Point Distribution Models for Pose Robust Face

Recognition: Advantages of Correcting Pose Parameters

Over Warping Faces to Mean Shape

Daniel Gonz

´

alez-Jim

´

enez and Jos

´

e Luis Alba-Castro

⋆

Departamento de Teor

´

ıa de la Se

˜

nal y Comunicaciones

Universidad de Vigo (Spain)

Abstract. In the context of pose robust face recognition, some approaches in the

literature aim to correct the original faces by synthesizing virtual images facing

a standard pose (e.g. a frontal view), which are then fed into the recognition sys-

tem. One way to do this is by warping the incoming face onto the average frontal

shape of a training dataset, bearing in mind that discriminative information for

classiﬁcation may have been thrown away during the warping process, specially

if the incoming face shape differs enough from the average shape. Recently, it

has been proposed a method for generating synthetic frontal images by modiﬁ-

cation of a subset of parameters from a Point Distribution Model (the so-called

pose parameters), and texture mapping. We demonstrate that if only pose param-

eters are modiﬁed, client speciﬁc information remains in the warped image and

discrimination between subjects is more reliable. Statistical analysis of the veri-

ﬁcation experiments conducted on the XM2VTS database conﬁrm the beneﬁts of

modifying only the pose parameters over warping onto a mean shape.

1 Introduction

It is well known that the performance of face recognition systems drops drastically

when pose differences are present within the input images, and it has become a major

goal to design algorithms that are able to cope with this kind of variations. Some of

these approaches aim to synthesize faces across pose in order to cope with viewpoint

differences. One of the earliest attempts was done by Beymer and Poggio [1]: from a

single image of a subject and making use of face class information, virtual views facing

different poses were synthesized. For the generation of the virtual views, two different

techniques were used: linear classes and parallel deformation. Vetter and Poggio also

took advantage of the concept of linear classes to synthesize face images from a single

example in [8]. Blanz et al. employed the 3D Morphable Model [6] to synthesize frontal

faces from non frontal views in [7], which were then fed into the recognition system.

In this same direction, other researchers have tried to generate frontal faces from non

frontal views, like the works proposed by Xiujuan Chai et al. in [4], via linear regression

⋆

This work was supported with funds provided partially by the Spanish ministry of education

under project TEC2005-07212/TCM and the European sixth framework programme under the

Network of Excellence BIOSECURE (IST-2002-507604)

González-Jiménez D. and Luis Alba-Castro J. (2007).

Point Distribution Models for Pose Robust Face Recognition: Advantages of Correcting Pose Parameters Over Warping Faces to Mean Shape.

In Proceedings of the 7th International Workshop on Pattern Recognition in Information Systems, pages 138-147

DOI: 10.5220/0002428001380147

Copyright

c

SciTePress

in each of the regions in which the face is divided, and in [5] where a 3D model is used.

More recently, Gonz

´

alez-Jim

´

enez and Alba-Castro [9] have proposed an approach for

generating frontal faces via modiﬁcation of a subset of parameters from a Point Dis-

tribution Model (so-called pose parameters) and texture mapping. Another possibility

is to warp the face image onto a frontal standard shape (e.g. the average frontal shape

of a training dataset) prior to recognition. This solution is adopted by methods that use

holistic features for face representation (e.g. Eigenfaces [2]), and that need all images to

be embedded into a constant reference frame. For example, Lanitis et al. [10] deformed

each face image to the mean shape using 14 landmarks, extracted shape and appearance

parameters and classiﬁed using the Mahalanobis distance.

