THEORIE DE LA DETECTION DU SIGNAL La Théorie de la Détection du Signal (TDS) est à la fois un instrument de mesure de la performance et un cadre théorique

THEORIE DE LA DETECTION DU SIGNAL

La Théorie de la Détection du Signal (TDS) est à la fois un instrument de mesure de la performance et un cadre théorique dans lequel cette performance est interprétée du point de vue des mécanismes sous-jacents. En tant que telle, la TDS peut être regardée comme étant à la base de la psychophysique moderne. Le cours développera les bases de la TDS, discutera sa relation avec les concepts de seuil sensoriel et de décision et exemplifiera son application dans des situations expérimentales allant depuis le sensoriel jusqu'au cognitif.

SIGNAL DETECTION THEORY AND PSYCHOPHYSICS

David M. Green & John A. Swets

1st published in 1966 by Wiley & Sons, Inc., New York

Reprint with corrections in 1974

Copyright © 1966 by Wiley & Sons, Inc.

Revision Copyright © 1988 by D.M. Green & J. A. Swets

1988 reprint edition published by Peninsula Publishing, Los Altos, CA 94023, USA

CONTINUUM SENSORIEL

PR

OB

AB

AB

ILIT

É

1

R

FA

Hits

p(‘yes’│N) = p(RN>c)

p(‘yes’│S) = p(RS>c)

p(N) p(S)STIMULUS

RÉ

PO

NS

E

Bruit Signal

Oui FA Hit

Non CR Omiss.c

R

LE MODEL STANDARD :LE MODEL STANDARD :THEORIE de la DETECTION du SIGNALTHEORIE de la DETECTION du SIGNAL

CR

Miss

0

S Rd' z(Hits) z(FA)

Bc .5 z(H) z(FA) ; c z FA

-

xz

Score zOu « score normal » ou « score standard »

-4.0 -3.0 -2.0 -1.0 0 +1.0 +2.0 +3.0 +4.0Z scores


CONTINUUM SENSORIEL

f R:

PR

OB

AB

AB

ILIT

É

FA

Hits

The likelihood ratioLe rapport de vraisemblance

c R

cf

cf

NcRp

ScRp)X(L

N

S

R

R

-4 -3 -2 -1 0 1 2 3 4 5 6

Sensory Continuum (z)

0

0,1

0,2

0,3

0,4

0,5

P(z

)

N S

d’=1

cA = c + d’/2 = 1.60 =cA

c = 1.10c


p(S) = .25

c

3

p

p

czp

czp

S

N

N

S

pN(z

=c

)

pS (z=

c)

-zFA

c0

= 1

p(S) = . 50

c = 0

z(FA)z(FA)

-z

1 - p > .5p < .5

1 - p > .5

+z

p > .51 - p < .5

p > .51 - p > .5

+z +z

z(H)z(H)

-z +zd’ = z(H) – [-z(FA)]

+z +zd’ = z(H) – z(FA)

d’ d’

z(.5) = 0z(p < .5) < 0z(p > .5) > 0z(1 - p) = -z(p)

d’ computation with Excel

d’ = LOI.NORMALE.STANDARD.INVERSE[p(H)] - LOI.NORMALE.STANDARD.INVERSE[p(FA)]

c0 = -0.5*{LOI.NORMALE.STANDARD.INVERSE[p(H)] + LOI.NORMALE.STANDARD.INVERSE[p(FA)]}

cA = -LOI.NORMALE.STANDARD.INVERSE[p(FA)]

= LOI.NORMALE(cA;d’;1;FAUX)/LOI.NORMALE(cA;0;1;FAUX)

HITS FA HITS FA HITS FA HITS FAn 70 30 90 10 83 5 60 20

out of 100 100 100 100 100 100 100 100

N_Tot

d'

c0ca 1.0000

0.3453 0.29410.5244 1.2816 1.6449 0.8416

200 200 200 200

1.0000 2.4536 1.3800

1.09502.59902.56311.0488

0.0000 0.0000

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 0

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 0

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 0

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 0

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 0

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 0

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 0

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 0

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 0

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 0

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 1

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 1

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 1

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 1

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 1

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 1

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 1

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 1

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 1

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 1

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 1

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 1

0

0.2

0.4

-8 -4 0 4 8


P(z

d' = 1

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 1

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 2

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 2

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 2

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 2

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 2

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 2

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 2

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 3

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 3

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 3

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 3

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 3

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 3

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 3

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 3

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 3

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 3

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 3

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 3

0

0.2

0.4

-8 -4 0 4 8


P(z

d'= 3

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

pFAp

H

d' = 3

d’d’

d’

Receiving Operating Characteristics (ROC)Receiving Operating Characteristics (ROC)

ROC & le Rating experimentROC & le Rating experiment1. Faire le choix entre Oui et Non;

375

375

Tot.

