ROBUST DEFORMABLE MODEL FOR SEGMENTING THE LEFT

VENTRICLE IN 3D VOLUMES OF ULTRASOUND DATA

Carlos Santiago, Jorge S. Marques and Jacinto Nascimento

Institute for Systems and Robotics, Instituto Superior Tecnico, Lisbon, Portugal

Keywords:

3D Echocardiography, Left ventricle, Segmentation, Deformable models, Feature extraction, Robust estima-

tion.

Abstract:

The segmentation of the left ventricle (LV) in echocardiographic data has proven itself a useful methodology

to assess cardiac function and to detect abnormalities. Traditionally, cardiologists segment the LV border at the

end-systolic and end-diastolic phases to determine the ejection fraction. However, the manual segmentation

of the LV is a tedious and time demanding task, which means automated segmentation systems can provide a

powerful tool to improve workﬂow in a clinical setup. This paper proposes a robust 3D segmentation system

consisting of a deformable model that uses a probabilistic data association ﬁlter (PDAF) to robustly detect the

LV border. Results show that the algorithm performs well in both synthetic and real data, without signiﬁcantly

compromising its performance. The obtained LV segmentations are compared with the manual segmentations

performed by an expert, yielding an average distance of 4 pixel between points from both segmentations.

1 INTRODUCTION

Echocardiography has arguably become amongst the

most preferred medical imaging modality to visualize

the left ventricle (LV). This is mainly due to several

reasons, such as, its low cost and portability(Juang

et al., 2011). The diagnosis usually comprises the

intervention of an expert who manually segments

the LV boundary at the end-systole and end-diastole

phases. This is a necessary step for further quanti-

tative analysis of the heart in order to detect possi-

ble cardiopathies present in the LV. Such procedure is

generally (i) tedious and time consuming, (ii) prone to

errors and (iii) has a signiﬁcant inter-variability of the

segmentation among specialists. Besides, this image

modality presents several challenges among which we

point out (i) the poor images quality (low SNR ratio),

(ii) the edge dropout specially in the diastole phase,

(iii) the presence of outliers, and (iv) the presence of

multiplicative noise (i.e, Rayleigh), see Fig. 1 for an

illustration. Consequently, only experts are able to

correctly locate the LV boundary.

The above mentioned problems can be alleviated

with the use of an automatic LV segmentation sys-

tem. Initially, automatic LV segmentation systems

were developed for 2D echocardiography. As soon as

the 3D echocardiography became available, methods

to perform the segmentation also became available in

Figure 1: Echocardiography - apical four-chamber view

(Chan and Veinot, 2011).

the literature. One approach to perform 3D segmen-

tation is to consecutively applying 2D segmentations

to each image plane and assembling them into a 3D

structure (Nillesen et al., 2006; Scowen et al., 2000) -

as cardiologists manually do in such cases. However,

such approaches require additional methods to pre-

vent inconsistencies in the surface. Other approaches

have performed the 3D segmentation using the level-

set method, such as in (Juang et al., 2011; Hang et al.,

2005; Yu et al., 2006), and even 3D tracking systems

(Yang et al., 2008; Orderud, 2010).

One of the above mentioned difﬁculties, is the

presence of outliers, i.e. the invalid features that do

333

Santiago C., S. Marques J. and Nascimento J..

ROBUST DEFORMABLE MODEL FOR SEGMENTING THE LEFT VENTRICLE IN 3D VOLUMES OF ULTRASOUND DATA.

DOI: 10.5220/0003858403330340

In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods (SADM-2012), pages 333-340

ISBN: 978-989-8425-98-0

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

not belong to the boundary of the object of inter-

est, in this case, the LV surface. The presence of

outliers should be avoided as far as possible, since

it often leads to meaningless shape estimation re-

sults. To overpass this difﬁculty, we propose a ro-

bust 3D segmentation algorithm capable of discern-

ing between valid and invalid image features. To

accomplish this, the algorithm is based on a proba-

bilistic data association ﬁlter (Bar-Shalom and Fort-

mann, 1988). Two main underlying ideas of the al-

gorithm are as follows. First middle level features

are considered. More speciﬁcally, patches are used.

Second, a labeling process (valid-invalid) is assigned

to each patch. Since we do not know beforehand,

the reliability of the patches, all possible labeling se-

quences of valid/invalid patch labels are considered.

Each patch sequence is called here as patch interpre-

tation. Finally, a probability (association probability)

is assigned to each patch interpretation. Thus, in the

adopted strategy, all the patches contribute to the evo-

lution of the deformable model with different weights.

