informed consent was evaluated. Two standard
metrics were used for quantitative error measurement.
Results Segmentation results are comparable to previously reported values in the lit-
erature. Since different points in the cardiac cycle and different slice levels were used
in this study, a detailed error analysis is possible. Better performance was obtained
at end diastole than at end systole, and on mid-ventricular slices than apical slices.
Localization of segmentation errors were highlighted through a study of their spatial
distribution.
Conclusions Ventricular segmentation based on region-driven active contours provided
satisfactory results in MRI, without the use of a priori knowledge. The study of error
distribution allows identification of potential improvements in algorithm performance.
Keywords Cardiac magnetic resonance imaging (CMRI) · Image segmentation ·
Ventricle segmentation · Validation · Active contours
D. Grosgeorge - C. Petitjean (B)
Universit´ e de Rouen, LITIS EA 4108
BP 12, 76801 Saint-Etienne-du-Rouvray, France
Tel: +33 232 955 215
Fax: +33 232 955 022
E-mail: caroline.petitjean@univ-rouen.fr
J. Caudron - J. Fares - J.-N. Dacher
University Hospital of Rouen, Department of Radiology
76031 Rouen, France

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1 Introduction
To study the cardiac function, MRI is a modality of choice that allows to obtain accu-
rate anatomical and functional information [1]. The computation of clinical parameters
to assess the cardiac function requires to segment the cardiac ventricles, as shown in
Figure 1, where the left (LV) and right (RV) ventricles are identified. As the heart
is a moving organ, images are acquired throughout the whole cardiac cycle, but two
precise instants are of particular interest for the clinician: the time of maximum filling,
when the heart is the most dilated (end diastole, ED) and the time of greatest contrac-
tion (end systole, ES). Although some relatively efficacious methods are commercially
available for segmenting the LV, such as MASS (Medis, Leiden, The Netherlands) [2]
and Argus (Siemens Medical Systems, Germany) [3], the segmentation of ED and ES
images of the RV is currently performed manually in clinical routine. This long and
tedious task, prone to intra and inter-expert variability, requires about 20 minutes per
ventricle by a clinician. The great need for automated methods has led to the develop-
ment of a wide variety of segmentation methods [4], among which thresholding [5], pixel
classification [6–8], deformable models. This latter family of methods have been greatly
used thanks to their flexibility, especially for this application [9–12], either on the form
of 2D active contours or 3D deformable surfaces, which are more computationnally
expensive [13,14]. Shape prior information can also be used to guide the segmentation
process, under the form of a statistical model, in a variational framework [15], by using
active shape and appearance models [16–20] or via an atlas, using registration-based
segmentation [21,22]. Note that the temporal dimension of cardiac data can be taken
into account to improve the segmentation process [13,23].
1.1 The LV and RV segmentation challenge
The challenges faced by all segmentation methods in cardiac MRI are: (i) fuzziness of
the cavity borders due to blood flow, acquisition artefacts, and partial volume effect
especially for apical slices [24], (ii) the presence of papillary muscles in the LV pool and
trabeculations (wall irregularities) in the RV, which have the same grey level as the
Fig. 1 LV, RV, papillary muscles and trabeculations on ED and ES images

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surrounding myocardium and yet must not be taken into account during segmentation,
as shown on Figure 1, (iii) the complex crescent shape of the RV, which varies according
to the imaging slice level (Figure 2). For this last reason, and because the RV function
is less vital than the LV’s, most research effort has focused on the LV, leaving the
problem of RV segmentation wide open.
1.2 Choice of a segmentation methodology
To face these issues, deformable models have appeared as one of the most efficient
approaches. Their principle is to iteratively deform an initial contour until it reaches
the object frontiers to be detected, i.e. the LV and RV cavities. The deformation of the
contour is driven by the minimization of an energy functional, that is designed to reach
a minimum on the ventricle boundaries. Classically, the energy functional comprises
two terms: a data-driven term that provides information about object frontiers and
a regularization term that controls the smoothness of the curve. Initially edge-based
and thus sensitive to noise, the data-driven term can be chosen to be region-based,
such as in the well-known active contours without edges (ACWE) [25]. Region-based
energy terms in a variational approach have been widely used in the literature of
cardiac MR image segmentation [26,12,11], since segmentation can sorely rely on the
ventricle borders only. In curve evolution, the level set framework allows for automatic
topological change, i.e. splitting and merging of the contour [27]. This enables multiple
object segmentation, an interesting property to detect both ventricle cavities.
The ACWE model is thus a segmentation method that is computationally efficient,
does not require user interaction, nor heavy postprocessing steps, nor the learning of
a priori shape. Furthermore, thanks to the design of a region-based energy functional,
the ACWE model can detect objects whose boundaries are not necessarily defined by
the image gradient. This has lead us to choose this well-tried, preliminary approach
for our segmentation problem.
Fig. 2 Schematic representation of ventricle volumes and associated MR images obtained on
basal and apical imaging slices

