Age Simulation in Young Face Images Yixiong Liang, Chengrong Li, Hongqiang Yue, Yangyu Luo Institute of Automation, Chinese Academy of Sciences, Beijing, 100080 China Email: {yxliang, lich, hqyue, yyluo}@hitic.ia.ac.cn

Abstract—In this paper, an example-based aging simulation method is proposed for modeling the age effects on young images. The technique is based upon a statistical appearance model and age trajectories. The statistical appearance model is designed to capture the appearance variations due to the aging effect in the young images and the age trajectories provide a statistical definition of facial changes with age that are biologically consistent across a sample population. SVM is trained to predict the age of subject in the test image and the appearance parameters at the target age can be obtained according to the estimated age and age trajectories and then the desired image can be reconstructed. Experimental results show that the proposed age transformation method can effectively change the age of face images and produce plausible, near photo-quality images.

I. I NTRODUCTION Aging is an inevitable process of human and it often causes the significant changes in the appearance of human faces. The capability to produce an accurately ”aged” face image in an automatic way could aid several fields such as face recognition across age (homeland security), automatic age estimation (age based Human-Computer interaction), prediction of one’s appearance across age (finding missing children, tracking and apprehension of criminal suspects and terrorists), etc. Generally, we are aged in a similar way: from infancy to teen years, changes due to the aging effect are manifested in the form of nonlinear shape variations involving the changes in the underlying skeletal features toward the formation of the adult skull and face, while during the adulthood, the age-related changes involves the minor skeletal variations and large textural variations such as wrinkles and other skin artifacts. However, the age progression is specific to a given individual. It occurs slowly and is affected significantly by other factors such as health, gender, race, and lifestyle, which makes modeling or simulating age progression in human faces very difficult. There are only a limited amount of literature outlining rigorous approaches to age progression. Pitterner et al. [1], [2] imposed age-related changes on human faces by using the coordinate transformations with a group of predefined cardioidal strain functions. Todd et al. [3] proposed the ’revised’ cardioidal strain transformation model to account for craniofacial growth. Ramanathan et al. [4] proposed a craniofacial growth model that takes into account both psychophysical evidences on how human perceive age progression in faces and anthropometric evidence on facial growth. Hutton et al. [5] constructed a shape model based on 3D facial meshes and defined growth trajectories in the model space. Using these trajectories, examples within the space can be

reconstructed at a target age. Wang et al. [6] trained a set of support vector machines (SVMs) to predict the shape in the future. The above mentioned methods only record the shape changes, while the texture changes are ignored. To overcome this problem, Burt et al. [7] applied aging transformations by superimposing on face images changes in both shape and color. They created facial prototypes for different age groups. A caricature algorithm is subsequently used in which the shape and color differences between prototypes of a young age group and an older age group are added to the subject image to increase the perceived age. However, such facial prototypes are ineffective in capturing wrinkles that are characteristic of elderly subjects. Tidderman et al. [8] extended the above method by using the wavelet-based method to improve the texture of the facial prototypes. Their work is primarily focused on texture enhancement and doesn’t use any aging model or learning scheme to perform the transform. Gandhi [9] trained a SVM for age prediction and extended the texture enhancement procedure [10] towards emphasizing or de-emphasizing wrinkles on face images. Ramanathan et al. [11] studied the textural effects of age progression on facial similarity measure and developed a Bayesian age-difference classifier. Their algorithm does not take the shape variations into account. In perhaps the most rigorous approach to age progression to date, Lanitis et al. [12] generated an active appearance model (AAM) for face and investigated aging functions which determine the relationship between the age and the model parameters. Their work is focused on the growth and the results are encouraging and provide important experiment for further study on this topic. Patterson et al. [13] exploited Lanitis’s method for modelling adult aging. Wang et al. [14] extended Lanitis’s method by integrating aging way classification and typical vector creating function. Hill et al. [15] constructed a shape model and a texture model to represent the face image and defined a set of aging directions through the model space. Using these directions, examples within the space can be reconstructed at the target age by linear or piecewise methods. In this paper, we propose a new example-based aging scheme to simulate the age effects on human faces during formative years. The remainder of this paper is structured as follows. In Section II, we both describe the construction of the statistical appearance model and the calculation of the average age trajectories. Section III discusses the use of SVM for age estimation while Section IV describes the aging simulation scheme. The experimental results are given in Section V and the last Section concludes the paper and outlines the future

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work.

whose components can be determined by projecting the map φ(x) onto the eigenvectors: II. S TATISTICAL AGING M ODEL bi = (ui · φ(x)) =

