Image and Vision Computing 28 (2010) 1039–1048

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Image and Vision Computing

journal homepage: www.elsevier .com/ locate / imavis

Facial gender classification using shape-from-shading q

Jing Wu *, William A.P. Smith, Edwin R. HancockDepartment of Computer Science, The University of York, York, YO10 5DD, UK

a r t i c l e i n f o

Article history:Received 14 June 2008Received in revised form 2 September 2009Accepted 14 September 2009

Keywords:Gender classificationPrincipal geodesic analysisShape-from-shading

0262-8856/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.imavis.2009.09.003

q Expanded version of a paper presented at theConference (Warwick, September 2007).

* Corresponding author. Tel.: +44 0 1904 432709; fE-mail addresses: jwu@cs.york.ac.uk (J. Wu), w

Smith), erh@cs.york.ac.uk (E.R. Hancock).

a b s t r a c t

The aim in this paper is to show how to use the 2.5D facial surface normals (needle-maps) recoveredusing shape-from-shading (SFS) to perform gender classification. We use principal geodesic analysis(PGA) to model the distribution of facial surface normals which reside on a Remannian manifold. Weincorporate PGA into shape-from-shading, and develop a principal geodesic shape-from-shading (PGSFS)method. This method guarantees that the recovered needle-maps exhibit realistic facial shape by satis-fying a statistical model. Moreover, because the recovered facial needle-maps satisfy the data-closenessconstraint as a hard constraint, they not only encode facial shape but also implicitly encode image inten-sity. Experiments explore the gender classification performance using the recovered facial needle-mapson two databases (Notre Dame and FERET), and compare the results with those obtained using intensityimages. The results demonstrate the feasibility of gender classification using the recovered facial shapeinformation.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction 1.1. Literature review

Correct gender identification plays a significant role duringface-to-face communication between humans, and improves theinteraction between humans and machines. An accurate and reli-able gender classification approach can also improve the perfor-mance of face identity recognition. Therefore face genderclassification has attracted significant attention in computer vision[1–16,39–45], as well as in psychology [17–20]. However, althoughstudies [18] have shown that gender is not only revealed by 2D fa-cial texture, but also has a close relationship with the 3D shape ofthe human face, relatively few studies have investigated the role of3D shape in gender classification [14]. To some extent this is due tothe more complex computations required in 3D face shape analy-sis, and the limited effectiveness and high cost of the 3D sensorscurrently available. In this paper, we explore the alternative ofusing a 2.5D representation based on facial surface normals (or fa-cial needle-maps) for gender classification. The needle-map is ashape representation which can be acquired from 2D intensityimages using shape-from-shading (SFS). Therefore it avoids prob-lems caused by the limitations of current 3D sensors, and providesshape information.

In this section, we first review the previous work on gender classi-fication in computer vision together with the literature on SFS. Then,we show how gender classification can be realized using facial nee-dle-maps. Finally, we outline the main contributions of this paper.

ll rights reserved.

18th British Machine Vision

ax: +44 0 1904 432767.smith@cs.york.ac.uk (W.A.P.

Depending on the type of features used, current gender classifi-cation methods fall into two main categories. The first is geometri-cally based gender classification which uses biometric featuressuch as the dimensions of the face, the salient features (eyes, nose,mouth, etc.), and the distances between the salient feature points.In [1], two competing HyperBF networks were trained using 16geometrical features. Burton et al. in [17] extracted 73 points fromfull-face photographs and 34 points from the profile views, andmeasured the 2D and 3D distances between points. The methodachieved an accuracy approaching human performance (94%accuracy).

The second class of methods are appearance based, and makeuse of facial image contents without extracting any geometricfeatures. In the case of low-resolution ’thumbnail’ images, theentire image is provided as features for gender classification[5,16]. An alternative approach is to use image subspace tech-niques to reduce the dimensionality of the problem. Jain andHuang [9] extracted features by applying independent compo-nent analysis to face images. Buchala etc. [10] applied principalcomponent analysis (PCA) and explored the PCA componentsthat gave the greatest gender discrimination using linear dis-criminant analysis (LDA). In [11], genetic algorithms were ap-plied to PCA feature vectors to select the gender discriminatingfeature subset. Recently, Lu et al. in [12] explored the use of apixel-pattern-based texture feature for gender classification. Thismethod is motivated by the idea that face images can be re-garded as a composition of micro-patterns. The pattern tem-plates were obtained through PCA, and Adaboost was used toselect the discriminating feature subset. Active appearance

1040 J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048

models (AAM) [21] have also been used as a feature extractionmechanism in gender classification. In [13], the AAM was com-pared with ICA for gender classification using four different clas-sifiers. In [15], Saatci and Town utilized AAM and support vectormachine (SVM) for gender and expression recognition.

