An information-theoretical look to facial attractiveness

Miguel Ibanez Berganza

Politecnico di Torino, 17th July 2017

[Durer, Four books on human proportion 1534]

Acknowledgements

Fabrizio Antenucci

Serena Di Santo

Vittorio Loreto

Giorgio Parisi

William Schuller

Massimiliano Viale

Outline

Facial attractiveness

An experimental proposal

Some results

Two ideas from ancient greek aesthetics

“Crisippo stays that beauty does not resideon the single elements but on the mutualproportions between them, [...] as it iswritten on Polycletos Canon” [Galeno,Placita Hippocratis et Platonis, 2ndcentury]

Polykleitos Canon. “He did his Canon,

consulted by artists to know the rules of art,

as a law to respect. He was the only one

able to materialise the whole art in a piece

of artwork” [Plinio, Naturalis Historia 1st

century

Two ideas from the renaissance

[Pacioli De Divina Proportione 1509] About

the ideal aesthetic proportions

Facial attractiveness hypothesis

I Common sense hypothesis (beauty is in the eye of thebeholder)

influenced by leaders, fashion, public media, personalpreferences (self-similarity?)

I Natural selection hypothesis (beauty as a health certificate)

facial attractiveness judgements evolved as assessments ofphenotypic condition

I Sexual selection [Darwin 1871] Signal-receiving co-evolution ofsome (possibly handicap) traits, because attractive to theopposite sex (sexual vs. natural selection compromise)

Are they subjective, or have a biological basis? Do they signalfertility, or reproductive value? (refs. in [Johnston Franklin1993])

The “health certificate hypothesis”

I More generaly, beauty as a sign of good phenotypic condition(GPC) [Symons 1979]

I No strong correlation between beauty and health observed(refs. in [Thornill Gangestad 1999]) (stronger in Environmentsof Evolutionary Adaptedness [Hill Hurtado 1996])

I Adaptationist approach: beauty as a GPC certificate shouldreflect in a correlation between facial attractiveness and:facial symmetry and averageness

Facial symmetry

I Reason: asymmetry is known to generally reflectmaladaptation (mutations, pathogens, toxins) (refs. in[Thornhill Gangestad 1999])

I Evidences: with images of identical twins [Mealey et al 1999];with artificially symmetrized faces [Perret et al 1999] [Rhodeset al 1998]; and with corrected double blemishes artefact[Swaddle Churthill 1995]

I Symmetry may be associated with attractiveness because ofother features co-varying with it [Sheib et al 1999].〈〈[...] the direct impact of symmetry [...] is not currentlyknown, but it could be small〉〉 [Thornhill Gangestad 1999]

Facial averageness

I Reason: averageness signals good performance in biologicaltasks [Symons 1979]

I Averaged composites of human faces are more attractive thanthe original faces [Grammer Thornhill 1994] [Langlois et al1994] [OToole et al 1994] (self-similarty clue: [Penton-VoakPerret 1999])

I But the reason may be that it correlates with skin texture andsymmetry. Moreover, the average can be improved withcomposites of beautiful people [Perret et al 1994, AlleyCunningham 1991]

I Sexually dimorphic traits (out-of-the average) are preferred[Perret et al 1998] [Thornhill Gangestad 1999] [JohnstonFrankiln 1993]

[Pallet et al 2010]

A set of faces is modified by changing the inter-eye (IED) and theeye-mouth (EM) distances, maintaining the features, and is scoredby 32 voters

[Pallet et al 2010]

I IED/(face width) 0.46, EM/(face hight) 0.36 (the goldenratio correspondsto ∼0.38)

I These values correspond to the average face: the resultssupport the averageness hypothesis (and the universality ofproportions)

I Are (vertical-horizontal) correlations important?

[Eisenthal et al 2006]

I Machine learning analysis: faces are dimension- reduced using1) a vector of landmark positions and 2) a PCA analysis(eigenfaces)

I Using the ratings of 28 voters, the beauty is estimated withthe KNN algorithm, from the distances between faces in thereduced space.

[Eisenthal et al 2006]

I The trained predictor achieves a significant correlation withhuman ratings: “beauty is objective, and learnable by amachine”

I The vector representation (1) is more effective (confirmed by[Gunes Piccardi 2006])

I The PCA eigenvectors correlated with beauty are not the onewith highest eigenvalue

Questions on facial attractiveness

I What are the relevant variables [proportions/facial featureshapes]?

I Can the most beautiful faces can be characterised as themaximum of some function?

I In this case, are there several maxima (or saddle points)?

I What are their essential properties? Are vertical-horizontalcorrelations important?

I To what extent such properties are universal?

An experimental proposal

I A priori dimensionality reduction: thefaces are described by the set ofdistances, ~x = (xi )

d1 , d = 11

0 1

2

3

4

5

6

7

8

9

10

I A genetic algorithm allows the subject to evolve a populationof N images, generated by a reference facial image and a by aset of N d-dim vectors {~xn}N1 (the genetic codes in thegenetic algorithm).

I The subject selects one out of two images, N times, theselected faces can reproduce (mutation+recombination) andcreate a next generation of images, and so on.

