How Unique Is a Face: An Investigative Study
Michal Balazia, S L Happy, Francois Bremond, Antitza Dantcheva
HHow Unique Is a Face: An Investigative Study
Michal Balazia , S L Happy , François Brémond , and Antitza Dantcheva
INRIA Sophia Antipolis - Méditerranée, 2004 Route des Lucioles, 06902 Sophia Antipolis, France {michal.balazia, s-l.happy, francois.bremond, antitza.dantcheva}@inria.fr
Abstract —Face recognition has been widely accepted as ameans of identification in applications ranging from bordercontrol to security in the banking sector. Surprisingly, whilewidely accepted, we still lack the understanding of uniqueness ordistinctiveness of faces as biometric modality. In this work, westudy the impact of factors such as image resolution, featurerepresentation, database size, age and gender on uniquenessdenoted by the Kullback-Leibler divergence between genuineand impostor distributions. Towards understanding the impact,we present experimental results on the datasets AT&T, LFW,IMDb-Face, as well as ND-TWINS, with the feature extraction al-gorithms VGGFace, VGG16, ResNet50, InceptionV3, MobileNetand DenseNet121, that reveal the quantitative impact of thenamed factors. While these are early results, our findings indicatethe need for a better understanding of the concept of biometricuniqueness and its implication on face recognition.
I. I
NTRODUCTION
Biometrics is the science of identifying humans based ontheir physical, behavioral or psycho-physiological characteris-tics [20], with one assumption being that such characteristicsare unique.
Uniqueness refers to the ability of a biometricmodality to distinguish between individuals, indicating how abiometric characteristic varies across the population. Conse-quently, an individual possesses high biometric uniqueness, ifthe distance distribution of their genuine (mated) comparisonscores is well separated from the distance distribution ofimpostor (non-mated) comparison scores. Hence, an individualis less unique if their genuine and impostor distributions signif-icantly overlap (see Figure 1). We note that while a similaritymatch score represents a genuine score if it is a result ofmatching two biometric samples of the same individual, an impostor score refers to comparing of two biometric samplesoriginating from different individuals [18].
Distance P r o b a b ili t y D e n s i t y genuineimpostor Distance P r o b a b ili t y D e n s i t y genuineimpostor Fig. 1. Genuine and impostor score distributions in a setting with relativelyunique subjects (left), as well as a setting with similar subjects (right).
The amount of biometric information is influenced by a setof factors including facial expression, pose, image resolution,distortion, noise or blur [9]. Moreover, the general population includes family members, a large number of twins (3% in theUS between 2014–2018 [25]), as well as doppelgangers (seeFigure 2), all of which inherently lower the overall uniquenessof faces in a dataset.However, the knowledge of distinctiveness of face is incom-plete and often relegated to anecdotal interpretation of errorrates rather than a systematic exploration of the biology of thecharacteristics [2], [19], [30]. Hence, we lack an estimate forthe upper bound of the amount of discriminatory informationcontained in a face. Fig. 2. Are faces unique? Images of identical twins (left) and doppelgangers(right). The anthropology project Twinstrangers has the goal to identifydoppelgangers across the world.
Such upper bound can be estimated on the level of extractedfeatures. Generally speaking, class separability of the featurespace directly corresponds to accuracy of the estimate. Inthe context of soft biometrics [6], distinctiveness has to dowith collision, or equivalently interference, which describesthe event where any two or more subjects belong in the samecategory of soft biometrics (e.g., female, dark hair, tall) [3]–[5], [7]. We note that this is related to the Birthday para-dox [11] and named works answered questions such as:
Howlarge can a population become before it is likelier than notthat at least two persons in the group collide biometrically?