Learning the classifier is another important issue in gender clas-sification. Fleming and Cottrell [2] used a two-layer neural network.The first layer was for image compression (feature extraction) andthe second for classification. Colomb etc. [3] adopted a similartwo-layer neural network called SexNet. Gutta etc. [4] used a mix-ture of experts consisting of ensembles of radial basis functions(RBFs). Here decision trees and support vector machines are usedto implement the gating network components. In [5], Moghaddamand Yang demonstrated the superiority of nonlinear SVMs over tra-ditional linear pattern classifiers together with RBFs and largeensemble-RBF networks. An accuracy of over 96% was reportedon the FERET face database. Kim et al. [6] performed gender classi-fication using Gaussian process classifiers, which are a class ofBayesian kernel classifiers. This technique overcame the difficultyencountered by SVMs in determining the hyperparameters for thekernels. A fuzzy SVM approach [45] has also been developed re-cently to improve the generalization ability for gender classifica-tion. Another popular approach to gender classification isAdaboost. This type of classifier is much faster than SVMs, and rep-resents a better choice for real-time applications. Shakhnarovichet al. [7] applied a thresholded weak classifier variant of Adaboostto detected face images for gender classification. Wu et al. [8] usedthe weak classifier Adaboost approach together with a look-up-ta-ble to learn gender classifiers. Baluja et al. [16] explored using Ada-boost on low resolution grayscale face images and achieved over93% gender classification accuracy with 50 times faster perfor-mance than the SVM-based classifiers. Recently, Makinen and Rai-samo [39,40] combined face detection and gender classification,and gave a comprehensive comparison of state-of-the-art genderclassification methods. Small differences in the classification ratesbetween the methods were reported. However a combination ofneural network and Adaboost classifiers were recommended whereclassification speed is important. Moreover, in [39], Makinen andRaisamo also suggested to improve the classification rate by com-bining the outputs of different gender classifiers.

Recent developments included gender classification from vid-eos [41] by combining facial appearance and motion. However,there is little work aimed at using 3D information for gender clas-sification. Lu and Chen [14] exploit range information extractedfrom human faces for gender classification, and combine the regis-tered range and intensity images. Their experimental results dem-onstrate that combining 3D range data provides betterclassification accuracy than using the 2D intensity images alone.In our previous work [42–44], we have investigated gender classi-fication using facial needle-maps taken from range images. In thispaper, we investigate the classification performance of using nee-dle-maps recovered using shape-from-shading.

Shape-from-shading provides a means of recovering 3D sur-faces from single 2D images. However, the local convexity-concav-ity instability and the bas-relief ambiguity have limited theeffectiveness of SFS in recovering realistic 3D facial shape. Oneway to overcome this problem is to use domain specific con-straints. Both Prados and Faugeras [23] and Castelan and Hancock[24] used the location of singular points to enforce convexity onthe recovered surfaces. Zhao and Chellappa [25], on the other hand,have introduced a geometric constraint which exploits the approx-imate bilateral symmetry of faces. Atick etc. [26] proposed a statis-tical shape-from-shading framework using principal componentanalysis to parameterise facial surfaces. Samaras and Metaxas[27] adopted a similar approach by incorporating reflectance con-straints derived from shape-from-shading into a deformable face-

model. However, none of these methods has been used for genderclassification.

1.2. Contribution

Although the determination of gender from facial images hasbeen the focus of sustained activity over the past 20 years, mostof the existing work is based on 2D intensity images alone. How-ever, few studies [14] have investigated the role of 3D facial shapein gender classification. In this paper we address this gap in the lit-erature, and present a statistical framework for gender classifica-tion based on 2.5D facial needle-maps. In this way facial shapecan be recovered from intensity images using SFS.

We use an iterative SFS method [28], referred to as principalgeodesic SFS (PGSFS), for the recovery of the facial needle-maps.This PGSFS method not only satisfies the data-closeness constraintas a hard constraint [29], but also guarantees that the recoveredneedle-maps satisfy the shape constraints provided by a statisticalmodel which captures the distribution of facial surface normals.

Facial needle-maps can be considered as points on the Rie-mannian manifold S2ðNÞ. For data residing on a Riemannian mani-fold, principal geodesic analysis (PGA) [30,31], which is ageneralization of principal component analysis, is better suited tothe analysis of data than PCA. We make use of PGA to constructa statistical model from a set of ground-truth facial needle-maps,and then combine the model with SFS to recover needle-maps fromthe intensity images. The recovered needle-maps are representedby their PGA parameters.

Our gender discrimination method is based on applying lineardiscriminant analysis (LDA) to the PGA parameters for a set oftraining data. In this way we extract a scalar gender discriminatingattribute from the set of PGA parameters using a LDA transformmatrix. From the training set, we also estimate the distributionof the scalar attribute for different genders. A Bayes classifier isused to discriminate gender for data in the test set. This classifica-tion strategy is simple, and the results are not necessarily betterthan those obtained using the state-of-the-art approaches. How-ever, the focus of this paper is to investigate the feasibility of gen-der classification using facial shape information recovered fromintensity images. The results reported in the experiments couldbe improved using more sophisticated classifiers such as SVMs.

We compare the results obtained with PGSFS with those ob-tained using PCA on intensity images and those obtained usingPGA on range data. Experimental results show that our methodachieves comparable and even improved gender classificationaccuracy to those achieved on intensity images or range data. Thisdemonstrates the feasibility of performing gender classification inconjunction with SFS. We also compare our method with the clas-sification results obtained by human subjects. The results showthat gender classification using PGSFS outperforms humanobservers.