A. Appearance Model

n


uij exp(−

j=1

Our construction of an appearance model includes devising a shape model and a texture model (independent of shape), which closely resembles that outlined by Hill et al. [15]. The shape information is represented by the coordinates of facial landmarks and is then aligned to the mean face shape through an iterative procrustes alignment method. The shapeindependent texture information can be generated by warping the face images to the mean shape using linear warping over the landmarks Delaunay triangulation (as shown in Fig. 1). Different from [15], we use kernel principal component

xi − x2 ), 2σ 2

(3)

where uij is the j-th component of ui . The texture model can be constructed by applying linear PCA on the shape-normalised texture vectors. Any texture vector t within the training set may be approximated by the sum of first q principal components: t ≈ ¯t + Vg,

(4)

where ¯t is the mean texture vector, the matrix V contains the q texture principal components and g is a set of texture model parameters. The two sets of model parameters, b and g, are relatively compact representation of the examples. B. Average Age Trajectories

(a) The source image with landmarks Fig. 1.

(b) The mean shape

(c) The shape-free texture

The shape and texture information.

analysis (KPCA) [16] for statistical shape analysis and PCA for statistical texture analysis. The rationale behind this is that our attention is mainly focused on age variations in the stage from infancy to teenage, which is characterized by significant, nonlinear shape variations and less texture variations. The critical idea behind KPCA is to use the kernel trick to map the input data into an implicit feature space F, φ : x ∈ Rh → φ(x) ∈ F, with a nonlinear dot product kernel function k(xi , xj ) = (φ(xi ) · φ(xj )), and then perform PCA in F to produce nonlinear principal components of input data. Here we adopt the Gaussian kernel 2 k(x, y) = exp(−
x−y
2σ 2 ). Considering the aligned training shape vector set X = (x1 , . . . , xn ), define a kernel matrix K by Kij := (φ(xi ) · φ(xj )) = k(xi , xj )1 . Performing the following eigen-decomposition: nλu = Ku,

(1)

yields eigenvectors u1 , . . . , un with eigenvalues λ1 ≥ . . . ≥ λn satisfying λi (ui · ui ) = 1. The map of shape x in the training set φ(x) can be approximated using a weighted sum of these deviations obtained from the first p modes: φ(x) ≈

p


bi ui = Ub,

(2)

i=1

where the matrix U = (u1 , . . . , up ) is the matrix of the first p eigenvectors, and b = (b1 , . . . , bp )T is a vector of weights

We calculate the average age trajectories both in shape model space and in texture model space. Since there is a difference in the timing and types of facial growth between men and women, we treat them respectively. Hence, in each model space, two age trajectories are defined, one for each gender. The path of the average age trajectory through the shape model space is calculated by: n w(t, ti )bi , (5) fs (t) = i=1 n i=1 w(t, ti ) where w(t, ti ) is the weighted function, which is parameterised by target age t, and ti and bi are respectively the age and location in the shape model space of the i-th subject. Again, the Gaussian function is adopted as the weighted function where the parameter σ is determined by the amount of input data and its distribution. In our experiments, the parameter σ is the standard deviation of the input data. The average age trajectories for the texture variations can be formed in an entirely analogous way to Eq.(5). III. AGE E STIMATION WITH S UPPORT V ECTOR M ACHINE SVM is a relatively new learning technique that learns the decision surface through a process of discrimination and has good generalization properties. It is originally developed to solve the classification problem, but recently, SVM has been successfully extended to regression [17]. In fact, SVM regression performs a linear function regression in an implicit feature space via the aforementioned kernel tricks. Here we use SVM regression to learn the relationship between the age and the coded representation of the face image, i.e. find the age function t = g(c), where c = (bT , gT )T is coded representation of the face image and g is the desired regression function, t is the predicted age of the subject in the image. Using the ε-insensitive loss function, the desired age function can be computed as follows:

1 For simplicity, we assume that the mapped data are centered in F . ˜ Otherwise, := φ(x) − n we have to go through the same algebra using φ(x) 1 φ(xi ). n i=1

495

g(c) =

n
i=1

(αi − αi∗ )k(ci , c) + b,

(6)

where αi and αi∗ are the Lagrange multipliers which can be determined by solving the following dual optimization problem:  n 1 (α − αi∗ )(αj − αj∗ )k(ci , cj )  max{− 2n i,j=1 ∗i n (7) −ε (αi + αi ) + i=1 ti (αi − αi∗ )} i=1   n s.t. i=1 (αi − αi∗ ) = 0, and αi , αi∗ ∈ [0, C], where the constant C > 0 determines the trade-off between the flatness of g(c) and the amount up to which deviations larger than ε are tolerated. The coefficient b is computed by exploiting the so called Karush-Kuhn-Tucker (KKT) conditions, which allow us to conclude that:  ε − ti + g(ci ) = 0, αi ∈ [0, C] (8) ε + ti − g(ci ) = 0, αi∗ ∈ [0, C]. IV. S YNTHESIZE THE FACE I MAGE AT TARGET AGE In this section, we describe how to synthesize the aged face images with the aid of the average age trajectories and age estimation discussed in the previous sections. Fig.2 illustrates the simulation process in a block diagram. First, the parameterized representation of the test image can be obtained by projecting its shape vectors and texture vectors onto the shape model space and texture model space, respectively. These parameters

