Research ArticleAge Estimation of Face Images Based onCNN and Divide-and-Rule Strategy

Haibin Liao 1 Yuchen Yan 2 Wenhua Dai1 and Ping Fan1

1School of Computer Science and Technology Hubei University of Science and Technology Xianning China2School of Electronic Information Wuhan University Wuhan Hubei China

Correspondence should be addressed to Yuchen Yan yycwhueducn

Received 7 March 2018 Revised 28 April 2018 Accepted 7 May 2018 Published 5 June 2018

Academic Editor Krzysztof Okarma

Copyright copy 2018 Haibin Liao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In recent years the research on age estimation based on face images has drawn more and more attention which includes twoprocesses feature extraction and estimation function learning In the aspect of face feature extraction this paper leverages excellentcharacteristics of convolution neural network in the field of image application by using deep learning method to extract facefeatures and adopts factor analysis model to extract robust features In terms of age estimation function learning age-basedand sequential study of rank-based age estimation learning methods is utilized and then a divide-and-rule face age estimator isproposed Experiments in FG-NET MORPH Album 2 and IMDB-WIKI show that the feature extraction method is more robustthan traditional age feature extraction method and the performance of divide-and-rule estimator is superior to classical SVM andSVR

1 Introduction

In the medical profession people rely mainly on the analysisof cholesterol high density cholesterol albumin and otherblood test indicators to determine a personrsquos ldquophysiologicalagerdquo and to study the degree of human aging Unfortunatelythis set of indicators is still very imperfect and of great incon-venience to use If we can use computer and image processingtechnology to analyze facial images to accurately predict apersonrsquos ldquophysiological agerdquo and compare ldquophysiological agerdquoand ldquoactual agerdquo we can knowwhether you are in ldquoYouth Per-manentrdquo or ldquoPremature Agingrdquo Then it will greatly improveresearch efficiency and reduce research costs By looking atthe ldquofacerdquo to estimate the age it can not only be used toquantify the aging but also be applied to smart city andsafe city construction In everyday language conversation thecontent and manner of conversation are often affected byother factors such as gender and age For example when facedwith the elderly the language of conversation will obviouslybe formal More generally humans quickly estimate eachotherrsquos gender age and identity through the appearance ofthe other personrsquos face in order to select different socialstyles

2 Related Work

Compared with face recognition age analysis has receivedmuch less attention However it does not mean that ageanalysis is not as important as face identification The useof face age analysis is always involved in the application inface recognition [1 2] and forensic science [3 4] In recentyears face age analysis has attractedmore interests and atten-tion from psychology aesthetics forensic science computergraphics computer vision [5ndash7] and so onThere is no doubtthat the coming applications of automatic age analysis will notjust include face recognition but will be widely used in intel-ligent ad delivery bioassays science biostatistics electroniccustomer relationship management recognition beauty lawenforcement security controls demographic census human-computer interaction and other fields

The two main issues in age estimation are ldquohow faceimages are represented and how ages are estimatedrdquo Namelythey are face representation and estimation function learningMost of the current estimation functions learning methodsare regarded as multiclass classification [8 9] or regressionproblems [10 11] to learn the classifier The multiclass clas-sification method takes the age value as a separate category

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 1712686 8 pageshttpsdoiorg10115520181712686

2 Mathematical Problems in Engineering

and then learns a classifier for age classification Therefore anumber of standard classicmethods such asK-NNmultilevelperception AdaBoost and SVM can be used to performaccurate age prediction and age grouping The regressionmethod fits the mapping of feature space to age spacemainly by regularization method to get the best regressionfunction Typical nonlinear regressionmethods are quadraticregression Gaussian Process and Support Vector Regression(SVR) which are used for age estimation problems Theclassification method only considers the independence ofdifferent age categories but ignores the internal relationsbetween them In fact it has a strong internal order betweenthe ages For example for a 15-year-old sample the age ismore likely to be 14 or 16 years rather than 10 or 20 yearsAlthough the regression method considers the connectionbetween different age categories it views age category asa linearly increasing relationship and does not reflect thediversity of the aging process For example in infancy ageaging is mainly reflected in the changes of bones while inadults it is mainly the changes in texture

Since the classification method naively treats the agecategory as an independent label the regression methodsimply regards the age category as equilibrium Therefore asalternatives to classification and regression methods recentrank-based (or ordinal regression) methods have been usedfor age estimation [12 13] This approach uses the age-axisstrategy for age-class estimation which is suitable for ageestimation because the relative order of age is properly used

As people of different ages have different age growth wecan divide the training data according to age and use differentsubmodels to predict the age data of different ages Thenthe penalty parameters are weighted to solve the problemof classification bias caused by the imbalance of the samplenumber which can make the accuracy of age estimationfurther improved In this paper we will study the rank-basedage estimation learning method and propose a divide-and-rule age estimation framework

Face features extraction is another important problem inimage age estimation In order to extract features of humanface early research is mainly focused on the face geome-try ratio feature extraction [14] In order to extract moredetailed features of facial features active appearance model(AAM) combined with principal component analysis (PCA)gradually replaces the face geometry characteristics of mainfeatures for age estimation [15 16] Since each test face imagehas been labelled as a specific age value this AAM-basedage estimation method is more suitable for higher-precisionage estimation system However the AAMmethod has someshortcomings because AAM is mainly based on shape andgray scale in which the average global feature of the trainingimage is extracted and the characterization of some textureinformation is not effective for some faces

All of the above methods require accurate key featurepoint detection and location technology However it is dif-ficult to meet the requirements in practical applicationTherefore with reference to the feature extraction methodin face recognition the current mainstreammethods directlyextract the face feature vector from human face For exampleAhonen et al [17] and Zhou et al [18] used local binary

model (LBP) and Haar-like wavelet transform to extractface features for age estimation respectively In additionimportant features such as flow-type learning [19 20] feature-based dimensionality reduction methods in face recognitionare also used to construct face age features One of the mosteffective methods for face feature extraction is BioinspiredFeatures (BIF) [21] This method imitates the single cellacceptability information domain of the primary visual cor-tex of vertebrate brain Firstly the Gabor filter with differentscales and directions is used to convolute the face to extractface features Then the extracted feature vector in first stepis merged However this method tends to generate localtransform invariance and reduce texture detail informationwhen combining Gabor convolution coefficients in secondstep [22]

More recently CNN-based methods [23ndash30] have beenwidely adopted for age estimation due to its superior per-formance over existing methods Yi et al [26] introduceda multitask learning method with a relatively shallow CNNand achieved good results however its multiscale networkrelies on accurate feature point positioning technology whichlimits its application Rothe et al [25] crawled a largest publicdataset (IMDB-WIKI dataset) for age prediction and tackledthe estimation of apparent age with CNN using the VGG-16architecture In [27] a six-layer CNN was used for genderand age grouping but it did not address the problem of ageestimation In [24] the six-layer CNN is used to extract theage feature of face and the manifold learning method is usedto estimate the age Instead of multiclass classification andregression methods ranking techniques were introduced tothe problem of age estimation In [29] Niu et al proposedto formulate age estimation as an ordinal regression problemwith the use of multiple outputs CNN In [30] Chen et alproposed a Convolutional Neural Network- (CNN-) basedframework ranking-CNN for age estimation In this paperwe will extract age feature fromAgeNet network according to[23] and then use the age-classifying strategy of divide-and-rule to estimate age

3 Face Age Feature Extraction

31 Face Age Description Based on Deep Learning Since deepCNN has been proved to be rich in scene and target repre-sentation ability it has intelligent and automatic performancecompared with the traditional manual feature extractionmethod In this paper the age network (AgeNet) in [23] isused to extract the face age descriptor and then the age esti-mation is carried out by using the divide-and-rule strategy

The AgeNet uses an approach based on regression andclassification to construct an age-estimated deep CNN Inorder to reduce the complexity of the network and trainingtime we only use the regression-based age estimation deepCNN Therefore the following Euclidean loss function canbe defined

119864 (119882) = 12119873119873sum119894=1

1003817100381710038171003817119910119899 minus 119910119899100381710038171003817100381722 (1)

where 119882 is the parameter of deep convolution network 119910119899is the age prediction value by the deep convolution network

Mathematical Problems in Engineering 3

Figure 1 GoogLeNetrsquos Deep CNN Hierarchy

119910119899 is the actual age value and 119873 is the batch number Thedeepnetworkmodel is based onGoogLeNet [22] designed byGoogle et al [31] which can improve the performance underthe same computing cost It is a very effective network designmodel as shown in Figure 1

In order to further speed up the convergence rate beforethe ReLU (activation function) operation we add the layerof scale normalization (Batch Normalization BN) whileremoving all the dropout operation In order to reduce therisk of overfitting the training of deep CNN is carried outby means of network migration learning Thus the networktraining consists of two stages pretrain based on the faceidentity data set and fine-tune based on the age data set

Pretrain stage Although face identity and age are twodifferent concepts they are related In addition there aremany public large-scale face identity databases Thereforewe use the large-scale face database CASIA-WebFace [32] topretrain the network Experiments show that the method ofnetwork pretraining in face database is better than that ofrandom network initialization

Fine-tune phase This stage uses the CACD [33] Morph-II [34] and WebFaceAge [35] face age libraries to fine-tunethe networkmodel generated by the pretrain stage to producea robust age-deep network

All training and test face images are normalized to256times256 sizes In the training stage the data is augmentedThat is images of 227times227 size are randomly cut out fromthe images of 256times256 size and the images are enlarged Inthe test for the input image of 256times256 size according tothe four corners and center point of the image we cut outfive images of 227times227 size then all the cropped images arehorizontally inverted to generate the corresponding imagea total of 10 images respectively into the depth of networklearning Finally the output of last layer of GoogLeNet is usedas the face age descriptor and features of the 10 images areconcatenated to form the final face feature vector

32 Feature Reduction Based on Factor Analysis Since thefacial feature vectors obtained by deepCNNnetwork learninghave high dimensionality (10 lowast 100 = 1000 dimensions)both redundancy and noise are inevitable in this process Inorder to extract the essence of the discriminative compactfeature subset we regard each age value as a class and use

factor analysis model to deal with original feature dimensionreduction

In the factor analysis model (FAM) [36 37] it is desirableto find the optimal projection matrix to minimize thedifference in style between homogeneous (same age) samplesand to maximize the difference in content between differentclasses (different ages) We consider the features reflectingface of the characteristics of age changes as a content factorwhich is defined as follows

119865119888 = 119862minus1sum119894=1

119862sum119895=119894+1

119901119894119901119895119908 (119894 119895) (120583119894 minus 120583119895) (120583119894 minus 120583119895)119879 (2)

where 119862 is the total number of classes 119901119894 is the priorprobability of classes 119894 120583119894 is the average of the original featurevectors of the class 119894th and 119908(119894 119895) = 1(119890119889)2 (119890119889 is Euclideandistance between two classes) are the weights of the 119894th andthe 119895th classWe consider the change of face illumination andexpression as a style factor which is defined as follows

119865119904 = 119862sum119894=1

119901119894 119873119894minus1sum119895=1

119873119894sum119896=119895+1

119908 (119895 119896) (119909(119894)119895 minus 119909(119894)119896 ) (119909(119894)119895 minus 119909(119894)119896 )119879 (3)

where119909(119894)119895 119909(119894)119896 are the 119895-th and 119896-th feature vectors of class119894 respectively and 119908(119895 119896) is the weight of the 119895-th and 119896-thvector defined as

119908 (119895 119896) = exp(minus10038171003817100381710038171003817119909119895 minus 11990911989610038171003817100381710038171003817221199052 ) (4)

where 119905 is the experience parameterGiven theweighted119865119888119865119904 for FAM the objective function

of the linear factors analysis model is represented as follows

119869119865 (119882) = argmax119908

119905119903 (119882119879119865119862119882)119905119903 (119882119879119865119878119882) (5)

where 119882 is the unresolved linear mapping transformationwhich can be obtained by solving the generalized eigenvalueproblem

119865119888119882 = 120582119865119904119882 (6)

4 Mathematical Problems in Engineering

Then we can extract low-dimensional simplified and dis-criminative features 119909 from the high-dimensional redun-dant disturbed and distorted original feature 119909

119909 = 119882119879119909 (7)

By FAM we finally get the 200 dimensional eigenvectors

4 Divide-and-Rule Age EstimationFunction Learning

After obtaining the feature vector of face image age the ageestimation function can be learned and the correspondingage estimator can be trained When we compare the two faceages it is easy for humans to identify which is older butto accurately guess the age of the face is not so easy Wheninferring a personrsquos exact age we may compare the inputface with the faces of many people whose ages are knownresulting in a series of comparisons and then estimate thepersonrsquos age by integrating the results This process involvesnumerous pairwise preferences each of which is obtained bycomparing the input face to the faces in the dataset Based onthis we propose a divide-and- rule age estimation functionlearning scheme

41 Divide Given the training set of images 119868 = [1198681 1198682sdot sdot sdot 119868119894 sdot sdot sdot 119868119872] suppose 119909119894 isin 119877119863 is a face feature vector(obtained by the method of the previous section) and 119870is the total number of categories (age tags) for which thecorresponding age category 119910119894 isin 1 2 sdot sdot sdot K is to be treatedas order ranks Suppose for a given age 119896 119883 can be dividedinto the following two subsets119883+119896 and119883minus119896

119883+119896 = (119909119894 +1) | 119910119894 gt 119896119883minus119896 = (119909119894 minus1) | 119910119894 lt 119896 (8)

Based on the above two subsets we can train two-classclassifier that only answers the problem of ldquowhether this faceis older than 119896rdquo Because it only needs to make a yes or noanswer in the classification process the complexity of theproblem is reduced In addition because 119883+119896 cup 119883minus119896 = 119883sufficient training samples are ensured for each classificationwhich overcomes the problem of lack of training samplesin classifiers such as parallel-hyperplanes or one-versus-oneclassifiers (this problem is more prominent in age estima-tion)

42 Rule Once more than one classifier has been trainedthe results of all the two-class classifiers can be aggregated toestimate the age rank as with the multiple hyperplane clas-sification methods Since there is an inconsistency in all ofthe two-class classifiers a classification function 119891119896(119909) withdiscriminating performance is defined for each of the two-class classifiersThe age rank estimation problem (ie the ageestimate) becomes

119903 (119909) = 1 + 119870minus1sum119896=1

⟨119891119896 (119909) gt 0⟩ (9)

In this case a logical decision is made by ⟨∙⟩ and if theinternal condition is satisfied it returns 1 and vice versa Sinceeach classification function uses its own feature space it iseasier to obtain the optimal solution than the method usinguniform feature space

43 Categorical Function Learning Based on the Sensitive CostFunction The estimation of the final age rank in the divide-and-rule age estimation scheme relies on a series of easilyclassifiable two-class classifiersTherefore it is very importantto design an appropriate cost function ofmissed classificationfor each classifier In the case of age estimation the error ratebased on 0-1 loss is not of interest In the 0-1 loss schemeall missed classifications are given the same price which isclearly not in line with the reality of the age estimates Forexample when a personrsquos age is 119896 the 0-1 loss does not identifythe miss classification between 119896 + 1 and 119896 + 20 classesObviously the latter is more serious Therefore we study theclassification function based on the sensitive cost function