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1.3 Validation issues
Validation of the segmentation algorithm against ground truth, i.e. manual delineation,
is of great importance. As manual segmentation is time-consuming, validation is often
restricted to a few dozens or hundreds of images in the literature, obtained on a few
patients. Additionally, results are often limited to mid-ventricular or basal slices, and
at ED, where the heart presents the most regular and largest shapes, or sometimes
provided on healthy volunteers, whereas images from pathological subjects are more
prone to noise and artefacts, and thus, more difficult to segment. For this work, we
propose the validation of our method over 1920 images, covering all slice levels, ac-
quired on patients presenting different pathologies. We also suggest to sudy the spatial
distribution of segmentation errors - which ventricle is easier to segment, which slice
level, and at which instant of the cardiac cycle - so as to gain some insight on the
segmentation difficulties and to identify where room for improvement is left. To the
best of our knowledge, no such extensive segmentation tests nor study of the error
distribution has been realized on these images.
In the remaining of the paper, we present the chosen segmentation method, based
on active contours without edges, in Section 2. Validation and results are presented in
Section 3 and conclusion and perspectives for this work are drawn in Section 4.
2 Cardiac image segmentation method
2.1 Method basic principle
The principle of our segmentation method is to define a single initial contour on our
cardiac image, that evolves according to an evolution equation. In the level set frame-
work, the contour automatically splits into several different regions, among which the
ventricle cavities. The ventricle pools are identified as being the two largest connected
components [28]. Residual components inside the cavities (if any) are removed. The
LV and RV are labeled according to the position of their center of gravity (the RV is
to the left of the LV). The different steps of our method are illustrated in Figure 3.
In the following, the theoretical background and implementation details regarding the
ACWE approach are provided.
(a) Initial
contour
(b) After ACWE
convergence
(c) After selection of the
2 largest components
(d) After removal of
inside contours
Fig. 3 The different steps of our method and corresponding evolution of the deformable
contour

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2.2 Theoretical background of the ACWE model
The aim of the ACWE approach is to separate the image into regions based on their
mean intensities. The image is considered as being composed of two regions of roughly
uniform intensity [25]: one region is the inside of the contour (the ventricle cavities or
foreground) of mean intensity c1, and the other one, the outside (the rest of the image
or background), of mean intensity c2. The foreground and background distributions
are assumed to be gaussian [26,29].
Let us denote by C the deformable contour, U the image, where U(x) represents
the pixel value at location x = (x,y). The region-based energy term is given by the
following equation:
?
where Ω ∈ ?2represents the image domain and ω the domain inside the contour. This
energy term is regularized by the contour curvature κ, a well-known regularizer [30],
and the total energy E(C) of the contour can thus be defined as:
ECV(C) =
ω
|U(x) − c1|2dx −
?
Ω\ω
|U(x) − c2|2dx (1)
E(C) = ECV(C) + µκ(2)
where µ is a user-defined weighting parameter. This energy functional is minimized by
implementing the Euler-Lagrange equations in a partial differential equation (PDE),
that allows to obtain the contour evolution equation. The minimization is performed
via gradient descent, a method that can get trapped in local minima, when the contour
is initialized too far from the boundaries to be reached [31–33].
The level set framework consists in considering the contour C as the zero level of
a two-dimensional function ψ: C = {x ∈ Ω : ψ(x) = 0} (Figure 4). The evolution of ψ
can then be written as [25]:
∂ψ
∂t= δ(ψ)(µκ − (U − c1)2+ (U − c2)2) = 0(3)
where δ(·) denotes the Dirac function. Average intensities c1 and c2 are updated
throughout the iterations as the contour evolves. The curvature κ of the contour can
be computed directly from ψ using:
κ = div(∇ψ
|∇ψ|)(4)
2.3 Implementation details of the ACWE model
The segmentation algorithm applied to each cardiac MR image is composed of the
following steps:
1. Contour initialization, as a circle centered on the image. The radius of the circle
is equal to one eigth of the image width, an empirical value that has proven to be
quite adequate in regard to the ventricle size.