V. E XPERIMENTAL R ESULTS A database containing 506 age progressive face images of 45 subjects (26 men and 19 women) were used in our experiments 2 . First, 56 landmarks were located in all images (see Fig. 1(a)) and the mean shape (see Fig. 1(b)) was determined by the Procrustes Analysis. A warping procedure was applied to all images to obtain the shape-free texture information (see Fig. 1(c)). Then the shape information and texture information are ultimately represented by a 112- and 53883-dimensional vector, respectively. We selected 387 images from the database for building the statistical appearance model. During the process of building the appearance model, the eigenspaces of shape and texture variation are truncated so that each explains 98% of total variation. All samples are projected onto the model space to obtain the model parameters b and g, and then the average trajectories can be easily computed using Eq.(5). Figure. 3 shows a plot of the two trajectories we computed against the Female Male

Female Male

−4

−4

x 10

x 10

1.5

6

1

5

0.5 4 0 −0.5

3

−1

2

−1.5 1 −2 0

−2.5 −3 5

−1 4 3 4

x 10

Parameterized Representation

Age estimation

Parameters changing

Aged image

Fig. 2.

−4

x 10

−4

(a) In the shape model space Fig. 3.

4 3

0 −4

x 10

0 −1 −2 −3 −5

5

1

1

−4

Test image

6

2

3 2

0

2

−1

1 0

−2

−1 −2

−3 −4

−4

x 10

−3 −4

(b) In the texture model space

The average age trajectories for male and female.

Block diagram of the age simulation process.

are then fed into the trained SVMs to estimate the current age t of the subject in the test image. The new shape parameters
corresponding to the target age t are given by:





b = b + (fs (t ) − fs (t)),

(9)




where b and b are the corresponding shape parameters of the target image and the current image in the shape model
space, respectively. The new texture parameters g can be generated in a similar way and the texture vector at target age can be easily reconstructed using Eq. (4). However, given
the new shape parameter b , we can not explicitly reconstruct


the desired shape vector x such as φ(x ) = Ub . In fact, such
a x will not always exist and if it exists, it need to be not unique. A straightforward solution to this problem [16] is to find a shape vector z who minimizes the following function:


E(z) = φ(z) − Ub 2 p
n = k(z, z) − 2 i=1 bi j=1 uij k(z, xj ) + Ω,

(10)

where Ω is the term independent of z. For the Gaussian kernel, we have k(z, z) = 1, then the above optimization problem is equal to maximize the second term with respect to z, which can be solved by the gradient descent method. Once aging has proceeded according to the age trajectories,
the resultant texture vector t is then warped to the approximate shape vector z using the Delaunay-based affine transform to generate the face image at the target age.

three strongest principal components of the shape model and texture model, which demonstrates that the trajectories for males and females are significantly different in both shape and texture. After determining the model space and the age trajectories, we set out to train and evaluate the performance of the SVMbased age function. Due to the sexual dimorphism in the aging of humans, we train two age functions, one for each gender. The set used for building the statistical appearance model are still used for training, while the remaining samples in our database are used for testing. Thus we have 387 training samples (163 for female and 206 for male) and 119 testing samples (46 for female and 73 for male). Here we still use the Gaussian kernel and the kernel parameter is determined by a 4-fold cross-validation method. The absolute mean error of the female age function was 2.58 (with a standard deviation 4.2) and that of the male age function was 2.92 (with a standard deviation 3.53). The last experiment was performed to evaluate the proposed age simulation scheme. The test images used in this experiment were not present in the set used for calculating the age trajectories and training the SVM-based age function. Fig. 4 illustrates age progress results on two subjects for various 2 Due to the availability of the images, this database may be not the ideal for the needs of our experiments because most of them displayed some other appearance variations such as pose, illumination and expression than age variation.

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(a) Original

(b) 6

(c) 9

(d) 12

(e) 15

(f) 18

(g) Original

(h) 6

(i) 9

(j) 12

(k) 15

(l) 18

Fig. 4.

