LEFT VENTRICLE IMAGE LANDMARKS EXTRACTION USING

SUPPORT VECTOR MACHINES

Miguel A. Vera

Laboratorio de F´ısica

Departamento de Ciencias, Universidad de Los Andes–T´achira, San Crist´obal 5001, Venezuela

Antonio J. Bravo

Grupo de Bioingenier´ıa

Decanato de Investigaci´on, Universidad Nacional Experimental del T´achira, San Crist´obal 5001, Venezuela

Keywords: Human heart, anatomical landmarks, left ventricle, patterns classiﬁcation, support vectors machines.

Abstract:

This paper introduces an approach for efﬁcient myocardial landmarks detection in angiograms. Several

anatomical landmarks located on the left ventricle are obtained by mean of a support vector machine. Training

set corresponds a dataset of landmark and non-landmark 31×31 pixel patterns. Our support vector machine

uses the structural risk minimization principle as inference rule and radial basis function kernel. In the training

phase false positives were not registered and in the detection phase 100% of recognition was obtained.

1 INTRODUCTION

Landmarks detection from medical images represents

a stage useful stage to extracting sufﬁcient informa-

tion which describes an examined anatomical struc-

ture. The extracted image landmarks are used in va-

rious applications of medical image analysis, such

as segmentation (Bosch et al., 2002), shape–model

construction (Frangi et al., 2002) and motion analy-

sis (Chandrashekara et al., 2004).

In clinical routine cardiologist uses heart cavities

images for the assessment of morphology and func-

tion of the heart (Marcus and Dellsperger, 1991).

Contrast cineangiography based on X–rays provide

a projected image of the cardiac structures (Macov-

ski, 1983). These images have enough information of

dimension and shape of heart cavities during the en-

tire cardiac cycle. The left ventricle is considered the

main cavity of the heart.

Left ventricle images are obtained from cinean-

giography, after the injection of a contrast medium in

the cavities of the heart aiming to enhance the contrast

with respect to other tissues. Ventriculographic ima-

ge analysis requires a precise description of ventricu-

lar shape in order to quantify the parameters associa-

ted with the cardiovascular function (Kennedy et al.,

1970) (Ratib, 2000) or alternatively for performing

the visualization of this anatomical structure (Medina

et al., 2004). The accurate description of ventricu-

lar shape and their quantitative analysis is important,

since cardiovascular disease (CVD) accounts for one

third of the deaths in the world (WHO, 2002).

Recently, several robust methods for ventricu-

lographic image segmentation have been proposed.

Suzuki et al. (Suzuki et al., 2004) have developed

a ventricular contour detector based on neural net-

works (NN). The detector was implemented using a

multilayer neural network which was trained through

a back–propagation algorithm. The training set in-

cludes left ventricle images and ventricular contours

traced by a cardiologist. Validation was performed by

comparison of the area enclosed by the estimated con-

tour with respect to the reference contour traced by

the cardiologist. The average contour error obtained

at end–diastole was 6.2%. Oost et al. (Oost et al.,

2005) have proposed a ventricular cavity automatic

segmentation method based on Active Appearance

Models (AAMs) and dynamic programming (DP).

The active appearance model is used to exploit the ex-

isting correlations in shape and texture between end-

diastole and end-systole images. A dynamic program-

ming algorithm was used to incorporate cardiac mo-

tion features to the method. The method was evalua-

ted by using 140 images. The average border posi-

tioning error was smaller than 1.45 mm. These me-

thods provided an accurate representation of ventri-

cular borders, however,they are not yet fully validated

and accepted by clinicians as a gold standard.

339

A. Vera M. and J. Bravo A. (2007).

LEFT VENTRICLE IMAGE LANDMARKS EXTRACTION USING SUPPORT VECTOR MACHINES.

In Proceedings of the Second International Conference on Computer Vision Theory and Applications - IFP/IA, pages 339-343

Copyright

c

SciTePress

Segmentation techniques some times require a

previous stage in which an initial set of points is lo-

cated near the shape to detect (Fu and Mui, 1981). In

cardiac imaging left ventricle anatomical landmarks

as apex, basal regions and aortic valve points are use-

ful to deﬁne the left ventricle shape.

The objective of this work is to develop an ap-

proach based on machines learning to detecting seve-

ral anatomical landmarks located on the left ventri-

cle (LV) contour. This is a classiﬁcation problem be-

cause the machine learning task is to classify example

among a discrete set of possible categories or classes.

Our approach utilizes densitometric information and

a support vector machine (SVM) for the reliable lo-

calization of landmarks in ventriculographic images.

2 SUPPORT VECTOR MACHINES

Support Vector Machine (SVM) is a learning tech-

nique based in the framework of statistical learning

theory (Vapnik, 1995). These machines learning can

be seen as a method for training polynomial, neural

network or radial basis function classiﬁers. The SVM

training process is based on the idea of minimizing

an upper bound on the generalization error by mean

structural risk minimization induction principle (Vap-

nik, 1982).