Given the training set 119883+119896 and 119883minus119896 of the 119896th class wedenote the cost function cos119905119896(119897) of the missed classificationof the age category 119897th in the subclass of the 119896th class And119862(119890119894) 119877+ cup 0 rarr 119877+ cup 0 is recorded as the cost thathas occurred in which 119890119894 = 119894 minus 119897119894 indicates the absoluteerror denoted between the estimated age and the real ageThetwo most commonly used evaluation criteria in the syntheticage estimation are the mean absolute error (MAE) and thecumulative integral (Cumulative Score CS) of the absoluteerror We define the costs that have already occurred asfollows

119862 (119890119894) = ⟨119890119894 gt 119871⟩ sdot (119890119894 minus 119871) (10)

where119871 is the acceptable tolerance for the age of the erroryou can take 3-5Therefore the cost function of the 119894th sample119909119894 in the 119896th subproblem in missed classification is expressedas

cost119905119896 (119909119894) = 119862 (119896 minus 119910119894 + 1) 119910119894 le 119896119862 (119910119894 minus 119896) 119910119894 gt 119896 (11)

With themissed classification cost function it can be usedas an important weight to adjust the data for training of thetwo-class classifier In this paper SVM is used to train thetwo-class classifier in the subproblems and the hinge loss isadjusted by using themissed classified cost function as weightitem

min119908119896 119887119896120577

12 ⟨119908119896 119887119896⟩ + 119862[sum119894

cos119905119896 (119909119896) 120577119894]119904119905 119904119896 (119894) (119908119879119896 120601119896 (119909119894) + 119887119896) ge 1 minus 120577119894

120577119894 ge 0 forall119894(12)

where 119904119896(119894) = +1 if 119909119894 isin 119883+119896 and 119904119896(119894) = -1 if 119909119894 isin X-k120601119896 denotes the mapping from feature space to Hilbert space

and ⟨119908119896 119887119896⟩ is hyperplane parameters of the hidden spaceFor age estimation problems a single kernel does not apply to

Mathematical Problems in Engineering 5

all subproblems And (12) selects different cores according tothe characteristics of the feature space in each subproblem sothat each subproblem can be well projectedThe discriminantclassification function based on the sensitive cost functioneventually becomes

119891119896 (119909) = ⟨119908119896 120601119896 (119909)⟩ + 119887119896 (13)

5 Experiments and Analysis

In this section three common age groups FG-NET [38]MORPH Album 2 [34] and IMDB-WIKI [39] are usedto test the validity of the proposed face feature extractionalgorithmand face age estimation functionTheFG-NET facedatabase consists of 1002 images of 82 different individualswith different expressions illumination and attitude changesEach one has 6 to 18 images of different ages ranging from0 to69 years old and FG-NET face age database is one of themostcommonly used public databases The MORPH2 databasecontains a total of 55000 pictures of 13000 volunteers aged16 to 77 years 45000 of which are used for network trainingand the remaining 10000 are used for testing IMDB-WIKIis the largest publicly available dataset of face images withgender and age labels for training and testing In total thereare 460723 face images from 20284 celebrities from IMDband 62328 fromWikipedia being thus 523051 in total

The age estimation indexes we used are mean absoluteerror (MAE) and cumulative index (Cumulative Score CS)and the expressions are as follows

119872119860119864 = sum119873119896=1 1003816100381610038161003816 119904119896 minus 1199041198961003816100381610038161003816119873 (14)

where 119904119896 is the actual age 119904119896 is the estimated age and 119873is the total number of pictures for testing

119862119878 (119871) = 119873119890lt119871119873 lowast 100 (15)

where 119873119890lt119871 denotes the number of test images whoseabsolute error is not larger than the set value

51 Experiment Based on FG-NET In this section we com-pare the novel face feature extraction method based ondeep learning (DLF + FAM) with Gabor + PCA LBP +PCA Gabor + LBP + PCA and BIF + PCA which are thecommon face feature extraction methods The effectivenessof the feature extraction and feature-based multidimensionalreduction algorithm is analyzedThe age estimation functionwe use is the classical SVRThe face database was trained andtested by the Leave-One-Person-Out (LOPO) strategy whichwas used to test all age images of the same person as the testset and all the others as trainingThe test procedure tests eachsample and does not overlap with the training set

Table 1 shows the comparison of MAE values of differentfeature extraction methods under SVR estimator Figure 2shows the CS comparison of different feature extractionmethods under SVR estimator It can be seen that the DLFfeatures adopted in this paper are obviously superior to

Table 1 Comparison of MAE values for different feature extractionmethods

Methods MAEAgeGabor+PCA 553LBP+PCA 592Gabor+ LBP+PCA 496BIF+PCA 477DLF+ PCA 457DLF+FAM 426

Figure 2 CS comparison of different feature extraction methods

Table 2 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 583SVR BIF + FAM 458Our Proposed BIF + FAM 432SVM DLF +FAM 477SVR DLF +FAM 426Our Proposed DLF +FAM 402

the traditional manual features In order to validate theeffectiveness of the method based on factor analysis thispaper gives the comparison of DLF + PCA and DLF + FAMIt can be seen that FAM is better than PCA This is becauseFAMmakes use of the category information of age tags

In order to verify the effectiveness of the proposed divide-and-rule age estimation function BIF and DLF face featureswith better performance are selected in this experiment andthe divide-and-rule method is compared with classical SVMand SVR methods The comparison results are shown inTable 2 and Figure 3 (using the DLF feature) and we can seethat the age estimator based on divide-and-rule method isabout 1 year better than the classic SVM and SVR

52 Experiment Based on MORPH Due to the small amountof FG-NET face databases recent studies have shown that

6 Mathematical Problems in Engineering

Figure 3 CS comparison of different estimators

Table 3 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 602SVR BIF + FAM 462Our Proposed BIF + FAM 377SVM DLF+FAM 514SVR DLF+FAM 417Our Proposed DLF+FAM 348

the corresponding algorithm in this database has very lim-ited space for improvement In order to further verify theeffectiveness of this algorithm this section will be furtherexperimented on the MORPHAlbum 2 face database 10000images were further divided 80 of which were randomlyselected for the training of the estimator and the remaining20 were used for test The average of 10 experiments wastaken as the final result

The experimental results of different feature extractionmethods are shown in Figure 4 andTable 3 Figure 4 is the ageestimation comparison under different features using SVRestimator Table 3 shows the comparison of the age estimationusing the better BIF and DLF features comparison It canbe seen that the feature extraction method proposed in thispaper is nearly 3 years better than the Gabor method andnearly 1 year better than the BIF Using this estimator is nearly2 years better than SVM and nearly 1 year better than SVRFigure 5 shows the comparison results of different estimatorsunder the DLF + FAM feature which further confirms thevalidity of the proposed estimator

53 Evaluation on Face in the Wild Experiments on faces inthe wild were conducted to demonstrate the performance ofdifferent approaches on real-world data The experiments onIMDB-WIKI [39] were carried out as follows For the taskto be equally discriminative for all ages we equalize the agedistribution ie we randomly ignore some of the imagesof the most frequent ages This leaves us with 260282 faceimages for our experiment Further the 260000 images are

Figure 4 Comparison ofMAE values of different feature extractionmethods

Figure 5 CS comparison of different estimators

split into 200000 for training 30000 images for validationand 30282 images for testing

In order to verify the advancement of this method wecompare the proposed method with the most advancedmethod based on deep learning [23ndash25] In [23] a deep net-work based on regression and classification is adopted In[24] a six-layer deep network is used to extract the age featureof the face and then the manifold learning method is usedto estimate the age In [25] a DEX network using the VGG-16 architecture is proposed which poses the age regressionproblem as a deep classification problem followed by asoftmax expected value refinement All the methods use thegeneral-to-specific deep transfer learning scheme for deepnetwork training which includes two stages ie pretrainwith face identities and fine-tune with real age

Stage 1 we firstly employ the large-scale face identitiesdatabase CASIA-WebFace [30] to pretrain the deep networkwhich is much better than random initialization

Stage 2 we employ IMDB-WIKI training set to fine-tunethe deep network from stage 1

Finally we employ IMDB-WIKI testing set (30282images) for age prediction

The results of MAE comparisons of different methods onthe IMDB-WIKI face database are shown in Table 4 It can beseen from Table 4 that the effect of using 1622-layer network

Mathematical Problems in Engineering 7

Table 4 Comparison of different methods based on deep learning

Methods MAEAge[23] 393[24] 422[25] 335Our Proposed 329

is better than that of 6-layer network which indicates thatface age is a complex nonlinear variation problem Althoughthe deep network in this paper is designed based on [23] thefinal estimation effect is better than that in [23] which showsthe validity of the divide-and-rule strategy proposed in thispaper

6 Conclusion

In this paper a robust face age feature extraction method isproposed based on the superior image representation abilityof depth convolution neural network In the aspect of fea-ture dimensionality the feature reduction method based onFAM is used to replace the PCA dimensionality reductionmethod In the estimator learning an ordinal regressionproblem is transformed into a series of binary classificationsubproblems which are collectively solved with the proposeddivide-and-rule learning algorithm By taking the ordinalrelation between ages into consideration it is more likelyto get smaller estimation errors compared with multiclassclassification approaches Experimental results show that themethod proposed in this paper is more discriminative androbust than traditional Gabor LBP and BIF methods Theperformance of the proposed age estimator is superior toSVM and SVR

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported partially by the National NaturalScience Fund (No 61373108) the Hubei Provincial NaturalScience Foundation of China (No 2017CFB168 and No2015CFC778) the Hubei Provincial Education Office Scienceand Technology Research Project youth talent project (NoQ20172805) the Hubei Provincial Education Science Plan-ning Project (No 2016GB086) and the Construction of aSpecial Scientific Research Project for Masterrsquos Point (No2018-19GZ050)

References

[1] A Lanitis and C J Taylor ldquoTowards automatic face identi-fication robust to ageing variationrdquo in Proceedings of the 4th

IEEE International Conference on Automatic Face and GestureRecognition FG 2000 pp 391ndash396 fra March 2000

[2] Z Li and A K Jain ldquoA discriminative model for age invariantface recognitionrdquo IEEE Transactions on Information Forensicsand Security vol 6 no 3 pp 1028ndash1037 2011

[3] N Dayan Skin aging handbook An Integrated Approach toBiochemistry and Product Development AndrewWilliam Press2008

[4] A Amadasi NMerusi andC Cattaneo ldquoHow reliable is appar-ent age at death on cadaversrdquo International Journal of LegalMedicine vol 129 no 4 pp 1437ndash1596 2015

[5] S B M Patzelt L K Schaible S Stampf and R J KohalldquoSoftware-based evaluation of human age A pilot studyrdquo Jour-nal of Esthetic and Restorative Dentistry vol 27 no 2 pp 100ndash106 2015

[6] W Chen W Qian G Wu et al ldquoThree-dimensional humanfacial morphologies as robust agingmarkersrdquoCell Research vol25 no 5 pp 574ndash587 2015

[7] Y Fu G Guo and T S Huang ldquoAge synthesis and estimationvia faces a surveyrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 32 no 11 pp 1955ndash1976 2010

[8] C-C Wang Y-C Su C-T Hsu C-W Lin and H Y M LiaoldquoBayesian age estimation on face imagesrdquo in Proceedings of theProceddings of the IEEE International Conference onMultimediaand Expo (ICME rsquo09) pp 282ndash285 July 2009

[9] X Geng Z Zhou and K Smith-Miles ldquoAutomatic age esti-mation based on facial aging patternsrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 29 no 12 pp2234ndash2240 2007

[10] GGuo Y Fu C RDyer andT SHuang ldquoImage-based humanage estimation bymanifold learning and locally adjusted robustregressionrdquo IEEE Transactions on Image Processing vol 17 no7 pp 1178ndash1188 2008

[11] Y Zhang andD-Y Yeung ldquoMulti-taskwarpedGaussian processfor personalized age estimationrdquo in Proceedings of the IEEEConference on Computer Vision Pattern Recognition pp 2622ndash2629 2010

[12] J Lu and Y-P Tan ldquoOrdinary preserving manifold analysis forhuman age and head pose estimationrdquo IEEE Transactions onHuman-Machine Systems vol 43 no 2 pp 249ndash258 2013

[13] K-YChang andC-S Chen ldquoA learning framework for age rankestimation based on face images with scattering transformrdquoIEEE Transactions on Image Processing vol 24 no 3 pp 785ndash798 2015

[14] Y H Kwon and N da Vitoria Lobo ldquoAge classification fromfacial imagesrdquo Computer Vision and Image Understanding vol74 no 1 pp 1ndash21 1999

[15] A Lanitis C J Taylor and T F Cootes ldquoToward automaticsimulation of aging effects on face imagesrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 24 no 4 pp442ndash455 2002

[16] A Martinez and S Du ldquoA model of the perception of facialexpressions of emotion by humans research overview andperspectivesrdquo Journal of Machine Learning Research vol 13 no1 pp 1589ndash1608 2012

[17] T Ahonen A Hadid and M Pietikainen ldquoFace descriptionwith local binary patterns application to face recognitionrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol28 no 12 pp 2037ndash2041 2006

[18] S K Zhou B Georgescu X S Zhou andD Comaniciu ldquoImagebased regression using boosting methodrdquo in Proceedings of the

8 Mathematical Problems in Engineering

10th IEEE International Conference on Computer Vision (ICCVrsquo05) pp 541ndash548 October 2005

[19] G Guo Y Fu T S Huang and C R Dyer ldquoLocally adjustedrobust regression for human age estimationrdquo in Proceedings ofthe IEEEWorkshop on Applications of Computer Vision (WACVrsquo08) pp 1ndash6 IEEE CopperMountain Colo USA January 2008

[20] Y Fu and T S Huang ldquoHuman age estimation with regressionon discriminative aging manifoldrdquo IEEE Transactions onMulti-media vol 10 no 4 pp 578ndash584 2008

[21] G Guo G Mu and Y Fu ldquoHuman age estimation using bio-inspired featuresrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition Work-shops (CVPR rsquo09) pp 112ndash119 IEEE June 2009

[22] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[23] X Liu S LiM Kan et alAgeNet Deeply Learned Regressor andClassifier for Robust Apparent Age Estimation ICCV rsquo16 2016

[24] X Wang R Guo and C Kambhamettu ldquoDeeply-LearnedFeature for Age Estimationrdquo in Proceedings of the 2015 IEEEWinter Conference on Applications of Computer Vision (WACV)pp 534ndash541 Waikoloa HI USA January 2015

[25] R Rothe R Timofte and L V Gool ldquoDEX Deep EXpectationof Apparent Age from a Single Imagerdquo in Proceedings of the 2015IEEE International Conference on Computer Vision Workshop(ICCVW) pp 252ndash257 Santiago Chile December 2015

[26] D Yi Z Lei and S Z Li ldquoAge Estimation by Multi-scale Con-volutional Networkrdquo in Computer Vision ndash ACCV 2014 vol9005 of LectureNotes in Computer Science pp 144ndash158 SpringerInternational Publishing 2015

[27] G Levi and T Hassncer ldquoAge and gender classification usingconvolutional neural networksrdquo in Proceedings of the IEEE Con-ference on Computer Vision and Pattern RecognitionWorkshopsCVPRW 2015 pp 34ndash42 usa June 2015