The outline of the paper is as follows. Section 2 describes how touse the PGA method to construct the statistical model for facialneedle-maps, and describes how to incorporate the statisticalmodel into SFS (PGSFS) to recover facial shapes. Section 3 reviewsthe LDA method and the Bayes classifier used in our work. In Sec-tion 4, firstly, a description of the data set and the normalizationmethod used to align the data is given. Secondly, the experimentalresults are presented and discussed. Finally, Section 5 concludesthe paper.

2. Facial shape recovery

We aim to recover facial needle-maps using an iterative SFSmethod, referred to as principal geodesic SFS (PGSFS). The idea is

J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048 1041

to augment shape-from-shading using a statistical model that cap-tures variations present in fields of surface normals extracted fromhuman faces. Being instances of this statistical model, the recoveredfacial needle-maps are guaranteed to be valid for human faces. In thissection, we first describe how to model the distribution of surfacenormals, and then introduce how to incorporate the statistical modelinto SFS.

2.1. A statistical surface normal model

A unit surface normal n may be considered as a point residingon a spherical manifold n 2 S2. Facial needle-maps, which are fieldsof N surface normals, may be considered as a point on the manifoldS2ðNÞ ¼

QNi¼1S2. To model the distribution of data on this manifold,

we turn to principal geodesic analysis (PGA) which makes use ofexponential/log maps and intrinsic means.

2.1.1. Exponential and log mapsIn the space S2, with the metric being the usual one induced by

embedding in 3D Euclidean space, geodesics correspond to greatcircles. Given u 2 TnS2, a non-zero vector on the tangent plane toS2 at the point n ðn 2 S2Þ, there exists a unique geodesic passingthrough n in the direction of u. The exponential map, denotedExpn, maps u to the point, denoted ExpnðuÞ, on the geodesic in thedirection of u at distance kuk from n. This is illustrated in Fig. 1.The log map, denoted Logn is the inverse of the exponential map.Making use of exponential/log maps, the geodesic distance be-tween two points n1 and n2 2 S2 can be expressed asdðn1;n2Þ ¼ kLogn1

ðn2Þk. In the S2ðNÞ space, the exponential andlog maps are simply the products of N copies of the maps for S2

given above.

2.1.2. Intrinsic meansTo characterize the mean of surface normals which are spheri-

cal directional data, we make use of intrinsic means. Intrinsicmeans minimize the sum-of-squared geodesic distances on a man-ifold M and satisfy the computation:

l ¼ arg minx2M

XK

i¼1

dðx; xiÞ2:

For a spherical manifold, the geodesic distance is the arc lengthdðx; xiÞ ¼ arccosðx � xiÞ, and the intrinsic mean of a set of surface nor-mals n1; . . . ;nK 2 S2 can be found using the gradient descent methodof Pennec [31]:

lðtþ1Þ ¼ ExplðtÞ1K

XK

i¼1

LoglðtÞ ðniÞ( )

: ð1Þ

The intrinsic mean l 2 S2ðNÞ of a set of K needle-maps can be foundby replacing the exponential and log maps in Eq. (1) with the corre-sponding maps for the space S2ðNÞ as mentioned above.

Fig. 1. The exponential map.

2.1.3. Principal geodesic analysisPGA is a generalization of PCA from data residing in a Euclid-

ean space to data residing on a Riemmanian manifold. The goalof PCA is to locate a linear subspace of the space in which thedata lies, and maximize the projected variance of the data. InPGA, the notion of linear subspace is replaced by that of a geode-sic submanifold. The geodesics that traverse the submanifold arereferred to as principal geodesics. They are analogous to theprincipal axes in PCA, except that each principal axis in PCA isa straight line. In the spherical case, a principal geodesic corre-sponds to a great circle. To project a point n1 2 S2 onto a greatcircle G is to find the point on G that is nearest to n1 in geodesicdistance. The projection pG : S2 ! G is defined as:

pGðn1Þ ¼ arg minn2G

dðn1;nÞ2:

For a geodesic G passing through the intrinsic mean l, this projec-tion can be approximated linearly in the tangent space TlS2:

LoglðpGðn1ÞÞ �Xd

i¼1

vi � Loglðn1Þ;

where v1; . . . vd is an orthonormal basis for TlS2, and can beobtained through standard PCA. Then, the principal geodesics forthe S2 space are obtained under exponential map ExplðviÞ; i ¼1 . . . d. This approximation enables us to compute the principal geo-desics by applying PCA in the tangent plane TlS2.

2.1.4. PGA for needle-mapsIn this section, we show how to apply PGA to a set of example fa-

cial needle-maps for the purpose of learning a statistical model of fa-cial shape. Suppose there are K example facial needle-maps eachhaving N pixel locations. The surface normal at the pixel location lfor the kth needle-map is nk

l . We calculate the intrinsic mean ll ofthe distribution of surface normals n1

l ; . . . nKl at each pixel location l.