The paper is organized as follows: Section 2

presents an overview of the proposed segmentation

system; Section 3 describes the deformable model

used; Section 4 addresses the feature extraction al-

gorithm and the middle-level features assemblage;

and Section 5 presents the robust model estimation

technique inspired in the S-PDAF algorithm. Sec-

tion 6 shows results of segmentation system applied

to synthetic data and to the segmentation of the LV

in echocardiographic images. Finally, Section 7 con-

cludes the paper with ﬁnal remarks about the devel-

oped system and future research areas.

2 SYSTEM OVERVIEW

The idea behind of the present approach is to tackle

the difﬁculties of classic deformable contour methods

associated with noisy images (such as ultrasound im-

ages) by introducing a robust estimation scheme. The

robust framework is inspired in the S-PDAF (Nasci-

mento and Marques, 2004), developed for shape

tracking in cluttered environments. Here we extend

it to the context of 3D shape estimation.

The proposed segmentation system uses a 3D de-

formable model to characterize the surface of the seg-

mentation. This deformable surface requires an ini-

tialization procedure that ensures it is initialized in the

vicinity of the LV boundary.

The adaptation procedure is an iterative process

that consists of the following steps: after initializa-

tion of the model, an adaptation cycle begins with

the detection of low-level features, searched in the

vicinity of the model. Then, these are grouped into

middle-level features (patches). Based on the assem-

bled patches, the S-PDAF algorithm determines all

possible interpretations of considering a patch valid or

invalid and assigns to each patch interpretation a con-

ﬁdence degree that is used to deﬁne the estimate of the

boundary location. The model estimate is then used to

ﬁt the surface to the LV boundary, ending an iteration

of the adaptation cycle. The process repeats until the

surface is considered close to the LV boundary. The

following ﬁgure shows a diagram of the adaptation

cycle.

Figure 2: Diagram of the proposed segmentation system.

3 SURFACE MODEL

The proposed segmentation system uses a simplex

mesh (Delingette, 1999) as the deformable model. A

3D simplex mesh is a meshed surface composed of

vertices and edges, where each vertex has three neigh-

boring vertices (i.e., belongs to three edges) (see Fig.

4). This particular structure allows to deﬁne geo-

metric relations between vertices that are used in the

adaptation procedure to ensure a smooth surface and

good vertices distribution.

3.1 Law of Motion

Each vertex adapts in an iterative process under the

inﬂuence of external and internal forces and its ﬁnal

position is determined by the equilibrium of forces of

the following equation (Delingette, 1999):

(k+1) = P

(k)+(1−γ)(P

(k)−P

(k−1))+α

int

(k)+β

ext

(k)

(1)

where the parameters γ, α and β are constants.

The internal force, F

int

, is responsible for main-

taining the smoothness of the surface, making use of

the geometric relations between vertices. On the other

hand, the external force, F

ext

, is responsible to attract

each vertex towards the object boundary.

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

334

3.2 Model Initialization

The initialization procedure has to meet the following

conditions: 1) the initial model should be initialized

in the vicinity of the LV boundary; and 2) it should be

a simplex mesh. These two conditions are met using

the following three step procedure.

First, to ensure that the model is initialized in the

vicinity of the LV boundary, the user manually deﬁnes

a coarse outline of the LV in three orthogonal planes.

A 3D region is then obtained by space carving (Kutu-

lakos and Seitz, 2000) (see Fig. 3).

Figure 3: Schematic example of the computation of the

carved volume (cylinder) (in light blue) by intersection of

the segmented projections (in red).

Second, the simplex mesh is initialized as a sphere

in the center of the carved volume. After uniformly

sampling sphere points, the convex hull algorithm

(Barber et al., 1996) is applied, resulting in a trian-

gular mesh on the sphere surface. Then, taking into

account the duality between simplex meshes and tri-

angulations (Delingette, 1999), an associated simplex

mesh can be formed by considering the center of each

triangle as vertices and linking each vertex with the

center of the three neighboring triangles, resulting in

the simplex mesh shown in Fig. 4.

Figure 4: Simplex mesh initialized as a sphere.

Finally we let the spherical simplex mesh deform

until it ﬁts the carved region. This region corresponds

to the silhouette of the LV boundary and simpliﬁes an

initial adaptation to the dataset since it is a noiseless

binary volume.

4 FEATURE EXTRACTION

The detection of the LV border is performed by the

feature extraction algorithm. First, the volume is pre-

processed using a median ﬁlter with a window size

of 4 × 4 pixels. Feature extraction is then performed

using a directional feature search in the vicinity of the

surface model.