The difference between the synthetic images obtained using the methods described

in [9] and [10] relies on the generation of the synthetic frontal shapes onto which the

original faces must be warped. It seems rather safe to think that warping faces onto

a mean shape may provoke discriminative information reduction, specially if the in-

coming face shape differs enough from the average shape (see Figure 1). On the other

hand, [9] did not analyze whether the modiﬁcation of the pose parameters had any in-

ﬂuence on non-rigid factors (such as expression and identity), which could provoke non

desirable effects in the synthesized faces. The goal of this paper is two-fold:

1. Show that, if the training set is chosen appropriately, pose parameters do not contain

important non-rigid (expression/identity) information, and

2. Propose an empirical comparison of the synthetic images obtained with the meth-

ods described in [9] and [10] respectively. Obviously, we need a non-subjective

way to compare the two approaches and, to this aim, we conducted face veriﬁca-

tion experiments on the XM2VTS database [11] using Gabor ﬁltering for feature

extraction.

Fig.1. Images from subject 013 of the XM2VTS. Left: Original image. Right: Image warped

onto the average shape. Observe that subject-speciﬁc information has been reduced (specially in

the lips region).

The paper is organized as follows. Next section brieﬂy reviews Point Distribution

Models, and introduces the concepts of Pose Eigenvectors and Pose Parameters. The

two techniques used to generate frontal face images are presented in Section 3. Section

4 shows the results of the veriﬁcation experiments conducted on the XM2VTS database

[11]. Finally, conclusions are drawn in Section 5.

139

2 A Point Distribution Model For Faces

A point distribution model (PDM) of a face is generated from a set of training ex-

amples. For each training image I

i

, N landmarks are located and their normalized

coordinates (by removing translation, rotation and scale) are stored, forming a vector

X

i

= (x

1i

, x

2i

, . . . , x

Ni

, y

1i

, y

2i

, . . . , y

Ni

). The pair (x

ji

, y

ji

) represents the normal-

ized coordinates of the j-th landmark in the i-th training image. Principal Components

Analysis (PCA) is performed to ﬁnd the most important modes of shape variation. As a

consequence, any training shape X

i

can be approximately reconstructed:

X

i

=

¯

X + Pb, (1)

where

¯

X stands for the mean shape, P = [φ

1

|φ

2

| . . . |φ

t

] is a matrix whose columns are

unit eigenvectors of the ﬁrst t modes of variation found in the training set, and b is the

vector of parameters that deﬁne the actual shape of X

i

. So, the k -th component from b

(b

k

, k = 1, 2, . . . , t) weighs the k-th eigenvector φ

k

. Also, since the columns of P are

orthogonal, we have that P

T

P = I, and thus:

b = P

T

X

i

−

¯

X

, (2)

i.e. given any shape, it is possible to obtain its vector of parameters b. We built a 62-

point PDM using manually annotated landmarks (some of them were provided by the

FGnet project

1

, while others were manually annotated by ourselves). Figure 2 shows

the position of the landmarks on an image from the XM2VTS database [11].

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

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60 61

62

Fig.2. Position of the 62 landmarks used in this paper on an image from the XM2VTS database.

2.1 Pose Eigenvectors and Pose Parameters

Among the obtained modes of shape variation, the authors of [9] identiﬁed the eigen-

vectors that were responsible for controlling the apparent changes in shape due to rigid

facial motion. However, it was not analyzed whether the modiﬁcation of these pose pa-

rameters had any inﬂuence on non-rigid factors (such as expression and identity), which

1

Available at http://www-prima.inrialpes.fr/FGnet/data/07-XM2VTS/xm2vts-markup.html

140

could provoke non desirable effects on the synthesized faces. In this section, we show

that if the training data are appropriately chosen, the identiﬁed pose parameters do only

account for pose variations.

Clearly, the eigenvectors (and their relative position) obtained after PCA strongly

depend on the training data and hence, the choice of the examples used to build the PDM

is critical. In fact, if all training meshes were strictly frontal, there would not appear any

eigenvector explaining rotations in depth. However, if we are sure that pose changes

are present in the training set, the eigenvectors explaining those variations will appear

among the ﬁrst ones, due to the fact that the energy associated to rigid facial motion

should be higher than that of most expression/identity changes (once again, depending

on the speciﬁc dataset used to train the PDM). With our settings, it turned out that φ

1

controlled up-down rotations (see Figure 3) while φ

2

(Figure 4) was the responsible

for left-right rotations. Hence, given a mesh X with a vector of shape parameters b =

[b

1

, b

2

, . . . , b

t

]

T

, we can change the values of b

1

and b

2

(i.e. the pose parameters), and

use equation (1) to generate a synthetic mesh X

2

facing a different pose.

