Head Yaw Estimation using Frontal Face Detector

Jos

e Mennesson

, Aﬁfa Dahmane

, Taner Danisman

and Ioan Marius Bilasco

Univ. Lille, CNRS, Centrale Lille, UMR 9189 - CRIStAL - Centre de Recherche en Informatique Signal et Automatique de

Lille, F-59000, Lille, France

Computer Science Department, USTHB University, Algiers, Algeria

Department of Computer Engineering, Akdeniz University, Antalya, Turkey

Keywords:

Head Pose, Yaw Angle Estimation, Frontal Face Detector, 3D Head Rotation, Ellipsoid.

Abstract:

Detecting accurately head orientation is an important task in systems relying on face analysis. The estimation

of the horizontal rotation of the head (yaw rotation) is a key step in detecting the orientation of the face. The

purpose of this paper is to use a well-known frontal face detector in order to estimate head yaw angle. Our

approach consists in simulating 3D head rotations and detecting face using a frontal face detector. Indeed,

head yaw angle can be estimated by determining the angle at which the 3D head must be rotated to be frontal.

This approach is model-free and unsupervised (except the generic learning step of VJ algorithm). The method

is experimented and compared with the state-of-the-art approaches using continuous and discrete protocols on

two well-known databases : FacePix and Pointing04.

1 INTRODUCTION

Head yaw estimation is one of the key components for

estimating the orientation of the face. Yaw rotation is

a rotational component of 3DoF (yaw, pitch, roll) and

deﬁned as rotation about the vertical z-axis. Accurate

estimation of the yaw angle has particular importance

in several domains such as analysing drivers’ driv-

ing behaviour, video surveillance and facial analysis

(e.g. face recognition, face detection, face tracking,

gender recognition and age estimation). In such con-

tents, the head pose can quickly change from frontal

upright position and generate out-of-plane rotations.

Out-of-plane rotations (yaw and pitch) are more chal-

lenging than in-plane rotations (roll) as they largely

inﬂuence the performances of underlying analysing

systems. Therefore, there is a need to recover the head

pose information when the face is not directly facing

to the camera.

Common typologies of approaches in head pose

estimation are summarized in (Murphy-Chutorian and

Trivedi, 2009). These methods can be roughly

grouped into two categories: Model-based and

appearance-based methods. Model-based meth-

ods use 3D information for head pose estimation

while appearance-based methods infer the relation-

ship among the 3D points and their projections on 2D.

According to the survey, the performance of head-

pose estimation systems signiﬁcantly degrades in out-

of-plane rotations than in-plane rotations. As indi-

cated in (Jung and Nixon, 2010) existing 2D mod-

els are not effective since they do not represent the

curved surfaces and they do not cope well with large

variations in 3D. Therefore, they are not robust to out-

of-plane rotations.

(Kwon et al., 2006) used cylindrical head model

to recover the 3D head pose information from a set of

images. They ﬁrst detect the face and then generate

an initial template for the head pose and cylindrical

head model. They dynamically update this template

to recover the problems in tracking. Head motion is

tracked based on optical ﬂow in sequential images.

For this reason, this method requires a set of sequen-

tial frames and cannot be applied to single images.

(Narayanan et al., 2014) studied yaw estimation

using cylindrical and ellipsoidal face models. Their

study on ellipsoidal framework provides MAE be-

tween 4

◦

and 8

◦

outperforming manifold-based ap-

proaches on FacePix dataset. Methods dealing with

yaw detection become more and more complex by

combining various techniques requiring most of the

time speciﬁc machine learning tools. This kind of

methods can suffer from the fact that combining

methods that are not completely precise and robust

individually, may eventually result in a lack of global

precision and tuning the system becomes complicated

Mennesson, J., Dahmane, A., Danisman, T. and Bilasco, I.

Head Yaw Estimation using Frontal Face Detector.

DOI: 10.5220/0005711905170524

In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 4: VISAPP, pages 517-524

ISBN: 978-989-758-175-5

517

Degree of head yaw rotation

Total face detections at 0 neighboorhood

Figure 1: Changes in total VJ face detections for different yaw angles at zero neighborhood. Each bar shows the number of

detections obtained from different scales of the VJ detector for speciﬁed degree of rotation.

as compromises between the drawbacks of underlying

methods might not be straight-forward. Besides, the

learning process in such methods can conduct to spe-

ciﬁc solutions that are tuned for a speciﬁc training set

and may behave differently in more generic context

such as in-the-wild unconstrained settings.