The surface normal nkl is then represented by its log map position

ukl ¼ Logll

ðnkl Þ in the tangent plane Tll

S2. Fig. 2 illustrates this pro-cess. On the left of the figure is the distribution of surface normalsat one pixel location l, which are shown as points on a unit sphere.The mean ll is shown as a red star. On the right is the log mappedpositions of the points with the mean as the center of the projection.For the kth training needle-map, we concatenate the x; y-coordinatesof uk

l at the N pixel locations, and form the log mapped long vectoruk ¼ ½uk

1x;uk1y; . . . ;uk

Nx;ukNy�

T in the tangent plane TlS2ðNÞ. The K longvectors form the column-wise data matrix U ¼ ½u1j . . . juK �, and thecovariance matrix is L ¼ 1

K UUT .Because N, the dimension of the facial needle-maps, is often too

large to make the calculation of L feasible, we use the numericallyefficient snap-shot method of Sirovich [32] to compute the eigen-vectors of L. Accordingly, we construct the matrix bL ¼ 1

K UT U, andlocate its eigenvalues and eigenvectors. The ith eigenvector ei of Lcan be computed from the ith eigenvector ei of bL using ei ¼ Uei.The ith eigenvalue ki of L equals the ith eigenvalue ki of bL wheni 6 K . When i > K; ki ¼ 0. In our experiments, we use the K � 1leading eigenvectors of L as the columns of the eigenvector matrix(projection matrix) U ¼ ðe1je2j . . . jeK�1Þ, where K is the number oftraining data samples.

Given a facial needle-map, we first compute its log mapped longvector u ¼ ½u1x;u1y; . . . ;uNx;uNy�T in the tangent plane TlS2ðNÞ, thenthe corresponding PGA parameter vector is b ¼ UT u. Given the PGAparameters b ¼ ½b1; . . . bK�1�T , we can generate a needle-map using:nl ¼ Expll

ððUbÞlÞ at each location l.

2.2. Incorporating the statistical model into SFS

With the mean l and projection matrix U of the statistical model,constructed using PGA from the sample facial needle-maps, at hand,

Fig. 2. Projection of surface normals on the unit sphere to points on the tangent plane at the mean.

Fig. 4. Restoring a normal to the closest position on the reflectance cone.

1042 J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048

we are able to augment SFS using this model in an iterative way. ThisSFS method is referred to as principal geodesic SFS (PGSFS). The stepsof this SFS method are illustrated in Fig. 3. The facial needle-map isinitialized as the intrinsic mean of the statistical model nð0Þ ¼ l. Ateach iteration, the facial needle-map satisfies a strict global con-straint by projection onto the statistical model (statistical con-straint), as well as a hard local constraint by satisfying the imageirradiance equation (brightness constraint).

2.2.1. Satisfying the statistical constraintGiven a current estimated facial needle-map nðtÞ, we can first

compute its log mapped long vector uðtÞ ¼ LoglnðtÞ, and then obtainits best fit PGA parameters bðtÞ ¼ UT uðtÞ. Then the half way updatedfacial needle-map, which is an instance of the statistical model, canbe generated as nðtÞ ¼ ExplðUbðtÞÞ. Because the statistical modelcaptures the variance structure of facial needle-maps, by satisfyingthe statistical constraint guarantees that the generated facial nee-dle-map has a realistic appearance. This overcomes the well-known local convexity-concavity instability problem in previousSFS methods [22].

2.2.2. Satisfying the brightness constraintLet Il 2 R denote the intensity at the pixel location l. According

to Worthington and Hancock [29], when the surface reflectancefollows Lambert’s law Il ¼ nl � s, then the surface normal is con-strained to fall on a cone whose axis is in the light source directions and whose opening angle is a ¼ arccos Il. With nðtÞ generated fromthe statistical model at hand, in order to enforce this brightnessconstraint, we rotate the normal at each pixel location l back toits closest on-cone position. This is equivalent to moving each sur-face normal nðtÞl 2 S2 along a passing geodesic from s 2 S2 a distancearccos Il. This is demonstrated in Fig. 4 which shows the tangentplane TsS

2. The updated surface normal at pixel location l is

nðtþ1Þl ¼ Exps arccosðIlÞ

LogsðnðtÞl Þ

kLogsðnðtÞl Þk

( ):

Fig. 3. The proce

Since the facial needle-map satisfies the brightness constraint as ahard constraint, they effectively encode the original image data. Inother words, the original image can be recovered from theneedle-map. As a result, the needle-map implicitly encodes imageintensity.

2.2.3. AlgorithmThe PGSFS algorithm can be summarized as follows:

1. Initialize: nð0Þ ¼ l, where l is the intrinsic mean of the model.Set iteration t ¼ 0.

2. Estimate PGA parameters: bðtÞ ¼ UT loglðnðtÞÞ. Generate best fitnormals: nðtÞ ¼ ExplðUbðtÞÞ.

3. Update normals: nðtþ1Þ ¼ Exps arccosðIÞ: � LogsðnðtÞÞkLogsðnðtÞÞk

n o, where the

operator :� denotes the component-wise product of any twovectors of the same length. Set t ¼ t þ 1.

4. Stop if t > max iterations.Upon convergence, the output n is the closest on-cone positionof its statistical model instance. Therefore it not only satisfies

ss of PGSFS.

J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048 1043

data-closeness constraint, but also satisfies the statistical modelwhich guarantees that the recovered shape realistically resem-bles a human face.

3. Feature extraction and gender classification

The recovered facial needle-maps are represented by the PGAparameters: b ¼ UT loglðnÞ. However, the parameter vectors inevi-tably contain information which is either redundant or irrelevantto the gender classification task, and cause a deterioration in clas-sification accuracy. To overcome this problem, we aim to extractthe most significant features for gender by applying a discriminantanalysis method to the PGA parameters. Classification is then per-formed on the extracted features. Linear discriminant analysis(LDA) is a widely used discriminant analysis method. It is simpleto implement and is computationally efficient. Moreover, its effec-tiveness for classification is guaranteed when the input data arelinearly separable. Therefore, in our gender classification task, wechoose LDA as the dimensionality reduction method.