It is known that users of a biometric system may exhibitstatistically different degrees of accuracy within the system,which relates to variations in uniqueness across subjects.While some users may experience challenges in authentica-tion, others may be particularly vulnerable to impersonation.The Doddington’s zoo [10], [29], [31] has been frequentlyused to quantify this phenomenon and specifically to classifyusers based on verification performance, when users are com-pared against themselves and against others. Associated majorclasses include: (a) sheep : users who are easy to recognize;(b) goats : users who are difficult to recognize; (c) lambs : userswho are easy to imitate; and (d) wolves : users who can easilyimitate others. Easy imitation contributes to False Acceptance https://twinstrangers.net/ a r X i v : . [ c s . C V ] F e b ate and difficult recognition to False Rejection Rate. Thisconcept was extended in the biometric menagerie [14] (seeFigure 3), with additional classes: (e) chameleons : users whoare easy to recognize and easy to imitate; (f) phantoms : userswho are difficult to recognize and difficult to imitate; (g) doves :users who are easy to recognize and difficult to imitate; and(h) worms : users who are difficult to recognize and easy toimitate. Hence, the distribution of a given dataset in suchclasses impacts the accuracy of a face recognition system onthe dataset. WolvesLambsWormsPhantomsGoats ChameleonsDovesSheepAverage Genuine Similarity A v e r age I m po s t o r S i m il a r i t y Personal Entropy P e r s ona l R e l a t i v e E n t r op y SheepDovesChameleons GoatsPhantomsWormsLambs
Fig. 3. Animal groups distinguished by Doddington’s zoo according to [14].Left figure shows the distribution for match-based classification and the rightone for entropy-based classification.
Motivated by the above, we here aim to provide new insighton the topic of facial uniqueness by investigating the impact offeature extractors (in particular six CNN-based feature extrac-tors: VGGFace, VGG16, ResNet50, InceptionV3, MobileNetand DenseNet121), dataset size (see Section VI-A), imageresolution (see Section VI-B), as well as age and gender (seeSection VI-C), on the four datasets AT&T, LFW, IMDb andTWINS. Additionally, we identify a potential limitation of theused uniqueness score and propose an additional uniquenessscore, which reflects the common occurrence of persons, wholook alike (twins, family members and doppelgangers).II. R
ELATED W ORK
There have been numerous early attempts to quantify bio-metric uniqueness, distinctiveness and entropy. A key esti-mator of biometric information related to uniqueness wasdefined by Adler et al. [1] as the decrease in uncertaintyabout the identity of a person due to a set of biomet-ric measurements . This measure was subsequently used bySutcu et al. [36], Takashi and Murakami [38], as well asGomez-Barrero et al. [12]. Similar uniqueness considerationswere applied towards improving template protection [12] andperformance of biometric systems [21]. Further, facial entropywas quantified and was found to range from . bits [26]to bits [1]. Recent work of Krivoku´ca and Marcel [22]on fingervein entropy estimated discriminatory information infingervein patterns by calculating the number of features usedto differentiate between different fingers.While such works have used different measures of biometricinformation, what they have in common is the calculation ofentropy, which relates to the inter-class variance that can be artificially increased by including a larger number of features.In order to be independent of the number of extracted featuresand thus to more accurately estimate the intrinsic information,we also need to consider intra-class variance. Both of thesevariances are encompassed in our proposed biometric unique-ness score based on the Kullback-Leibler divergence [24], alsodenoted as relative entropy , between genuine and impostordistributions. By