INTRODUCTION A LA PSYCHOPHYSIQUE*

Andrei Gorea

*La science régulant le choix des stimuli, des méthodes et des plans expérimentaux permettant de répondre à une question précise en rapport avec les processus sous-jacents aux sensations/perceptions induites par le monde extérieur.

*The science regulating the choice of stimuli, the methods and experimental designs meant to answer specific questions concerning the mechanisms/processes underlying the sensations/perceptions evoqued by external events.

(I. Histoire)

II. Stimuli & Méthodes Stimuli élémentaires et leurs paramètres Visibilité, enveloppe spatio-temporelle de la visibilité Autre stimuli, autres problématiques Seuil, Bruit, Fonction Psychométrique et Transduction

III. Méthode de mesure de seuils Classification des méthodes et des tâches Fonction psychométrique Paradigmes oui/non et choix forcé Méthodes de mesure de seuil

Méthodes des limites Ajustement Stimuli constants Fonction psychométrique Méthodes adaptative ‘Scaling’ et ‘magnitude estimation’

Plans expérimentaux Quelques paradigmes classiques

IV. Un peu de pratique

V. Théorie de la Détection du Signal

PLAN DU COURS

II. STIMULI « ELEMENTAIRES »

En Psychophysique, le Stimuli doivent être précisément définis…

…leur forme, leur taille, leur couleur, leur orientation, leur contraste (intensité)…

…leur fréquence temporelle/spatiale, leur disparité binoculaire, leur vitesse…

Rule of the thumb:

= 57.3/d

Visual Angle

'dd

Tarctan

'dd

Ttan

2

2

T/2T/2

T

The Snellen charts (1862)

L0

L0-LL0+L

Dots and BarsWeber’s Contrast

CWEBER = LL0

LO

L0+L

L

L

x

CWEBER =L

L0

Gaussian blobsWeber’s Contrast

G []

2

2

22

1 xexp

dB

dB = 20log10 (I / I)

I = I10dB/20

1dB I/I = 1.122

Vernier Acuity Pierre Vernier (1580-1637) mathématicien français

x xSeuil = 5’’

Minimum separabile

x

xSeuil ≈ 36’’

Spatial Frequency (Gratings)Michelson Contrast

-1,5

-1

-0,5

0

0,5

1

1,5

0 5 10 15 20 25 30Am

pli

tud

e

AmplitudeLMAX

Lmin

L0

CMichelson =LMAX - Lmin

LMAX + Lmin

A

L0

=

SF [cycles/degree]

L(x,t) = L0[1 + mcos(2fx 2t)]

Elements of Fourier Analysis

2A

2Afx

fy

0

fx

fy

0

1f, A

3f, A/3

fx

fy

0

fx

fy

0

fx

fy

0

1f, 2A 3f, 2A/3 5f, 2A/5

Dans un système linéaire, mesurer l’amplitude du signal de sortie du système pour une amplitude d’entrée constante (l’approche de l’ingénieur) équivaut à mesurer l’amplitude entrante requise afin d’obtenir un signal de sortie constant (le seuil; l’approche du psychophysicien).

Constant Input amplitude

Variable Output amplitude

Ou

tpu

t am

pli

tud

e

Frequency (c/deg)

Fonction de transfert d’une lentille

Low-pass

Band-pass

Low-pass

Band-pass

C

SF

The Human Contrast Transfer Function (CSF)

≈ 36’’

Classical acuityminimum separabile

( 50 c/deg)

S (

= 1

/C)

INHIBITION

?

Speed deg/sDirection degVelocity = Speed + Direction

Speed [deg/s] =Space [deg]

Time [s]=

TF [cycles/s]

SF [cycles/deg]

Gratings move…Direction, speed, velocity

THJRESHOLD&

SENSITIVITY

Kelly, 1978

Sensitivity = 1/Threshold

Temporal Frequencycycles/s Hz

1 Hz

6 Hz

16 Hz

22 Hz

0.5 c/°

4 c/°

22 c/°

Robson, 1966

16 c/°

Equiluminant gratings

Examples of gratings with S-cone positive (left) and S-cone negative (right) contrast.

Chromatic grating & sensitivity

Contrast sensitivities as a function of spatial frequency for a blue-yellow grating (◊; 470, 577 nm) and a red-green grating (□; 602, 526 nm).

Contrast sensitivity as a function of spatial frequency for the red-green grating (□; 526, 602 nm) and a green monochromatic grating (○; 526 nm).

Contrast sensitivity as a function of spatial frequency for the blue-yellow grating (□; 470, 577 nm) and a yellow monochromatic grating (○; 577 nm).

Mullen, K.T. (1985) J. Physiol. 359, 381-400

Color vision testsIsihara plates

FILTRAGE MULTIECHELLE

FaceSF

FaceSF + Ori

Lu

min

ance

x

Mach bands

Brig

htn

ess

Mach bands

An illusion by Vasarely, left, and a bandpass filtered version, right.

(b) Fourier transform of the

image (1-D Fourier spectrum)

(a) Image 1-D luminance profile

(c) Human SF sensitivity

(d) Dot product of (b) & (c)

(e) ‘Reconstructed image 1-D

luminance profile (inverse Fourier

transform)

Incoming light

Photoreceptors

Neurons

Axons

RECEPTIVE FIELD

PHYSICAL SPACE

Recording site

RETINOTOPICAL SPACE

Recording site

Photoreceptors

Neurons

Axons

PHYSICAL SPACE

IMPULSE RESPONSE

RETINOTOPICAL SPACE

Incoming light

The RF is equivalent to the system’s Impulse Response

Dans un système linéaire rétinotopique,

La représentation d’un ensemble de points (image)

par un seul neurone

est strictement identique à la représentation d’un point dans l’espace physique

par l’ensemble des neurones qui le traitent.