3.1. Linear discriminant analysis

Given a set of labeled training data, LDA [33,34] utilizes the la-bel information to find the directions in the underlying space thatbest discriminate among classes. The transformation matrix Wopt ischosen in such a way that the ratio of the between class scatter andthe within class scatter is maximized, i.e.

Wopt ¼ arg maxWTraceðWT SbWÞTraceðWT SwWÞ

where Sb is the between class scatter matrix, and Sw is the withinclass scatter matrix. The solution is given by

Wopt ¼ ½w1jw2j . . . jwm�

where wiði ¼ 1 . . . mÞ are the generalized eigenvectors which satisfy

Sbwi ¼ kiSwwi; i ¼ 1;2; . . . ;m ð2Þ

For our gender classification, there are 2 classes denotetd asc ¼ ffemale;maleg. The training data are the PGA parameters ofthe recovered facial needle-maps. Suppose class c has Kc labeledsamples fbkjk ¼ 1 . . . Kcg in the training set. Then, the between classand within class scatter matrices are defined as follows,

Sb ¼X

c

Kcðbc � bÞðbc � bÞT

Sw ¼X

c

XKc

k¼1

ðbk � bcÞðbk � bcÞT

where b is the global mean for the training samples and bc is themean for class c.

A direct way to solve the generalized eigen-problem of Eq. (2) isto compute the inverse of Sw, and to perform eigen decompositionon the matrix S�1

w Sb. However, for gender classification using faceimages, the image dimension is often larger than the number oftraining samples K. Since the rank of Sw is at most K � 2, then Sw

is often singular. To avoid this problem, in most applications it isusual to first apply subspace techniques such as PCA to the trainingimages to reduce the dimensionality of the original data. In ourwork, LDA is applied to the PGA parameters of the facial needle-maps used for training. These PGA parameters are truncated tobe K � 2 dimensional by keeping the first K � 2 components. Sincethe PGA parameters are already of zero-mean over the trainingsamples, the between class scatter can be simplified by ignoring

the centering operation, which involves subtracting the globalmean b.

There are only one nonzero generalized eigenvalues for the gen-eralized eigen-problem (2) for gender classification. Therefore weextract a scalar attribute for each facial needle-map using thetransformation matrix Wopt .

3.2. Classification

Using PGA and LDA, we obtain a scalar attribute for each facialneedle-map. A Bayes classifier can be applied to these scalar attri-butes to classify the test faces on the basis of gender.

Let c ¼ ffemale;maleg denote the female and male gender clas-ses, x denote the scalar attribute of a test facial needle-map. Thenaccording to the Bayes rule, the probability that the test face is ofclass c is:

PðcjxÞ ¼ PðxjcÞPðcÞPcPðxjcÞ : ð3Þ

We assume that x follows a Gaussian distribution for the differentgenders, and that the mean and the covariance of class c are xc

and rc . Assuming equal a priori class probability PðcÞ ¼ 0:5, and

PðxjcÞ ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffi2pr2

c

p exp �ðx� xcÞ2

2r2c

( ): ð4Þ

The a posteriori probabilities PðcjxÞ are computed by applying Eq.(4) and substituting the a priori probability into Eq. (3). IfPðfemalejxÞ > PðmalejxÞ, then the face is classified as female. Other-wise, the face is classified as male.

4. Experiments and discussion

This section is organized as follows. We first describe the dataset and the normalization method used in our experiments. Wethen evaluate the performance of PGSFS by visualizing the recov-ered facial needle-maps. The results of gender classification basedon the recovered needle-maps are presented and compared withthose obtained using intensity images and those obtained fromground-truth needle-maps. We also compare our method withthe classification results obtained by human observers. Finally,we present the gender classification results using facial needle-maps recovered from FERET images.

4.1. Data set and normalization

The data set used in our experiments consists of range images(3D) and frontal facial images (2D) for 200 subjects (100 femalesand 100 males) selected from the University of Notre Dame Bio-metrics Database [35,36]. To construct the statistical model re-quired for PGSFS, the range images and the frontal facial imagefor each subject must be aligned and normalised.

Geometric alignment is required for the range scans which con-sist of height values z sampled at different image locations (x,y). Se-ven points are manually selected (as shown in Fig. 5). These are theinside and the outside corners of the left eye (1,2), the inside andthe outside corners of the right eye (3,4), the nose tip (N), the mid-dle of the lips (M), and the center of the chin (C). The centers of theleft and the right eyes (denoted as El and ErÞ are calculated as themidpoints of points 1 and 2, and 3 and 4 respectively. We first ro-tate and translate the face scans so that the plane passing throughEl, Er and C is perpendicular to the Z-axis, the line passing throughEl and Er is horizontal, and the XY position of N is ð0; 0Þ. The rota-tion matrix R is as defined in [14]. If N1 denotes the position of Nafter rotation, the translation matrix is defined as,

Fig. 5. Seven control points.

Fig. 6. Examples of normalized 2D images (1st row) and surface normals (2nd row).