SVMs have been applied successfully in practical

problems such as pattern classiﬁcation (Osuna et al.,

1997b) and nonlinear function estimation problems

(Smola, 1998). A classiﬁer based on SVM is a ma-

chine learning that uses a hyperplane to separate pa-

tterns classes (Burges, 1998). If the classiﬁcation task

is a two–class pattern recognition problem, where we

assume that we have a set of examples:

z

i

=

{x

i

,y

i

} | x

i

∈ R

N

∧ y

i

∈ {−1,+1} ∧ i = 1..l

the hyperplane corresponds to a decision function:

f

α

(x) : R

N

−→ {−1,+1} . (1)

which provides the smallest possible value for the risk

(Sch¨olkopf et al., 1995). The SVM classiﬁer is de-

ﬁned by the family function f

α

(x) which mappings

x

i

7→ y

i

. A deterministic process is implanted to reach

the machine’s task: to learn the mapping x

i

7→ y

i

. In

this process given a set of examples x, a particular

value of the α parameter is chosen for the same out-

put f

α

(x). The process to choice a α that mapping

x

i

7→ f

α

(x) is an optimization process called Training

a Support Vector Machine (Osuna et al., 1997b).

For linearly separable data, the classiﬁcation pro-

blem is solved ﬁnding the best hyperplane that sep-

arates the data. Osuna and collaborators (Osuna

et al., 1997a) show that the decision surface in the

linear case using Lagrange Multipliers like optimiza-

tion technique can be written as:

f

α

(x) = sign

l

∑

i=1

y

i

λ

i

(x· x

i

) + b

!

, (2)

where λ

i

are non–negative Lagrange multipliers.

The main problem in real classiﬁcation task is that

linear decision surfaces (hyperplane) are not appro-

priate. In this case is necessary to map the dataset to

higher dimensional feature space (some other Euclid-

ean space ℜ) using the following mapping:

Φ : R

N

7→ ℜ . (3)

In the feature space we work with linear classiﬁ-

cation. For that reason, the so–called kernel function

(K) is introduced to compute scalar products of the

form Φ(x

i

) · Φ(x

j

):

K(x

i

,x

j

) ≡ Φ(x

i

) · Φ(x

j

) . (4)

Using (2) and (4) the SVM solution is expressed

as:

f

α

(x) = sign

l

∑

i=1

y

i

λ

i

(K(x,x

i

)) + b

!

. (5)

In pattern recognition problem several kernels

have been applied (Burges, 1998). The kernels for

which (3) is veriﬁed are all those that satisfy the Mer-

cers’s condition (Vapnik, 1995; Williamson et al.,

1999). Some commonly used kernels:

K(x

i

,x

j

) = (x

i

· x

j

+ 1)

p

. (6)

K(x

i

,x

j

) = tanh(x

i

· x

j

− θ) . (7)

K(x

i

,x

j

) = e

−kx

i

−x

j

k

2

/2σ

2

. (8)

A SVM polynomial classiﬁer of degree p is cons-

tructed using (6). (7) results in a particular multi layer

perceptron only for some values of θ, and (8) gives

a radial basis function classiﬁer. Other valid kernel

functions that satisfy Mercer’s conditions are (Gunn,

1997):

• Exponential radial basis function:

K(x

i

,x

j

) = e

−kx

i

−x

j

k/2σ

2

• Fourier series:

K(x

i

,x

j

) =

sin

N +

1

2

(x

i

− x

j

)

sin(

1

2

(x

i

− x

j

)

• B–splines:

K(x

i

,x

j

) = B

2N+1

(x

i

− x

j

)

• Additive kernels:

K(x

i

,x

j

) =

∑

l

K

l

(x

i

,x

j

)

• Tensor product:

K(x

i

,x

j

) =

∏

l

K

l

(x

i

,x

j

)

3 PROPOSED APPROACH

The learning task here involves classifying patterns

that represent left ventricle landmarks on ventriculo-

graphycs images.

3.1 Data Source

The images used are sequences of ventriculographics

images acquire on patients using a digital ﬂat–panel

X–ray system (Innova

TM

4100 General Electric Me-

dical System). These images were acquired from

Right Anterior Oblique (RAO 30

◦

) direction. Each

image with resolution of 420×420 pixels and with

each image pixel described by a greyscale intensity

value between 0 (black) and 255 (white). Figure 1

shows angiographics images of the left ventricle in

RAO incident.

Figure 1: Left ventricle images. Systole phase (left). Dias-

tole phase (right).

3.2 Training Set Selection

American Heart Association (AHA) establishes ﬁf-

teen anatomical landmarks for the left ventricle shape

deﬁnition on the angiographic images acquired from

RAO 30

◦

direction.

