3-D Shape Matching for Face Analysis and Recognition

Wei Quan, Bogdan J. Matuszewski and Lik-Kwan Shark

Robotics and Computer Vision Research Laboratory, Applied Digital Signal and Image Processing (ADSIP) Research

Centre, University of Central Lancashire, Preston PR1 2HE, U.K.

Keywords: Face Recognition, Shape Matching and Modelling, Isometric Embedding Representation, Non-Rigid

Deformation Registration.

Abstract: The aims of this paper are to introduce a 3-D shape matching scheme for automatic face recognition and to

demonstrate its invariance to pose and facial expressions. The core of this scheme lies on the combination of

non-rigid deformation registration and statistical shape modelling. While the former matches 3-D faces

regardless of facial expression variations, the latter provides a low-dimensional feature vector that describes

the deformation after the shape matching process, thereby enabling robust identification of 3-D faces. In

order to assist establishment of accurate dense point correspondences, an isometric embedding shape

representation is introduced, which is able to transform 3-D faces to a canonical form that retains the

intrinsic geometric structure and achieve shape alignment of 3-D faces independent from individual’s facial

expression. The feasibility and effectiveness of the proposed method was investigated using standard

publicly available Gavab and BU-3DFE databases, which contain faces expressions and pose variations.

The performance of the system was compared with the existing benchmark approaches and it demonstrates

that the proposed scheme provides a competitive solution for the face recognition task with real-world

practicality.

1 INTRODUCTION

Human face is one of the widely used biometric

features. It is used for subject identification with

advantages, including: naturalness, non-contact and

non-intrusiveness. Face recognition and related

research have been for many years of great interest

to computer vision and image processing

communities, which has been exploited for

applications such as public security (Chellappa,

1995), fraud prevention (Jafri, 2009) and crime

prevention and detection (Kong, 2005). A fair

amount of efforts have been made on the

development of 2-D face recognition systems using

intensity images as input data in the past. Despite 2-

D face recognition systems have a capability to

achieve good performance under controlled

conditions, they are still facing great difficulties as

facial appearances can vary significantly even for

the same individual due to differences in pose,

lighting conditions and expressions (Lu, 2003).

By using 3-D face information, it is expected to

overcome the challenges faced by 2-D face

recognition systems and improve the performance of

face recognition, since the 3-D faces contain explicit

3-D geometry which can be used to handle the

variations of face pose and expressions (Lu, 2008).

Unlike simple image normalisation and alignment in

2-D face recognition, 3-D systems usually require

more sophisticated shape matching methodologies in

order to standardise data prior to feature extraction.

This is a major challenge in 3-D face recognition as

facial shapes of the same person can be very

different due to diverse expressions (Jenkins, 2011).

Face recognition based on range images has been

investigated by a number of researchers in order to

simplify 3-D face recognition and avoid the

complicated shape matching process (Pan, 2003),

(Chang, 2003; Huang, 2012). This type of method

does not use all the 3-D information available from a

face and often ignores the shape deformation caused

by the facial expression. Chua et al. (Chua, 2002)

introduced a modified version of Point Signature to

recognize 3-D face scans with facial expressions. A

method based on the integration of matching results

from multiple regions around the nose was presented

by Chang et al. (Chang, 2006). Bronstein et al.

(Bronstein, 2005) introduced an isometric model of

facial surfaces in order to derive an expression-

invariant face representation for 3-D face

Quan W., Matuszewski B. and Shark L..

3-D Shape Matching for Face Analysis and Recognition.

DOI: 10.5220/0005180300450052

In Proceedings of the International Conference on Pattern Recognition Applications and Methods (ICPRAM-2015), pages 45-52

ISBN: 978-989-758-077-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

(a)

(b)

(c)

(d)

Figure 1: Examples of isometric embedding

transformation: (a) original faces from the same subject

across facial expressions; (b) transformed faces from row

(a); (c) original faces from different subjects; (d)

transformed faces from row (c).

recognition. The method relies on the assumption

that face is approximately isometric and the geodesic

distances among the points on the facial surface are

preserved under facial expressions. Lu et al. (Lu,

2008) proposed a 3-D deformation modelling

scheme that is capable of handling facial expression

variations. With assistance of automatically

extracted landmarks, a deformable model was built

linearly, and the method has been applied to the

problem of matching multiview facial scans to a

neutral facial model. Mpiperis et al. (Mpiperis,

2007) proposed a geodesic polar parameterisation of

the facial surface. With the parameterisation, the

intrinsic surface attributes do not change under the

isometric deformation caused by facial expressions.

