Transcript L 0 - Andrei GOREA

INTRODUCTION A LA PSYCHOPHYSIQUE*
Andrei Gorea
*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.
*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.
PLAN DU COURS
(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
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…
Visual Angle
T

T/2 
T/2
tanq 
T
2d  d'
 T 
q  arctan

 2d  d'
Rule of the thumb:
q = 57.3/d
The Snellen charts (1862)
Dots and Bars
Weber’s Contrast
L0+DL
L0-DL
L0
DL
CWEBER =
L0
Gaussian blobs
Weber’s Contrast
 x  m 2 
1

exp 
2
2s 
s 2

L
L0+DL
CWEBER =
DL
G  [m, s]
DL
LO
L0
x
dB
dB = 20log10 (DI / I)
DI = I10dB/20
1dB  DI/I = 1.122
Vernier Acuity
Pierre Vernier (1580-1637) mathématicien français
Dx
DxSeuil = 5’’
Minimum separabile
DxSeuil ≈ 36’’
Dx
Spatial Frequency (Gratings)
Michelson Contrast
SF [cycles/degree]
1,5
L0
Amplitude
1
Amplitude
0,5
LMAX
0
0
5
10
15
20
25
30
-0,5
Lmin
-1
-1,5
L(x,t) = L0[1 + mcos(2fx  2wt)]
Angle
CMichelson =
LMAX - Lmin
LMAX + Lmin
=
A
L0
Elements of Fourier Analysis
2A
fy
2A
0
fx
1f, A
fy
3f, A/3
0
S
fx
fy
0
fx
fy
0
fx
fy
0
1f, 2A
3f, 2A/3
5f, 2A/5
fx
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).
Low-pass
Variable Output amplitude
Output amplitude
Band-pass
Constant Input amplitude
Fonction de transfert d’une
lentille
Frequency (c/deg)
C
S (= 1/Cq)
The Human Contrast Transfer Function (CSF)
Classical acuity
minimum separabile
( 50 c/deg)
≈ 36’’
?
SF
Gratings move…
Direction, speed, velocity
Speed
 deg/s
Direction
 deg
Velocity = Speed + Direction
Speed [deg/s] =
Space [deg]
Time [s]
=
TF [cycles/s]
SF [cycles/deg]
6 Hz
4 c/°
1 Hz
16 Hz
0.5 c/°
16 c/°
Robson, 1966
22 Hz
22 c/°
THJRESHOLD
&
SENSITIVITY
Kelly, 1978
Sensitivity = 1/Threshold
Temporal Frequency
cycles/s  Hz
Equiluminant gratings
Examples of gratings with S-cone positive (left) and S-cone negative (right) contrast.
Chromatic grating & sensitivity
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).
Contrast sensitivities as
a function of spatial
frequency for a blueyellow grating (◊; 470,
577 nm) and a redgreen grating (□; 602,
526 nm).
Mullen, K.T. (1985) J. Physiol. 359, 381-400
Color vision tests
Isihara plates
FILTRAGE MULTIECHELLE
Face
SF
Face
SF + Ori
Mach bands
Luminance
Brightness
x
Mach bands
An illusion by Vasarely, left, and a bandpass
filtered version, right.
(a) Image 1-D
luminance profile
(b) Fourier
transform of the
image (1-D Fourier
spectrum)
(c) Human SF
sensitivity
(d) Dot product of
(b) & (c)
(e) ‘Reconstructed
image 1-D
luminance profile
(inverse Fourier
transform)
The RF is equivalent to the system’s Impulse Response
PHYSICAL SPACE
RECEPTIVE
FIELD
Incoming light
Photoreceptors
Dans un système linéaire
rétinotopique,
Axons
Neurons
La représentation d’un
ensemble de points (image)
Recording site
RETINOTOPICAL SPACE
par un seul neurone
PHYSICAL SPACE
est strictement identique à la
représentation d’un point
dans l’espace physique
Incoming light
Photoreceptors
par l’ensemble des
neurones qui le traitent.
Axons
Neurons
Recording site
IMPULSE
RESPONSE
RETINOTOPICAL SPACE
CONVOLUTION
1
1
1
1
-1
3
-1
2
3
4
5
5
5
5
1
1
1
-1
3
-1
3
-1
-1
3
-1
1
2
3
4
5
5
5
5
-5
15
-5
-5
15
Champ récepteur
Réponse impulsionnelle

S
1
1
SX   E  h   E(X  x)  h(x)dx

0
2
3
4
6
5
5
-1
3
-1
-1
3
-2
-1
6
-3
-2
9
-4
-3
12
-5
-4
15
-5

SX   E  h   E(X)  h(X  x)dx
-5
15
-5

E(X) = Entrée (fct. de X)
S(X) = Sortie (fct. de X)
CR = h(x) = Réponse Implle (fct. de x)
S
1
1
0
2
3
4
6
5
5
Gabors: cos(x)  Gauss(x)
L(x,t) = L0[1 + mcos(2fx  2wt)] 
s (deg)
Spatial Frequency (c/deg)
Carrier (porteuse) c/deg, phase
 contrast
Envelope  m, s  deg
Orientation
Plaids
(tartans)
fy
0
fy
fx
0
+
fy
0
fx
fy
fx
0
+
fy
0
fx
fx
Plaids in motion
Speed [deg/s] =
Space [deg]
Time [s]
=
TF [cycles/s]
SF [cycles/deg]
White noise
Pink noise
Appearance
S(f)  1 / f 0
=k
Amplitude (dB)
S(f)  1 / f 1
1-D
Fourier
spectrum
1
10
100 1
10
100
Frequency (Hz or c/deg)
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)
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
Root mean square Contrast
Crms 
n
  Li  L 0 
i1
n
2
rms Contrast
(root mean square)
n
Crms 
  Li  L 0 
i1
n
2
SF gratings in Noise
Assessing the internal noise
Contraste au Seuil
Élévation du Seuil
Noise rms Contrast
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=nois
e&template=thumbs_details&join=or&field2
=imageDescription&op=contains&value2=n
oise&sorton=Filename&catalog=proto1&su
bmit2.x=0&submit2.y=0&submit2=Search
Random Dots Stereograms
(RDS – Julesz, 1961)
I. Create a random dot image.
II. Copy image side by side.
The Random Dot Stereogram is ready.
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.
To “reveal” the “hidden” square
the brain presumably computes
the cross-correlation between
the 2 images.
Binocular disparity
P
p
p’
Binocular disparity  x – x’ [deg]
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
Amplitude Modulation (AM) ContrastContrast (2nd order modulations)
http://viperlib.york.ac.uk/scripts/Po
rtWeb.dll?field=keywords&op=con
tains&value1=second+order+moti
on&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
CMAX + Cmin
CMAX
Amplitude
CCMichelson =
CMAX - Cmin
http://www.michaelbach.de/ot/lum
_contrast-contrast/index.html
Cmin
x
Amplitude Modulation (AM)
Contrast-Contrast
Other approaches… other stimuli…
Lois d’organisation
Figure-Fond
Rubin, 1915
Figure-Fond
Necker cube
Luis Albert Necker, 1832
Sort commun, Mouvement et Forme
2D HIDDEN IMAGE
Optic flaw
Biological motion
Hollow Mask
Light from above
Illusions
http://www.michaelbach.de/ot/