The selected landmarks correspond to apex (AP),

the basal regions (BA2, BP3, BP4) and the aortica

valve sides (VA, VP). Dataset of landmarks patterns

Figure 2: AHA anatomical landmarks.

is constructed from a ventriculographic image se-

quence. A manually process driven by a cardiolo-

gist is applied to locate 31×31 pixel patterns corres-

ponding to each LV landmark. A total of 300 pa-

tterns constitutes the landmarks dataset, 50 images of

31×31 pixel for each landmark. Applying a similar

procedure, a dataset of 1200 non–landmark images

was generated from angiographic images of coronary

vessel and kidney. A training set is formed in rela-

tion 1:4, by each pattern that represents an anatomical

landmark, four non–landmark images are introduced.

Class +1 is assigned to identify a landmark and class

-1 for the non–landmark.

3.3 Training a Support Vector Machine

In this Section we design a SVM using the library

for Support Vector Machines of MatLab 7.0. The

idea is to construct a SVM classiﬁer using one of the

most popular parametric kernel: Gaussian radial basis

function (8).

This implementation considers a unique parame-

ter σ. Additionality, our SVM classiﬁer considers a

misclassiﬁcation tolerance parameter C that penali-

zing the most undesirables errors. A large value of

this parameter corresponding a higher penalty errors.

The SVM is trained using a training set of 1500

patterns (see section 3.2). The training process is used

to construct a decision surface that allows to classify

the input images as left ventricle landmark or non–

landmark.

The bootstrapping step is applied. The decision

surface obtained in the training process is used to

classify images that do not contain landmarks. The

false positive obtained in this process are incorporated

to dataset of non–landmark images and used in sub-

sequent training phases. This bootstrapping process

helps to characterize and deﬁne the non–landmark

class in order to obtain the decision surface than better

separates the classes. Non–landmark class is abun-

dant and broader in this sense more complex that

landmark class.

3.4 The Svm Left Ventricle Landmark

Detection Approach

Our landmark extraction problem can be deﬁned as

follows: Given a ventriculographic image which is

consider as input data, determine where the LV’s

landmarks in this image are located and return an en-

coding of their location. Our encoding is to represent

each anatomical landmark on the image by means of

31×31 pixel bounding box whose center represents

the exact location of the landmark.

This approach detects left ventricle landmarks by

exhaustively scanning an image for landmark–like

patterns, by splitting the original image into overla-

pping sub–images and classifying them using a SVM

(see section 3.3) to determine the appropriate class

(landmark or non–landmark).

4 RESULTS

The training of support vector machine was per-

formed using the MATLAB Support Vector Machine

toolbox developed by Gunn (Gunn, 1997) from the

Information: Signals, Images, Systems (ISIS) Re-

search Group at the University of Southampton. A

SVM classiﬁer was trained considering σ = 0.002 and

C = 10.

The landmark detection stage was implemented in

MatLab. The support vector obtained in the training

stage are used to construct the decision surface that

we use to discriminate if each subimage (see section

3.4) of the original image is a left ventricle landmark

or non–landmark.

The proposed approach has been tested with ven-

triculograms acquired at several instants of the car-

diac cycle. During the training procedure false posi-

tives were not registered. In the landmark extraction

phase 100 % of recognition was obtained. In ﬁgure

3, results of the left ventricle images landmarks ex-

traction approach for the end–systole to end–diastole

ventriculogram sequence are shown.

Validation of the approach is performed by quan-

tifying the difference between the left ventricle land-

mark location obtained with respect to the left ventri-

cle landmark located by a cardiologist. The error is

expressed as the distance between the manual and au-

tomatic landmark location. The error obtained (mean

± standard deviation) for a sequence of ventriculo-

grams in the RAO view, including 21 images is 2.47

Figure 3: Left ventricle image sequence. Bounding boxes

represents the anatomical landmarks obtained.

mm ± 1.61 mm, with a maximum value of 4.84 mm

and a minimum value of 1.03 mm.

5 CONCLUSIONS

An automatic approach for left ventricle anatomical

landmarks extraction has been implemented. The

classiﬁcation approach does not require any prior

knowledge about the ventriculograms and not require

some preprocessing of the input data.

A quantitative validation stage is implemented.

The estimated landmarks from the detection approach

show a good match with the landmarks located by

specialist. This application would be a useful tool for

detecting the left ventricle landmark in conventional

Left Anterior Oblique (LAO) 60

◦

view.

Further research involves incorporationof the pro-

posed classiﬁer to an approach for left ventricle con-

tour detection using deformable models.

ACKNOWLEDGEMENTS

The authors would like to thank the CDCHT from

Universidad de Los Andes–T´achira and Investigation

Dean’s Ofﬁce of Universidad Nacional Experimental

del T´achira. Authors would also like to thank the Cen-

tro M´edico Caracas in Caracas, Venezuela for provi-

ding the human ventriculographic databases.

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