A major problem, inherent to the underlying PCA analysis, relies on the fact that

a given pose-eigenvector may not only contain rigid facial motion (pose) but also non-

rigid (expression/identity) information, mostly depending on the training data used to

build the PDM. The reconstructed shapes in Figure 4, show that expression changes are

not noticeable when sweeping b

2

. Regarding φ

1

, it has been shown [15] that there exists

a dependence between the vertical variation in viewpoint (nodding) and the perception

of facial expression, as long as faces that are tilted forwards (leftmost shape in Figure

3) are judged as happier, while faces tilted backwards (rightmost shape in Figure 3) are

judged as sadder. Apart from this subjective perception, we provide visual evidence in

the next section suggesting that the inﬂuence of non-rigid factors within φ

1

and φ

2

is

small.

Fig.3. Effect of changing the value b

1

on the reconstructed shapes. φ

1

controls the up-down

rotation of the face.

Fig.4. Effect of changing the value b

2

on the reconstructed shapes. φ

2

controls the left-right

rotation of the face.

141

2.2 Experiment on a Video-sequence: Decoupling of Pose and Expression

In order to demonstrate that the presence of non-rigid factors within the identiﬁed pose-

eigenvectors is minimal, we used a manually annotated video-sequence of a man during

conversation

2

(hence, rich in expression changes). For each frame f in the video, the

vector of shape parameters

b(f ) = [b

1

(f) , b

2

(f) , . . . , b

t

(f)]

T

of the corresponding mesh X(f) was calculated and splitted into the rigid (pose) part

b

pose

(f) = [b

1

(f) , b

2

(f) , 0, . . . , 0]

T

and the non-rigid (expression) part

b

exp

(f) = [0, 0, b

3

(f) , . . . , b

t

(f)]

T

Finally, we calculated the reconstructed meshes X

pose

(f) and X

exp

(f) using equa-

tion (1) with b

pose

(f) and b

exp

(f) respectively. Ideally, X

pose

(f) should only contain

rigid mesh information, while X

exp

(f) should reﬂect changes in expression and con-

tain identity information. As shown in Figure 5, it is clear that although there exists

some coupling (specially in the seventh row with small eyebrow bending in X

pose

(f)),

X

exp

(f) is responsible for expression changes and identity information (face shape

is clearly encoded in X

exp

(f)) while X

pose

(f) does mainly contain rigid motion in-

formation. For instance, the original shapes from the ﬁrst and second rows share ap-

proximately the same pose, but differ substantially in their expression. Accordingly, the

X

pose

’s are approximately the same while the X

exp

’s are clearly different.

3 Synthesizing Frontal Faces

Given two faces I

A

and I

B

to be compared, the system must output a measure of simi-

larity (or dissimilarity) between them. Straightforward texture comparison between I

A

and I

B

may not produce desirable results as differences in pose could be quite impor-

tant. In this section, we describe the two approaches proposed in [10] and [9] for frontal

face synthesis. These two methods share one common feature: given one face image I,

the coordinates of its respective ﬁtted mesh, X, and a new set of coordinates, X

2

, a syn-

thetic face image must be generated by warping the original face onto the new shape.

For this purpose, we used a method developed by Bookstein [13], based on thin plate

splines. Provided the set of correspondences between X and X

2

, the original face I is

allowed to be deformed so that the original landmarks are moved to ﬁt the new shape.