its definition below, KL-divergence weighsresistance to both false acceptance and false rejection.In the context of iris and iris code in particular, an irisuniqueness has been determined by Daugman [8], [9]. Therein of the bits in two IrisCodes are allowed to disagreewhile still accepting them as a match, resulting in a falsematch rate of in billion. Given the fixed length ofthe standardized IrisCode, we consider this rate as an exactindicator of uniqueness in irises.For the purpose of texture-based generation of fingerprintimages, Yankov et al. [42] used generative models to estimateupper bounds on the image entropy for systems with smallsensor acquisition. They estimated the identification capacityof such systems using the mutual information between differ-ent samples from the same finger.We proceed with describing the uniqueness measure toquantify the identification capacity of faces based on a similarconcept. III. U NIQUENESS AS A D IVERGENCE
Takahashi et al. [39] showed that a decrease in uncertaintywith respect to identity of an unknown biometric characteristiccan be formulated in terms of mutual information I ( X ; Y ) = H ( X ) − H ( X | Y ) (1)with H ( X ) as the marginal entropy, i.e., uncertainty of X ,and H ( X | Y ) as the conditional entropy, i.e., uncertainty of X given the observation of Y . In addition, the authors showedthat I ( X ; Y ) can be approximated by the Kullback-Leiblerdivergence of genuine P G ( d ) and impostor P I ( d ) probabilitydistributions I ( X ; Y ) ≈ D (cid:0) P G (cid:13)(cid:13) P I (cid:1) = (cid:88) d P G ( d ) log P G ( d ) P I ( d ) , (2)where d denote observed dissimilarities between pairs ofsamples constituting a genuine or impostor observations.We here note that an average norm estimator can be used tocalculate the value of D (cid:0) P G (cid:13)(cid:13) P I (cid:1) from the dissimilarities ofsamples without computing any probability models [35]. Let G and I be i.i.d. sets of samples with mutual dissimilaritiesforming the distributions P G and P I , respectively. Then, theaverage norm estimator of the KL-divergence is defined as D (cid:0) P G (cid:13)(cid:13) P I (cid:1) ≈ ˆD( G, I ) = 1 | G | (cid:88) g ∈ G log δ g ( I ) δ g ( G ) + log | I || G | − , (3)where δ s ( S ) = 1 | S \ { s }| (cid:88) s (cid:48) ∈ S \{ s } (cid:107) s − s (cid:48) (cid:107) (4)epresents mean of the Euclidean norms between a sample s and all samples from the set S eventually without s .Calculation of D (cid:0) P G (cid:13)(cid:13) P I (cid:1) can be sped up by approximationwith random sampling. In order to ensure that the score is notbiased towards the distribution of a certain random subset, wecalculate the divergence as the average of n different randomsubset choices. We note that random samples are a sounderrepresentation of the underlying distribution as compared tofor example nearest neighbors. Furthermore, for the divergenceto mainly depend on the genuine-impostor distributions ratherthan the count distribution, we choose the subsets G (cid:48) ⊆ G and I (cid:48) ⊆ I to contain r + 1 and r random samples from G and I ,respectively. Equation 3 then transforms to ˆD n,r ( G, I ) = 1 n n (cid:88) k =1 r (cid:88) g ∈ G (cid:48) log δ g ( I (cid:48) ) δ g ( G (cid:48) ) + log rr = 1 nr n (cid:88) k =1 (cid:88) g ∈ G (cid:48) log δ g ( I (cid:48) ) δ g ( G (cid:48) ) . (5)In our experiments, we calculate KL-divergence from theabove definition using all available genuine data r = min( | G | − , | I | ) (6)so as to obtain the most accurate approximation of the genuineand impostor distributions and n = (cid:100) / r (cid:101) (7)random subset choices which we believe is sufficiently largeto prevent a potential bias. For very large datasets that havetoo many samples of individual subjects, one can take asmaller r to estimate the divergence for reasons of efficiency.Slightly abusing annotation, in the following we will refer to ˆD (cid:100) / min( | G |− , | I | ) (cid:101) , min( | G |− , | I | ) as to simply ˆD .Let a dataset S have c subjects and let S p ⊂ S denote aset of samples that belong to subject p . The KL-divergenceestimate on this dataset is defined as the average ˆD across allsubjects ¯D( S ) = 1 c c (cid:88) p =1 ˆD( S p , S \{ S p } ) , (8)where impostor distribution is calculated from the wholeremainder of the dataset S \{ S p } .Finally, since there is a common practice of normalizingbiometric scores to the interval (0 , , we define the impostor-based biometric uniqueness U of a given dataset S as theestimated and sigmoid-normalized divergence U( S ) = 11 + e − ¯D( S ) . (9)Note that while U( S ) close to 1 indicates that subjects arehighly unique, a lower uniqueness indicates that the genuineand impostor distributions are increasingly overlapping. Alsonote that the uniqueness score is defined as an exponentialfunction with base e , which means that even a small variationin the uniqueness score has a rather significant effect. IV. D ATASETS
In this section we briefly present the four used datasets:AT&T, LFW, IMDb and TWINS. We summarize details inTable I. • AT&T Database of Faces (AT&T) [33] contains faceimages acquired in the laboratory conditions, with adark homogeneous background. Subjects are capturedin an upright, frontal position. There are 10 differentimages of each of 40 subjects. Covariates include lighting,facial expressions, open or closed eyes, as well as facialaccessories such as glasses. • Labeled Faces in the Wild (LFW) [17] was designedfor studying the problem of unconstrained face recog-nition. The dataset contains 5,749 distinct subjects with13,233 images of faces collected from the web and henceincorporates highly unconstrained conditions. We select9,164 images of 1,680 subjects, with two or more imagesin the dataset. Faces were detected and cropped by theViola-Jones face detector [40]. • IMDb-Face (IMDb) [41] is a large-scale noise-controlleddataset for face recognition research, containing about1.7M faces of 59K identities, which is a manually cleanedsubset of the original 2M raw images. All images wereobtained from the IMDb website. We select 1,167,509images associated to 10,347 identities. IMDb containsgender and age annotations, which allow us to performadditional experiments on subsets pertained to gender andage. See statistics in Table II. • ND-TWINS-2009-2010 (TWINS) [28] dataset was col-lected by the University of Notre Dame in the years2009-2010 and comprises 24,050 color photographs of435 attendee faces captured at the Twins Days Festivalunder natural light in indoor and outdoor configurations.Facial yaw varies from − to +90 degrees in steps of degrees. We use a set of cropped 23,762 images, wherewe detect faces with the MTCNN detector [43]. TABLE IS
IZES OF DATASETS WITH MEAN AND STANDARD DEVIATION STATISTICS , GENDER AND ETHNICITY DISTRIBUTIONS .AT&T LFW IMDb TWINStotal number of subjects 40 1,680 10,347 435total number of samples 400 9,164 1,167,509 23,762mean/st.d. samples per subject 10.0/0.0 5.5/16.3 112.8/70.5 54.6/36.1% female/male 10/90 23/77 40/60 75/25% African/Asian/Caucasian 2/0/98 9/8/83 12/23/65 12/1/84TABLE IIN
UMBERS OF SUBJECTS IN
IMD
B BY AGE AND GENDER .full male female 0-9 10-19 20-29 30-3910,347 6,215 4,132 159 856 2558 303140-49 50-59 60-69 70-79 80-89 90-99 100-1091876 1024 522 227 77 14 2 . A
LGORITHMS