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Fig. 4 The level set function ψ at two different instants t1 and t2 and the contour C as its
zero level (from [34])
2. Initialization of the ψ function with the signed distance map to the initial contour.
3. Updating of ψ at each iteration, using the discrete version of Equation 3:
ψn+1= ψn+ ∆tV
where ∆t is the time step and V is the discrete version of δ(ψ)(µκ − (U − c1)2+
(U −c2)2) in which µ is classically set to 0.3. For further information regarding the
formulation of V , the reader is refered to [25]. The time step value must be large
enough not to slow the level set evolution, and small enough to ensure the stability
of the numerical scheme [35]. The maximum value for the time step is given by the
Courant-Friedrichs-Lewy (CFL) condition:
∆t <
∆x
maxΩV
where maxΩV is the maximum value of V on the image domain and ∆x is the
spatial step. This equation is usually enforced by introducing a CFL number α,
usually set to 0.5 [36]: ∆t = α
maxΩV. To guarantee the stability of numerical
solutions, the CFL condition requires the boundary move no further than one
spatial step after each time step [35]. The value of the time step is thus:
∆x
∆t =
0.5
maxΩV
We thus have an adaptative time step which verifies the CFL condition without
adding an extra parameter to tune. The contour C is obtained by identifying points
x which are on the zero level of the level set function, i.e. such as ψ(x) = 0.

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In order to keep the regularity of ψ at each iteration, the ψ function is reinitialized
to the distance function through the resolution of the following PDE [37]:
∂ψ
∂t= sign(ψ0)(1 − |∇ψ|) (5)
where ψ0is the initial value of ψ. Note that methods without re-initialization of the
level set function have been proposed [38], that decrease computation time. In order
to speed up computation, ψ is not updated on the whole image but only in the neigh-
borhood of the contour points [39], i.e. on a narrow band. The width of this band
should be equal to the frontier width of the object to be segmented as suggested by
the literature [39]. According to MRI spatial resolution, the cavity borders have been
assessed to be 1.2 pixels wide, the value chosen for the narrow band width.
After a certain number of iterations, the algorithm has converged: the level set does
not evolve anymore. For sake of simplicity, we have chosen a fixed number of iterations
(set to 120), a number large enough to guarantee that the ventricle borders have been
reached.
We shall now introduce the database of cardiac images and study the performance
of the segmentation method on this large dataset, as well as the spatial distribution of
segmentation errors.
3 Experimental results
3.1 Cardiac image database and validation method
Our validation database is composed of 59 patients who gave informed consent, with
identified pathologies, such as myocarditis, myocardial infarction and dilated cardiomy-
opathy. All MRI examinations are performed using a 1.5T MR scanner (Magnetom
Symphony TIM; Siemens Healthcare, Erlangen, Germany). Images are 256 pixels x
216 pixels with a spatial resolution of 0.7mm per pixel. For each patient, imaging slices
cover the whole heart from the apex to the base of the heart, providing between 6 and
10 slice levels depending on the size of the heart, with a slice thickness of 7mm. The
most basal short-axis slice is selected using the 4-chamber view, as the one crossing the
tricuspid valve. The most apical slice is selected as the last slice showing white blood
in the LV pool.
At each slice level, images at ED and at ES are selected, for a total of 1038 im-
ages of the LV and 882 for the RV. For each of them, the left ventricle and the right
ventricle contours were manually drawn by a 4-year experienced cardiac radiologist
of the University Hospital of Rouen, in clinical routine conditions. In order to study
the influence of the slice level on segmentation errors, three groups of slices have been
defined, following a standard nomenclature [40]: apical, mid-ventricular, and basal slice
levels. For each patient, all imaging slices have been split into these three levels, and
results on each group of slices have been obtained by averaging results obtained on
individual slices in the corresponding group. The detailed number of images per group
of slices is given in Table 1.
Results obtained using our algorithm have been compared to manual segmentation
through the computation of two standard and complementary error measurements:

