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Miguel Ib anez~ Berganza Politecnico di Torino, 17 July · PDF fileMiguel Ib anez~ Berganza Politecnico di Torino, 17th July 2017 [Durer, Four books on human proportion 1534] Acknowledgements

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  • 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, , :

    I ucn = xcn1 + (x

    cn2 x

    cn3)

    I ucn x(c)n with prob. (1 )

    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|2(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 = xixje xi exje

    (standarized variable xi = xi /i )

    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 = xixje xi exje

    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 xjP ,

    where xi = xi xi e. It is:

    P(~x) =1

    Zexp

    12

    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 =

    dk=1

    f(k)i f

    (k)j k (3)

    Jij =k 6=0

    f(k)i f

    (k)j

    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.

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