We select six state-of-the-art convolutional neural networks(CNNs), which have excelled in a number of face recognitionand classification tasks that we proceed to describe. • VGGFace [27] is a 16-layer CNN, trained on the VG-GFace dataset comprising over 2M celebrity images.Given a × input image, the network extracts 4,096image features from the output of the 6-th fully connectedlayer. • VGG16 [34] constitutes the same 16-layer CNN, how-ever trained on over 1M images from the ImageNetdatabase [32]. We use 4,096 features, provided as outputby the second fully connected layer. • ResNet50 [13] represents a 50-layer CNN, also trained onImageNet. As a result of having a large amount of layers,the network has learned rich feature representations fora wide range of images. Similar as the above networks,ResNet50 accepts as input an image of size × .The 2,048 related ResNet50 features are provided by thelast convolutional layer. • InceptionV3 [37] is a 48-layer CNN trained on Im-ageNet. We obtain 2,048 features from the last fullyconnected layer. • MobileNet [15] is a 56-layer CNN trained on ImageNet,which has been optimized for mobile devices. MobileNetextracts a 1,000-dimensional feature vector. • DenseNet121 [16] is a 121-layer CNN trained on Ima-geNet. The layer structure involves more narrow layersas opposed to ResNet50. The total number of layers isdetermined by 5 plus two blocks of 58 layers, the last ofwhich results in a 1,024-dimensional feature vector.VI. E
XPERIMENTS
We conduct a set of experiments on the above enlisteddatasets with the above named algorithms. We report in eachexperiment the uniqueness score U , as denoted in Equation 9.We note that small variations in U can indicate large differ-ences in uniqueness due to the exponential function in thedenominator in Equation 8. We proceed to investigate U withrespect to following factors. A. Datasets
In the first experiment, we study the uniqueness scoreacross datasets of different size and setting. Related scores arereported in Table III. We note that dataset size is pertinent,as in large datasets it is more likely to encounter similarfaces, and the related probability of collision is higher asopposed to small datasets. As expected, AT&T encompasseshigher uniqueness scores, due to its small size, as well asconstrained acquisition conditions. With respect to features, wesee that VGGFace features are systematically outperformingthe other networks w.r.t. uniqueness and hence distinctiveness.We believe it is because VGGFace was trained on faces asopposed to other models trained on ImageNet.
TABLE IIIU
NIQUENESS EVALUATED ON FULL
AT&T, LFW, IMD
B AND
TWINS,
WITH RESOLUTION × .AT&T LFW IMDb TWINSVGGFace 0.6710 0.5637 0.5420 0.5591VGG16 0.6417 0.5364 0.5381 0.5339ResNet50 0.6650 0.5364 0.5330 0.5574InceptionV3 0.5915 0.5293 0.5272 0.5242MobileNet 0.6204 0.5353 0.5299 0.5301DenseNet121 0.6338 0.5302 0.5309 0.5268 B. Image Resolution
We proceed to investigate five image resolutions, namely × , × , × , × and × , of thecropped face images of our datasets, all of them in RGB. Giventhat some of the CNNs take an input of size × , weapply a lossy data conversion by first downscaling the imageto a given resolution and subsequently upscaling it to × , in order to fit the standardized input size. We observethat resolution has a surprisingly low effect on uniqueness, asshown in Table IV.For this experiment we provide an additional measurerelated to uniqueness, namely the image entropy calculatedby H = − C (cid:88) c =1 p c · log ( p c ) , (10)where C is the color depth, p c is probability of color c , that is,number of pixels of color c by total number of pixels. We seethat while H decreases proportionally with resolution, U( S ) is not substantially affected. TABLE IVU
NIQUENESS ( AND MEAN IMAGE ENTROPY ) EVALUATED ON FULL
AT&T,LFW, IMD
B AND
TWINS,
WITH
VGGF
ACE FEATURE EXTRACTIONALGORITHM .AT&T LFW IMDb TWINS × × × × × C. Subsets
We investigate the effect of gender and age on the unique-ness score in the dataset IMDb, since related annotations areprovided. Results for the gender split are depicted in Table V.Intuitively, the full dataset reflects a higher uniqueness thanthe gender subsets, which are likely to include more similarfaces of only females and only males.A similar claim can be made w.r.t. age split. Results inFigure 4 show a decrease in uniqueness in all 10-year age-subsets compared to the full IMDb dataset. Moreover, weobserve a slight trend of lower uniqueness scores associatedwith all algorithms for infants and seniors, and of higheruniqueness for middle-aged people. This can be related to theother-age-effect observed in psychology [23]. ull 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-1090.500.510.520.530.540.55 VGGFaceVGG16 ResNet50InceptionV3 MobileNetDenseNet121