We discuss apart approaches that are dealing with

the discrete yaw estimation and continuous yaw es-

timation. Discrete pose represents the orientation at

ﬁxed intervals (e.g., ±15°) and they are only capa-

ble of estimating coarse pose space. On the other

hand continuous estimations can handle ﬁne (precise)

poses. In each of this two categories we are consider-

ing approaches that study the yaw estimation. The

yaw discrete estimation approaches can be consid-

ered, most of the time, as regular classiﬁcation prob-

lems where each discrete pose speciﬁc training and

analysis is done. In the yaw continuous estimation

regression methods and/or tracking mechanisms ini-

tialized from known/predeﬁned frontal are commonly

used.

Using a similar idea as (Danisman and Bilasco,

2015) which estimate roll pose estimation, we focus

on yaw pose estimation from still images using frontal

Viola-Jones (Viola and Jones, 2001) face detector us-

ing a two-stage approach. The frontal Viola-Jones

detector responds positively to faces that are nearly

frontal. However, the number of candidate face re-

gions responding to the Viola-Jones detector is gen-

erally more important for frontal faces than for non-

frontal faces and falls zero for proﬁle faces. Figure 1

shows total VJ face detections for different yaw an-

gles at zero neighbourhood. It is clear that the maxi-

mum of detected frontal faces is obtained with a yaw

angle near zero degree (a frontal face). When one

moves away from frontal face, the number of detected

frontal faces decreases to zero with a Gaussian decay.

In order to take advantage of this fact, we present the

same face under different perspectives corresponding

to candidate yaw angles to the Viola-Jones detector.

This idea is illustrated in Figure 2 where a face (whose

yaw angle is −30°) is projected onto a 3D ellipsoid

and rotated artiﬁcially from −90° to 90°. As a nearly-

frontal face still activates the Viola-Jones detector, we

consider the whole span of perspectives angles that

responded positively to Viola-Jones in order to esti-

mate the yaw by considering several acceptance cri-

teria : continuous detection over a given yaw range,

average over all positive candidate angles. Another

says is that regardless of the yaw angle of the anal-

ysed face, we apply a set of transformation to the face

and we study how the VJ detector behaves with regard

to applied transformation. The inverse yaw transfor-

mation yielding the best behaviour with regard to a

given detector (Viola-Jones frontal face detector in

our case) and a given criteria (number of consecutive

detections, for instance) is a fairly good candidate for

the yaw detection. The main idea is not to character-

ize the object, but the inverse transformation applied

on the object in order to bring the object in a state

where expected behaviour is met. The strength of

this approach resides also in the use of a well-known

method largely studied and used in the literature. In

addition, this method does not require speciﬁc learn-

ing step other than the one used for training the un-

derlying frontal Viola-Jones face detector.

The remaining part of this paper is organized as

follows. Section 2 discuss the existing typologies of

yaw estimation approaches. Section 3 presents our

approach including head segmentation, 2D projection

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

518

Degree of rotation of the 3D head

Total face detections at 0 neighborhood

Original

image

Yaw = -30°

min=-80°

max=20°

-30°

Estimated

yaw angle

Figure 2: Changes in total VJ face detections for different yaw angles at zero neighborhood. Each bar shows the number of

detections obtained from different scales of the VJ detector for speciﬁed degree of rotation of the ellipsoid.

on ellipsoid, face detection and head yaw estimation.

Section 4 explains the experimentation datasets and

presents evaluation results on a continuous and dis-

crete perspective.

2 STATE OF THE ART

A common functional taxonomy covering the large

variations in face orientation estimation studies can

be found in (Murphy-Chutorian and Trivedi, 2009).