[28] Y Dong Y Liu and S Lian ldquoAutomatic age estimation basedon deep learning algorithmrdquo Neurocomputing vol 187 pp 4ndash10 2016

[29] Z Niu M Zhou L Wang X Gao and G Hua ldquoOrdinalRegression with Multiple Output CNN for Age Estimationrdquo inProceedings of the 2016 IEEE Conference on Computer Visionand Pattern Recognition (CVPR) pp 4920ndash4928 Las Vegas NVUSA June 2016

[30] S Chen C Zhang M Dong J Le and M Rao ldquoUsingRanking-CNN for Age Estimationrdquo in Proceedings of the 2017IEEE Conference on Computer Vision and Pattern Recognition(CVPR) pp 742ndash751 Honolulu HI July 2017

[31] C Szegedy W Liu Y Jia et al ldquoGoing deeper with convolu-tionsrdquo inProceedings of the IEEEConference onComputer Visionand Pattern Recognition (CVPR rsquo15) pp 1ndash9 BostonMass USAJune 2015

[32] D Yi Z Lei S Liao and S Li ldquoLearning face representationfrom scratchrdquo httpsarxivorgabs14117923

[33] B-C Chen C-S Chen and W H Hsu ldquoCross-age referencecoding for age-invariant face recognition and retrievalrdquo LectureNotes in Computer Science (including subseries Lecture Notesin Artificial Intelligence and Lecture Notes in Bioinformatics)Preface vol 8694 no 6 pp 768ndash783 2014

[34] K Ricanek and T Tesafaye ldquoMORPH A Longitudinal ImageDatabase of Normal Adult Age-Progressionrdquo in Proceedings ofthe 7th International Conference on Automatic Face and GestureRecognition (FGR rsquo06) pp 341ndash345 2006

[35] B Ni Z Song and S Yan ldquoWeb image and video miningtowards universal and robust age estimatorrdquo IEEE Transactionson Multimedia vol 13 no 6 pp 1217ndash1229 2011

[36] G Zhile Z Shaolong and L Haibin ldquoLinear dimensionalityreduction method for factor analysis criterionrdquo Computer Engi-neering and Applications vol 52 no 3 pp 145ndash149 2016

[37] N Hao J Yang H Liao et al ldquoA unified factors analysisframework for discriminative feature extraction and objectrecognitionrdquo Mathematical Problems in Engineering pp 1ndash122016

[38] ldquoThe FGNET Aging Databaserdquo 2013 httpwwwprimainrialpesfrFGnet

[39] R Rothe R Timofte and LVanGool ldquoDeep expectation of realand apparent age from a single image without facial landmarksrdquoInternational Journal of Computer Vision pp 1ndash14 2016

Mathematical Problems in Engineering 3

Figure 1 GoogLeNetrsquos Deep CNN Hierarchy

119910119899 is the actual age value and 119873 is the batch number Thedeepnetworkmodel is based onGoogLeNet [22] designed byGoogle et al [31] which can improve the performance underthe same computing cost It is a very effective network designmodel as shown in Figure 1

In order to further speed up the convergence rate beforethe ReLU (activation function) operation we add the layerof scale normalization (Batch Normalization BN) whileremoving all the dropout operation In order to reduce therisk of overfitting the training of deep CNN is carried outby means of network migration learning Thus the networktraining consists of two stages pretrain based on the faceidentity data set and fine-tune based on the age data set

Pretrain stage Although face identity and age are twodifferent concepts they are related In addition there aremany public large-scale face identity databases Thereforewe use the large-scale face database CASIA-WebFace [32] topretrain the network Experiments show that the method ofnetwork pretraining in face database is better than that ofrandom network initialization

Fine-tune phase This stage uses the CACD [33] Morph-II [34] and WebFaceAge [35] face age libraries to fine-tunethe networkmodel generated by the pretrain stage to producea robust age-deep network

All training and test face images are normalized to256times256 sizes In the training stage the data is augmentedThat is images of 227times227 size are randomly cut out fromthe images of 256times256 size and the images are enlarged Inthe test for the input image of 256times256 size according tothe four corners and center point of the image we cut outfive images of 227times227 size then all the cropped images arehorizontally inverted to generate the corresponding imagea total of 10 images respectively into the depth of networklearning Finally the output of last layer of GoogLeNet is usedas the face age descriptor and features of the 10 images areconcatenated to form the final face feature vector

32 Feature Reduction Based on Factor Analysis Since thefacial feature vectors obtained by deepCNNnetwork learninghave high dimensionality (10 lowast 100 = 1000 dimensions)both redundancy and noise are inevitable in this process Inorder to extract the essence of the discriminative compactfeature subset we regard each age value as a class and use

factor analysis model to deal with original feature dimensionreduction

In the factor analysis model (FAM) [36 37] it is desirableto find the optimal projection matrix to minimize thedifference in style between homogeneous (same age) samplesand to maximize the difference in content between differentclasses (different ages) We consider the features reflectingface of the characteristics of age changes as a content factorwhich is defined as follows

119865119888 = 119862minus1sum119894=1

119862sum119895=119894+1

119901119894119901119895119908 (119894 119895) (120583119894 minus 120583119895) (120583119894 minus 120583119895)119879 (2)

where 119862 is the total number of classes 119901119894 is the priorprobability of classes 119894 120583119894 is the average of the original featurevectors of the class 119894th and 119908(119894 119895) = 1(119890119889)2 (119890119889 is Euclideandistance between two classes) are the weights of the 119894th andthe 119895th classWe consider the change of face illumination andexpression as a style factor which is defined as follows

119865119904 = 119862sum119894=1

119901119894 119873119894minus1sum119895=1

119873119894sum119896=119895+1

119908 (119895 119896) (119909(119894)119895 minus 119909(119894)119896 ) (119909(119894)119895 minus 119909(119894)119896 )119879 (3)

where119909(119894)119895 119909(119894)119896 are the 119895-th and 119896-th feature vectors of class119894 respectively and 119908(119895 119896) is the weight of the 119895-th and 119896-thvector defined as

119908 (119895 119896) = exp(minus10038171003817100381710038171003817119909119895 minus 11990911989610038171003817100381710038171003817221199052 ) (4)

where 119905 is the experience parameterGiven theweighted119865119888119865119904 for FAM the objective function

of the linear factors analysis model is represented as follows

119869119865 (119882) = argmax119908

119905119903 (119882119879119865119862119882)119905119903 (119882119879119865119878119882) (5)

where 119882 is the unresolved linear mapping transformationwhich can be obtained by solving the generalized eigenvalueproblem

119865119888119882 = 120582119865119904119882 (6)

4 Mathematical Problems in Engineering

Then we can extract low-dimensional simplified and dis-criminative features 119909 from the high-dimensional redun-dant disturbed and distorted original feature 119909

119909 = 119882119879119909 (7)

By FAM we finally get the 200 dimensional eigenvectors

4 Divide-and-Rule Age EstimationFunction Learning

After obtaining the feature vector of face image age the ageestimation function can be learned and the correspondingage estimator can be trained When we compare the two faceages it is easy for humans to identify which is older butto accurately guess the age of the face is not so easy Wheninferring a personrsquos exact age we may compare the inputface with the faces of many people whose ages are knownresulting in a series of comparisons and then estimate thepersonrsquos age by integrating the results This process involvesnumerous pairwise preferences each of which is obtained bycomparing the input face to the faces in the dataset Based onthis we propose a divide-and- rule age estimation functionlearning scheme

41 Divide Given the training set of images 119868 = [1198681 1198682sdot sdot sdot 119868119894 sdot sdot sdot 119868119872] suppose 119909119894 isin 119877119863 is a face feature vector(obtained by the method of the previous section) and 119870is the total number of categories (age tags) for which thecorresponding age category 119910119894 isin 1 2 sdot sdot sdot K is to be treatedas order ranks Suppose for a given age 119896 119883 can be dividedinto the following two subsets119883+119896 and119883minus119896

119883+119896 = (119909119894 +1) | 119910119894 gt 119896119883minus119896 = (119909119894 minus1) | 119910119894 lt 119896 (8)

Based on the above two subsets we can train two-classclassifier that only answers the problem of ldquowhether this faceis older than 119896rdquo Because it only needs to make a yes or noanswer in the classification process the complexity of theproblem is reduced In addition because 119883+119896 cup 119883minus119896 = 119883sufficient training samples are ensured for each classificationwhich overcomes the problem of lack of training samplesin classifiers such as parallel-hyperplanes or one-versus-oneclassifiers (this problem is more prominent in age estima-tion)

42 Rule Once more than one classifier has been trainedthe results of all the two-class classifiers can be aggregated toestimate the age rank as with the multiple hyperplane clas-sification methods Since there is an inconsistency in all ofthe two-class classifiers a classification function 119891119896(119909) withdiscriminating performance is defined for each of the two-class classifiersThe age rank estimation problem (ie the ageestimate) becomes

119903 (119909) = 1 + 119870minus1sum119896=1

⟨119891119896 (119909) gt 0⟩ (9)

In this case a logical decision is made by ⟨∙⟩ and if theinternal condition is satisfied it returns 1 and vice versa Sinceeach classification function uses its own feature space it iseasier to obtain the optimal solution than the method usinguniform feature space

43 Categorical Function Learning Based on the Sensitive CostFunction The estimation of the final age rank in the divide-and-rule age estimation scheme relies on a series of easilyclassifiable two-class classifiersTherefore it is very importantto design an appropriate cost function ofmissed classificationfor each classifier In the case of age estimation the error ratebased on 0-1 loss is not of interest In the 0-1 loss schemeall missed classifications are given the same price which isclearly not in line with the reality of the age estimates Forexample when a personrsquos age is 119896 the 0-1 loss does not identifythe miss classification between 119896 + 1 and 119896 + 20 classesObviously the latter is more serious Therefore we study theclassification function based on the sensitive cost function

Given the training set 119883+119896 and 119883minus119896 of the 119896th class wedenote the cost function cos119905119896(119897) of the missed classificationof the age category 119897th in the subclass of the 119896th class And119862(119890119894) 119877+ cup 0 rarr 119877+ cup 0 is recorded as the cost thathas occurred in which 119890119894 = 119894 minus 119897119894 indicates the absoluteerror denoted between the estimated age and the real ageThetwo most commonly used evaluation criteria in the syntheticage estimation are the mean absolute error (MAE) and thecumulative integral (Cumulative Score CS) of the absoluteerror We define the costs that have already occurred asfollows

119862 (119890119894) = ⟨119890119894 gt 119871⟩ sdot (119890119894 minus 119871) (10)

where119871 is the acceptable tolerance for the age of the erroryou can take 3-5Therefore the cost function of the 119894th sample119909119894 in the 119896th subproblem in missed classification is expressedas

cost119905119896 (119909119894) = 119862 (119896 minus 119910119894 + 1) 119910119894 le 119896119862 (119910119894 minus 119896) 119910119894 gt 119896 (11)

With themissed classification cost function it can be usedas an important weight to adjust the data for training of thetwo-class classifier In this paper SVM is used to train thetwo-class classifier in the subproblems and the hinge loss isadjusted by using themissed classified cost function as weightitem

min119908119896 119887119896120577

12 ⟨119908119896 119887119896⟩ + 119862[sum119894

cos119905119896 (119909119896) 120577119894]119904119905 119904119896 (119894) (119908119879119896 120601119896 (119909119894) + 119887119896) ge 1 minus 120577119894

120577119894 ge 0 forall119894(12)

where 119904119896(119894) = +1 if 119909119894 isin 119883+119896 and 119904119896(119894) = -1 if 119909119894 isin X-k120601119896 denotes the mapping from feature space to Hilbert space

and ⟨119908119896 119887119896⟩ is hyperplane parameters of the hidden spaceFor age estimation problems a single kernel does not apply to

Mathematical Problems in Engineering 5

all subproblems And (12) selects different cores according tothe characteristics of the feature space in each subproblem sothat each subproblem can be well projectedThe discriminantclassification function based on the sensitive cost functioneventually becomes

119891119896 (119909) = ⟨119908119896 120601119896 (119909)⟩ + 119887119896 (13)

5 Experiments and Analysis

In this section three common age groups FG-NET [38]MORPH Album 2 [34] and IMDB-WIKI [39] are usedto test the validity of the proposed face feature extractionalgorithmand face age estimation functionTheFG-NET facedatabase consists of 1002 images of 82 different individualswith different expressions illumination and attitude changesEach one has 6 to 18 images of different ages ranging from0 to69 years old and FG-NET face age database is one of themostcommonly used public databases The MORPH2 databasecontains a total of 55000 pictures of 13000 volunteers aged16 to 77 years 45000 of which are used for network trainingand the remaining 10000 are used for testing IMDB-WIKIis the largest publicly available dataset of face images withgender and age labels for training and testing In total thereare 460723 face images from 20284 celebrities from IMDband 62328 fromWikipedia being thus 523051 in total

The age estimation indexes we used are mean absoluteerror (MAE) and cumulative index (Cumulative Score CS)and the expressions are as follows

119872119860119864 = sum119873119896=1 1003816100381610038161003816 119904119896 minus 1199041198961003816100381610038161003816119873 (14)

where 119904119896 is the actual age 119904119896 is the estimated age and 119873is the total number of pictures for testing

119862119878 (119871) = 119873119890lt119871119873 lowast 100 (15)

where 119873119890lt119871 denotes the number of test images whoseabsolute error is not larger than the set value

51 Experiment Based on FG-NET In this section we com-pare the novel face feature extraction method based ondeep learning (DLF + FAM) with Gabor + PCA LBP +PCA Gabor + LBP + PCA and BIF + PCA which are thecommon face feature extraction methods The effectivenessof the feature extraction and feature-based multidimensionalreduction algorithm is analyzedThe age estimation functionwe use is the classical SVRThe face database was trained andtested by the Leave-One-Person-Out (LOPO) strategy whichwas used to test all age images of the same person as the testset and all the others as trainingThe test procedure tests eachsample and does not overlap with the training set

Table 1 shows the comparison of MAE values of differentfeature extraction methods under SVR estimator Figure 2shows the CS comparison of different feature extractionmethods under SVR estimator It can be seen that the DLFfeatures adopted in this paper are obviously superior to

Table 1 Comparison of MAE values for different feature extractionmethods

Methods MAEAgeGabor+PCA 553LBP+PCA 592Gabor+ LBP+PCA 496BIF+PCA 477DLF+ PCA 457DLF+FAM 426

Figure 2 CS comparison of different feature extraction methods

Table 2 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 583SVR BIF + FAM 458Our Proposed BIF + FAM 432SVM DLF +FAM 477SVR DLF +FAM 426Our Proposed DLF +FAM 402

the traditional manual features In order to validate theeffectiveness of the method based on factor analysis thispaper gives the comparison of DLF + PCA and DLF + FAMIt can be seen that FAM is better than PCA This is becauseFAMmakes use of the category information of age tags

In order to verify the effectiveness of the proposed divide-and-rule age estimation function BIF and DLF face featureswith better performance are selected in this experiment andthe divide-and-rule method is compared with classical SVMand SVR methods The comparison results are shown inTable 2 and Figure 3 (using the DLF feature) and we can seethat the age estimator based on divide-and-rule method isabout 1 year better than the classic SVM and SVR