1 1 1 1 2 3 4 5 5 5 5

Champ récepteur-1 3 -1

11 0 2 3 4 6 5 5

1 1 1 1 2 3 4 5 5 5 5

Réponse impulsionnelle-1 3 -1

11 0 2 3 4 6 5 5 -1 3 -1

-1 3 -1

-1 3 -1

-2 6 -2

-3 9 -3

-4 12 -4

-5 15 -5

-5 15 -5

-5 15

-13

-5

-5 15

CONVOLUTION

dx)xX(h)X(EhEXS

dx)x(h)xX(EhEXS

E(X) = Entrée (fct. de X)S(X) = Sortie (fct. de X)CR = h(x) = Réponse Implle (fct. de x)

Gabors: cos(x) Gauss(x)

Sp

atia

l F

req

uen

cy (

c/d

eg)

Orientation

Carrier (porteuse) c/deg, phase contrast

Envelope , deg

(d

eg)

L(x,t) = L0[1 + mcos(2fx 2t)]

 Plaids (tartans)

+ +

fx

fy

0 fx

fy

0 fx

fy

0

fx

fy

0 fx

fy

0 fx

fy

0 fx

fy

0

Speed [deg/s] =Space [deg]

Time [s]=

TF [cycles/s]

SF [cycles/deg]

 Plaids in motion

Pink noise or 1/f noise is a signal or process with a frequency spectrum such that the power spectral density is proportional to the reciprocal of the frequency. For pink noise, each octave carries an equal amount of noise power. The name arises from being intermediate between white noise (1/f0) and red noise (1/f2, more commonly known as Brownian noise)

S(f) 1 / f 0

= kS(f) 1 / f 1

White noise Pink noise

Am

pli

tud

e (d

B)

Frequency (Hz or c/deg)

1 10 1001 10 100

Appearance

1-D Fourier

spectrum

Filtered noise

Appearance 2-D Fourier spectrum

1-D Fourier spectrum

White

Filtered with a 0.5 octave* isotropic filter

* Octave: Frequency doubling

Figure 4. Illustration of spatial whitening. (a) A natural image whose amplitude spectrum, plotted in (c), falls approximately as “1/F” on log–log axes with a slope of j1.4. Whitening the amplitude spectrum produces an image (b) that appears sharpened, but otherwise structurally quite similar. (d) The amplitude spectrum of the whitened image has approximately the same amplitude at all spatial frequencies and a resultant spectral slope close to 0. The rms contrasts of the source and whitened images have been fixed at 0.25.

Bex, Solomon & Dakin, (2009). Journal of Vision, 9(10):1, 1–19.

White noise Natural Image

n 2

i 0i 1

rms

L LC

n

Root mean square Contrast

n 2

i 0i 1

rms

L LC

n

rms Contrast(root mean square)

Con

tras

te a

u S

euil

Noise rms Contrast

Élévation du S

euil

Equivalent NoiseSeuil « absolu »

SF gratings in NoiseAssessing the internal noise

A visual assessment chart consisting of letters in noise that is designed to test for some neural deficits while being unaffected by optical deficits.

Denis Pelli (NYU, USA) & John Hoepner (Depart. of Opthalmology, Health Science Center, Syracuse, NY, USA.)

http://viperlib.york.ac.uk/scripts/PortWeb.dll?field=keywords&op=contains&value1=noise&template=thumbs_details&join=or&field2=imageDescription&op=contains&value2=noise&sorton=Filename&catalog=proto1&submit2.x=0&submit2.y=0&submit2=Search

I. Create a random dot image.

II. Copy image side by side.

III. Select a region of one image.

IV. Shift (horizontally) this region and fill in the blank space left behind with the random dots to be replaced ahead.

The Random Dot Stereogram is ready.

To “reveal” the “hidden” square the brain presumably computes the cross-correlation between the 2 images.

Random Dots Stereograms(RDS – Julesz, 1961)

Figure 1. The binocular fusion problem: in the simple case of the diagram shown on the left, there is no ambiguity and stereo reconstruction is a simple matter. In the more usual case shown on the right, any of the four points in the left picture may, a priori, match any of the four points in the right one. Only four of these correspondences are correct, the other ones yielding the incorrect reconstructions shown as small grey discs

Binocular disparity

Binocular disparity x – x’ [deg]

P

p’

x x’

p

Amplitude Modulation (AM) Contrast-Contrast (2nd order modulations)

x

Am

plit

ud

e

CMAX

Cminhttp://viperlib.york.ac.uk/scripts/PortWeb.dll?field=keywords&op=contains&value1=second+order+motion&template=thumbs_details&join=or&field2=imageDescription&op=contains&value2=second+order+motion&sorton=Filename&catalog=proto1&submit2.x=41&submit2.y=12&submit2=Search

CCMichelson =CMAX - Cmin

CMAX + Cmin

http://www.michaelbach.de/ot/lum_contrast-contrast/index.html

Amplitude Modulation (AM) Contrast-Contrast

Other approaches… other stimuli…

Lois d’organisation

Rubin, 1915

Figure-Fond

Figure-Fond

Necker cube

Luis Albert Necker, 1832

Sort commun, Mouvement et Forme

2D HIDDEN IMAGE

Biological motionOptic flaw

Hollow Mask

Light from above

Illusions

http://www.michaelbach.de/ot/