In the current work, we selected representative ap-

proaches that report results on yaw estimation on pub-

lic datasets such as FacePix (Black et al., 2002) and

Pointing04 (Gourier et al., 2004). In particular, we

selected the works giving the best results in (Murphy-

Chutorian and Trivedi, 2009) and in (Dahmane et al.,

2014) on these two databases. Among the numerous

approaches for head pose estimation, one can cite :

Model-based approaches include geometric and

ﬂexible model approaches. For example, (Narayanan

et al., 2014) propose to use cylindrical and ellipsoidal

face models to estimate yaw angle. (Tu et al., 2007)

perform head pose estimation based on a pose tensor

model.

Regression based approaches consider pose an-

gles as regression values. In (Stiefelhagen, 2004), a

neural network is trained for ﬁne head pose estima-

tion over a continuous pose range. (Gourier et al.,

2007) propose to train an associative neural network

using data from facial feature locations while (Ji et al.,

2011) use convex regularized sparse regression.

Manifold Embedding approaches produce a low

dimensional representation of the original facial fea-

tures and then learn a mapping from the low dimen-

sional manifold to the angles. In (Balasubramanian

et al., 2007), biased manifold embedding for super-

vised manifold learning is performed and (Liu et al.,

2010) propose a K-manifold clustering method, inte-

grating manifold embedding and clustering.

Symmetry-based approaches use the symmetrical

properties of the head to estimate yaw angle as in

(Dahmane et al., 2014).

3 OUR APPROACH

Our approach is based on the classical Viola-Jones

(Viola and Jones, 2001) frontal face detector. Indeed,

this detector is able to detect frontal faces in images.

Assuming that a frontal face is a face with a head yaw

angle ∈ [-45°;45°], head yaw can be estimated by ar-

tiﬁcially turning head in 3D space from -90° to 90°

about the vertical z-axis and detect at each step if there

is a frontal face in the image plane. Head yaw angle

can be estimated by determining the angle at which

the 3D head must be rotated to be frontal. Using this

assumption, our method is highlighted in Figure 3.

First, the head must be segmented as much accu-

rately as possible because our method depends highly

on this step. The head can be segmented for example

using GrabCut (Rother et al., 2004) or a skin detector

(Zaidan et al., 2014). In this paper, GrabCut is chosen

because it is a well-known and widely used method to

segment images. Then, the head is cropped and pro-

jected on a 3D sphere to simulate the 3D shape of the

head. It can be done using complex methods which

estimate the real shape of the face as in (Blanz and

Vetter, 1999). In order to keep the method as efﬁcient

as possible, we choose to project the face on an ellip-

Head Yaw Estimation using Frontal Face Detector

519

-90° +90°

+90°-90° -30° +0° +30°

... ... ... ...

FACE DETECTION

NO NOYES NOYES

... ... ... ...

+90°

-90°

+0°

Min

Max

-66° +6°

Yaw Est.

-30°

...

Head

segmentation

Head

crop

Original

image

Projection

on ellipsoid

Figure 3: Overview of our method.

soid. The ellipsoid is then turned from −90° to 90°

about the z-axis to simulate a 3D head face turn and,

at each angle, face detection is performed. Results of

detection and non-detection are stored in a binary vec-

tor. After a ﬁltering step, we consider the minimum

and the maximum angles where the face has been de-

tected. Several criteria can be applied (consecutive

frames detection, mode, mean, etc.), but here we re-

tain the mean of the detection angles.

3.1 Head Segmentation

Our approach depends on the segmentation of the

face. In fact, if there is unbalanced background on

the right and on the left of the face, this will skew

the estimation of the head yaw. In order to solve this

problem, the face must be accurately segmented be-

fore the projection on the ellipsoid.

One of the most well-known and robust algorithm

to segment objects in images is GrabCut (Rother

et al., 2004). This algorithm needs to be initialized

with an area (a rectangle for example) which probably

corresponds to the foreground (here, it is the head of

the person). Everything outside the rectangle is con-

sidered as the background.

In this paper, we assumed that the face is centered.

So, the area given to the GrabCut is a rectangle in the

center of the image. The size of the rectangle is half

of the size of the image. This constraint can be low-

ered if we assume that the yaw angle ∈ [−45°; 45°]

and an initial VJ can be used instead. Outside this

range, other versions of VJ or other techniques must

be employed to ﬁnd the ﬁrst candidate face boundary

box. RACV library (Auguste, 2014) is used to op-

timize the head rectangle given to GrabCut using the

skin proportion therein. Finally, the convex hull of the

head is computed.