A representation of patch geodesic moment for 3-D

face recognition was proposed by Hajati (Hajati,

2012). This patch-based local pattern combines local

and global geodesic paths with patches in a coarse to

fine hierarchical computation for each surface point.

One of the common approaches for 3-D face

recognition is to register a probe face to each gallery

face and then calculate the sum of the distances

between their points. This is computationally

expensive and sensitive to facial expresion

variations. To improve the efficiency,

Mohammadzade et al. (Mohammadzade, 2013)

introduced an iterative normal point method for

finding the corresponding points between a probe

face and gallery faces. The method can also cope

with the changes of facial expressions.

The statistical-model based face recognition has

been one of the most successful techniques over the

past few decades. In this paper, a 3-D shape

matching scheme is proposed, which works in

conjunction with statistical shape modelling to

complete the task of face recognition. An isometric

embedding shape representation is used for the

neutralisation of 3-D faces with facial expressions so

that the non-rigid deformation problem caused by

facial expressions can be handled and the locality

preserving projection (LPP) is used in the

dimensionality reduction process to construct the

statisitical shape model. One of the novel

contribution of the paper is the use of the isometric

embedding transformation. It not only enables the

shape representation of 3-D faces indepdenet from

individual’s facial expressions, but also reduces the

complexity of the dense point correspondence search

in the shape matching. Further more, the proposed

methods uses only 3-D point clouds with texture not

being used at all. The method is therefore inherently

invariant to variations in scenes illumination

conditions, background clutter and to some extent

angle of view. This is in striking contrast to the

method based on texture where these factors

severely limit their practical applicability.

The remainder of the paper is organised as

follows. Section 2 introduces the concept of the

isometric embedding shape representation. Then,

further shape alignment based on thin-plate spline

(TPS) surface warping is described in Section 3.

Section 4 explains the LLP dimensionality reduction

method. Section 5 describes the fitting approach for

new dataset. The experimental results are shown in

Section 6 with concluding remarks in Section 7.

2 ISOMETRIC EMBEDDING

SHAPE REPRESENTATION

Expression-invariance is of particular importance as

most of the face recognition systems have to cope

with various facial expressions. Isometric

embedding shape representation was proposed by

Elad and Kimmel (Elad, 2003), which provides a

possibility for expression-invariant face recognition.

In this work, the isometric embedding shape

representation is used to minimise the shape

ICPRAM2015-InternationalConferenceonPatternRecognitionApplicationsandMethods

(a)

(b)

Figure 2: Further shape alignment: (a) canonical faces

with 83 facial landmarks; (b) reference faces after

alignment.

variation across different 3-D faces from the same

individual, with the shape variations mainly caused

by facial expressions. Isometric embedding shape

representation assumes that different 3-D facial

scans from the same individual are isometric to

his/her 3-D facial scan of the neutral expression,

therefore they can be transformed to approximate the

shape of the neutral face. The new representation

provided by the isometric embedding transformation

is known as canonical form, which has the Euclidean

metric structure of the facial surface with the

geodesic replaced by Euclidean distance (Bronstein,

2007).

Figure 3: 3-D projection of LPP feature subspace for six

subjects with various facial expressions.