1044 J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048

T ¼ ð�N1x;�N1y; 0ÞT :

After rotation and translation, the point (x,y,z) transforms to

ðx0; y0; z0ÞT ¼ R � ðx; y; zÞT þ T:

We calculate the mean positions of the five feature pointsEl0; Er0;N0;M0, and C0 from the 200 scans, and use them as the refer-ence points. Then, we scale the scans to make the distance betweenEl0 and Er0 identical to the reference. The nose tip N0 gives the cen-terline for cropping a 114� 100 region from the raw 3D scan to cre-ate a range image from the depth values. Then, we use the principalwarps method described in [37] to warp the cropped range imagesso that the XY positions of the five points ðEl0; Er0;N0;M0;C0Þ are iden-tical to those of the reference points. Linear interpolation is thenused to fill the holes. The geometric normalization for the 2Dimages is almost identical to that used for the 3D scans, except thatthe rotation and cropping are performed in the XY plane only.

In addition to the geometric normalization, the 2D images alsorequire brightness normalization. First, the colored images are con-verted into grey scale by averaging the values of the three colorchannels. The intensity contrast is then linearly stretched to nor-malize the ambient lighting variations using the formula

Inormalizedðx; yÞ ¼Iðx; yÞ � Imin

Imax � Imin

where Iðx; yÞ denotes the intensity value at position ðx; yÞ; Imin andImax are the minimum and maximum intensity values in the image.Finally, we use the method proposed in [38] to apply photometriccorrection and specularity subtraction to the stretched intensityimages in order to improve the results of PGSFS (which relies on aLambertian reflectance model). Note that although histogramequalization is widely used for image brightness normalization,we cannot use it in our application since it modifies the distributionof intensity and hence the reflectance properties of the viewed fa-cial surface. This in turn will affect the shape recovered using SFS.

After normalization, we can calculate ground-truth facial nee-dle-maps using the range scans. Because the cropping step in thegeometric normalization involves re-sampling, some noise is intro-duced into the needle-maps. Examples of the rendered needle-maps and the normalized 2D facial images are shown in Fig. 6.

4.2. Performance of PGSFS

We use the ground-truth facial needle-maps extracted from thealigned range images to construct the statistical model required inPGSFS to recover facial needle-maps from the normalized intensityimages. The needle-maps and the integrated surfaces recoveredusing PGSFS for eight facial images are shown in Fig. 7. Theground-truth needle-maps and the corresponding surfaces (i.e.range images) are also shown for comparison. Since the recovered

needle-map satisfies data-closeness, when rendered with a frontallight source it would yield an image identical to the input frontalview of the face. For this reason, we show the image rendered bythe recovered needle-maps re-illuminated with a light sourcemoved 30� from the viewing direction along the positive x-axis.For convenience of comparison, the ground-truth needle-mapsare also re-illuminated in the same way. From the figure, we makea number of conclusions. First, by using PGSFS, both the recoveredneedle-maps and the surfaces give realistic shape. Moreover, theyovercome the well-known local convexity-concavity instabilityproblem evident in several previous SFS methods [22]. Second,the recovered needle-maps and the surfaces are similar toground-truth. This is especially the case at the cheek and mouthlocations in which important gender information is encoded.Thirdly and importantly, gender information is conveyed in therecovered facial needle-maps. This underpins the feasibility of gen-der classification based on the recovered facial needle-maps.

Of course, there is noise in the recovered needle-maps. Thereason is that the ground-truth data are distorted because ofthe re-sampling step employed in the alignment step. Moreover,the statistical model used in SFS is constructed from the ground-truth data which is itself noisy. The model captures this andreintroduces it into the recovered needle-maps. Another draw-back of the recovered needle-maps is that the recovered shapeof the nose cannot attain its actual height. This is especiallythe case for male faces. This is because these images are not ta-ken under single light source conditions, and ambient light re-duces the shadow around the nose. As a result, the nose shaperecovery is not accurate.

4.3. Gender classification on notre dame data

In this section, we examine the gender classification perfor-mance when a controlled fraction p (where p=10%, 30%, 50%, and70%) of the 200 available faces (ground-truth needle-maps and cor-responding intensity images) are used for training. The test data setis of fixed size and contains 60 faces that are randomly selectedfrom the 200 available faces. The set of training data is randomlyselected from the remaining faces. When p=10%, 30%, 50%, the re-ported results are estimated using 10-fold cross validation. Thesteps are as follows

� The statistical model for PGSFS is constructed using the ground-truth needle-maps (extracted from the aligned range images)reserved for training.

� PGSFS is applied to both the training and test intensity images torecover their facial needle-maps.

� We then apply PGA to the recovered needle-maps in the trainingset to obtain the projection matrix. We represent both the nee-dle maps recovered from the training-set and the test-set usingtheir PGA parameters.

Fig. 7. Examples of the results of SFS. From left to right are: the input intensity images, the recovered facial needle-maps, the ground-truth needle-maps, the recoveredsurfaces, and the ground-truth surfaces.

J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048 1045

� LDA is applied to the PGA parameters of the training-set toobtain the scalar gender discriminating attribute. Using the sca-lar attributes of the training-set the Bayes classifier is con-structed and used to discriminate the gender for the set of testfaces.

� We repeat the random selection of the test faces 10 times foreach value of p.