3.2 Projection on Ellipsoid

In order to simulate the rotation of the face, the seg-

mented face is projected on an ellipsoid. In this pa-

per, we have used OpenGL (Open Graphics Library)

as in (Aissaoui et al., 2014). The height of the ellip-

soid is 1.5 times the width in order to approximate

the general proportions of faces. The ellipsoid is ro-

tated from −90° to 90° about the z-axis to cover all

the angles where the frontal face can be detected. The

incremental parameter of the rotation angle, denoted

step-factor, can vary from 1° to 10° in order to ac-

celerate the process. The effect of this parameter on

the results is shown in section 4. Finally, the image

we consider is a projection of the 3D ellipsoid on the

image plane.

3.3 Frontal Face Detection

Whenever the face is rotated, a face detection is per-

formed. In this paper, the classical VJ detector (Viola

and Jones, 2001) who proposes to use Haar Feature-

based Cascade Classiﬁers to detect faces, is used.

Each frontal face detection is then stored in a binary

vector.

In order to increase the chance of a matching size

with the model for detection, we use a small step for

resizing (scale factor=1.1). To eliminate false posi-

tives and get the proper face rectangle out of detec-

tions, the minimum neighbours parameter is set to 1.

3.4 Head Yaw Estimation

As it is said before, a binary vector containing the de-

tection results is obtained. In Figure 4, these vectors

are represented by binary images where white (resp.

black) pixel depicts that a face is detected (resp. not

detected). Each image corresponds to a different clip,

each line corresponds to a head image with a particu-

lar yaw angle and each columns corresponds to a ro-

tation angle of the ellipsoid. If we assume that there

is no error in the detection results, head yaw angles

can be estimated by considering the minimum and the

maximum angles the head is detected. Indeed, the VJ

detector being symmetric, it will detect the face as

well if it is slightly rotated to the right or left (See Fig-

ure 4 - Clip7 and Clip25 ). A morphological opening

of size 3 to suppress noise is performed. Estimated

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

520

-45°

45°

0°

Ground-truth No detection Detection

-45°

45°

0°

-90°

90°

0°

-90°

0°

-90°

90°

Clip 7 : Good detections Clip 25 : Good detections

Clip 16 : Many false positive Clip 21 : Many false negative

Figure 4: Detection results on FacePix dataset. White pixel: detection, black pixel: non detection, blue line: ground-truth.

head yaw is the angle between the minimum and the

maximum angles at which the frontal face is detected.

Several solutions can be proposed :

• HYE1 : In order to make our approach robust to

false positive detection (see Figure 4 - Clip16),

connected detections are labeled. Then, only the

largest connected component is considered to es-

timate head yaw angle as in Figure 5.

... 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 ...

... 0 0 1 1 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 ...

... -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ...

Angles in °

3°

Detection

Labelling

Figure 5: Labeling connected detections and choosing the

largest connected component.

• HYE2 : The center of mass of the binary vector

can be computed. This version is more robust to

false negative detections (see Figure 4 - Clip21).

In the following section, we are conducting exper-

iments to evaluate our methods. The objectives are

to compare the results of our approach with the state

of the art and to evaluate the inﬂuence of the param-

eters, initial yaw angles and different face shapes on

the results.

4 EXPERIMENTS

Tests are made on FacePix (Black et al., 2002) and

Pointing04 (Gourier et al., 2004) datasets. Two proto-

cols (continuous and discrete) have been deﬁned. The

continuous like protocol aims to evaluate the capacity

of the proposed method to offer ﬁne grain characteri-

zation of yaw movements. The discrete like protocol

considers the yaw movements problem as a classiﬁ-

cation problem, where 15° yaw interval classes are

considered.

4.1 Datasets

In order to validate our approach, head yaw estima-

tion is tested on several databases :

- FacePix Dataset

This dataset contains 3 sets of face images for each

of 30 people included in the dataset. In Figure 6, we

present frontal views of four persons that where in-

cluded in Figure 4 experiments. We have selected this

four persons in order to study closely the impact of

eye glasses, long hair and skin color on the results.

However, the whole dataset is considered for the re-

sults presented in the following. The ﬁrst set contains

181 color face images which corresponds to yaw an-

gle which vary across a range from +90° to −90°.