Multidimensional Scaling (MDS) is one of the

popular approaches for obtaining the canonical form

of faces (Bronstein, 2006). Given a smooth surface

that has been sampled at N points

{ ,..., }



(typically, N is approximately 3000 for a reasonable

surface description of a human face), with a matrix

of geodesic distance

[]



 between each pair of

surface points, each point



in the embedding space



is given by

(, )

kkk





 . The geodesic distances

are calculated by some explicit or efficiently

approximated function

(, ) (, )

ij ij ij



 





where

represents geodesic distance. MDS solves

the following optimisation problem

arg min ( , )









(1)

where

( ,..., )







is an

3N 

matrix of

coordinates in



corresponding to points

{ ,..., }



on the surface, and



is an embedding error

criterion function, measuring the discrepancies

between the original geodesic distances and the

embedding space Euclidean distances. The most

common choices include the raw stress

(,) ( () )

raw ij ij





   



(2)

and the normalised stress

(() )

(,)

()

ij ij

norm









 





(3)

where

()



is the short notation for

(, )





. The

usual algorithms for solving the MDS problem are

Newton, Quasi-Newton and gradient-descent

optimisation (Bronstein, 2006). In this work, the

Newton optimisation approach is applied to achieve

the isometric embedding transformation. Figure 1

shows examples of 3-D faces before and after the

transformation. From Figure 1(b), it is seen that the

3-D shapes of the same subject with different facial

expressions appear to be similar after the

transformation, and this illustrates the goodness of

shape variance offered by the transformation for

recognition of a person independent from

individual’s facial expressions.

3 FURTHER SHAPE

ALIGNMENT

Alignment of 3-D faces in the training dataset is

essential for statistical model construction since

inappropriate alignment will result in erroneous

dense point correspondences. As the shape

deformation related to the facial expression is much

reduced by the isometric embedding transformation,

the remaining differences is the shape across the

faces of different subjects in the training dataset as

shown in Figures 1 (c) and (d). A further shape

alignment is achieved by Thin-Plate Spline (TPS)

surface warping (Quan, 2009). The alignment starts

3-DShapeMatchingforFaceAnalysisandRecognition

with the selection of a reference face from the

training dataset. The reference canonical face

usually contains a neutral facial expression. It is then

warped to align with other canonical faces in the

training dataset using the TPS transformation, which

is calculated based on the selected landmarks on the

faces. For the results reported here, 83 landmarks

provided in the BU-3DFE database (Yin, 2006),

were used for that purpose. For the Gavab database

(Moreno, 2004), the same 83 landmarks were

manually labelled on each training face. Figure 2

shows examples of the further shape alignment. It

can be seen that after the alignment the transformed

canonical reference faces of different subjects in

Figure 2(a) are closely matched to each other in

Figure 2(b). Thus the pair-wise dense point

correspondences between the warped canonical

reference face and other canonical faces from the

training dataset can be established by pairing points

based on the closest distance metric (Quan, 2009).

These corresponding points later provide the basis

for building a statistical shape model.

4 DIMENSIONALITY-

REDUCTION METHOD

Dimensionality-reduction is usually applied with

statistical shape modelling approaches. Principal

component analysis (PCA) and linear discriminant

analysis (LDA) are the popular choices, when data

lie in the linear subspace of a high dimensional

space. The locality preserving projection (LPP) is

able to handle a wider range of data variability while

preserving local structure, which often links the

structure of the manifold (He, 2005). Therefore it

suggests that LPP can perform well on the task of

face recognition even under the influence of facial

expressions.

LPP is a technique with isometric mapping from

the original data space to the reduced low

dimensional space (Hastie, 2001). The optimality

criterion to minimise,

() () 2

()

, , 1, 2,..., , 1, 2, ,

kij

ij N k d 





(4)

where

()

y ax

describes the k-th coordinate of

vector

y 

representing the j-th training face

x 

in a lower dimensional space, dn



 .

[]

Ss is the adjacency matrix, which defines the

weighted similarity graph for all connected vertices,

and can be computed as,

exp( / 2 )

ij i j

sxx





(5)

where



is calculated as,

min

jx x











(6)

To enforce a non-trivial solution to the problem

posed in Equation 4, vectors

a should fulfil the

following constraint,

TTT

XDX aa. In this case, the

solution is given by solving the following

generalised eigenvalue problem:

ii i

XLX XDXaa



(7)

where X contains all the training faces,

LDS





with

[]



ii i j





d 

, for all

,ijdD





An example from the separability study of the

LPP-based method by reducing the dimensionality

for visualisation is provided in Figure 3, where the

LPP features of 150 faces from six persons with 25

expressions per person (taken from BU-3DFE

database) are projected to a 3-D space. As can be

seen, the output samples are well grouped in six

clusters corresponding to the six individuals and

exhibitings a good inter-person separability against

facial expressions even in a low dimensional space.