The average classification error rates found using this procedureare shown in Fig. 8 and listed in Table 1. The results are also

compared with those obtained by applying PGA and LDA to theground-truth needle-maps together with those obtained by apply-ing PCA and LDA to the intensity images.

There are several features of the data reported in Fig. 8 andTable 1 that are worth noting. First, the three methods are all effec-tive for gender classification. However, using the needle-mapsrecovered from the facial images achieves a higher classificationaccuracy than either using the ground-truth needle-maps ex-tracted from range images or using the intensity images alone.For example, when using 70% of the data for training the accuracy

Table 1Classification accuracy on Notre Dame data.

Ground-truth Needle-maps (%)

IntensityImages (%)

Recovered Needle-maps (%)

10% fortraining

69:98 3:41 79:13 2:78 80:22 3:09

30% fortraining

79:83 3:69 84:57 3:16 85:50 3:10

50% fortraining

83:17 3:40 85:63 3:09 87:63 3:45

70% fortraining

85:00 3:09 86:00 2:88 88:50 3:12

Fig. 8. Classification results on Notre Dame data.

1046 J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048

achieved using ground-truth needle-maps is 85.00% and thatachieved by using intensity images is 86.00%. When using therecovered needle-maps, on the other hand, the classification accu-racy is 88.50%. Although the improvement of using recovered nee-dle-maps over intensity images is not statistically significant, itstill confirms the feasibility of gender classification using the facialshape information encoded in the recovered facial needle-maps.Second, when less than 30% of the data is used for training, theimprovement in accuracy obtained by using recovered facial nee-dle-maps over that obtained using intensity images is not obvious.The reason for this, is that without sufficient needle-maps fortraining, the constructed statistical model in PGSFS cannot captureaccurately the structure of the facial shape. As a result the recov-ered facial needle-maps cannot reveal accurate shape information.Hence, the advantage of using shape information is limited. As a re-sult, the classification accuracy obtained using the recovered facialneedle-maps is close to that obtained using intensity images whenthe amount of training data used is small. Thirdly, the highest gen-der classification accuracy we achieve is 88.50%, which is lowerthan that (96.6%) of the state-of-the-art ’support faces’ method

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

Probability to be Female

Num

ber

of F

aces

FemaleMale

0 0.1 0.2 0.3 0.4 0.0

5

10

15

20

Probability to

Num

ber

of F

aces

Fig. 9. Histogram of female gender probability of one classification. From left to right aimages.

[5]. However in [5], SVMs were used as classifiers, which are muchmore sophisticated than the simple Bayes classifier used in our ap-proach. Finally, because the use of recovered facial needle-maps re-quires a shape recovery procedure, there are concerns about thecomputational efficiency of the method. In our experiments therecovery of the shapes for 200 images takes less than 5 minutes.Moreover, the recovery of needle-maps for a large quantity train-ing samples needs to be completed only once in advance. For eachgender classification operation, we only need to recover a single fa-cial needle-map.

In Fig. 9, we show the histogram of the female gender probabil-ity for both males and females. This is obtained using 70% of thedata for training, and we have averaged the histogram over 10 ran-domised selections of the data. From the figure, it is clear that irre-spective of the method used, the distributions for the two gendersare approximately symmetric. When we use the maximum proba-bility selection criterion, then the total number of misclassified fe-males (probability smaller than 50%) is slightly larger than thenumber of misclassified males (probability larger than 50%). Whenaveraged over the 10 different randomised selections of trainingdata, the following numbers of males and females are misclassi-fied: a) when using recovered needle-maps 4 females and 2.9males are misclassified, b) when using intensity images 4.4 femalesand 2.7 males are misclassified, and c) when using ground-truthneedle-maps 5.4 females and 4.1 males are misclassified. This indi-cates that the classification error rate is smaller for males than fe-males. This may be attributable to the fact that we are only usingthe central portion of the face, and the facial outline may help toimprove the classification of females.

In Fig. 10(a) and (b) we visualize the results of one randomiza-tion which uses 70% of the data for training. The test images are ar-ranged into a series with decreasing female probability. We select10 images from the series for visualization. The selection is as fol-lows, there are two images where the probability is greater than95%, two images with where the probability is approximately75%, one image where the probability is slightly larger than 50%,one image where the probability is just below 50% probability,two images where the probability is close to 25%, and two imageswhere the probability is below 5%. Fig. 10(a) shows the results ob-tained when the recovered facial needle-maps are used to computethe probabilities, and Fig. 10(b) those obtained when intensityimages are used instead. The vertical line is the Bayes decisionboundary between the two genders (females to the left and malesto the right). Each image is annotated with its female probabilityfollowed by the actual gender.

From the figures, the two series of images exhibit at least someconsistency with subjective human judgement. The images ateither end are clearly male or female, while those in the middleare more ambiguous. To investigate this more systematically, wehave presented the 20 images (with the 5 replications removed)to 12 naive human observers. The observers were asked to assignthe images to one of the following classes: a) definitely female, b)possible female, c) not sure, d) possible male and e) definitely

5 0.6 0.7 0.8 0.9 1 be Female

FemaleMale

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

Probability to be Female

Num

ber

of F

aces

FemaleMale

re using recovered needle-maps, using ground-truth needle-maps, using intensity

Fig. 10. Visualization of classifications.