Fig. 4. Uniqueness evaluated on full IMDb compared to its split into 10-year blocks.TABLE VU
NIQUENESS EVALUATED ON FULL
IMD
B WITH RESOLUTION × COMPARED TO ITS SPLITS INTO GENDERS .full female maleVGGFace 0.542 0.535 0.532VGG16 0.538 0.520 0.521ResNet50 0.533 0.519 0.525InceptionV3 0.527 0.511 0.514MobileNet 0.530 0.514 0.516DenseNet121 0.531 0.515 0.517
VII. L
IMITATION OF ¯U AND I NTRODUCTION OF ¯U MIN
We recall the definition of the uniqueness score in Equa-tion 8, where impostors are randomly drawn from the wholeremainder of the dataset. Under this definition, given a datasetof N subjects, replacing half of the subjects with twins ofthe already included subjects, would lower the divergence bya factor of / N . Hence the divergence of a dataset of 100twins will be about 99% of the divergence of non-twin dataset,which is negligible and therefore represents a limitation of theused divergence estimate ¯D . For an application that requiresa significant impact of occurrence of twins on the uniquenessscore, we propose a revised divergence estimate ¯D MIN , whichplaces emphasis on the most similar impostor instead ofall remaining people. This amendment moves the impostordistribution towards genuine mildly for general populationdatasets and significantly for twin datasets.Let a dataset S have c subjects and S p ⊂ S denote a setof samples that belong to the subject p . As an alternative, theminimum KL-divergence estimate on this dataset is defined asthe minimum ˆD across all pairs of subjects ¯D MIN ( S ) = 1 c c (cid:88) p =1 min c q =1 q (cid:54) = p ˆD( S p , S q ) , (11)where impostor distribution is calculated from the samples S q of only the subject q with the closest distribution to S p . Thecorresponding alternative uniqueness scores U MIN , calculatedusing ¯D MIN as U MIN ( S ) = 11 + e − ¯D MIN ( S ) , (12) are reported in Table VI. We observe that while theAT&T dataset based on ¯D MIN has a slightly lower U MIN (AT&T) score than
U(AT&T) , the TWINS datasetdrops ¯D MIN (TWINS) ≈ and so U MIN (TWINS) ≈ . ,as desired. TABLE VIU
NIQUENESS EVALUATED ON × RESOLUTION WITH ORIGINALAND MINIMUM DIVERGENCE ESTIMATES . U U
MIN
AT&T TWINS AT&T TWINSVGGFace 0.671 0.559 0.632 0.507VGG16 0.642 0.534 0.582 0.491ResNet50 0.665 0.557 0.542 0.449InceptionV3 0.592 0.524 0.542 0.485MobileNet 0.620 0.530 0.570 0.498DenseNet121 0.634 0.527 0.577 0.494
VIII. C
ONCLUSIONS
In this work we presented preliminary results on the impactof factors such as image resolution, gender, age, datasets, aswell as feature extraction algorithms on facial uniqueness.This is the first work that systematically studies such fac-tors. We provided clear experimental evidence of decrease inthe uniqueness score, in the case that (a) image resolutiondecreases, (b) a single gender is observed, (c) a smallerage group is observed, (d) a larger dataset is used, as wellas (e) different feature extractors are used. We illustratedthat while feature representation and dataset size significantlyaffect the uniqueness score, image resolution has a negligi-ble impact. Further, we proposed an alternative uniquenessestimate, which reflects on the presence of twins. Future workwill involve establishing a more detailed experimental protocolthat among others will aim at quantifying the impact of facialsymmetry on uniqueness. Further, common notions of facialentropy, distinctiveness, diversity, complexity, averageness andattractiveness, and their associated relations are to be explored.A
CKNOWLEDGMENT
This work was supported by the French National ResearchAgency (ANR) under grants ENVISION ANR-17-CE39-0002and IDEX UCA
JEDI
ANR-15-IDEX-01.
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