2

http://www-prima.inrialpes.fr/FGnet/data/01-TalkingFace/

talking

face.html

142

Original shape (X)

X

exp

X

pose

Original shape (X)

X

exp

X

pose

Original shape (X)

X

exp

X

pose

Original shape (X)

X

exp

X

pose

Original shape (X)

X

exp

X

pose

Original shape (X)

X

exp

X

pose

Original shape (X)

X

exp

X

pose

Fig.5. Experiment on the video sequence. Each row shows, for a given frame f, the original shape

X(f) and the reconstructed shapes (X

exp

(f) and X

pose

(f)) using b

exp

(f) and b

pose

(f) respec-

tively. Clearly, X

exp

(f) controls expression and identity while X

pose

(f) is mostly responsible

for rigid changes.

3.1 Warping to Mean Shape (WMS) [10]

Once the meshes have been ﬁtted to I

A

and I

B

, both faces are warped onto the average

shape of the training set,

¯

X, which corresponds to setting all shape parameters to 0, i.e.

b

A

= b

B

= 0. Thus, the images are deformed so that a set of landmarks are moved

to coincide with the correspondent set of landmarks on the average shape, obtaining

¯

I

A

and

¯

I

B

. The number of landmarks used as “anchor” points is another variable to be

ﬁxed. For the experiments, we used two different sets:

– The whole set of 62 points.

– The set of 14 landmarks used in [10].

As the number of “anchor” points grows, the synthesized image is more likely to

present artifacts because more points are forced to be moved to landmarks of a mean

shape (which may differ signiﬁcantly from the subject’s shape). On the other hand, with

few “anchor” points, little pose correction can be made.

143

3.2 Normalizing to Frontal Pose and Warping (NFPW) [9]

Once demonstrated that the pose parameters do only account for pose variations (Sec-

tions 2.1 and 2.2), we suggest that normalizing only these parameters should produce

better results than warping images onto a mean shape, as long as we are not modifying

identity information. In Figure 6, we can see a block diagram of this method. Given b

A

and b

B

, only the pose parameters are ﬁxed to the typical values of frontal faces from the

training set (as the average shape corresponds to a frontal face, we ﬁxed pose parame-

ters to zero, i.e. b

pose

A

= b

pose

B

= 0). New coordinates are computed using Equation 1,

and virtual images,

ˆ

I

A

and

ˆ

I

B

, are synthesized.

Normalization

Pose

Normalization

Pose

TPS Warping

Comparison

Final

TPS Warping

Input image

Face Alignment

Face Alignment

Training

image

ONLINE

OFFLINE

Fig.6. Block diagram for pose correction using NFPW. After face alignment, the obtained meshes

are corrected to frontal pose (Pose Normalization block), and virtual faces are obtained through

Thin Plate Splines (TPS) warping. Finally, both synthesized images are compared. It is important

to note that the processing of the training image could (and should) be done ofﬂine, thus saving

time during recognition.

4 Face Authentication on the XM2VTS Database

Using the XM2VTS database [11], authentication experiments were performed on con-

ﬁguration I of the Lausanne protocol [12] in order to conﬁrm the advantages of modi-

fying only pose parameters over warping onto a mean shape.

4.1 Feature Extraction

Holistic approaches such as eigenfaces [2] need all images to be embedded into a con-

stant reference frame (an average shape for instance), in order to represent these images

as vectors of ordered pixels. This constraint is violated by the faces obtained through

NF P W , leading us to the use of local features: Gabor jets as deﬁned in [3] are ex-

tracted at each of the pose corrected mesh coordinates and stored for further compari-

son.

144

4.2 Database and Experimental Setup

The XM2VTS database contains face images recorded on 295 subjects (200 clients, 25

evaluation impostors, and 70 test impostors) during four sessions taken at one month

intervals. The database was divided into three sets: a training set, an evaluation set, and

a test set. The training set was used to build client models, while the evaluation set

was used to estimate thresholds. Finally, the test set was employed to assess system

performance.