28590N

157218S

NonOui

2. Donner son niveau de certitude de 1 (peu sûr) à (par ex.) 3 (très sûr); l’on calcule les p pour chaque case en divisant sa fréq. par le no. total

1.00

1.00

Tot.

N, FA

S, H

*

.301

.059

“3”

.301

.200

“2”

.160

.160

“1”

Non

.200.251.131

.120.099.021

“1”“2”“3”

Oui

3. Pr chaque case, l’on calcule les p cumulés de gauche à droite, les scores z, les d’ et c

FA

H

1.00

1.00

“1”

.701

.942

“2”

.400

.742

“3”

.582.382.131

.240.120.021

“4”“5”“6”

Oui

-1.050-0.1980.2500.7381.579c

1.0460.9020.9130.8740.916d’

zFA

zH

0.527

1.573

-0.253

0.6490.207-0.301-1.121

-0.706-1.175-2.037

-4 -3 -2 -1 0 1 2 3 4 5 6Sensory Continuum (z)

0

0.1

0.2

0.3

0.4

0.5

P(z

)

N S

d’=.91

c

.202-(-.706) = .908d’

zH-zFA

-.706

zFA

-.5(.202 - .706) =.252c

-.5(zH + zFA)

90/375 = .24

.202218/375

= .58

pFAzHpH

2. Calculer le pH, pFA; puis d’ & c.

*Notez que l’échelle « Oui/Non » ci-dessus est équivalente à une échelle «Oui» avec 6 graduations, du plus sûr («6») au moins sûr («1»):

Tot.“1”“2”“3”“4”“5”“6”

Oui

ROC & le Rating experimentROC & le Rating experiment

-4 -3 -2 -1 0 1 2 3 4 5 6


0

0.1

0.2

0.3

0.4

0,5

P(z

)

N S

d’=.91

p z p z p z p z p z p zH 0.131 -1.122 0.382 -0.300 0.582 0.207 0.742 0.650 0.942 1.572 1.000 ######

FA 0.021 -2.034 0.120 -1.175 0.240 -0.706 0.400 -0.253 0.701 0.527 1.000 ######d'c0

OUI NON

#NOMBRE!1.0450.9030.9130.8750.912

"2""3"

#NOMBRE!-1.050-0.1980.2500.7381.578

"3""2""1""1"

Note that a symmetrical ROC indicates that d’ is independent of c0

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

pFA

pH

ROC & le Rating experimentROC & le Rating experiment

p z p z p z p z p z p zH 0.131 -1.122 0.382 -0.300 0.582 0.207 0.742 0.650 0.942 1.572 1.000 ######

FA 0.021 -2.034 0.120 -1.175 0.240 -0.706 0.400 -0.253 0.701 0.527 1.000 ######d'c0

OUI NON

#NOMBRE!1.0450.9030.9130.8750.912

"2""3"

#NOMBRE!-1.050-0.1980.2500.7381.578

"3""2""1""1"

ROC in z units

-2.5

-1.5

-0.5

0.5

1.5

-2.5 -0.5 1.5z(FA)

z(H

)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

pFA

pH

d’ with unequal variancesd’ with unequal variances

CONTINUUM SENSORIEL

PR

OB

AB

AB

ILIT

É

FA

Hits

c

?'d

1

2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

pFA

pH

d’ ?

0

0.2

0.4

0.6

0.8

1

pH

d’

-2

-1

0

1

2

-2 -1 0 1 2

zFA

zH

in N units

'1d

'2d in S units

'N/Yd

d’a

d’a

-2

-1

0

1

2

zH

'2d

in N units

in S units

'1d

d’2 < d’a < d’1

d’

wit

h u

neq

ual

var

ian

ces

d’

wit

h u

neq

ual

var

ian

ces

The index da has the properties we want.

1. It is intermediate in size between d1 and d‘2.2. It is equivalent to d' when the ROC slope is 1,

for then the perpendicular line of length DY/N coincides with the minor diagonal, and the two lines of length da coincide with the d'1, and d'2 segments.

3. It turns out to be equivalent to the difference between the means in units of the root-mean-square (rms) standard deviation, a kind of average equal to the square root of the mean of the squares of the standard deviations of S1 and S2.