52 Experiment Based on MORPH Due to the small amountof FG-NET face databases recent studies have shown that

6 Mathematical Problems in Engineering

Figure 3 CS comparison of different estimators

Table 3 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 602SVR BIF + FAM 462Our Proposed BIF + FAM 377SVM DLF+FAM 514SVR DLF+FAM 417Our Proposed DLF+FAM 348

the corresponding algorithm in this database has very lim-ited space for improvement In order to further verify theeffectiveness of this algorithm this section will be furtherexperimented on the MORPHAlbum 2 face database 10000images were further divided 80 of which were randomlyselected for the training of the estimator and the remaining20 were used for test The average of 10 experiments wastaken as the final result

The experimental results of different feature extractionmethods are shown in Figure 4 andTable 3 Figure 4 is the ageestimation comparison under different features using SVRestimator Table 3 shows the comparison of the age estimationusing the better BIF and DLF features comparison It canbe seen that the feature extraction method proposed in thispaper is nearly 3 years better than the Gabor method andnearly 1 year better than the BIF Using this estimator is nearly2 years better than SVM and nearly 1 year better than SVRFigure 5 shows the comparison results of different estimatorsunder the DLF + FAM feature which further confirms thevalidity of the proposed estimator

53 Evaluation on Face in the Wild Experiments on faces inthe wild were conducted to demonstrate the performance ofdifferent approaches on real-world data The experiments onIMDB-WIKI [39] were carried out as follows For the taskto be equally discriminative for all ages we equalize the agedistribution ie we randomly ignore some of the imagesof the most frequent ages This leaves us with 260282 faceimages for our experiment Further the 260000 images are

Figure 4 Comparison ofMAE values of different feature extractionmethods

Figure 5 CS comparison of different estimators

split into 200000 for training 30000 images for validationand 30282 images for testing

In order to verify the advancement of this method wecompare the proposed method with the most advancedmethod based on deep learning [23ndash25] In [23] a deep net-work based on regression and classification is adopted In[24] a six-layer deep network is used to extract the age featureof the face and then the manifold learning method is usedto estimate the age In [25] a DEX network using the VGG-16 architecture is proposed which poses the age regressionproblem as a deep classification problem followed by asoftmax expected value refinement All the methods use thegeneral-to-specific deep transfer learning scheme for deepnetwork training which includes two stages ie pretrainwith face identities and fine-tune with real age

Stage 1 we firstly employ the large-scale face identitiesdatabase CASIA-WebFace [30] to pretrain the deep networkwhich is much better than random initialization

Stage 2 we employ IMDB-WIKI training set to fine-tunethe deep network from stage 1

Finally we employ IMDB-WIKI testing set (30282images) for age prediction

The results of MAE comparisons of different methods onthe IMDB-WIKI face database are shown in Table 4 It can beseen from Table 4 that the effect of using 1622-layer network

Mathematical Problems in Engineering 7

Table 4 Comparison of different methods based on deep learning

Methods MAEAge[23] 393[24] 422[25] 335Our Proposed 329

is better than that of 6-layer network which indicates thatface age is a complex nonlinear variation problem Althoughthe deep network in this paper is designed based on [23] thefinal estimation effect is better than that in [23] which showsthe validity of the divide-and-rule strategy proposed in thispaper

6 Conclusion

In this paper a robust face age feature extraction method isproposed based on the superior image representation abilityof depth convolution neural network In the aspect of fea-ture dimensionality the feature reduction method based onFAM is used to replace the PCA dimensionality reductionmethod In the estimator learning an ordinal regressionproblem is transformed into a series of binary classificationsubproblems which are collectively solved with the proposeddivide-and-rule learning algorithm By taking the ordinalrelation between ages into consideration it is more likelyto get smaller estimation errors compared with multiclassclassification approaches Experimental results show that themethod proposed in this paper is more discriminative androbust than traditional Gabor LBP and BIF methods Theperformance of the proposed age estimator is superior toSVM and SVR

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported partially by the National NaturalScience Fund (No 61373108) the Hubei Provincial NaturalScience Foundation of China (No 2017CFB168 and No2015CFC778) the Hubei Provincial Education Office Scienceand Technology Research Project youth talent project (NoQ20172805) the Hubei Provincial Education Science Plan-ning Project (No 2016GB086) and the Construction of aSpecial Scientific Research Project for Masterrsquos Point (No2018-19GZ050)

References

[1] A Lanitis and C J Taylor ldquoTowards automatic face identi-fication robust to ageing variationrdquo in Proceedings of the 4th

IEEE International Conference on Automatic Face and GestureRecognition FG 2000 pp 391ndash396 fra March 2000

[2] Z Li and A K Jain ldquoA discriminative model for age invariantface recognitionrdquo IEEE Transactions on Information Forensicsand Security vol 6 no 3 pp 1028ndash1037 2011

[3] N Dayan Skin aging handbook An Integrated Approach toBiochemistry and Product Development AndrewWilliam Press2008

[4] A Amadasi NMerusi andC Cattaneo ldquoHow reliable is appar-ent age at death on cadaversrdquo International Journal of LegalMedicine vol 129 no 4 pp 1437ndash1596 2015

[5] S B M Patzelt L K Schaible S Stampf and R J KohalldquoSoftware-based evaluation of human age A pilot studyrdquo Jour-nal of Esthetic and Restorative Dentistry vol 27 no 2 pp 100ndash106 2015

[6] W Chen W Qian G Wu et al ldquoThree-dimensional humanfacial morphologies as robust agingmarkersrdquoCell Research vol25 no 5 pp 574ndash587 2015

[7] Y Fu G Guo and T S Huang ldquoAge synthesis and estimationvia faces a surveyrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 32 no 11 pp 1955ndash1976 2010

[8] C-C Wang Y-C Su C-T Hsu C-W Lin and H Y M LiaoldquoBayesian age estimation on face imagesrdquo in Proceedings of theProceddings of the IEEE International Conference onMultimediaand Expo (ICME rsquo09) pp 282ndash285 July 2009

[9] X Geng Z Zhou and K Smith-Miles ldquoAutomatic age esti-mation based on facial aging patternsrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 29 no 12 pp2234ndash2240 2007

[10] GGuo Y Fu C RDyer andT SHuang ldquoImage-based humanage estimation bymanifold learning and locally adjusted robustregressionrdquo IEEE Transactions on Image Processing vol 17 no7 pp 1178ndash1188 2008

[11] Y Zhang andD-Y Yeung ldquoMulti-taskwarpedGaussian processfor personalized age estimationrdquo in Proceedings of the IEEEConference on Computer Vision Pattern Recognition pp 2622ndash2629 2010

[12] J Lu and Y-P Tan ldquoOrdinary preserving manifold analysis forhuman age and head pose estimationrdquo IEEE Transactions onHuman-Machine Systems vol 43 no 2 pp 249ndash258 2013

[13] K-YChang andC-S Chen ldquoA learning framework for age rankestimation based on face images with scattering transformrdquoIEEE Transactions on Image Processing vol 24 no 3 pp 785ndash798 2015

[14] Y H Kwon and N da Vitoria Lobo ldquoAge classification fromfacial imagesrdquo Computer Vision and Image Understanding vol74 no 1 pp 1ndash21 1999

[15] A Lanitis C J Taylor and T F Cootes ldquoToward automaticsimulation of aging effects on face imagesrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 24 no 4 pp442ndash455 2002

[16] A Martinez and S Du ldquoA model of the perception of facialexpressions of emotion by humans research overview andperspectivesrdquo Journal of Machine Learning Research vol 13 no1 pp 1589ndash1608 2012

[17] T Ahonen A Hadid and M Pietikainen ldquoFace descriptionwith local binary patterns application to face recognitionrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol28 no 12 pp 2037ndash2041 2006

[18] S K Zhou B Georgescu X S Zhou andD Comaniciu ldquoImagebased regression using boosting methodrdquo in Proceedings of the

8 Mathematical Problems in Engineering

10th IEEE International Conference on Computer Vision (ICCVrsquo05) pp 541ndash548 October 2005

[19] G Guo Y Fu T S Huang and C R Dyer ldquoLocally adjustedrobust regression for human age estimationrdquo in Proceedings ofthe IEEEWorkshop on Applications of Computer Vision (WACVrsquo08) pp 1ndash6 IEEE CopperMountain Colo USA January 2008

[20] Y Fu and T S Huang ldquoHuman age estimation with regressionon discriminative aging manifoldrdquo IEEE Transactions onMulti-media vol 10 no 4 pp 578ndash584 2008

[21] G Guo G Mu and Y Fu ldquoHuman age estimation using bio-inspired featuresrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition Work-shops (CVPR rsquo09) pp 112ndash119 IEEE June 2009

[22] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[23] X Liu S LiM Kan et alAgeNet Deeply Learned Regressor andClassifier for Robust Apparent Age Estimation ICCV rsquo16 2016

[24] X Wang R Guo and C Kambhamettu ldquoDeeply-LearnedFeature for Age Estimationrdquo in Proceedings of the 2015 IEEEWinter Conference on Applications of Computer Vision (WACV)pp 534ndash541 Waikoloa HI USA January 2015

[25] R Rothe R Timofte and L V Gool ldquoDEX Deep EXpectationof Apparent Age from a Single Imagerdquo in Proceedings of the 2015IEEE International Conference on Computer Vision Workshop(ICCVW) pp 252ndash257 Santiago Chile December 2015

[26] D Yi Z Lei and S Z Li ldquoAge Estimation by Multi-scale Con-volutional Networkrdquo in Computer Vision ndash ACCV 2014 vol9005 of LectureNotes in Computer Science pp 144ndash158 SpringerInternational Publishing 2015

[27] G Levi and T Hassncer ldquoAge and gender classification usingconvolutional neural networksrdquo in Proceedings of the IEEE Con-ference on Computer Vision and Pattern RecognitionWorkshopsCVPRW 2015 pp 34ndash42 usa June 2015

[28] Y Dong Y Liu and S Lian ldquoAutomatic age estimation basedon deep learning algorithmrdquo Neurocomputing vol 187 pp 4ndash10 2016

[29] Z Niu M Zhou L Wang X Gao and G Hua ldquoOrdinalRegression with Multiple Output CNN for Age Estimationrdquo inProceedings of the 2016 IEEE Conference on Computer Visionand Pattern Recognition (CVPR) pp 4920ndash4928 Las Vegas NVUSA June 2016

[30] S Chen C Zhang M Dong J Le and M Rao ldquoUsingRanking-CNN for Age Estimationrdquo in Proceedings of the 2017IEEE Conference on Computer Vision and Pattern Recognition(CVPR) pp 742ndash751 Honolulu HI July 2017

[31] C Szegedy W Liu Y Jia et al ldquoGoing deeper with convolu-tionsrdquo inProceedings of the IEEEConference onComputer Visionand Pattern Recognition (CVPR rsquo15) pp 1ndash9 BostonMass USAJune 2015

[32] D Yi Z Lei S Liao and S Li ldquoLearning face representationfrom scratchrdquo httpsarxivorgabs14117923

[33] B-C Chen C-S Chen and W H Hsu ldquoCross-age referencecoding for age-invariant face recognition and retrievalrdquo LectureNotes in Computer Science (including subseries Lecture Notesin Artificial Intelligence and Lecture Notes in Bioinformatics)Preface vol 8694 no 6 pp 768ndash783 2014

[34] K Ricanek and T Tesafaye ldquoMORPH A Longitudinal ImageDatabase of Normal Adult Age-Progressionrdquo in Proceedings ofthe 7th International Conference on Automatic Face and GestureRecognition (FGR rsquo06) pp 341ndash345 2006

[35] B Ni Z Song and S Yan ldquoWeb image and video miningtowards universal and robust age estimatorrdquo IEEE Transactionson Multimedia vol 13 no 6 pp 1217ndash1229 2011

[36] G Zhile Z Shaolong and L Haibin ldquoLinear dimensionalityreduction method for factor analysis criterionrdquo Computer Engi-neering and Applications vol 52 no 3 pp 145ndash149 2016

[37] N Hao J Yang H Liao et al ldquoA unified factors analysisframework for discriminative feature extraction and objectrecognitionrdquo Mathematical Problems in Engineering pp 1ndash122016

[38] ldquoThe FGNET Aging Databaserdquo 2013 httpwwwprimainrialpesfrFGnet

[39] R Rothe R Timofte and LVanGool ldquoDeep expectation of realand apparent age from a single image without facial landmarksrdquoInternational Journal of Computer Vision pp 1ndash14 2016

4 Mathematical Problems in Engineering

Then we can extract low-dimensional simplified and dis-criminative features 119909 from the high-dimensional redun-dant disturbed and distorted original feature 119909

119909 = 119882119879119909 (7)

By FAM we finally get the 200 dimensional eigenvectors

4 Divide-and-Rule Age EstimationFunction Learning

After obtaining the feature vector of face image age the ageestimation function can be learned and the correspondingage estimator can be trained When we compare the two faceages it is easy for humans to identify which is older butto accurately guess the age of the face is not so easy Wheninferring a personrsquos exact age we may compare the inputface with the faces of many people whose ages are knownresulting in a series of comparisons and then estimate thepersonrsquos age by integrating the results This process involvesnumerous pairwise preferences each of which is obtained bycomparing the input face to the faces in the dataset Based onthis we propose a divide-and- rule age estimation functionlearning scheme

41 Divide Given the training set of images 119868 = [1198681 1198682sdot sdot sdot 119868119894 sdot sdot sdot 119868119872] suppose 119909119894 isin 119877119863 is a face feature vector(obtained by the method of the previous section) and 119870is the total number of categories (age tags) for which thecorresponding age category 119910119894 isin 1 2 sdot sdot sdot K is to be treatedas order ranks Suppose for a given age 119896 119883 can be dividedinto the following two subsets119883+119896 and119883minus119896

119883+119896 = (119909119894 +1) | 119910119894 gt 119896119883minus119896 = (119909119894 minus1) | 119910119894 lt 119896 (8)

Based on the above two subsets we can train two-classclassifier that only answers the problem of ldquowhether this faceis older than 119896rdquo Because it only needs to make a yes or noanswer in the classification process the complexity of theproblem is reduced In addition because 119883+119896 cup 119883minus119896 = 119883sufficient training samples are ensured for each classificationwhich overcomes the problem of lack of training samplesin classifiers such as parallel-hyperplanes or one-versus-oneclassifiers (this problem is more prominent in age estima-tion)

42 Rule Once more than one classifier has been trainedthe results of all the two-class classifiers can be aggregated toestimate the age rank as with the multiple hyperplane clas-sification methods Since there is an inconsistency in all ofthe two-class classifiers a classification function 119891119896(119909) withdiscriminating performance is defined for each of the two-class classifiersThe age rank estimation problem (ie the ageestimate) becomes

119903 (119909) = 1 + 119870minus1sum119896=1

⟨119891119896 (119909) gt 0⟩ (9)

In this case a logical decision is made by ⟨∙⟩ and if theinternal condition is satisfied it returns 1 and vice versa Sinceeach classification function uses its own feature space it iseasier to obtain the optimal solution than the method usinguniform feature space