J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048 1047

male. We assigned female probabilities to these classes as follows:a) 100%, b) 75%, c) 50%, d) 25%, and e) 0%. The reported results areaveraged over the 12 observers. We arranged the 15 images into aseries with descending average female probability, and this isshown in Fig. 10(c). The images to the left of the first vertical lineare female, and those to the right of the second vertical line aremale. These results are consistent with those obtained using theBayes classifier.

We presented the 12 human subjects the entire test-set of 60facial images with the same random selectation as above. The sub-jects were asked to determine the gender of each of the testimages. The average correct classification accuracy was 88.19%with a standard deviation of 5.4%. In Table 2, we compare thisaccuracy with those obtained using recovered facial needle-mapsand intensity images for the same random selection of test data.From the table it is clear that using recovered needle-maps givesbetter gender classification accuracy than either given by humansubjects or by using intensity images.

4.4. Gender classification on FERET images

In the above experiments, the range data used to construct the3D model in SFS and the intensity images are from the same data-base and are taken at the same time. The simultaneous capture ofrange and intensity data may assist accurate facial shape recovery,and give further benefits for gender classification using the recov-ered facial needle-maps. In the following experiments, we use the3D model constructed from the Notre Dame range data to recoverfacial needle-maps from FERET images. We examine the genderclassification performance using the FERET images and the recov-ered facial needle-maps. In total, 200 (100 male and 100 female)grayscale images were selected from the fa (regular frontal image)set of the FERET database [47]. Each of the 384� 256 pixel imagesis normalized using the same normalization method as used withthe Notre Dame images, and is cropped to be of size 114� 100 pix-els. Facial needle-maps are recovered from the normalized imagesusing the PGSFS method in conjunction with the 3D statisticalmodel constructed from the Notre Dame range data. The genderclassification performance is examined in the same way as withthe Notre Dame data. That is, 60 of the 200 images are randomly

Table 2Comparison with human classification.

Using RecoveredNeedle-maps(%)

Using IntensityImages(%)

Humanclassification(%)

Classification accuracy 91:67 88:33 88:19

selected as test data. A controlled fraction p (where p=10%, 30%,50%, and 70% of 200) of the remaining images are selected as train-ing data. The classification results are estimated with 10-fold crossvalidation (when p=10%, 30%, 50%), and are shown in Fig. 11 andsummarized in Table 3. From the results, there are two featuresworth noting. First, there is no improvement to be gained fromusing recovered facial needle-maps when compared with usingintensity images. It seems that the facial needle-maps are not accu-rately recovered using a 3D model constructed from a differentdatabase. As a result, the poor recovered shape information addsno benefit to gender classification. This phenomenon also occurredwhen relatively little training data are used to construct the 3Dmodel (as shown in Fig. 8). Secondly, that when p 6 50%, the clas-sification accuracies are much lower than those achieved on theNotre Dame data. This may be attributable to the high diversityof the FERET images taken under different lighting conditions.Without sufficient training data, the data variance is not accuratelycaptured, and affects the gender classification accuracy. Moreover,most of the state-of-the art gender classification approaches testedon the FERET database [5,16,46] use 80% of over 1000 FERETimages for training, and 20% for test.

The experiments on the FERET images show that the use of thePGSFS method to recover facial shapes for gender classification isof limited generalization ability. If accurate facial shape cannotbe recovered using the 3D statistical model, gender classificationusing the recovered facial shapes has no advantages over usingintensity images. On the other hand, the results shown in Figs. 8and 11 support the important role of the SFS method in our gender

Fig. 11. Classification results on FERET data.

Table 3Classification accuracy on FERET data.

Intensity Images (%) Recovered Needle-maps (%)

10% for training 50:83 4:32 50:00 4:3430% for training 58:64 2:72 59:64 1:7350% for training 64:10 1:81 63:50 2:2070% for training 84:17 3:10 84:33 2:00

1048 J. Wu et al. / Image and Vision Computing 28 (2010) 1039–1048

classification approach. Improvement of the SFS method wouldfurther improve the gender classification performance obtainedusing the recovered facial needle-maps.

5. Conclusion

In this paper, we have shown how gender classification can be ef-fected using 2.5D facial needle-maps. The needle-maps are extractedfrom intensity images using a model-based shape-from-shadingalgorithm. The algorithm relies on a statistical model of facial shapeformulated in the needle-map domain using principal geodesic anal-ysis. It is formulated using ideas from differential geometry and cap-tures the non-Euclidean statistical nature of fields of unit-vectors.The shape-from-shading algorithm is used to iteratively recoverneedle-maps that realistically capture facial shape and also satisfythe image irradiance equation as a hard constraint. Therefore, therecovered facial needle-maps both encode facial shape and alsoimplicitly capture facial intensity information. Linear discriminantanalysis together with a Bayes classifier is applied to the PGA param-eters of the needle-maps to perform gender classification.

Our experimental results demonstrate the feasibility of genderclassification using recovered facial needle-maps, and offer a newroute to gender classification based on facial shape information.We make suggestions as to how the achieved gender classificationaccuracy could be improved. The first approach is to use moresophisticated classifiers such as SVMs. The second approach is to im-prove the current SFS method so as to achieve more accurate facialshape recovery.

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