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Table 1 Mean Dice Metric ± standard deviation (DM) and false segmentation rates obtained
for the LV and RV on different slice levels
Nb. of imagesSlice level
Base
Mid
Apex
Base
Mid
Apex
Base
Mid
Apex
Base
Mid
Apex
DMFalse Seg.
0.07
0.02
0.14
0.16
0.11
0.35
0.05
0.13
0.44
0.28
0.29
0.58
LV
0.82±0.01
0.75±0.01
0.67±0.02
0.70±0.03
0.58±0.00
0.46±0.00
0.80±0.01
0.71±0.00
0.46±0.00
0.59±0.01
0.55±0.02
0.25±0.04
ED 569
ES 469
RV
ED 506
ES 376
– the Dice Metric [30], a measure of contour overlap, obtained by computing the
intersection divided by the union of the two surfaces. Let us denote by Aa (respec-
tively Am) the area enclosed by the automatic (respectively manual) segmentation,
and A∩ = Am∩Aathe intersection of both areas. The Dice Metric (DM) is defined
as:
DM(Aa,Am) =
2A∩
Aa+ Am
The DM varies from 0 (total mismatch) to 1 (perfect match).
– the Point to Curve (P2C) error, which is the mean perpendicular distance between
both contours. Let us denote by Ca (resp. Cm) the automatically (resp. manually)
obtained contour. For each Cacontour point pi
pj
mare computed. The minimum distance is retained and all minima are averaged
into the P2C error, over all Na points of contour Ca:
a, distances to all Cmcontour points
P2C(Ca,Cm) =
1
Na
Na
?
i=1
min
j
d(pi
a,pj
m)
where d(·,·) denotes Euclidean distance. A high value of P2C error indicates that
contours do not match well.
3.2 Segmentation results and analysis
Some typical segmentation results obtained on the LV are presented in Figure 5 and on
the RV on Figure 6. A false segmentation rate is computed, that indicates the number
of missegmentation cases (when the automatic contour and the manual contour do
not overlap at all) over the total number of segmentation results. Note that these
missegmentation cases are not taken into account for the Dice Metric computation.
The Dice Metric and false segmentation rates obtained on our validation database are
summarized in Table 1 and mean P2C errors are presented in Table 2, along with
segmentation errors collected from the literature. Note that many of the presented
results were obtained using 3D segmentation algorithms, whereas our approach is a 2D
segmentation method.
As one can see, segmentation results on cardiac images have been obtained on dif-
ferent number of patients, having diverse conditions, either only on ED, or restricted

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Table 2 Mean segmentation errors reported in the literature and for our approach. %P:
percentage of pathological subjects.aNo standard deviation provided.bRMS error.cLeave-
one-out protocol.∗3D segmentation methodology.
Authors
Lynch et al. [7]
El Berbari et al. [9]
Nb. subj.
25
13
%P.
-
-
Phases
ED, ES
ED
ED
ES
ED
ED
ED
ED
all
ED
ED
Slice nb.
5-12
3
LV (mm)
0.69±0.88
0.6±0.3
2.45±0.75
2.84±1.05
1.71±0.82b
2.75±0.86
1.97±0.54
-
2.21±2.22
1.88±2.00
2.01±0.31
2.45±1.57
2.27±2.02
5.00±2.12
2.33± 1.78
2.91± 2.25
3.52± 2.05
RV (mm)
-
-
-
-
2.46±1.39b
-
-
1.1a
2.89±2.56
2.26±2.13
2.37±0.5
1.85±1.42
2.38±1.89
3.5±2.38
2.6±2.46
2.27±2.02
3.28±2.54
Kaus et al. [15]
∗
121 100% 7-10
Mitchell et al. [16]
Mitchell et al. [17]∗
Van Assen et al. [18]∗
Abi-Nahed et al. [19]∗
20
56c
15
13
45%
32%
0%
-
3 Mid
8-14
10-12
-
Lorenzo-V. et al. [21]∗
10100% 3 Mid
Lotjonen et al. [22]∗
25c
100% 4-5
Our study 59 100%
ES
Base
6-10 Mid
Apex
Base
ED6-10 Mid
Apex
to a few mid-ventricular slices, thus making it difficult to conclude on the efficiency
or the superiority of one method over the others. Accurate segmentation results would
be expected to reach intra and inter-observer variability of manual segmentation, that
is, around 2mm [18]. On the whole, P2C errors obtained with our approach compare
favorably to this value, and are honorable compared to other results in the literature,
but room for improvement exists, in particular on apical slices. We can also remark
that papillary muscles are sometimes considered as part of the myocardium (when they
are very close to the wall) by the algorithm, whereas the corresponding manual con-
touring excludes them from the segmentation, which contributes to increase the P2C
errors. Note that our approach is totally generic and is not based on a priori knowledge,
whereas most of the approaches that are presented here use a statistical shape prior to
help the segmentation.
Considering the DM and the false segmentation rate, results are better on the LV
than on the RV, mainly due to the LV regular ring shape and lesser variability. Never-
theless, P2C errors tend to show that segmentation is more accurate on the RV. This
is due to the residual presence of papillary muscles in LV automatic contouring, which
considerably increases P2C values, since manual contours are very smooth. Actually,
the common current segmentation standards recommend to consider them as part as
the ventricle pool and to contour only the wall, because manual segmentation is more
reproductible in this case, than when papillary muscles are segmented as well. This
provides smooth manual contouring, but the exact cavity volume computation should
exclude the volume occupied by the papillary muscles. Indeed, in some automatic seg-
mentation methods, papillary muscles are segmented as well, authors arguing that the
radiologist should decide whether to incorporate them or not [6,7].
Let us now study the spatio-temporal distribution of segmentation errors. Figures
7 and 8 show histograms of the distribution of the DM values over the whole image
database, for the LV and RV, respectively. The distributions of P2C errors are shown
in Figure 9 and 10. From these figures, one can observe that ED results are better than
ES ones for any ventricle and any slice level. This can be explained by the fact that