43 Categorical Function Learning Based on the Sensitive CostFunction The estimation of the final age rank in the divide-and-rule age estimation scheme relies on a series of easilyclassifiable two-class classifiersTherefore it is very importantto design an appropriate cost function ofmissed classificationfor each classifier In the case of age estimation the error ratebased on 0-1 loss is not of interest In the 0-1 loss schemeall missed classifications are given the same price which isclearly not in line with the reality of the age estimates Forexample when a personrsquos age is 119896 the 0-1 loss does not identifythe miss classification between 119896 + 1 and 119896 + 20 classesObviously the latter is more serious Therefore we study theclassification function based on the sensitive cost function

Given the training set 119883+119896 and 119883minus119896 of the 119896th class wedenote the cost function cos119905119896(119897) of the missed classificationof the age category 119897th in the subclass of the 119896th class And119862(119890119894) 119877+ cup 0 rarr 119877+ cup 0 is recorded as the cost thathas occurred in which 119890119894 = 119894 minus 119897119894 indicates the absoluteerror denoted between the estimated age and the real ageThetwo most commonly used evaluation criteria in the syntheticage estimation are the mean absolute error (MAE) and thecumulative integral (Cumulative Score CS) of the absoluteerror We define the costs that have already occurred asfollows

119862 (119890119894) = ⟨119890119894 gt 119871⟩ sdot (119890119894 minus 119871) (10)

where119871 is the acceptable tolerance for the age of the erroryou can take 3-5Therefore the cost function of the 119894th sample119909119894 in the 119896th subproblem in missed classification is expressedas

cost119905119896 (119909119894) = 119862 (119896 minus 119910119894 + 1) 119910119894 le 119896119862 (119910119894 minus 119896) 119910119894 gt 119896 (11)

With themissed classification cost function it can be usedas an important weight to adjust the data for training of thetwo-class classifier In this paper SVM is used to train thetwo-class classifier in the subproblems and the hinge loss isadjusted by using themissed classified cost function as weightitem

min119908119896 119887119896120577

12 ⟨119908119896 119887119896⟩ + 119862[sum119894

cos119905119896 (119909119896) 120577119894]119904119905 119904119896 (119894) (119908119879119896 120601119896 (119909119894) + 119887119896) ge 1 minus 120577119894

120577119894 ge 0 forall119894(12)

where 119904119896(119894) = +1 if 119909119894 isin 119883+119896 and 119904119896(119894) = -1 if 119909119894 isin X-k120601119896 denotes the mapping from feature space to Hilbert space

and ⟨119908119896 119887119896⟩ is hyperplane parameters of the hidden spaceFor age estimation problems a single kernel does not apply to

Mathematical Problems in Engineering 5

all subproblems And (12) selects different cores according tothe characteristics of the feature space in each subproblem sothat each subproblem can be well projectedThe discriminantclassification function based on the sensitive cost functioneventually becomes

119891119896 (119909) = ⟨119908119896 120601119896 (119909)⟩ + 119887119896 (13)

5 Experiments and Analysis

In this section three common age groups FG-NET [38]MORPH Album 2 [34] and IMDB-WIKI [39] are usedto test the validity of the proposed face feature extractionalgorithmand face age estimation functionTheFG-NET facedatabase consists of 1002 images of 82 different individualswith different expressions illumination and attitude changesEach one has 6 to 18 images of different ages ranging from0 to69 years old and FG-NET face age database is one of themostcommonly used public databases The MORPH2 databasecontains a total of 55000 pictures of 13000 volunteers aged16 to 77 years 45000 of which are used for network trainingand the remaining 10000 are used for testing IMDB-WIKIis the largest publicly available dataset of face images withgender and age labels for training and testing In total thereare 460723 face images from 20284 celebrities from IMDband 62328 fromWikipedia being thus 523051 in total

The age estimation indexes we used are mean absoluteerror (MAE) and cumulative index (Cumulative Score CS)and the expressions are as follows

119872119860119864 = sum119873119896=1 1003816100381610038161003816 119904119896 minus 1199041198961003816100381610038161003816119873 (14)

where 119904119896 is the actual age 119904119896 is the estimated age and 119873is the total number of pictures for testing

119862119878 (119871) = 119873119890lt119871119873 lowast 100 (15)

where 119873119890lt119871 denotes the number of test images whoseabsolute error is not larger than the set value

51 Experiment Based on FG-NET In this section we com-pare the novel face feature extraction method based ondeep learning (DLF + FAM) with Gabor + PCA LBP +PCA Gabor + LBP + PCA and BIF + PCA which are thecommon face feature extraction methods The effectivenessof the feature extraction and feature-based multidimensionalreduction algorithm is analyzedThe age estimation functionwe use is the classical SVRThe face database was trained andtested by the Leave-One-Person-Out (LOPO) strategy whichwas used to test all age images of the same person as the testset and all the others as trainingThe test procedure tests eachsample and does not overlap with the training set

Table 1 shows the comparison of MAE values of differentfeature extraction methods under SVR estimator Figure 2shows the CS comparison of different feature extractionmethods under SVR estimator It can be seen that the DLFfeatures adopted in this paper are obviously superior to

Table 1 Comparison of MAE values for different feature extractionmethods

Methods MAEAgeGabor+PCA 553LBP+PCA 592Gabor+ LBP+PCA 496BIF+PCA 477DLF+ PCA 457DLF+FAM 426

Figure 2 CS comparison of different feature extraction methods

Table 2 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 583SVR BIF + FAM 458Our Proposed BIF + FAM 432SVM DLF +FAM 477SVR DLF +FAM 426Our Proposed DLF +FAM 402

the traditional manual features In order to validate theeffectiveness of the method based on factor analysis thispaper gives the comparison of DLF + PCA and DLF + FAMIt can be seen that FAM is better than PCA This is becauseFAMmakes use of the category information of age tags

In order to verify the effectiveness of the proposed divide-and-rule age estimation function BIF and DLF face featureswith better performance are selected in this experiment andthe divide-and-rule method is compared with classical SVMand SVR methods The comparison results are shown inTable 2 and Figure 3 (using the DLF feature) and we can seethat the age estimator based on divide-and-rule method isabout 1 year better than the classic SVM and SVR

52 Experiment Based on MORPH Due to the small amountof FG-NET face databases recent studies have shown that

6 Mathematical Problems in Engineering

Figure 3 CS comparison of different estimators

Table 3 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 602SVR BIF + FAM 462Our Proposed BIF + FAM 377SVM DLF+FAM 514SVR DLF+FAM 417Our Proposed DLF+FAM 348

the corresponding algorithm in this database has very lim-ited space for improvement In order to further verify theeffectiveness of this algorithm this section will be furtherexperimented on the MORPHAlbum 2 face database 10000images were further divided 80 of which were randomlyselected for the training of the estimator and the remaining20 were used for test The average of 10 experiments wastaken as the final result

The experimental results of different feature extractionmethods are shown in Figure 4 andTable 3 Figure 4 is the ageestimation comparison under different features using SVRestimator Table 3 shows the comparison of the age estimationusing the better BIF and DLF features comparison It canbe seen that the feature extraction method proposed in thispaper is nearly 3 years better than the Gabor method andnearly 1 year better than the BIF Using this estimator is nearly2 years better than SVM and nearly 1 year better than SVRFigure 5 shows the comparison results of different estimatorsunder the DLF + FAM feature which further confirms thevalidity of the proposed estimator

53 Evaluation on Face in the Wild Experiments on faces inthe wild were conducted to demonstrate the performance ofdifferent approaches on real-world data The experiments onIMDB-WIKI [39] were carried out as follows For the taskto be equally discriminative for all ages we equalize the agedistribution ie we randomly ignore some of the imagesof the most frequent ages This leaves us with 260282 faceimages for our experiment Further the 260000 images are

Figure 4 Comparison ofMAE values of different feature extractionmethods

Figure 5 CS comparison of different estimators

split into 200000 for training 30000 images for validationand 30282 images for testing

In order to verify the advancement of this method wecompare the proposed method with the most advancedmethod based on deep learning [23ndash25] In [23] a deep net-work based on regression and classification is adopted In[24] a six-layer deep network is used to extract the age featureof the face and then the manifold learning method is usedto estimate the age In [25] a DEX network using the VGG-16 architecture is proposed which poses the age regressionproblem as a deep classification problem followed by asoftmax expected value refinement All the methods use thegeneral-to-specific deep transfer learning scheme for deepnetwork training which includes two stages ie pretrainwith face identities and fine-tune with real age

Stage 1 we firstly employ the large-scale face identitiesdatabase CASIA-WebFace [30] to pretrain the deep networkwhich is much better than random initialization

Stage 2 we employ IMDB-WIKI training set to fine-tunethe deep network from stage 1

Finally we employ IMDB-WIKI testing set (30282images) for age prediction

The results of MAE comparisons of different methods onthe IMDB-WIKI face database are shown in Table 4 It can beseen from Table 4 that the effect of using 1622-layer network

Mathematical Problems in Engineering 7

Table 4 Comparison of different methods based on deep learning

Methods MAEAge[23] 393[24] 422[25] 335Our Proposed 329

is better than that of 6-layer network which indicates thatface age is a complex nonlinear variation problem Althoughthe deep network in this paper is designed based on [23] thefinal estimation effect is better than that in [23] which showsthe validity of the divide-and-rule strategy proposed in thispaper

6 Conclusion

In this paper a robust face age feature extraction method isproposed based on the superior image representation abilityof depth convolution neural network In the aspect of fea-ture dimensionality the feature reduction method based onFAM is used to replace the PCA dimensionality reductionmethod In the estimator learning an ordinal regressionproblem is transformed into a series of binary classificationsubproblems which are collectively solved with the proposeddivide-and-rule learning algorithm By taking the ordinalrelation between ages into consideration it is more likelyto get smaller estimation errors compared with multiclassclassification approaches Experimental results show that themethod proposed in this paper is more discriminative androbust than traditional Gabor LBP and BIF methods Theperformance of the proposed age estimator is superior toSVM and SVR

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported partially by the National NaturalScience Fund (No 61373108) the Hubei Provincial NaturalScience Foundation of China (No 2017CFB168 and No2015CFC778) the Hubei Provincial Education Office Scienceand Technology Research Project youth talent project (NoQ20172805) the Hubei Provincial Education Science Plan-ning Project (No 2016GB086) and the Construction of aSpecial Scientific Research Project for Masterrsquos Point (No2018-19GZ050)

References

[1] A Lanitis and C J Taylor ldquoTowards automatic face identi-fication robust to ageing variationrdquo in Proceedings of the 4th

IEEE International Conference on Automatic Face and GestureRecognition FG 2000 pp 391ndash396 fra March 2000

[2] Z Li and A K Jain ldquoA discriminative model for age invariantface recognitionrdquo IEEE Transactions on Information Forensicsand Security vol 6 no 3 pp 1028ndash1037 2011

[3] N Dayan Skin aging handbook An Integrated Approach toBiochemistry and Product Development AndrewWilliam Press2008

[4] A Amadasi NMerusi andC Cattaneo ldquoHow reliable is appar-ent age at death on cadaversrdquo International Journal of LegalMedicine vol 129 no 4 pp 1437ndash1596 2015

[5] S B M Patzelt L K Schaible S Stampf and R J KohalldquoSoftware-based evaluation of human age A pilot studyrdquo Jour-nal of Esthetic and Restorative Dentistry vol 27 no 2 pp 100ndash106 2015

[6] W Chen W Qian G Wu et al ldquoThree-dimensional humanfacial morphologies as robust agingmarkersrdquoCell Research vol25 no 5 pp 574ndash587 2015

[7] Y Fu G Guo and T S Huang ldquoAge synthesis and estimationvia faces a surveyrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 32 no 11 pp 1955ndash1976 2010

[8] C-C Wang Y-C Su C-T Hsu C-W Lin and H Y M LiaoldquoBayesian age estimation on face imagesrdquo in Proceedings of theProceddings of the IEEE International Conference onMultimediaand Expo (ICME rsquo09) pp 282ndash285 July 2009

[9] X Geng Z Zhou and K Smith-Miles ldquoAutomatic age esti-mation based on facial aging patternsrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 29 no 12 pp2234ndash2240 2007

[10] GGuo Y Fu C RDyer andT SHuang ldquoImage-based humanage estimation bymanifold learning and locally adjusted robustregressionrdquo IEEE Transactions on Image Processing vol 17 no7 pp 1178ndash1188 2008

[11] Y Zhang andD-Y Yeung ldquoMulti-taskwarpedGaussian processfor personalized age estimationrdquo in Proceedings of the IEEEConference on Computer Vision Pattern Recognition pp 2622ndash2629 2010

[12] J Lu and Y-P Tan ldquoOrdinary preserving manifold analysis forhuman age and head pose estimationrdquo IEEE Transactions onHuman-Machine Systems vol 43 no 2 pp 249ndash258 2013

[13] K-YChang andC-S Chen ldquoA learning framework for age rankestimation based on face images with scattering transformrdquoIEEE Transactions on Image Processing vol 24 no 3 pp 785ndash798 2015

[14] Y H Kwon and N da Vitoria Lobo ldquoAge classification fromfacial imagesrdquo Computer Vision and Image Understanding vol74 no 1 pp 1ndash21 1999

[15] A Lanitis C J Taylor and T F Cootes ldquoToward automaticsimulation of aging effects on face imagesrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 24 no 4 pp442ndash455 2002

[16] A Martinez and S Du ldquoA model of the perception of facialexpressions of emotion by humans research overview andperspectivesrdquo Journal of Machine Learning Research vol 13 no1 pp 1589ndash1608 2012

[17] T Ahonen A Hadid and M Pietikainen ldquoFace descriptionwith local binary patterns application to face recognitionrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol28 no 12 pp 2037ndash2041 2006

[18] S K Zhou B Georgescu X S Zhou andD Comaniciu ldquoImagebased regression using boosting methodrdquo in Proceedings of the

8 Mathematical Problems in Engineering

10th IEEE International Conference on Computer Vision (ICCVrsquo05) pp 541ndash548 October 2005

[19] G Guo Y Fu T S Huang and C R Dyer ldquoLocally adjustedrobust regression for human age estimationrdquo in Proceedings ofthe IEEEWorkshop on Applications of Computer Vision (WACVrsquo08) pp 1ndash6 IEEE CopperMountain Colo USA January 2008

[20] Y Fu and T S Huang ldquoHuman age estimation with regressionon discriminative aging manifoldrdquo IEEE Transactions onMulti-media vol 10 no 4 pp 578ndash584 2008

[21] G Guo G Mu and Y Fu ldquoHuman age estimation using bio-inspired featuresrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition Work-shops (CVPR rsquo09) pp 112ndash119 IEEE June 2009

[22] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[23] X Liu S LiM Kan et alAgeNet Deeply Learned Regressor andClassifier for Robust Apparent Age Estimation ICCV rsquo16 2016

[24] X Wang R Guo and C Kambhamettu ldquoDeeply-LearnedFeature for Age Estimationrdquo in Proceedings of the 2015 IEEEWinter Conference on Applications of Computer Vision (WACV)pp 534ndash541 Waikoloa HI USA January 2015

[25] R Rothe R Timofte and L V Gool ldquoDEX Deep EXpectationof Apparent Age from a Single Imagerdquo in Proceedings of the 2015IEEE International Conference on Computer Vision Workshop(ICCVW) pp 252ndash257 Santiago Chile December 2015