22

21

'N/Y

'a /Rd2d

To find da from an ROC that is linear in z coordinates, it is easiest to first estimate d’1, d’2 and the slope s = d’1/d’2. Because the standard deviation of the S1 distribution is s times as large as that of S2, we can set the standard deviation of S1 to s and that of S2 to 1.

To find da directly from one point on the ROC once s is known:

-2

-1

0

1

2

-2 -1 0 1 2

zFA

zH

in N units

'1d

'2d in S units

'N/Yd

d’a

d’a

d’

wit

h u

neq

ual

var

ian

ces

d’

wit

h u

neq

ual

var

ian

ces

5.

'25.

'2'

a ²s1

2d

²s15.

dd

5.

'a ²s1

2FszHzd

Sometimes a measure of performance expressed as a proportion is preferred to one expressed as a distance. The index Az, is such a proportion and is simply DYN transformed by the cumulative normal distribution function , i.e. (DYN):

Az is the area under the normal-model ROC curve, which increases from .5 at zero sensitivity to 1.0 for perfect performance. It is basically equal to %Correct in a 2AFC experiment. It is a truly nonparametric index of sensitivity.

d’

wit

h u

neq

ual

var

ian

ces

d’

wit

h u

neq

ual

var

ian

ces

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

pFA

pH

d’

2dDAz,ROCunderArea a

YN

High-Threshold

Sum Absolute Difference (SAD)

Max Absolute Difference (MAD)

Schematic of a single trial used for the set size and the target number experiments. In the orientation and spatial frequency experiments, the colored squares were replaced with Gabor patches.

Wilken, P. & Ma, W.J (2004). A detection theory account of change detection. J. Vision 4, 1120-1135.

ROCs obtenus avec une méthode de « rating » sur une échelle de 1 à 4. Different symbols represent performance at different set sizes: set-size 2 for color, orientation and SF – red stars; set-size 4 for color and SF, set-size 3 for orientation – green triangles; set-size 6 for color and SF, set-size 4 for orientation – blue circles; set-size 8 for color and SF, set-size 5 for orientation – purple squares.

Hits & FA

HT

SAD

MAD

H

FA

H

FA

H

FA

LA RELATION ENTRE Y/N & 2AFC

See MacMillan & Creelman (2005, 2nd ed.) pp 166-170.

0 S

1 2

S 0

1 2

A = « 1 » - « 2 » -S

B = « 1 » - « 2 » S22SD

S2BA

'N/Y

'AFC2 d2

2S

2

S2d

LA RELATION ENTRE Y/N & 2AFC

d’

d’

d’2

RéponseCorrectIncorrectDroite

IncorrectCorrectGauche

DroiteGauche

Stimulus

%Correct Hits%Incorrect FA

d’ 2AFC

d’2AFC = 2d’Oui/Non

D

0

G

Yes/No

Yes

/No

See MacMillan & Creelman (2005, 2nd ed.) pp 166-170.

So, objects may be “invisible” for only 2 + 1 reasons;

because the internal activity they yield upon presentation:

because Sj’s report on the presence/absence of the stimulus is solicited within a time delay beyond his/her mnemonic capacity (the case of change blindness).

is below Sj’s criterion the objet is ignored, or

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

is undistinguishable from noise (null sensitivity) d' = 0,

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

d' = 3

c =1.5

Reasons for “invisibility”Reasons for “invisibility”

Failure of discriminating Signal from Noise has a triple edge:

Stimuli may be out of the standard window of visibility [] (Signal Internal noise)

e.g. ultraviolet light, SF > 40 c/deg, TF > 50 Hz reduced window of visibility (experimental or pathological –

e.g. blindsight)

Stimuli may be "masked" by external noise [] so that the S/N ratio is decreased by means of:

increasing N (external noise impinges on the detecting mechanism the classical pedestal effect, or increases spatial/temporal uncertainty e.g. the "mud-splash effect")

decreasing S (external noise activates an inhibitory

mechanism lateral masking/metacontrast) [] Change of the transducer [](experimentally or neurologically

induced gain-control effects, normalization failure …)

SENSITIVITYSENSITIVITY 0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

can be manipulated in a number of ways: probability pay-off

can be affected by experience in general

and, possibly, by some neurological conditions blindsight neglect / extinction attentional deficit syndromes

CRITERIONCRITERION

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

49.4%50%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

98.7%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

91.5%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

73.9%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

56.1%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

49.4%50%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

42.5%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

24.1%

0

0,1

0,2

0,3

0,4

0,5

-4 -3 -2 -1 0 1 2 3 4 5 6

P(z

)

-4 -3 -2 -1 0 1 2 3 4 5 6

Criterion (zFA)

% Y

ES

d' = 3

7.3%

The response criterion can be assimilated to response bias (and everything that goes with it, i.e. predisposition, context effects, etc.)