4.1 Feature Detection

At each vertex, P

, of the simplex mesh, we com-

pute the normal to the surface and deﬁne a search line

parallel to the normal vector that passes through P

Then, the intensity signal along the search line is an-

alyzed. The LV border features are detected using an

edge detector ﬁlter, as described in (Blake and Isard,

1998). The ﬁlter output’s maxima are extracted us-

ing a threshold and a non-maximum suppression tech-

nique.

Although this methodology has good results,

many undesired features are still detected, depending

on the threshold used. In our experimental setup we

obtained, for each vertex, an average number of fea-

tures that varies from one up to four. Recall that, only

one of these features corresponds to the LV boundary.

4.2 Middle-level Features

To increase the robustness of the feature detec-

tion, these are grouped into middle-level features

(patches). To assemble these patches, we use a label-

ing algorithm that assumes that features should be-

long to the same patch if: 1) the corresponding ver-

tices are neighbors in some level (i.e., the patch is a

connected graph of its features); 2) all features associ-

ated with the same vertex have different labels; and 3)

the distance between neighboring features in a patch

must not exceed a chosen threshold. Fig. 5 shows an

example of the labeling result.

Figure 5: Example of middle-level features. Each color rep-

resents a different patch.

In order to achieve the desired label conﬁgura-

tion, L, an energy function is used composed of three

ROBUST DEFORMABLE MODEL FOR SEGMENTING THE LEFT VENTRICLE IN 3D VOLUMES OF

ULTRASOUND DATA

335

terms:

E(L) = E

(L) + E

(L) (2)

This energy is computed as a sum of the energy of

each individual label.

The ﬁrst term, E

(L), is minimum when features

with the same label are the closest features associ-

ated with the neighboring vertices. The second term,

(L), prevents patches from having features too far

apart. This is done by assigning an energy of ∞ to la-

bels where the distance between neighboring features

exceeds the labeling threshold. If the distance is lower

than the threshold, the energy yields the value 0. Fi-

nally, the third term, E

(L), prevents repeated labels

in features associated with the same vertex, again as-

signing an energy value of ∞ if this occurs and 0 oth-

erwise.

The label conﬁguration L that minimizes the total

energy function (2) corresponds to the conﬁguration

that obeys all the conditions.

The energy minimization algorithm uses a region

growing scheme where a label is seeded in a random

feature and it propagates to the surrounding features

whenever an energy decrease is possible. This pro-

cess repeats until all features have been labeled. The

pseudocode in Table 1 describes the developed label-

ing algorithm:

Table 1: Labeling algorithm.

Q = {} % labeling queue

C = {} % labeled features

repeat

If Q is empty

seed a new label l in a random feature y

/∈ C

add y

to C

for each feature y

neighbor of y

if y

/∈ C & labeling y

with l lowers E(L)

add y

to Q

Else

repeat

= Q(1)

label y

with l

add y

to C

remove y

from Q

for each feature y

neighbor of y

if y

/∈ C & labeling y

with l lowers E(L)

add y

to Q

until Q is empty

until all features have been labeled

The size of the resulting patches and their distance

to the surface provides good differentiation measures

to assess if the features in that patch belong to the LV

boundary or if they were produced by the background.

5 ROBUST MODEL ESTIMATION

The robust model estimation used is an extension of

the S-PDAF algorithm described in (Nascimento and

Marques, 2004) to the 3D case. In each iteration k,

this estimation technique considers all possible com-

binations of considering each patch as valid or in-

valid. Assuming M

patches were detected, there

are m

= 2

possible interpretations. Each com-

bination is deﬁned as a patch interpretation I

(k) =

(k), .. .,I

(k)}, where I

(k) = 0 if the

nth patch in the ith interpretation is considered invalid

and I

(k) = 1 otherwise.

The model assumes that the LV boundary position

is described by

x(k) = x(k − 1) + w(k) (3)

where w(k) ∼ N(0,Q) is white Gaussian noise with

normal distribution.

For each interpretation I

(k), the observations

(k) are generated by a different model. If an obser-

vation y

(k) is considered invalid (outlier), the model

assumes it is generated by uniform distribution. Oth-

erwise, the model assumes it relates to the boundary

points x(k) by:

(k) = x(k) + v

(k) (4)

where v

(k) ∼ N(0, R

) is a white Gaussian noise with

normal distribution associated with the valid features

(k) of the interpretation I

(k).