The synthesized images at various age (years).

target ages. The synthesis demonstrates realistic examples of the aged portraits, preserving the identity of the subject and precisely aging the images. VI. C ONCLUSIONS AND F UTURE W ORK In this paper, we present a novel aging simulation scheme for young face images. We first construct a statistical appearance model to represent the face images and then computer the average age trajectories in the model space. After that we train SVM-based age functions to estimate the age of the input image. Based on the estimated age and the age trajectories, we can get the vectors at the target age and synthesize the aged image. The experiments show that our method can synthesis reasonable face image at various ages. Although the results are promising, there are a number of problems to be focused. First, in order to age a face in a more accurate way, not only the average tendencies but also the person-specific factors should be took into account. Moreover, our statistical appearance model fails to capture the variation of wrinkle information, which make our method not suitable for the adult aging simulation. Furthermore, the selection of the kernel function and its parameters is still an open problem.

[6] J. N. Wang, C. J. Ling, ”Artificial Aging of Faces by Support Vector Machines”, Advances in Artificial Intelligence, Lecture Notes in Computer Science, Vol. 3060. New York: Springer-Valag, 2004, pp. 499–503. [7] D. M. Burt, D. I. Perrett, ”Perception of Age in Adult Caucasian Male Faces: Computer Graphic Manipulation of Shape and Color Information”, J. Roy. Soc., vol. 259, pp. 137–143, 1995. [8] B. Tiddeman, D. M. Burt, and D. Perrett, ”Prototyping and transforming facial textures for perception research”, IEEE Comput. Graph. Appl., vol. 21, pp. 42–50, 2001. [9] M. Gandhi, A Method for Automatic Synthesis of Aged Human Facial Images, M.S. Thesis, McGill Univ., Montreal, QC, Canada, 2004. [10] Y. Shan, Z. Liu, and Z. Zhang, ”Image Based Surface Detail Transfer”, in IEEE Conf. Computer Vision and Pattern Recognition, 2001, pp. 794– 799. [11] N. Ramanathan, R. Chellappa, ”Face Verification Across Age Progressioin”, IEEE Trans. Imag. Proc., vol. 15, pp. 3349–3361, 2006. [12] A. Lanitis, C. J. Taylor, and T. F. Cootes, ”Toward Automatic Simulation of Aging Effects on Face Images”, IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, pp. 422–455, 2002. [13] E. Paterson, K. Ricanek, E. Boone, ”Automatic Representation of Adult Aging in Facial Images”, in Proceedings of Visualization, Imaging, and Image Processing, 2006, Palma de Mallorca, Spain. [14] J. Y. Wang, Y. Shang, G. D. Su, X. G. Lin, ”Age Simulation for Face Recognition”, in Proceedings of IEEE Conference on Pattern Recognition, vol. 3, pp. 913–916, 2006. [15] C. M. Hill, C. J. Solomon, and S. J. Gibos, ”A Person-Specific, Rigorous Aging Model of the Human Face”, Pattern Recognition Letters, vol. 27, pp. 1776–1787, 2006. [16] S. Mika, B. Scholkopf, A. Smola, K. R. Muller, M. Scholz, and G. Ratsch, ”Kernel PCA and De-Noising in Feature Spaces”, Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 1999, pp. 536–542. [17] A. J. Smola, B. Scholkopf, ”A tutorial on support vector regression”, Stat. Comput., vol. 14, pp. 199–222, 2004.

ACKNOWLEDGMENTS The image database used in courtesy of the FGNET consortium (http://sting.cycollege.ac.cy/˜alanitis/ fgnetaging/index.htm), with kind permission of Dr. Andreas Lanitis. R EFERENCES [1] J. B. Pittenger, R. E. Shaw, ”Aging Faces as Viscal-Elastic Events: Implications for a Theory of Nonrigid Shape Perception”, J. Exp. Psych.: Human Perception and Performance, vol. 1, pp. 374–382, 1975. [2] J. B. Pittenger, R. E. Shaw, L. S. Mark, ”Perceptual Information for the Age Level of Faces as a Higher Order Invariant of Growth”, J. Exp. Psych.: Human Perception and Performance, vol. 5, pp. 478–493, 1979. [3] J. T. Todd, L. S. Mark, R. E. Shaw, J. B. Pittenger, ”The Perception of Human Growth”, Scientific American, vol. 242, pp. 132–144, 1980. [4] N. Ramanathan, R. Chellappa, ”Modeling Age Progression in Young Faces”, in IEEE Conf. Computer Vision and Pattern Recognition, pp. 387–394, 2006. [5] T. J. Hutton, B. F. Buxton, P. Hammond, and H. W. W. Potts, ”Estimating Average Growth Trajectories in Shape-Space using Kernel Smoothing”, IEEE Trans. Med. Imag., vol. 22, pp. 747–753, 2003.

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