[26] D Yi Z Lei and S Z Li ldquoAge Estimation by Multi-scale Con-volutional Networkrdquo in Computer Vision ndash ACCV 2014 vol9005 of LectureNotes in Computer Science pp 144ndash158 SpringerInternational Publishing 2015

[27] G Levi and T Hassncer ldquoAge and gender classification usingconvolutional neural networksrdquo in Proceedings of the IEEE Con-ference on Computer Vision and Pattern RecognitionWorkshopsCVPRW 2015 pp 34ndash42 usa June 2015

[28] Y Dong Y Liu and S Lian ldquoAutomatic age estimation basedon deep learning algorithmrdquo Neurocomputing vol 187 pp 4ndash10 2016

[29] Z Niu M Zhou L Wang X Gao and G Hua ldquoOrdinalRegression with Multiple Output CNN for Age Estimationrdquo inProceedings of the 2016 IEEE Conference on Computer Visionand Pattern Recognition (CVPR) pp 4920ndash4928 Las Vegas NVUSA June 2016

[30] S Chen C Zhang M Dong J Le and M Rao ldquoUsingRanking-CNN for Age Estimationrdquo in Proceedings of the 2017IEEE Conference on Computer Vision and Pattern Recognition(CVPR) pp 742ndash751 Honolulu HI July 2017

[31] C Szegedy W Liu Y Jia et al ldquoGoing deeper with convolu-tionsrdquo inProceedings of the IEEEConference onComputer Visionand Pattern Recognition (CVPR rsquo15) pp 1ndash9 BostonMass USAJune 2015

[32] D Yi Z Lei S Liao and S Li ldquoLearning face representationfrom scratchrdquo httpsarxivorgabs14117923

[33] B-C Chen C-S Chen and W H Hsu ldquoCross-age referencecoding for age-invariant face recognition and retrievalrdquo LectureNotes in Computer Science (including subseries Lecture Notesin Artificial Intelligence and Lecture Notes in Bioinformatics)Preface vol 8694 no 6 pp 768ndash783 2014

[34] K Ricanek and T Tesafaye ldquoMORPH A Longitudinal ImageDatabase of Normal Adult Age-Progressionrdquo in Proceedings ofthe 7th International Conference on Automatic Face and GestureRecognition (FGR rsquo06) pp 341ndash345 2006

[35] B Ni Z Song and S Yan ldquoWeb image and video miningtowards universal and robust age estimatorrdquo IEEE Transactionson Multimedia vol 13 no 6 pp 1217ndash1229 2011

[36] G Zhile Z Shaolong and L Haibin ldquoLinear dimensionalityreduction method for factor analysis criterionrdquo Computer Engi-neering and Applications vol 52 no 3 pp 145ndash149 2016

[37] N Hao J Yang H Liao et al ldquoA unified factors analysisframework for discriminative feature extraction and objectrecognitionrdquo Mathematical Problems in Engineering pp 1ndash122016

[38] ldquoThe FGNET Aging Databaserdquo 2013 httpwwwprimainrialpesfrFGnet

[39] R Rothe R Timofte and LVanGool ldquoDeep expectation of realand apparent age from a single image without facial landmarksrdquoInternational Journal of Computer Vision pp 1ndash14 2016

Mathematical Problems in Engineering 5

all subproblems And (12) selects different cores according tothe characteristics of the feature space in each subproblem sothat each subproblem can be well projectedThe discriminantclassification function based on the sensitive cost functioneventually becomes

119891119896 (119909) = ⟨119908119896 120601119896 (119909)⟩ + 119887119896 (13)

5 Experiments and Analysis

In this section three common age groups FG-NET [38]MORPH Album 2 [34] and IMDB-WIKI [39] are usedto test the validity of the proposed face feature extractionalgorithmand face age estimation functionTheFG-NET facedatabase consists of 1002 images of 82 different individualswith different expressions illumination and attitude changesEach one has 6 to 18 images of different ages ranging from0 to69 years old and FG-NET face age database is one of themostcommonly used public databases The MORPH2 databasecontains a total of 55000 pictures of 13000 volunteers aged16 to 77 years 45000 of which are used for network trainingand the remaining 10000 are used for testing IMDB-WIKIis the largest publicly available dataset of face images withgender and age labels for training and testing In total thereare 460723 face images from 20284 celebrities from IMDband 62328 fromWikipedia being thus 523051 in total

The age estimation indexes we used are mean absoluteerror (MAE) and cumulative index (Cumulative Score CS)and the expressions are as follows

119872119860119864 = sum119873119896=1 1003816100381610038161003816 119904119896 minus 1199041198961003816100381610038161003816119873 (14)

where 119904119896 is the actual age 119904119896 is the estimated age and 119873is the total number of pictures for testing

119862119878 (119871) = 119873119890lt119871119873 lowast 100 (15)

where 119873119890lt119871 denotes the number of test images whoseabsolute error is not larger than the set value

51 Experiment Based on FG-NET In this section we com-pare the novel face feature extraction method based ondeep learning (DLF + FAM) with Gabor + PCA LBP +PCA Gabor + LBP + PCA and BIF + PCA which are thecommon face feature extraction methods The effectivenessof the feature extraction and feature-based multidimensionalreduction algorithm is analyzedThe age estimation functionwe use is the classical SVRThe face database was trained andtested by the Leave-One-Person-Out (LOPO) strategy whichwas used to test all age images of the same person as the testset and all the others as trainingThe test procedure tests eachsample and does not overlap with the training set

Table 1 shows the comparison of MAE values of differentfeature extraction methods under SVR estimator Figure 2shows the CS comparison of different feature extractionmethods under SVR estimator It can be seen that the DLFfeatures adopted in this paper are obviously superior to

Table 1 Comparison of MAE values for different feature extractionmethods

Methods MAEAgeGabor+PCA 553LBP+PCA 592Gabor+ LBP+PCA 496BIF+PCA 477DLF+ PCA 457DLF+FAM 426

Figure 2 CS comparison of different feature extraction methods

Table 2 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 583SVR BIF + FAM 458Our Proposed BIF + FAM 432SVM DLF +FAM 477SVR DLF +FAM 426Our Proposed DLF +FAM 402

the traditional manual features In order to validate theeffectiveness of the method based on factor analysis thispaper gives the comparison of DLF + PCA and DLF + FAMIt can be seen that FAM is better than PCA This is becauseFAMmakes use of the category information of age tags

In order to verify the effectiveness of the proposed divide-and-rule age estimation function BIF and DLF face featureswith better performance are selected in this experiment andthe divide-and-rule method is compared with classical SVMand SVR methods The comparison results are shown inTable 2 and Figure 3 (using the DLF feature) and we can seethat the age estimator based on divide-and-rule method isabout 1 year better than the classic SVM and SVR

52 Experiment Based on MORPH Due to the small amountof FG-NET face databases recent studies have shown that

6 Mathematical Problems in Engineering

Figure 3 CS comparison of different estimators

Table 3 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 602SVR BIF + FAM 462Our Proposed BIF + FAM 377SVM DLF+FAM 514SVR DLF+FAM 417Our Proposed DLF+FAM 348

the corresponding algorithm in this database has very lim-ited space for improvement In order to further verify theeffectiveness of this algorithm this section will be furtherexperimented on the MORPHAlbum 2 face database 10000images were further divided 80 of which were randomlyselected for the training of the estimator and the remaining20 were used for test The average of 10 experiments wastaken as the final result

The experimental results of different feature extractionmethods are shown in Figure 4 andTable 3 Figure 4 is the ageestimation comparison under different features using SVRestimator Table 3 shows the comparison of the age estimationusing the better BIF and DLF features comparison It canbe seen that the feature extraction method proposed in thispaper is nearly 3 years better than the Gabor method andnearly 1 year better than the BIF Using this estimator is nearly2 years better than SVM and nearly 1 year better than SVRFigure 5 shows the comparison results of different estimatorsunder the DLF + FAM feature which further confirms thevalidity of the proposed estimator

53 Evaluation on Face in the Wild Experiments on faces inthe wild were conducted to demonstrate the performance ofdifferent approaches on real-world data The experiments onIMDB-WIKI [39] were carried out as follows For the taskto be equally discriminative for all ages we equalize the agedistribution ie we randomly ignore some of the imagesof the most frequent ages This leaves us with 260282 faceimages for our experiment Further the 260000 images are

Figure 4 Comparison ofMAE values of different feature extractionmethods

Figure 5 CS comparison of different estimators

split into 200000 for training 30000 images for validationand 30282 images for testing

In order to verify the advancement of this method wecompare the proposed method with the most advancedmethod based on deep learning [23ndash25] In [23] a deep net-work based on regression and classification is adopted In[24] a six-layer deep network is used to extract the age featureof the face and then the manifold learning method is usedto estimate the age In [25] a DEX network using the VGG-16 architecture is proposed which poses the age regressionproblem as a deep classification problem followed by asoftmax expected value refinement All the methods use thegeneral-to-specific deep transfer learning scheme for deepnetwork training which includes two stages ie pretrainwith face identities and fine-tune with real age

Stage 1 we firstly employ the large-scale face identitiesdatabase CASIA-WebFace [30] to pretrain the deep networkwhich is much better than random initialization

Stage 2 we employ IMDB-WIKI training set to fine-tunethe deep network from stage 1

Finally we employ IMDB-WIKI testing set (30282images) for age prediction

The results of MAE comparisons of different methods onthe IMDB-WIKI face database are shown in Table 4 It can beseen from Table 4 that the effect of using 1622-layer network

Mathematical Problems in Engineering 7

Table 4 Comparison of different methods based on deep learning

Methods MAEAge[23] 393[24] 422[25] 335Our Proposed 329

is better than that of 6-layer network which indicates thatface age is a complex nonlinear variation problem Althoughthe deep network in this paper is designed based on [23] thefinal estimation effect is better than that in [23] which showsthe validity of the divide-and-rule strategy proposed in thispaper

6 Conclusion

In this paper a robust face age feature extraction method isproposed based on the superior image representation abilityof depth convolution neural network In the aspect of fea-ture dimensionality the feature reduction method based onFAM is used to replace the PCA dimensionality reductionmethod In the estimator learning an ordinal regressionproblem is transformed into a series of binary classificationsubproblems which are collectively solved with the proposeddivide-and-rule learning algorithm By taking the ordinalrelation between ages into consideration it is more likelyto get smaller estimation errors compared with multiclassclassification approaches Experimental results show that themethod proposed in this paper is more discriminative androbust than traditional Gabor LBP and BIF methods Theperformance of the proposed age estimator is superior toSVM and SVR

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported partially by the National NaturalScience Fund (No 61373108) the Hubei Provincial NaturalScience Foundation of China (No 2017CFB168 and No2015CFC778) the Hubei Provincial Education Office Scienceand Technology Research Project youth talent project (NoQ20172805) the Hubei Provincial Education Science Plan-ning Project (No 2016GB086) and the Construction of aSpecial Scientific Research Project for Masterrsquos Point (No2018-19GZ050)

References

[1] A Lanitis and C J Taylor ldquoTowards automatic face identi-fication robust to ageing variationrdquo in Proceedings of the 4th

IEEE International Conference on Automatic Face and GestureRecognition FG 2000 pp 391ndash396 fra March 2000

[2] Z Li and A K Jain ldquoA discriminative model for age invariantface recognitionrdquo IEEE Transactions on Information Forensicsand Security vol 6 no 3 pp 1028ndash1037 2011

[3] N Dayan Skin aging handbook An Integrated Approach toBiochemistry and Product Development AndrewWilliam Press2008

[4] A Amadasi NMerusi andC Cattaneo ldquoHow reliable is appar-ent age at death on cadaversrdquo International Journal of LegalMedicine vol 129 no 4 pp 1437ndash1596 2015

[5] S B M Patzelt L K Schaible S Stampf and R J KohalldquoSoftware-based evaluation of human age A pilot studyrdquo Jour-nal of Esthetic and Restorative Dentistry vol 27 no 2 pp 100ndash106 2015

[6] W Chen W Qian G Wu et al ldquoThree-dimensional humanfacial morphologies as robust agingmarkersrdquoCell Research vol25 no 5 pp 574ndash587 2015

[7] Y Fu G Guo and T S Huang ldquoAge synthesis and estimationvia faces a surveyrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 32 no 11 pp 1955ndash1976 2010

[8] C-C Wang Y-C Su C-T Hsu C-W Lin and H Y M LiaoldquoBayesian age estimation on face imagesrdquo in Proceedings of theProceddings of the IEEE International Conference onMultimediaand Expo (ICME rsquo09) pp 282ndash285 July 2009

[9] X Geng Z Zhou and K Smith-Miles ldquoAutomatic age esti-mation based on facial aging patternsrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 29 no 12 pp2234ndash2240 2007

[10] GGuo Y Fu C RDyer andT SHuang ldquoImage-based humanage estimation bymanifold learning and locally adjusted robustregressionrdquo IEEE Transactions on Image Processing vol 17 no7 pp 1178ndash1188 2008

[11] Y Zhang andD-Y Yeung ldquoMulti-taskwarpedGaussian processfor personalized age estimationrdquo in Proceedings of the IEEEConference on Computer Vision Pattern Recognition pp 2622ndash2629 2010

[12] J Lu and Y-P Tan ldquoOrdinary preserving manifold analysis forhuman age and head pose estimationrdquo IEEE Transactions onHuman-Machine Systems vol 43 no 2 pp 249ndash258 2013

[13] K-YChang andC-S Chen ldquoA learning framework for age rankestimation based on face images with scattering transformrdquoIEEE Transactions on Image Processing vol 24 no 3 pp 785ndash798 2015

[14] Y H Kwon and N da Vitoria Lobo ldquoAge classification fromfacial imagesrdquo Computer Vision and Image Understanding vol74 no 1 pp 1ndash21 1999

[15] A Lanitis C J Taylor and T F Cootes ldquoToward automaticsimulation of aging effects on face imagesrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 24 no 4 pp442ndash455 2002

[16] A Martinez and S Du ldquoA model of the perception of facialexpressions of emotion by humans research overview andperspectivesrdquo Journal of Machine Learning Research vol 13 no1 pp 1589ndash1608 2012

[17] T Ahonen A Hadid and M Pietikainen ldquoFace descriptionwith local binary patterns application to face recognitionrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol28 no 12 pp 2037ndash2041 2006

[18] S K Zhou B Georgescu X S Zhou andD Comaniciu ldquoImagebased regression using boosting methodrdquo in Proceedings of the

8 Mathematical Problems in Engineering

10th IEEE International Conference on Computer Vision (ICCVrsquo05) pp 541ndash548 October 2005

[19] G Guo Y Fu T S Huang and C R Dyer ldquoLocally adjustedrobust regression for human age estimationrdquo in Proceedings ofthe IEEEWorkshop on Applications of Computer Vision (WACVrsquo08) pp 1ndash6 IEEE CopperMountain Colo USA January 2008

[20] Y Fu and T S Huang ldquoHuman age estimation with regressionon discriminative aging manifoldrdquo IEEE Transactions onMulti-media vol 10 no 4 pp 578ndash584 2008

[21] G Guo G Mu and Y Fu ldquoHuman age estimation using bio-inspired featuresrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition Work-shops (CVPR rsquo09) pp 112ndash119 IEEE June 2009

[22] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[23] X Liu S LiM Kan et alAgeNet Deeply Learned Regressor andClassifier for Robust Apparent Age Estimation ICCV rsquo16 2016