The second and the third sets contain just frontal faces

and just concern illumination variations.

In this paper, we consider a subset of the ﬁrst set

which contains only faces which are in [−45°; 45°]

(i.e. 2730 images) due to the frontal face detector

used. Indeed, if too much information about the face

is missing, the frontal face detector is no longer able

to detect the face, even if the head is artiﬁcially ro-

tated.

Clip7 Clip16 Clip21 Clip25

Figure 6: Several images from facePix dataset.

- Pointing04 Dataset

The head pose database contains 15 sets of im-

ages. Each set consists in two series of 93 images of

the same person at different poses. There are 15 peo-

ple in the database, wearing glasses or not and hav-

ing various skin color. The pose, or head orientation

is determined by 2 angles (yaw,pitch), which varies

from −90° to +90°. The ﬁrst serie is used and only

faces which are in [−45°; 45°] (i.e. 105 images) are

considered due to the face detector used.

4.2 Evaluation

In this paper, the following experiments are conducted

on continuous (i.e. evaluated every degree on FacePix

dataset) and discrete space (i.e. evaluated every 15

degree on Pointing04 dataset).

Head Yaw Estimation using Frontal Face Detector

521

4.2.1 Experiments on FacePix

In these tests, continuous experiments are conducted

using well-known measures as the Mean Average Er-

ror (MAE), the Root Mean Square Error (RMSE) and

the Standard Deviation (STD).

In Table 1, one can see that our approach pro-

vides comparable MAE with classical approaches of

the state of the art. But our approach is model-

free, person-free and unsupervised (except the generic

learning step of VJ algorithm). One can also add

that a signiﬁcant drawback of manifold learning tech-

niques is the lack of a projection matrix to treat

new data points (Balasubramanian et al., 2007). The

HYE2 method gives the best result on this database.

The following charts show the results computed with

this solution.

Table 1: FacePix : Comparison with the state of the art.

Method MAE

(Balasubramanian et al., 2007)

Biased Isomap 5.02°

Biased LLE 2.11°

Biased LE 1.44°

(Liu et al., 2010)

Manifold clustering 3.16°

(Ji et al., 2011)

Regression 6.1°

(Dahmane et al., 2014)

Symmetry classiﬁcation 3.14°

(Narayanan et al., 2014)

CE 5.55°

Center CE 5.26°

Boundary CE 5.28°

Proposed Method

HYE1 5.2°

HYE2 4.8°

In Figure 7, a boxplot which represents estimated

yaw angles with regard to the groundtruth is shown.

It is clear that most of estimated yaw angles are near

the groundtruth. Widest errors are found nearby −45°

and 45°. This is due to the VJ detector which has

difﬁculties to detect frontal faces at these angles even

if the face is turned artiﬁcially. Indeed, there can be a

lack of face information (e.g. an eye is hidden) which

can prevent the frontal face detection when the head

is turned to -45° or 45°.

In order to evaluate our method in function of per-

sons and head yaw angles, MAE measures are com-

puted and shown in Figure 8 and 9. Figure 8 shows

that most angles (between −35° and 33°) have a MAE

under 5.5°. The worst results are obtained when head

yaw angles are greater than 35° due to the frontal face

-80

-60

-40

-20

Groundtruth

Estimated angles

Figure 7: FacePix : boxplot of head yaw angle estimation.

Ground-truth yaw angles

MAE

Figure 8: FacePix : Histogram of head yaw angles estima-

tion MAE for ground-truth yaw angles.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Clips

MAE

Figure 9: FacePix : Histogram of head yaw angles estima-

tion MAE for Clip1-30.

detector properties.

In Figure 9, most Clips have low MAE (< 8°) ex-

cept Clip5, 6, 11, 16, 21. Frontal faces in these clips

are sometimes difﬁcult to detect. For example, in

Clip21 (see Figure 6 and 4), the person wear glasses,

and in Clip11, the person closes almost completely

her eyes, which prevent neat face detection.

We have seen in section 3.2 that our method de-

pends of a parameter which controls the incremen-

tal step of the rotation of the face (i.e. step-factor).