We compared the performance of the different methods presented in section 3: a)

WMS 14: Warping images onto a mean shape using the same set of 14 “anchor” points

employed in [10], b) WMS 62: Warping images onto a mean shape using the full set of

62 “anchor” points, and c) NFPW: Normalizing only the subset of pose parameters to

generate a frontal mesh. Table 1 shows the False Acceptance Rate (FAR), False Rejec-

tion Rate (FRR) and Total Error Rate (TER=FAR+FRR) over the test set for the above

mentioned methods. Moreover, the last row from this table presents the baseline results

when no pose correction is applied (Baseline).

Table 1. False Acceptance Rate (FAR), False Rejection Rate (FRR) and Total Error Rate (TER)

over the test set for different methods.

METHOD FAR(%) FRR(%) TER(%)

WMS 14 2.31 5.00 7.31

WMS 62 2.64 4.50 7.14

NFPW 2.17 2.75 4.92

Baseline 2.93 4.25 7.18

Table 2. Conﬁdence interval around ∆

HT ER

= HT ER

A

− HT ER

B

for Z

α/2

= 1.645.

METHOD WMS 62 NFPW Baseline

WMS 14 [−1.15%, 1.32%] [0.07%, 2.32%] [−1.16%, 1.29%]

WMS 62 [0.02%, 2.20%] [−1.21%, 1.17%]

NFPW [−2.20%, −0.06%]

4.3 Statistical Analysis of the Results

In [14], the authors adapt statistical tests to compute conﬁdence intervals around Half

Total Error Rates (HT ER = T ER/2) measures, and to assess whether there exist

statistically signiﬁcant differences between two approaches or not. Given methods A

and B with respective performances HT ER

A

and HT ER

B

, we compute a conﬁdence

interval (CI) around ∆

HT ER

= HT ER

A

− HT ER

B

. Clearly, if the range of ob-

tained values is symmetric around 0, we can not say the two methods are different. The

conﬁdence interval is given by ∆

HT ER

± σ · Z

α/2

, where

σ =

s

F AR

A

(1−F AR

A

)+F AR

B

(1−F AR

B

)

4·NI

+

F RR

A

(1−F RR

A

)+F RR

B

(1−F RR

B

)

4·NC

(3)

145

and

Z

α/2

=

1.645 for a 90% CI

1.960 for a 95% CI

2.576 for a 99% CI

(4)

In equation (3), NC stands for the number of client accesses, while NI stands for

the number of imposter trials. For each comparison between the methods presented in

table 1, we calculated conﬁdence intervals which are shown in table 2. From both tables

we can conclude:

1. Although pose variation is not a major characteristic of the XM2VTS database, it is

clear that the use of NFPW signiﬁcantly improved system performance compared

to the baseline method.

2. Warping images to a mean shape suffers from the greatest degradation in perfor-

mance. It is clear that synthesizing face images with WMS does seriously distort

the “identity” of the warped image, as long as the performances of the baseline al-

gorithm and the two WMS’s methods are very similar (robustness to pose provokes

subject-speciﬁc information supression, leading to no improvement at all). Further-

more, we assess that signiﬁcant differences are present when comparing WMS with

NFPW, as the conﬁdence intervals do not include 0 in their range of values.

3. There are no statistically signiﬁcant differences between WMS

14 and WMS 62, as

the conﬁdence interval is symmetric around 0.

It was previously stated that NFPW was not suitable for holistic feature extraction, but

this is not the case of WMS. In order to assess the performance of a (baseline) holistic

method on W MS faces, we applied eigenfaces [2] and obtained a TER of 16.27%,

which is signiﬁcantly worse than that of the local feature extraction on WMS faces,

with a conﬁdence interval around ∆

HT ER

of [2.95%, 6.01%].

5 Conclusions

We have demonstrated that, if the training set is appropriately chosen, the pose eigen-

vectors as introduced in [9] are mostly responsible for rigid mesh changes, and do not

contain important non-rigid (expression/identity) information that could severely distort

the synthetic meshes. Moreover, we have conﬁrmed, with experimental results on the

XM2VTS database, the advantages of modifying these pose parameters over warping

faces onto a mean shape.

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