AN EXAMPLE: CHANGE BLINDNESSAN EXAMPLE: CHANGE BLINDNESS

Dinner

Money

Airplane

CANAUX, BRUIT

et

THÉORIE DE LA DÉTECTION DU SIGNAL

« Qualité » ()Intensité ou « qualité » du StimulusRé

po

ns

e d

’un

fil

tre

(s

/s o

u a

utr

e)

Le principe de l’UNIVARIANCE

Un Canal,Filtre.

Chp Récep.

R V

Snn

n

max RI

IRR

I = stimulus intensityR = responseRmax = max resp.N = max slopeS = semi-saturation cst.Rs = spontaneous R

Un autreR

ép

on

se

d’u

n f

iltr

e

Normalization works (here) by

dividing each output

by the sum of all outputs.

Heeger, D.J. (1992). Normalization of cell responses in cat striate cortex. Visual Neuroscience, 9, 181-197.

RESPONSE NORMALIZATION

Divisive inhibition

R V

RÉPONSE

CANAUX & PROBABILITÉ DE RÉPONSEIntensity Discrimination

p(s/s)

RE

PO

NS

E (

e.g

. s

/s)

pmin

pMax

pmin

pMax

p(s/s)

R V

RÉPONSE

CANAUX & PROBABILITÉ DE RÉPONSEWithin & Across Channels Discrimination

p(s/s)

p(s/s)

RE

PO

NS

E (

e.g

. s

/s)

pmin

pMax

pmin

pMax

CANAUX & PROBABILITÉ DE RÉPONSE« OFF-LOOKING » CHANNEL

RÉPONSE

R Vp(s/s)

RE

PO

NS

E (

e.g

. s

/s)

p(s/s)R

EP

ON

SE

(e

.g.

s/s

)R V

I0 I1

kIR = cst.

kI

.)cstiff;at(kR

IR

IR

log (I)lo

g (I

)

slope

= 1

NO Weber ’s LawI = k

k

Input

R =

kI

p(R)

II1

R

II0

R

TRANSDUCTION

Input

R =

log

(I)

I0 I1

II1

R

II0

R

)Fechner()Ilog(R = cst.

p(R)log (I)

log

(I

)

slope

= 1

Weber ’s LawI = kI

)Laws'Weber(I'kI

.)cstiff;at(kRI

IR

)Fechner()Ilog(R

TRANSDUCTION

Input

R =

log

(I)

I0 I1

)0βiffLaws'Weber(IlogkII

)Rσ;θat(RRI

IR

)Fechner(IlogR

βθ

ββθ

II0

R

p(R)

R

II1

log (I)lo

g (I

)

slop

e >

1

Weber ’s LawI = kI

)Fechner(IlogR R

TRANSDUCTION

VISUAL SEARCH

and

SIGNAL DETECTION THEORY

T

emp

s. R

éact

ion

No. Éléments

ORIENTATION

Parallèle (?!)

Tem

ps.

Réa

ctio

n

No. Éléments

Sériel (?!)

ORI + COL

Le paradigme type

Treisman A.M. & Gelade G. (1980)

LE MODÉLE STANDARD : LA THÉORIE DE LA DÉTECTION DU SIGNAL

« COULEUR »

L

R V

RE

SP

ON

SE

RE

SP

ON

SE

CONTINUUM SENSORIEL (R-V)

PR

OB

AB

.

R

d’ n’est pas mesurable

« COULEUR »

L

R V

RE

SP

ON

SE

CONTINUUM SENSORIEL (R-V)

PR

OB

AB

.

R

Rd’=

T

emp

s. R

éact

ion

No. Éléments

ORIENTATION

Parallèle (?!)

Tem

ps.

Réa

ctio

n

No. Éléments

Sériel (?!)

Procs. Coopératifs

Tem

ps.

Réa

ctio

n

No. Éléments

COULEUR

Parallèle (?!)

Tem

ps.

Réa

ctio

nNo. Éléments

Sériel (?!)

Procs. Coopératifs

Documents

THEORIE DE LA DETECTION DU SIGNAL La Théorie de la Détection du Signal (TDS) est à la fois un instrument de mesure de la performance et un cadre théorique