Genetic algorithm: Differential Evolution

N agents with d components, {~xn}Nn=1. The DEA with mutationand recombination constants, µ, ρ:

I ucn = xcn1 + µ(xcn2 − xcn3)

I ucn ≡ x(c)n with prob. (1− ρ)

I if F [~un] < F [~xn] then ~xn ≡ ~un

Image deformation

Image deformation using moving least squares. The ref. points{pi} → {qi}. The transformation fy(x) minimizing:∑

i

wi |fy(pi )− qi |2 wi =1

|y − pi|2α(1)

of the form fy(x) = My · x

The image deformation map that one looks for is M(x) = fx(x)The solution is given by the normal equations solution:

M =

[∑i

wipp†

]−1·

[∑i

wipq†

](2)

Algorithm

Consistency check

0 2 4 6 8 10 12 14generation index

0.002

0.004

0.006

0.008

0.010di

st. t

o th

e 9-

th g

ener

atio

n

023456789101112

0 2 4 6 8 10 12 14generation index

0.000

0.001

0.002

0.003

0.004

0.005

dist

. to

the

9-th

gen

erat

ion

023456789101112

0.36 0.37 0.38 0.39 0.40 0.41 0.421-th coordinate

0.27

0.28

0.29

0.30

0.31

0.32

0.33

2-th

coo

rdin

ate

9gen.1gen. after reshuffling6gen. after reshuffling

Second consistency check

0 1 2 3experiment day index

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

stan

dard

dev

. of i

nter

-pop

dist

ance

11-less PC-metrics

wrt face (av. over voter)wrt voter

0 1 2 3experiment day index

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

stan

dard

dev

. of i

nter

-pop

dist

ance

10-less PC-metricswrt face (av. over voter)wrt voter

Large variability...

Large variability...

0 2 4 6 8 10face coordinate

0.00

0.01

0.02

0.03

0.04

0.05

0.06(euclidean) distance between face vectors

intra-S distance, 1st exp.intra-S distance between 1st and 2nd exps.inter-S distance, 1st exp.

Two-distance correlations

C(2)ij = 〈xixj〉e − 〈xi 〉e〈xj〉e

(standarized variable xi = x ′i /σi )

0 2 4 6 8 10

0.6

0.4

0.2

0.0

0.2

0.4

0.6 01610

Two-distance correlations

C(2)ij = 〈xixj〉e − 〈xi 〉e〈xj〉e

0 2 4 6 8 10

0

2

4

6

8

100.4

0.2

0.0

0.2

0.4

Two distance correlations

Most correlated pairs and their Cij :- vv nose h. – forehead h. -0.491- vv chin h. – forehead h. -0.485+ hh jaw w. – face w. 0.418- vv chin h. – nose h. -0.386+ hh eye w. – mouth w. 0.343- vv nose-lips d. – forehead h. -0.333+ hh jaw w. – eye w. 0.327+ hh jaw w. – mouth w. 0.325

Remarkable correlations:+ hv mouth w. – chin h. 0.251- hv jaw w. – nose h. -0.248- hv inter-eye d. – forehead h. -0.149- hv mouth w. – nose h. -0.181+ hv mouth w. – zyg.-b.h. 0.178- hv nose w. – forehead h. -0.233+ hv nose w. – chin h. 0.188

Inference in LRA

One looks for the most probable P(~x) such that C(2)ij = 〈xi xj〉P ,

where xi = xi − 〈xi 〉e. It is:

P(~x) =1

Zexp

−1

2

∑i ,j

Jijxixj

In linear response approximation:

J = [C (2)]−1

Inference in LRAThe matrix C (2) cannot be inverted because of the presence of a0-mode.J can be obtained by pseudo-inverting it:

C(2)ij =

d∑k=1

f(k)i f

(k)j λk (3)

Jij =∑λk 6=0

f(k)i f

(k)j λ−1k (4)

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

9

10

0.4

0.2

0.0

0.2

0.4

Inference in LRA

Most strongly interacting pairs (higher Jij)+ hh jaw w. – face w. 0.540+ hh eye w. – mouth w. 0.416+ vv chin h. – nose-lips d. 0.415+ hv mouth w. – chin h. 0.326+ vv nose h. – forehead h. 0.299+ hh inter-eye d. – face w. 0.277+ vv chin h. – nose h. 0.248

Remarkable interactions:+ hh inter-eye d. – face w. 0.2771- hv inter-eye d. – forehead h. -0.128+ hv inter-eye d. – nose h. 0.153+ hv mouth w. – chin h. 0.326- hv jaw w. – nose h. -0.209- hv nose w. – forehead h. -0.242

Inference in LRAEigenvalues and eigenvectors

0 2 4 6 8 10eigenvalue index

0.0

0.5

1.0

1.5

2.0

2.5

Clustering

0.65 0.70 0.75 0.80 0.85 0.905-th coord

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

0-th

coo

rd

012345

Clustering

Ongoing work

1. Exact inference (Monte-Carlo sampling the hyperplanarmodel): look for a correlation between clusters andHamiltonian eigenvectors

2. Compute 3,4-distance correlations and compare them with theexperimental ones→Does the “real” effective interaction H involve 3,4-distanceinteraction terms?

3. Study the influence of the sex of the voter

4. Assessing the validity of the a priori dimensionality reduction.→Study the influence of the reference protrait

5. Consider the subject choice as a cognitive process→ coherence and response times→ other discrimination criteria

A long-term project: a systematic inference of the relevantvariables

Outline of results

The experimental setup may allow

1. for an inference of the criteria with which we assess theattractiveness, and

2. for an investigation on its universality

3. and on the dependence of attractiveness perception on thesubject sex, age, ethnicity and origin

4. It can be extended to evaluate different qualities, other thanattractiveness (and determine the relevant quantities tocharacterise them)