The state estimate is then deﬁned by:

ˆx(k) =

∑

i=0

ˆx

(k)α

(k) (5)

where ˆx

(k) is the updated state conditioned on the hy-

pothesis that I

(k) is correct (which is the same as the

update state equation of a traditional Kalman ﬁlter),

and α

(k) is the association probability of the interpre-

tation I

(k). A similar analysis is done to predict and

update the covariance matrix (Nascimento and Mar-

ques, 2004).

5.1 Association Probabilities

The association probabilities, α

(k), deﬁne the

strength of the corresponding interpretation I

(k) in

each iteration k of the adaptation procedure (from this

point on we omit the dependence of k for the sake of

simplicity). It is deﬁned as

= P(I

|Y,L, ˆx) (6)

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

336

where Y and L are the set of the detected features

and patches, respectively. Using a Bayesian approach,

this probability can be decomposed into:

P(Y |I

,L, ˆx) × P(I

|L, ˆx)

(7)

where β = P(Y |L, ˆx) is a normalization constant that

does not depend on I

, P(Y |I

,L, ˆx) is the likelihood

of the set of features Y and P(I

|L, ˆx) is the prior

probability of the interpretation I

conditioned on the

patches (i.e., based on its valid and invalid patches).

Note that interpretations with overlapping patches

will be assigned an association probability of 0, and

patches considerably smaller then the larger ones will

be promptly discarded to avoid an exponential growth

of possible interpretations.

Assuming that the patches are independently gen-

erated, the likehood P(Y |I

,L, ˆx) is expressed as the

product of each individual probability of having a

patch l

at an average distance d to the surface. How-

ever, this probability is dependent on the hypothesis

that l

is considered valid or invalid: if I

= 0 it is

assumed that the probability distribution is uniform

along the search line, whereas if I

= 1 the probability

distribution is assumed Gaussian with mean 0 and co-

variance proportional to the length of the search line,

V . Formally:

P(l

,L, ˆx) ∼



−1

if I

= 0

−1

N(d; 0,σ) otherwise

(8)

where ρ is the normalization constant.

As to the prior probability of each interpretation

, it is related to the size of its valid and invalid

patches. The probability P(I

|L, ˆx) is also decomposed

as the product of each individual probability of the

patches, P(I

|L, ˆx). It is assumed that larger patches

are more likely to belong to the LV boundary. There-

fore, these should receive a higher probability. On the

other hand, when considered invalid, these should be

assigned a small probability.

The resulting prior probability yields:

P(I

|L, ˆx) =

∏

[alog(A

+ 1) + b] ×

∏

1 − [a log(A

+ 1) + b)] (9)

where:

a =

−P

1−log(A

max

+1)

b = P

− a log(A

max

+ 1).

(10)

and P

, P

and A

max

are constants, and A

is the

area of the patch l

(number of features it comprises).

These assumptions assure that patches above a certain

area A are preferably considered.

6 RESULTS

The proposed system was tested using several differ-

ent datasets, both real and synthetic. The purpose of

the synthetic data was to assess the functionality of

the model, for which we will present more insight of

the framework. The real data corresponds to echocar-

diographic volumes (courtesy of Dr. Jacinto Nasci-

mento). The algorithm was applied to four different

echocardigraphic volumes. A quantitative assessment

of the system’s performance will be provided using

error metrics between the obtained segmentation and

the manual segmentation performed by an expert - the

ground truth (GT).

6.1 Evaluation Metrics

We use four similarity metrics to compare the output

of the algorithm with the reference contours, namely:

the Hammoude metric (Hammoude, 1988), d

HMD

, the

average metric, d

, the Hausdorff metric (Hutten-

locher et al., 1993), d

HDF

, and mean absolute distance

metric, d

MAD

. These are deﬁned as follows: consider

as the region delimited by model segmentation

and R

Ω

as the region delimited by the GT. The Ham-

moude metric is deﬁned by:

HMD

(Ψ,Ω) =

#((R

∪ R

Ω

) − (R

∩ R

Ω

)

#((R

∪ R

Ω

))

(11)

This error metric corresponds to the fraction of area

between the two contours using a XOR operator. Low

values of d

HMD

indicate high similarity between both

regions.

Now consider the border of the model segmenta-

tion deﬁned by the points Ψ = {ψ

,. ..,ψ

} and the

border of the GT Ω = {ω

,. ..,ω

}. The average

metric between two contours is deﬁned as the average

distance between each point ψ

to the closest point in

Ω, d(ψ

,Ω) = min

||ω

− ψ

||,

∑

i=1

d(ψ

,Ω) (12)

where N

is the length of Ψ. The Hausdorff metric

is deﬁned as the maximum value of d(ψ

,Ω) between

the two contours:

HDF

(Ψ,Ω) = max



max

{d(ψ

,Ω)}, max

{d(ω, Ψ)}



(13)

Finally, the MAD metric is deﬁned by:

MAD

(Ψ,Ω) =

∑

i=1

||ψ

− ω

|| (14)

which corresponds to the maximum absolute dis-

tance’s average between corresponding points in the

boundaries.