Figure 10 shows the evolution of MAE, MRSE and

STD obtained on FacePix using several step-factor

settings. One can easily see that the results vary only

slightly if step-factor is less or equal to 4°. Hence for

speed up purposes, we can divide the number of rota-

tions of the 3D head by four while maintaining a good

accuracy.

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

522

1 2 3 4 5 6 7 8 9 10

MAE

MRSE

STD

Step-factor

Values in degree

Figure 10: FacePix : Effect of step-factor(see section 3.2)

on MAE, MRSE and STD.

4.2.2 Experiments on Pointing04

In this section, we consider discrete yaw classiﬁca-

tion. Hence, the results correspond to the number of

well estimated yaw over the total number of head yaw

to estimate. In order to cluster the estimated head yaw

into discrete classes, it is associated to the nearest yaw

class. There are 7 head yaw classes : −45°, −30°,

−15°, 0°, 15°, 30°, 45°.

In Table 2, results on Pointing04 dataset are shown

in terms of MAE and recognition rates. It is clear that

our method outperforms most of the approaches of the

state of the art. Again, other methods require a learn-

ing step for estimating head yaw while our method

does not. Concerning this dataset, the HYE1 method

outperform the HYE2 one, so the following charts

show the results computed with this solution. This is

due to many false detections which appears in several

detection results for this dataset. As we said before,

HYE1 is more robust to that problem.

Table 2: Pointing04 : Comparison with the state of the art.

Method MAE Reco. rates

(Stiefelhagen, 2004) 9.5° 52%

(Gourier et al., 2007)

Human Performance 11.8° 40.7%

Associative Memories 10.1° 50.0%

(Tu et al., 2007)

High-order SVD 12.9° 49.25%

PCA 14.11° 55.20%

LEA 15.88° 45.16%

(Ji et al., 2011)

Regression 8.6° -

(Narayanan et al., 2014)

CE 7.2° -

Center CE 6.82° -

Boundary CE 6.9° -

Proposed Method

HYE1 6.96° 63.81%

HYE2 7.15° 59.05%

As it is shown in Figure 11, the worst recognition

rates are obtained with angles −45° and 45°. Again,

this is due to the properties of the VJ detector we used

in this paper. The results for other angles are better or

equal 60%.

-45 -30 -15 0 15 30 45

0,00%

10,00%

20,00%

30,00%

40,00%

50,00%

60,00%

70,00%

80,00%

90,00%

100,00%

Ground-truth yaw angles

Recognition rates

Figure 11: Pointing04 : Histogram of recognition rates for

ground-truth yaw angles.

In Figure 12, one can note that for most persons,

the results are good (> 50%). Worst results are ob-

tained for persons 2,7,8,9. The reason is a bad seg-

mentation of the head of these persons due, among

other things, to their hair which cover their ears.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0,00%

10,00%

20,00%

30,00%

40,00%

50,00%

60,00%

70,00%

80,00%

90,00%

100,00%

Personne

Recognition rates

Figure 12: Pointing04 : Histogram of recognition rates for

Personne1-30.

5 CONCLUSION

A new approach to estimate head yaw angle is pre-

sented in this paper. Face images are projected on 3D

ellipsoid and artiﬁcially turned about the vertical z-

axis. The goal is to determine the angle the head must

be turned to be frontal. Frontal faces are detected us-

ing a well-known frontal face detector. Advantages

are that it is a person-free, model-free and unsuper-

vised approach. It is not a black box, so every param-

eters can be set easily. Experiments on well-known

datasets have shown that this method gives compara-

ble or better results than the state of the art. In future

works, other methods to segment heads and detect

frontal faces can be explored. Also, the 3D modeling

Head Yaw Estimation using Frontal Face Detector

523

of the 3D face could be improved using more accurate

3D shape than a simple ellipsoid. This method could

also be extended to pitch angle estimation. In this pa-

per, we propose two methods to estimate head yaw

angles (HYE1 and HYE2). A hybrid method which

uses HYE1 or HYE2 depending on the size of the

connected component could be deﬁned to take advan-

tages of both approaches.

ACKNOWLEDGEMENTS

This work was supported by ”Empathic Products”,

ITEA2 1105 and the authors thank IRCICA USR

3380 for ﬁnancial support.

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