[24] X Wang R Guo and C Kambhamettu ldquoDeeply-LearnedFeature for Age Estimationrdquo in Proceedings of the 2015 IEEEWinter Conference on Applications of Computer Vision (WACV)pp 534ndash541 Waikoloa HI USA January 2015

[25] R Rothe R Timofte and L V Gool ldquoDEX Deep EXpectationof Apparent Age from a Single Imagerdquo in Proceedings of the 2015IEEE International Conference on Computer Vision Workshop(ICCVW) pp 252ndash257 Santiago Chile December 2015

[26] D Yi Z Lei and S Z Li ldquoAge Estimation by Multi-scale Con-volutional Networkrdquo in Computer Vision ndash ACCV 2014 vol9005 of LectureNotes in Computer Science pp 144ndash158 SpringerInternational Publishing 2015

[27] G Levi and T Hassncer ldquoAge and gender classification usingconvolutional neural networksrdquo in Proceedings of the IEEE Con-ference on Computer Vision and Pattern RecognitionWorkshopsCVPRW 2015 pp 34ndash42 usa June 2015

[28] Y Dong Y Liu and S Lian ldquoAutomatic age estimation basedon deep learning algorithmrdquo Neurocomputing vol 187 pp 4ndash10 2016

[29] Z Niu M Zhou L Wang X Gao and G Hua ldquoOrdinalRegression with Multiple Output CNN for Age Estimationrdquo inProceedings of the 2016 IEEE Conference on Computer Visionand Pattern Recognition (CVPR) pp 4920ndash4928 Las Vegas NVUSA June 2016

[30] S Chen C Zhang M Dong J Le and M Rao ldquoUsingRanking-CNN for Age Estimationrdquo in Proceedings of the 2017IEEE Conference on Computer Vision and Pattern Recognition(CVPR) pp 742ndash751 Honolulu HI July 2017

[31] C Szegedy W Liu Y Jia et al ldquoGoing deeper with convolu-tionsrdquo inProceedings of the IEEEConference onComputer Visionand Pattern Recognition (CVPR rsquo15) pp 1ndash9 BostonMass USAJune 2015

[32] D Yi Z Lei S Liao and S Li ldquoLearning face representationfrom scratchrdquo httpsarxivorgabs14117923

[33] B-C Chen C-S Chen and W H Hsu ldquoCross-age referencecoding for age-invariant face recognition and retrievalrdquo LectureNotes in Computer Science (including subseries Lecture Notesin Artificial Intelligence and Lecture Notes in Bioinformatics)Preface vol 8694 no 6 pp 768ndash783 2014

[34] K Ricanek and T Tesafaye ldquoMORPH A Longitudinal ImageDatabase of Normal Adult Age-Progressionrdquo in Proceedings ofthe 7th International Conference on Automatic Face and GestureRecognition (FGR rsquo06) pp 341ndash345 2006

[35] B Ni Z Song and S Yan ldquoWeb image and video miningtowards universal and robust age estimatorrdquo IEEE Transactionson Multimedia vol 13 no 6 pp 1217ndash1229 2011

[36] G Zhile Z Shaolong and L Haibin ldquoLinear dimensionalityreduction method for factor analysis criterionrdquo Computer Engi-neering and Applications vol 52 no 3 pp 145ndash149 2016

[37] N Hao J Yang H Liao et al ldquoA unified factors analysisframework for discriminative feature extraction and objectrecognitionrdquo Mathematical Problems in Engineering pp 1ndash122016

[38] ldquoThe FGNET Aging Databaserdquo 2013 httpwwwprimainrialpesfrFGnet

[39] R Rothe R Timofte and LVanGool ldquoDeep expectation of realand apparent age from a single image without facial landmarksrdquoInternational Journal of Computer Vision pp 1ndash14 2016

6 Mathematical Problems in Engineering

Figure 3 CS comparison of different estimators

Table 3 Comparison of MAE values for different estimators

Estimators Feature MMMAEAgeSVM BIF + FAM 602SVR BIF + FAM 462Our Proposed BIF + FAM 377SVM DLF+FAM 514SVR DLF+FAM 417Our Proposed DLF+FAM 348

the corresponding algorithm in this database has very lim-ited space for improvement In order to further verify theeffectiveness of this algorithm this section will be furtherexperimented on the MORPHAlbum 2 face database 10000images were further divided 80 of which were randomlyselected for the training of the estimator and the remaining20 were used for test The average of 10 experiments wastaken as the final result

The experimental results of different feature extractionmethods are shown in Figure 4 andTable 3 Figure 4 is the ageestimation comparison under different features using SVRestimator Table 3 shows the comparison of the age estimationusing the better BIF and DLF features comparison It canbe seen that the feature extraction method proposed in thispaper is nearly 3 years better than the Gabor method andnearly 1 year better than the BIF Using this estimator is nearly2 years better than SVM and nearly 1 year better than SVRFigure 5 shows the comparison results of different estimatorsunder the DLF + FAM feature which further confirms thevalidity of the proposed estimator

53 Evaluation on Face in the Wild Experiments on faces inthe wild were conducted to demonstrate the performance ofdifferent approaches on real-world data The experiments onIMDB-WIKI [39] were carried out as follows For the taskto be equally discriminative for all ages we equalize the agedistribution ie we randomly ignore some of the imagesof the most frequent ages This leaves us with 260282 faceimages for our experiment Further the 260000 images are

Figure 4 Comparison ofMAE values of different feature extractionmethods

Figure 5 CS comparison of different estimators

split into 200000 for training 30000 images for validationand 30282 images for testing

In order to verify the advancement of this method wecompare the proposed method with the most advancedmethod based on deep learning [23ndash25] In [23] a deep net-work based on regression and classification is adopted In[24] a six-layer deep network is used to extract the age featureof the face and then the manifold learning method is usedto estimate the age In [25] a DEX network using the VGG-16 architecture is proposed which poses the age regressionproblem as a deep classification problem followed by asoftmax expected value refinement All the methods use thegeneral-to-specific deep transfer learning scheme for deepnetwork training which includes two stages ie pretrainwith face identities and fine-tune with real age

Stage 1 we firstly employ the large-scale face identitiesdatabase CASIA-WebFace [30] to pretrain the deep networkwhich is much better than random initialization

Stage 2 we employ IMDB-WIKI training set to fine-tunethe deep network from stage 1

Finally we employ IMDB-WIKI testing set (30282images) for age prediction

The results of MAE comparisons of different methods onthe IMDB-WIKI face database are shown in Table 4 It can beseen from Table 4 that the effect of using 1622-layer network

Mathematical Problems in Engineering 7

Table 4 Comparison of different methods based on deep learning

Methods MAEAge[23] 393[24] 422[25] 335Our Proposed 329

is better than that of 6-layer network which indicates thatface age is a complex nonlinear variation problem Althoughthe deep network in this paper is designed based on [23] thefinal estimation effect is better than that in [23] which showsthe validity of the divide-and-rule strategy proposed in thispaper

6 Conclusion

In this paper a robust face age feature extraction method isproposed based on the superior image representation abilityof depth convolution neural network In the aspect of fea-ture dimensionality the feature reduction method based onFAM is used to replace the PCA dimensionality reductionmethod In the estimator learning an ordinal regressionproblem is transformed into a series of binary classificationsubproblems which are collectively solved with the proposeddivide-and-rule learning algorithm By taking the ordinalrelation between ages into consideration it is more likelyto get smaller estimation errors compared with multiclassclassification approaches Experimental results show that themethod proposed in this paper is more discriminative androbust than traditional Gabor LBP and BIF methods Theperformance of the proposed age estimator is superior toSVM and SVR

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported partially by the National NaturalScience Fund (No 61373108) the Hubei Provincial NaturalScience Foundation of China (No 2017CFB168 and No2015CFC778) the Hubei Provincial Education Office Scienceand Technology Research Project youth talent project (NoQ20172805) the Hubei Provincial Education Science Plan-ning Project (No 2016GB086) and the Construction of aSpecial Scientific Research Project for Masterrsquos Point (No2018-19GZ050)

References

[1] A Lanitis and C J Taylor ldquoTowards automatic face identi-fication robust to ageing variationrdquo in Proceedings of the 4th

IEEE International Conference on Automatic Face and GestureRecognition FG 2000 pp 391ndash396 fra March 2000

[2] Z Li and A K Jain ldquoA discriminative model for age invariantface recognitionrdquo IEEE Transactions on Information Forensicsand Security vol 6 no 3 pp 1028ndash1037 2011

[3] N Dayan Skin aging handbook An Integrated Approach toBiochemistry and Product Development AndrewWilliam Press2008

[4] A Amadasi NMerusi andC Cattaneo ldquoHow reliable is appar-ent age at death on cadaversrdquo International Journal of LegalMedicine vol 129 no 4 pp 1437ndash1596 2015

[5] S B M Patzelt L K Schaible S Stampf and R J KohalldquoSoftware-based evaluation of human age A pilot studyrdquo Jour-nal of Esthetic and Restorative Dentistry vol 27 no 2 pp 100ndash106 2015

[6] W Chen W Qian G Wu et al ldquoThree-dimensional humanfacial morphologies as robust agingmarkersrdquoCell Research vol25 no 5 pp 574ndash587 2015

[7] Y Fu G Guo and T S Huang ldquoAge synthesis and estimationvia faces a surveyrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 32 no 11 pp 1955ndash1976 2010

[8] C-C Wang Y-C Su C-T Hsu C-W Lin and H Y M LiaoldquoBayesian age estimation on face imagesrdquo in Proceedings of theProceddings of the IEEE International Conference onMultimediaand Expo (ICME rsquo09) pp 282ndash285 July 2009

[9] X Geng Z Zhou and K Smith-Miles ldquoAutomatic age esti-mation based on facial aging patternsrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 29 no 12 pp2234ndash2240 2007

[10] GGuo Y Fu C RDyer andT SHuang ldquoImage-based humanage estimation bymanifold learning and locally adjusted robustregressionrdquo IEEE Transactions on Image Processing vol 17 no7 pp 1178ndash1188 2008

[11] Y Zhang andD-Y Yeung ldquoMulti-taskwarpedGaussian processfor personalized age estimationrdquo in Proceedings of the IEEEConference on Computer Vision Pattern Recognition pp 2622ndash2629 2010

[12] J Lu and Y-P Tan ldquoOrdinary preserving manifold analysis forhuman age and head pose estimationrdquo IEEE Transactions onHuman-Machine Systems vol 43 no 2 pp 249ndash258 2013

[13] K-YChang andC-S Chen ldquoA learning framework for age rankestimation based on face images with scattering transformrdquoIEEE Transactions on Image Processing vol 24 no 3 pp 785ndash798 2015

[14] Y H Kwon and N da Vitoria Lobo ldquoAge classification fromfacial imagesrdquo Computer Vision and Image Understanding vol74 no 1 pp 1ndash21 1999

[15] A Lanitis C J Taylor and T F Cootes ldquoToward automaticsimulation of aging effects on face imagesrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 24 no 4 pp442ndash455 2002

[16] A Martinez and S Du ldquoA model of the perception of facialexpressions of emotion by humans research overview andperspectivesrdquo Journal of Machine Learning Research vol 13 no1 pp 1589ndash1608 2012

[17] T Ahonen A Hadid and M Pietikainen ldquoFace descriptionwith local binary patterns application to face recognitionrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol28 no 12 pp 2037ndash2041 2006

[18] S K Zhou B Georgescu X S Zhou andD Comaniciu ldquoImagebased regression using boosting methodrdquo in Proceedings of the

8 Mathematical Problems in Engineering

10th IEEE International Conference on Computer Vision (ICCVrsquo05) pp 541ndash548 October 2005

[19] G Guo Y Fu T S Huang and C R Dyer ldquoLocally adjustedrobust regression for human age estimationrdquo in Proceedings ofthe IEEEWorkshop on Applications of Computer Vision (WACVrsquo08) pp 1ndash6 IEEE CopperMountain Colo USA January 2008

[20] Y Fu and T S Huang ldquoHuman age estimation with regressionon discriminative aging manifoldrdquo IEEE Transactions onMulti-media vol 10 no 4 pp 578ndash584 2008

[21] G Guo G Mu and Y Fu ldquoHuman age estimation using bio-inspired featuresrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition Work-shops (CVPR rsquo09) pp 112ndash119 IEEE June 2009

[22] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[23] X Liu S LiM Kan et alAgeNet Deeply Learned Regressor andClassifier for Robust Apparent Age Estimation ICCV rsquo16 2016

[24] X Wang R Guo and C Kambhamettu ldquoDeeply-LearnedFeature for Age Estimationrdquo in Proceedings of the 2015 IEEEWinter Conference on Applications of Computer Vision (WACV)pp 534ndash541 Waikoloa HI USA January 2015

[25] R Rothe R Timofte and L V Gool ldquoDEX Deep EXpectationof Apparent Age from a Single Imagerdquo in Proceedings of the 2015IEEE International Conference on Computer Vision Workshop(ICCVW) pp 252ndash257 Santiago Chile December 2015

[26] D Yi Z Lei and S Z Li ldquoAge Estimation by Multi-scale Con-volutional Networkrdquo in Computer Vision ndash ACCV 2014 vol9005 of LectureNotes in Computer Science pp 144ndash158 SpringerInternational Publishing 2015

[27] G Levi and T Hassncer ldquoAge and gender classification usingconvolutional neural networksrdquo in Proceedings of the IEEE Con-ference on Computer Vision and Pattern RecognitionWorkshopsCVPRW 2015 pp 34ndash42 usa June 2015

[28] Y Dong Y Liu and S Lian ldquoAutomatic age estimation basedon deep learning algorithmrdquo Neurocomputing vol 187 pp 4ndash10 2016

[29] Z Niu M Zhou L Wang X Gao and G Hua ldquoOrdinalRegression with Multiple Output CNN for Age Estimationrdquo inProceedings of the 2016 IEEE Conference on Computer Visionand Pattern Recognition (CVPR) pp 4920ndash4928 Las Vegas NVUSA June 2016

[30] S Chen C Zhang M Dong J Le and M Rao ldquoUsingRanking-CNN for Age Estimationrdquo in Proceedings of the 2017IEEE Conference on Computer Vision and Pattern Recognition(CVPR) pp 742ndash751 Honolulu HI July 2017

[31] C Szegedy W Liu Y Jia et al ldquoGoing deeper with convolu-tionsrdquo inProceedings of the IEEEConference onComputer Visionand Pattern Recognition (CVPR rsquo15) pp 1ndash9 BostonMass USAJune 2015

[32] D Yi Z Lei S Liao and S Li ldquoLearning face representationfrom scratchrdquo httpsarxivorgabs14117923

[33] B-C Chen C-S Chen and W H Hsu ldquoCross-age referencecoding for age-invariant face recognition and retrievalrdquo LectureNotes in Computer Science (including subseries Lecture Notesin Artificial Intelligence and Lecture Notes in Bioinformatics)Preface vol 8694 no 6 pp 768ndash783 2014

[34] K Ricanek and T Tesafaye ldquoMORPH A Longitudinal ImageDatabase of Normal Adult Age-Progressionrdquo in Proceedings ofthe 7th International Conference on Automatic Face and GestureRecognition (FGR rsquo06) pp 341ndash345 2006