Figure 4: Rank-1 recognition accuracy versus feature

subspace dimensions.

5 NEW DATASET FITTING

After the eigenvectors of the constructed models are

extracted, the estimation of feature vectors can be

ICPRAM2015-InternationalConferenceonPatternRecognitionApplicationsandMethods

Figure 5: CMC curves of recognition accuracy for the

proposed and exiting benchmark methods.

undertaken in order to synthesize faces in a new set

of data. This is usually achieved by recursive data

registration, such as modified Iterative Closest Point

(ICP), in which the shape and pose parameters are

iteratively estimated in turn. While pose parameters

control the orientation and position of the model,

shape parameters encapsulate deformation of the

model. In order to solve all unknown parameters

effectively, the following standard optimisation

scheme is used:

1. Apply isometric embedding transformation to

the new face.

2. Align model and new face by using their

centroid point, to minimise translation

difference.

3. Apply isometric embedding transformation to

both model and new face.

4. Use ICP algorithm to estimate dense point

correspondences between transformed model

and new face.

5. Estimate feature vector

α for the new face

using back-projection based on the original

data, described as



opt

Aα x

(8)

where



is the estimated dense point

correspondences for a test face and A

opt

is the

matrix containing eigenvectors.

6. Generate a new instance of the statistical model

using the feature vector and repeat steps 2 to 5

until the pre-set convergence condition is

reached.

In this optimisation scheme, the isometric

embedding shape representation serves the similar

purpose as applied to the training dataset, which

reduces partial shape difference on both model and

new face. This potentially improves the dense point

correspondence search and provides better

estimation for the later stages of the optimisation.

Since vector

α controls the shape of the model, it

can be used as the feature vector for classifying face

identity.

6 EXPERIMENTAL RESULTS

To demonstrate the effectiveness of the proposed

method for the purpose of face verification and

recognition, two public databases, BU-3DFE (Yin,

2006) and Gavab (Moreno, 2004), were utilised for

the evaluation in this work. While the former was

used for evaluating performance related to the

dimensions of feature subspace and facial expression

changes; the latter was used to further observe its

robustness to facial expression changes as well as

pose variations. For the sake of simplicity, the

nearest-neighbour classifier was chosen for the

feature classification in this study. The two popular

dimensionality-reduction methods, PCA and LDA,

are also compared along with other benchmark

approaches.

6.1 Experiments on BU-3DFE

Database

The BU-3DFE database consists of 2,500 3-D faces

from 100 subjects, ranging from 18 to 70 years old,

with a variety of ethnic origins including White,

Black, East-Asian, Middle East Asian, Indian and

Hispanic Latino. Each subject has seven

expressions, one neutral and six universal

expressions: anger, fear, disgust, happiness, sadness

and surprise. With the exception of the neutral

expression, each of the six universal expressions

includes four levels of intensity.

6.1.1 Feature Subspace Dimensions

The first experiment looks at the face recognition

performance against feature subspace dimension. All

2,500 faces available in BU-3DFE database were

used in the experiments. The faces were divided into

ten subsets with each subset containing the same 100

subjects and all seven kinds of expressions. For each

feature subspace dimension, one subset is selected

for testing while the remaining subsets were used for

training. Such experiments were repeated ten times

with a different subset selected for testing each time.

The faces in the training set are not used in testing.

3-DShapeMatchingforFaceAnalysisandRecognition

Table 1: Recognition comparison on BU-3DFE database.

Figure 4 shows the plots of rank-1 recognition rate

versus the dimensions of the feature-subspace. It is

seen that the LPP-based approach significantly

outperforms PCA and is able to achieve similar

results to LDA-based methods but with lower

dimensional subspace used. The highest recognition

rate for PCA is 79%, whereas both LDA and LPP

can reach 100% with 15 and 10 dimensional

subspace used, respectively.