ROBUST DEFORMABLE MODEL FOR SEGMENTING THE LEFT VENTRICLE IN 3D VOLUMES OF

ULTRASOUND DATA

337

6.2 Parameter Deﬁnition

All the presented results were obtained using the pa-

rameters that achieve better overall results:

• In (1), we used α = 0.7, β = 0.05 and γ = 0.9; the

stopping criterion was the average displacement

of the vertices k

stop

< 0.005;

• In the feature extraction algorithm, the thresh-

old using the maxima detection was t

= 0.5c

max

where c

max

is the highest peak of the ﬁlter out-

put; as to the labeling threshold (i.e., the maxi-

mum distance allowed between neighboring fea-

tures with the same label) used was t

= 8;

• Finally, in (9) we used P

= 0.05, P

= 0.95 and

max

= 700 (the number of vertices in the surface).

6.3 Synthetic Data

We will present one particular test using a synthetic

volume. This synthetic volume contains a sphere cor-

rupted by white Gaussian noise with zero mean (see

Fig. 7). Although many features are detected (an av-

erage of approximately 3 features associated with a

single vertex), only one large patch is extracted (see

Fig. 6) and all the other smaller noise-originated

patches are discarded. The association probabilities

of the existing interpretations are the following:

= P(I

= {I

= 0}) = 0.04

= P(I

= {I

= 1}) = 0.96

which means a high conﬁdence degree is assigned to

the large (correct) patch. Fig. 7 shows that the model

is able to correctly adapt to the desired sphere.

6.4 Echocardiographic Data

As mentioned before, the segmentations of the LV

in four different echocardiographic volumes are pre-

sented in Fig. 8. For each volume, a single slice is

shown twice: one containing the obtained segmen-

tation and one containing the GT. The ﬁnal three-

dimensional surface is also presented.

6.5 Quantitative Assessment

Although the previous results show that the devel-

oped segmentation system performs reasonably well,

quantiﬁcation measurements are required to compare

its performance with other similar methods. Table 2

presents the values of the similarity metrics.

The table shows high similarity between the esti-

mated contour and the GT, indicating a good match.

Figure 6: Patch detection in a synthetic noisy sphere.

Figure 7: Slice view of the ﬁnal conﬁguration of the surface

(yellow contour).

Table 2: Results of the evaluation methods for each volume

(the distance values are expressed in pixels).

Volume 1 Volume 2

HMD

0.15 ± 0.03 0.20 ± 0.10

3.8 ± 0.7 3.1 ± 1.3

HDF

11.2 ± 2.5 8.7 ± 3.2

MAD

5.5 ± 1.3 4.7 ± 2.8

Volume 3 Volume 4

HMD

0.16 ± 0.02 0.24 ± 0.04

3.3 ± 0.6 4.6 ± 0.7

HDF

8.4 ± 2.1 13.7 ± 2.3

MAD

4.4 ± 1.1 8.1 ± 2.5

7 CONCLUSIONS

This paper addresses the automatic LV segmentation

problem in 3D echocardiographic data. Due to the

nature of the volumes, many of the detected fea-

tures usually do not belong to the LV boundary. The

proposed system uses a robust estimation technique

based on PDAF that prevents the segmentation to be

misguided by those outliers.

The results shown demonstrate that the proposed

system performs a good segmentation of the LV, with

potential application to accurately compute cardiac

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

338

Volume 1

Volume 2

Volume 3

Volume 4

Figure 8: Slice from the echocardiographic showing (on the left) the GT and (on the center) the obtained segmentation. Final

conﬁguration of the surface (on the right).

measurements such the systemic and diastolic vol-

umes and the corresponding ejection fraction.

Further tests shows that the developed system is

slightly over-dependent on the initialization proce-

ROBUST DEFORMABLE MODEL FOR SEGMENTING THE LEFT VENTRICLE IN 3D VOLUMES OF

ULTRASOUND DATA

339

dure, which does not help improving the repeatabil-

ity of LV segmentations. This could be avoided using

an automatic initialization scheme, such as in (Yang

et al., 2008).

ACKNOWLEDGEMENTS

This work was supported by project [PTDC/EEA-

CRO/103462/2008] (project HEARTRACK) and

FCT [PEst-OE/EEI/LA0009/2011].

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