[35] B Ni Z Song and S Yan ldquoWeb image and video miningtowards universal and robust age estimatorrdquo IEEE Transactionson Multimedia vol 13 no 6 pp 1217ndash1229 2011

[36] G Zhile Z Shaolong and L Haibin ldquoLinear dimensionalityreduction method for factor analysis criterionrdquo Computer Engi-neering and Applications vol 52 no 3 pp 145ndash149 2016

[37] N Hao J Yang H Liao et al ldquoA unified factors analysisframework for discriminative feature extraction and objectrecognitionrdquo Mathematical Problems in Engineering pp 1ndash122016

[38] ldquoThe FGNET Aging Databaserdquo 2013 httpwwwprimainrialpesfrFGnet

[39] R Rothe R Timofte and LVanGool ldquoDeep expectation of realand apparent age from a single image without facial landmarksrdquoInternational Journal of Computer Vision pp 1ndash14 2016

Mathematical Problems in Engineering 7

Table 4 Comparison of different methods based on deep learning

Methods MAEAge[23] 393[24] 422[25] 335Our Proposed 329

is better than that of 6-layer network which indicates thatface age is a complex nonlinear variation problem Althoughthe deep network in this paper is designed based on [23] thefinal estimation effect is better than that in [23] which showsthe validity of the divide-and-rule strategy proposed in thispaper

6 Conclusion

In this paper a robust face age feature extraction method isproposed based on the superior image representation abilityof depth convolution neural network In the aspect of fea-ture dimensionality the feature reduction method based onFAM is used to replace the PCA dimensionality reductionmethod In the estimator learning an ordinal regressionproblem is transformed into a series of binary classificationsubproblems which are collectively solved with the proposeddivide-and-rule learning algorithm By taking the ordinalrelation between ages into consideration it is more likelyto get smaller estimation errors compared with multiclassclassification approaches Experimental results show that themethod proposed in this paper is more discriminative androbust than traditional Gabor LBP and BIF methods Theperformance of the proposed age estimator is superior toSVM and SVR

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported partially by the National NaturalScience Fund (No 61373108) the Hubei Provincial NaturalScience Foundation of China (No 2017CFB168 and No2015CFC778) the Hubei Provincial Education Office Scienceand Technology Research Project youth talent project (NoQ20172805) the Hubei Provincial Education Science Plan-ning Project (No 2016GB086) and the Construction of aSpecial Scientific Research Project for Masterrsquos Point (No2018-19GZ050)

References

[1] A Lanitis and C J Taylor ldquoTowards automatic face identi-fication robust to ageing variationrdquo in Proceedings of the 4th

IEEE International Conference on Automatic Face and GestureRecognition FG 2000 pp 391ndash396 fra March 2000

[2] Z Li and A K Jain ldquoA discriminative model for age invariantface recognitionrdquo IEEE Transactions on Information Forensicsand Security vol 6 no 3 pp 1028ndash1037 2011

[3] N Dayan Skin aging handbook An Integrated Approach toBiochemistry and Product Development AndrewWilliam Press2008

[4] A Amadasi NMerusi andC Cattaneo ldquoHow reliable is appar-ent age at death on cadaversrdquo International Journal of LegalMedicine vol 129 no 4 pp 1437ndash1596 2015

[5] S B M Patzelt L K Schaible S Stampf and R J KohalldquoSoftware-based evaluation of human age A pilot studyrdquo Jour-nal of Esthetic and Restorative Dentistry vol 27 no 2 pp 100ndash106 2015

[6] W Chen W Qian G Wu et al ldquoThree-dimensional humanfacial morphologies as robust agingmarkersrdquoCell Research vol25 no 5 pp 574ndash587 2015

[7] Y Fu G Guo and T S Huang ldquoAge synthesis and estimationvia faces a surveyrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 32 no 11 pp 1955ndash1976 2010

[8] C-C Wang Y-C Su C-T Hsu C-W Lin and H Y M LiaoldquoBayesian age estimation on face imagesrdquo in Proceedings of theProceddings of the IEEE International Conference onMultimediaand Expo (ICME rsquo09) pp 282ndash285 July 2009

[9] X Geng Z Zhou and K Smith-Miles ldquoAutomatic age esti-mation based on facial aging patternsrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 29 no 12 pp2234ndash2240 2007

[10] GGuo Y Fu C RDyer andT SHuang ldquoImage-based humanage estimation bymanifold learning and locally adjusted robustregressionrdquo IEEE Transactions on Image Processing vol 17 no7 pp 1178ndash1188 2008

[11] Y Zhang andD-Y Yeung ldquoMulti-taskwarpedGaussian processfor personalized age estimationrdquo in Proceedings of the IEEEConference on Computer Vision Pattern Recognition pp 2622ndash2629 2010

[12] J Lu and Y-P Tan ldquoOrdinary preserving manifold analysis forhuman age and head pose estimationrdquo IEEE Transactions onHuman-Machine Systems vol 43 no 2 pp 249ndash258 2013

[13] K-YChang andC-S Chen ldquoA learning framework for age rankestimation based on face images with scattering transformrdquoIEEE Transactions on Image Processing vol 24 no 3 pp 785ndash798 2015

[14] Y H Kwon and N da Vitoria Lobo ldquoAge classification fromfacial imagesrdquo Computer Vision and Image Understanding vol74 no 1 pp 1ndash21 1999

[15] A Lanitis C J Taylor and T F Cootes ldquoToward automaticsimulation of aging effects on face imagesrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 24 no 4 pp442ndash455 2002

[16] A Martinez and S Du ldquoA model of the perception of facialexpressions of emotion by humans research overview andperspectivesrdquo Journal of Machine Learning Research vol 13 no1 pp 1589ndash1608 2012

[17] T Ahonen A Hadid and M Pietikainen ldquoFace descriptionwith local binary patterns application to face recognitionrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol28 no 12 pp 2037ndash2041 2006

[18] S K Zhou B Georgescu X S Zhou andD Comaniciu ldquoImagebased regression using boosting methodrdquo in Proceedings of the

8 Mathematical Problems in Engineering

10th IEEE International Conference on Computer Vision (ICCVrsquo05) pp 541ndash548 October 2005

[19] G Guo Y Fu T S Huang and C R Dyer ldquoLocally adjustedrobust regression for human age estimationrdquo in Proceedings ofthe IEEEWorkshop on Applications of Computer Vision (WACVrsquo08) pp 1ndash6 IEEE CopperMountain Colo USA January 2008

[20] Y Fu and T S Huang ldquoHuman age estimation with regressionon discriminative aging manifoldrdquo IEEE Transactions onMulti-media vol 10 no 4 pp 578ndash584 2008

[21] G Guo G Mu and Y Fu ldquoHuman age estimation using bio-inspired featuresrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition Work-shops (CVPR rsquo09) pp 112ndash119 IEEE June 2009

[22] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[23] X Liu S LiM Kan et alAgeNet Deeply Learned Regressor andClassifier for Robust Apparent Age Estimation ICCV rsquo16 2016

[24] X Wang R Guo and C Kambhamettu ldquoDeeply-LearnedFeature for Age Estimationrdquo in Proceedings of the 2015 IEEEWinter Conference on Applications of Computer Vision (WACV)pp 534ndash541 Waikoloa HI USA January 2015

[25] R Rothe R Timofte and L V Gool ldquoDEX Deep EXpectationof Apparent Age from a Single Imagerdquo in Proceedings of the 2015IEEE International Conference on Computer Vision Workshop(ICCVW) pp 252ndash257 Santiago Chile December 2015

[26] D Yi Z Lei and S Z Li ldquoAge Estimation by Multi-scale Con-volutional Networkrdquo in Computer Vision ndash ACCV 2014 vol9005 of LectureNotes in Computer Science pp 144ndash158 SpringerInternational Publishing 2015

[27] G Levi and T Hassncer ldquoAge and gender classification usingconvolutional neural networksrdquo in Proceedings of the IEEE Con-ference on Computer Vision and Pattern RecognitionWorkshopsCVPRW 2015 pp 34ndash42 usa June 2015

[28] Y Dong Y Liu and S Lian ldquoAutomatic age estimation basedon deep learning algorithmrdquo Neurocomputing vol 187 pp 4ndash10 2016

[29] Z Niu M Zhou L Wang X Gao and G Hua ldquoOrdinalRegression with Multiple Output CNN for Age Estimationrdquo inProceedings of the 2016 IEEE Conference on Computer Visionand Pattern Recognition (CVPR) pp 4920ndash4928 Las Vegas NVUSA June 2016

[30] S Chen C Zhang M Dong J Le and M Rao ldquoUsingRanking-CNN for Age Estimationrdquo in Proceedings of the 2017IEEE Conference on Computer Vision and Pattern Recognition(CVPR) pp 742ndash751 Honolulu HI July 2017

[31] C Szegedy W Liu Y Jia et al ldquoGoing deeper with convolu-tionsrdquo inProceedings of the IEEEConference onComputer Visionand Pattern Recognition (CVPR rsquo15) pp 1ndash9 BostonMass USAJune 2015

[32] D Yi Z Lei S Liao and S Li ldquoLearning face representationfrom scratchrdquo httpsarxivorgabs14117923

[33] B-C Chen C-S Chen and W H Hsu ldquoCross-age referencecoding for age-invariant face recognition and retrievalrdquo LectureNotes in Computer Science (including subseries Lecture Notesin Artificial Intelligence and Lecture Notes in Bioinformatics)Preface vol 8694 no 6 pp 768ndash783 2014

[34] K Ricanek and T Tesafaye ldquoMORPH A Longitudinal ImageDatabase of Normal Adult Age-Progressionrdquo in Proceedings ofthe 7th International Conference on Automatic Face and GestureRecognition (FGR rsquo06) pp 341ndash345 2006

[35] B Ni Z Song and S Yan ldquoWeb image and video miningtowards universal and robust age estimatorrdquo IEEE Transactionson Multimedia vol 13 no 6 pp 1217ndash1229 2011

[36] G Zhile Z Shaolong and L Haibin ldquoLinear dimensionalityreduction method for factor analysis criterionrdquo Computer Engi-neering and Applications vol 52 no 3 pp 145ndash149 2016

[37] N Hao J Yang H Liao et al ldquoA unified factors analysisframework for discriminative feature extraction and objectrecognitionrdquo Mathematical Problems in Engineering pp 1ndash122016

[38] ldquoThe FGNET Aging Databaserdquo 2013 httpwwwprimainrialpesfrFGnet

[39] R Rothe R Timofte and LVanGool ldquoDeep expectation of realand apparent age from a single image without facial landmarksrdquoInternational Journal of Computer Vision pp 1ndash14 2016

8 Mathematical Problems in Engineering

10th IEEE International Conference on Computer Vision (ICCVrsquo05) pp 541ndash548 October 2005

[19] G Guo Y Fu T S Huang and C R Dyer ldquoLocally adjustedrobust regression for human age estimationrdquo in Proceedings ofthe IEEEWorkshop on Applications of Computer Vision (WACVrsquo08) pp 1ndash6 IEEE CopperMountain Colo USA January 2008

[20] Y Fu and T S Huang ldquoHuman age estimation with regressionon discriminative aging manifoldrdquo IEEE Transactions onMulti-media vol 10 no 4 pp 578ndash584 2008

[21] G Guo G Mu and Y Fu ldquoHuman age estimation using bio-inspired featuresrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition Work-shops (CVPR rsquo09) pp 112ndash119 IEEE June 2009

[22] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[23] X Liu S LiM Kan et alAgeNet Deeply Learned Regressor andClassifier for Robust Apparent Age Estimation ICCV rsquo16 2016

[24] X Wang R Guo and C Kambhamettu ldquoDeeply-LearnedFeature for Age Estimationrdquo in Proceedings of the 2015 IEEEWinter Conference on Applications of Computer Vision (WACV)pp 534ndash541 Waikoloa HI USA January 2015

[25] R Rothe R Timofte and L V Gool ldquoDEX Deep EXpectationof Apparent Age from a Single Imagerdquo in Proceedings of the 2015IEEE International Conference on Computer Vision Workshop(ICCVW) pp 252ndash257 Santiago Chile December 2015

[26] D Yi Z Lei and S Z Li ldquoAge Estimation by Multi-scale Con-volutional Networkrdquo in Computer Vision ndash ACCV 2014 vol9005 of LectureNotes in Computer Science pp 144ndash158 SpringerInternational Publishing 2015

[27] G Levi and T Hassncer ldquoAge and gender classification usingconvolutional neural networksrdquo in Proceedings of the IEEE Con-ference on Computer Vision and Pattern RecognitionWorkshopsCVPRW 2015 pp 34ndash42 usa June 2015

[28] Y Dong Y Liu and S Lian ldquoAutomatic age estimation basedon deep learning algorithmrdquo Neurocomputing vol 187 pp 4ndash10 2016

[29] Z Niu M Zhou L Wang X Gao and G Hua ldquoOrdinalRegression with Multiple Output CNN for Age Estimationrdquo inProceedings of the 2016 IEEE Conference on Computer Visionand Pattern Recognition (CVPR) pp 4920ndash4928 Las Vegas NVUSA June 2016

[30] S Chen C Zhang M Dong J Le and M Rao ldquoUsingRanking-CNN for Age Estimationrdquo in Proceedings of the 2017IEEE Conference on Computer Vision and Pattern Recognition(CVPR) pp 742ndash751 Honolulu HI July 2017

[31] C Szegedy W Liu Y Jia et al ldquoGoing deeper with convolu-tionsrdquo inProceedings of the IEEEConference onComputer Visionand Pattern Recognition (CVPR rsquo15) pp 1ndash9 BostonMass USAJune 2015

[32] D Yi Z Lei S Liao and S Li ldquoLearning face representationfrom scratchrdquo httpsarxivorgabs14117923

[33] B-C Chen C-S Chen and W H Hsu ldquoCross-age referencecoding for age-invariant face recognition and retrievalrdquo LectureNotes in Computer Science (including subseries Lecture Notesin Artificial Intelligence and Lecture Notes in Bioinformatics)Preface vol 8694 no 6 pp 768ndash783 2014

[34] K Ricanek and T Tesafaye ldquoMORPH A Longitudinal ImageDatabase of Normal Adult Age-Progressionrdquo in Proceedings ofthe 7th International Conference on Automatic Face and GestureRecognition (FGR rsquo06) pp 341ndash345 2006

[35] B Ni Z Song and S Yan ldquoWeb image and video miningtowards universal and robust age estimatorrdquo IEEE Transactionson Multimedia vol 13 no 6 pp 1217ndash1229 2011

[36] G Zhile Z Shaolong and L Haibin ldquoLinear dimensionalityreduction method for factor analysis criterionrdquo Computer Engi-neering and Applications vol 52 no 3 pp 145ndash149 2016

[37] N Hao J Yang H Liao et al ldquoA unified factors analysisframework for discriminative feature extraction and objectrecognitionrdquo Mathematical Problems in Engineering pp 1ndash122016

[38] ldquoThe FGNET Aging Databaserdquo 2013 httpwwwprimainrialpesfrFGnet

[39] R Rothe R Timofte and LVanGool ldquoDeep expectation of realand apparent age from a single image without facial landmarksrdquoInternational Journal of Computer Vision pp 1ndash14 2016

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