6.1.2 Facial Expression

The robustness to facial expression variation is an

important aspect in the face recognition task. To see

how the proposed methods cope with this issue, a

comparison was made with that of the state-of-the-

art methods, including patch geodesic moments

(Mpiperis, 2007), geodesic polar representation

(Hajati, 2012) and canonical image representation

(Bronstein, 2005). The same experimental protocol

used in (Hajati, 2012) was applied in this work. The

performance was measured in terms of rank-1

recognition accuracy and the Cumulative Matching

Characteristics (CMC) (Rizvi, 1998). All the faces

with the neutral expression were used for training,

while the rest of database was used as the testing

faces. The rank-1 recognition rates were tabulated in

Table 1. From the table, it can be seen that among

the proposed methods the LPP-based approach

achieved the highest recognition rate with an

average accuracy of 92%, outperforming the other

state-of-the-art expression-invariant techniques by

around 8%. It is worth noticing that its recognition

rates for different expressions range from 88% to

96%. This shows that the proposed scheme can

handle facial expression changes well. The CMC of

the proposed methods together with those

benchmark methods are shown in Figure 5. From the

figure, it can be noticed that the recognition rate of

the LPP-based method is always higher.

6.2 Experiments on Gavab Database

The Gavab database is one of the most expression-

rich and noise-prone 3-D face datasets available to

the public (Moreno, 2004). It consists of 549 scans

from 61 different subjects. The subjects, of which 45

are male and 16 are female, are all Caucasian. Each

subject was scanned 9 times for different poses and

expressions, giving six neutral scans and three scans

with an expression. The scan with pose variations

contains one scan while looking up (+35

), one

while looking down (-35

), one for the left profile (-

), one for the right profile (+90

) as well as one

with random poses. The scans without pose changes

include two different frontal facial scans, one with

smile, and one with an accentuated laugh.

In order to evaluate the expression and pose

invariance, the proposed approach is compared with

the results achieved by the existing benchmark

methods reported in (Drira, 2010). The same

experimental protocol introduced in (Drira, 2010)

was used here. The benchmark methods include

sparse representation (Li, 2009), 3-D ridge images

(Mahoor, 2009), concave and convex regions

(Berretti, 2006) and elastic radial curves (Drira,

2010). In the experiment, one of the two frontal

scans with the neutral expression provided for each

person was taken as the training data. The rest of the

scans were used for testing. Since the proposed

approach is not designed for working on facial scans

with large part of missing data, the scans for the left

and right profiles were not included for testing.

Table 2 illustrates the results of the rank-1

recognition accuracy for different categories of

testing faces. From the table, it can be seen that the

proposed approach provides a high recognition

accuracy on both expression and pose variations,

and outperforms majority of the existing methods

with its performance very close to the best

recognition accuracy achieved by the elastic radial

curves (Drira, 2010).

ICPRAM2015-InternationalConferenceonPatternRecognitionApplicationsandMethods

Table 2: Recognition comparison on Gavab database.

7 CONCLUSIONS

An effective 3-D shape matching scheme for pose

and expression-invariant face recognition has been

presented in this paper. The key contribution of the

proposed work is to use isometric embedding shape

representation and statistical modelling techniques to

achieve accurate dense point correspondences and

generate appropriate shapes for new 3-D face data.

From the experimental results on the Gavab and BU-

3DFE database, it can be concluded that the LPP-

based approach offers a recognition rate that can be

as high as nearly 100% and is more expression-

invariant compared with the existing benchmark

approaches. The research will be extended further by

taking into consideration more practical factors. One

possible extension for the work is to evaluate the

ability of the proposed algorithm using more

databases that are produced by different devices

operated under various acquisition environments.

The missing data problem can also be introduced

and dealt with by modifying the shape matching

scheme. Finally, more sophisticated pattern

recognition methods can be applied to increase the

overall performance of the proposed method.

ACKNOWLEDGEMENTS

The work presented in this paper was supported by

the Engineering and Physical Sciences Research

Council (Grant numbers EP/D077540/1 and

EP/H024913/1) and the EU FP7 Project

SEMEOTICONS.

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ICPRAM2015-InternationalConferenceonPatternRecognitionApplicationsandMethods