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at ED, the ventricles are larger and less subject to noise. Results also depend upon
slice levels: basal and mid-ventricular slice levels are simpler to segment than apical
levels, where ventricle cavities are really small. Apical slices are more prone to partial
volume effect, a consequence of which is a certain fuziness on the ventricle frontiers.
Segmentation errors in apical images may originate from the initialization of the de-
formable contour, because of its fixed size that might not be optimal for these images.
A solution would be to have an adaptative size for the initial contour, corresponding
to the different slice levels [41].
Regarding computational cost, our algorithm is implemented in Java without any
particular optimization and requires less than 7 seconds on a regular PC hardware
to segment a single image, which represents less than 4 minutes for a patient, a time
compatible with clinical practice.
Fig. 5 Example of segmentation results on two different patients for the LV at ED (top)
and ES (bottom). Red (resp. green) contours are obtained with manual (resp. automatic)
segmentation. Note the missegmentation case for the last apical image.
Fig. 6 Example of segmentation results on two different patients for the RV at ED (top)
and ES (bottom). Red (resp. green) contours are obtained with manual (resp. automatic)
segmentation. Note the missegmentation case for the last apical images.

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Fig. 7 Distribution of DM values for the LV over the whole image database
Fig. 8 Distribution of DM values for the RV over the whole image database

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Fig. 9 Distribution of P2C error values for the LV over the whole image database
Fig. 10 Distribution of P2C error values for the RV over the whole image database
4 Conclusion and perspectives
In this paper, we have been presenting the validation of an automatic method to per-
form the segmentation of both the left and right ventricles in cardiac MRI, by combining
active contours without edges followed by a morphological step to smooth the result-
ing contour. This method allows for segmentation of both ventricle cavities. No user
interaction is required since contour initialization is automatic. Validation has been

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performed on a very large database of 1920 images. An original study of segmentation
errors show satisfying results on basal and mid-ventricular slices, compared to results
provided by other segmentation methods in the litterature, and to manual segmenta-
tion accuracy. Nevertheless, segmentation errors obtained on apical slices and on the
RV leave room for improvement. On some images, especially at the apex, myocardium
borders are very fuzzy and ill-defined, and it is very difficult to rely on the image alone
to perform segmentation. Perspectives for this work include (i) improving the accuracy
of our segmentation approach by extending it to a 3D framework, which would allow
the removal of residual papillary muscle contouring and improve apical segmentation
results, (ii) applying the method to segment the epicardium of the heart, i.e. the outer
border of the myocardium and comparing automatic results to manual ones, and (iii)
the computation of clinical parameters: ventricule volume, mass and ejection fraction,
and the correlation between manual tracing and our automatic method through linear
regression and Bland-Altman analysis.
Acknowledgements The authors wish to thank Valentin Lefebvre, S´ ebastien Dubois and
Que Nguyen for manually collecting the image data. They also would like to thank the anony-
mous reviewers whose insightful comments greatly helped to improve their paper. Damien
Grosgeorge was supported by a grant from the Centre de Recherche et de Lutte Contre le
Cancer (CRLCC) Henri Becquerel, Rouen, France.
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