introduction a la psychophysique* andrei gorea *la science régulant le choix des stimuli, des...
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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/