lecture 13
Psychophysics
Psychometric curve (function)
"Psychophysics" : (loose definition)
the study of mappings from physical variables to perceptual
variables (measured by behavior)
- psychometric curves
- thresholds
- contrast sensitivity
subject's
response
e.g. setting of
some knob
or (more
commonly) a
statistic such as
percent correct
- disparity sensitivity
Tuesday, Oct. 27, 2015
Example task: decide if there is a
bright patch in the center surround i.e.
detect if an increment is present.
Suppose that that there is an increment
present half the time.
stimulus
response
(physical)
(perception, behavior)
stimulus (independent variable,
set by experimenter)
Example task:
Example task (depth from binocular stereo) :
Decide whether the center is brighter or
darker than the surround.
Decide whether the 'test' is further or closer than a fixed 'reference'
(also called 'standard').
Percent correct now goes from 0 to 100.
test
reference
"brighter"
pct response
"test is further"
percent
correct
test
depth
reference depth
"darker"
ASIDE:
?
Why are psychometric curves not step functions
Contrast
Recall lecture 6, slide 20 : blurring a step edge
psychometric function is
sometimes modelled as a
blurred step edge
e.g. cumulative Gaussian
distribution
- noise in the display or stimulus (sometimes added)
- noise in the sensors
Other "S shaped" (sigmoid) models are used as well e.g. logistic function.
- limited resolution (finite sampling)
- noise in behavior (subjects press the wrong button, stop
paying attention)
The key is to have a small number of parameters (two for Gaussian).
There is no special 'law of psychophysics' that says a cumulative Gaussian
should be used.
Michelson
contrast
Imax - Imin
I max + Imin
Let
Michelson
contrast
I
( Imax - Imin ) / 2
Example of a different task that measures contrast
sensitivity:
I0
( Imax + Imin ) / 2
Is the sinusoid 'grating' vertical or horizontal?
( Imax - Imin ) / 2
( I max + Imin ) / 2
Psychophysical Threshold
Often we don't care about the whole psychometric curve. Instead,
we might just ask what is the stimulus level (threshold) that gives a
particular performance level e.g. 75% correct.
I
I0
percent
correct
stimulus
level
threshold
Methods for Estimating a Threshold
1)
2)
"Method of Constant Stimuli" :
3)
"Method of Adjustment" and "Method of Limits"
fit curve
Here I give a hybrid version of these two methods ...
https://en.wikipedia.org/wiki/Psychophysics
Turns a 'knob' until a threshold is reached.
test level
"Staircase Method"
Sometimes we don't know in advance which levels to use.
An adaptive method is needed here.
Decrease level (make task harder) whenever subject responds
correctly (say 2x in a row), and increase the level (make task easier)
when subject responds incorrectly.
threshold
stimulus level
"trial"
e.g. the sinusoid grating becomes visible (increasing)
or no longer is visible (when decreasing)
You may get different results going from high to low than low to high.
Take the average (of red levels). You could define the threshold by
the average of these settings.
Contrast detection thresholds
On each trial, test level is chosen in random order from a small set of
predetermined values (e.g. five test levels above). This way,
subjects cannot predict the level.
level
Often the method of adjustment is used beforehand to find a suitable
range of levels.
Threshold is obtained by fitting a curve and finding value e.g. 75%.
The image below illustrates the idea that contrast
detection depends on spatial frequency.
Is the sine grating vertical or
horizontal ?
trial
Threshold could be defined as the average of the last 2N "reversal"
levels.
In an experiment, we would measure a threshold
separately at each spatial frequency (as in two slides
ago).
The threshold depends on
the spatial frequency.
contrast
threshold
contrast
percent
correct
contrast
spatial frequency
spatial frequency
k
k (cycles per degree)
Contrast "sensitivity" is defined as :
What is the neural basis for the contrast sensitivity function ?
1
Contrast sensitivity depends on mean luminance I 0
.
Retinal ganglion cells are bandpass, and there is a limited
range of cell sizes (and hence bands).
threshold
peaks at 3-5 cycles per degree
DOG
cycles per
degree
rods only
spatial frequency
cones only
k
Contrast sensitivity depends on eccentricity.
For any spatial frequency k, contrast sensitivity
decreases as eccentricity increases.
Chromatic contrast sensitivity
Recall how an RGB image can be transformed into a luminance
(R+G+B), red-green (R-G), and yellow-blue (R+G-2B), i.e.
Chromatic contrast sensitivity:
Consider a sinusoid that has constant luminance and varies along
either the R + G - 2B or R - G axes.
R + G - 2B
R-G
R + G - 2B
What is the contrast sensitivity for each, as a function of spatial
frequency k ?
Chromatic contrast sensitivity (at constant luminance) is lowpass, not
bandpass.
Depth from binocular disparity
We cannot see a sinusoidal grating above ~5 cycles per degree of
visual angle, which is where peak sensitivity in luminance occurs.
test
reference
Disparity Sensitivity
spatial frequency of
depth (or disparity)
"Stereoacuity" thresholds for deciding
whether a test is in front of or behind a
reference are often quite low (e.g. < 1
arcmin).
60 arcmin = 1 degree
60 arcsec = 1 arcmin
The next few slides will look at the case of
depth perception along surfaces, rather
than for isolated points.
Disparity Contrast Sensitivity
Peak (lowest threshold) occurs at about 1/10 of the peak of contrast
sensitivity we saw earlier. Is this surprising?
This spatial frequency is very low (about 1 cycle per 60 deg).
For this spatial frequency (about 1 cycle per 5 deg), you can detect a
much smaller amplitude sinusoid.
You need a big amplitude to do the task.
Why ?
I have exagerrated the
amplitude. If I showed the
true amplitude, the curve would
look like a straight line.
Bradshaw and Rogers 1999
http://www.ncbi.nlm.nih.gov/pubmed/10664803
For this spatial frequency (about 5 cycles per deg), you need a larger
amplitude sinusoid again.
Disparity contrast sensitivity depends on eccentricity.
3600 arcsec = 1 deg
so 1000 arc = 1/3 deg
Note they don't measure beyond 20
degrees. (I'm not sure why.
Presumably we have some
disparity sensitivity in periphery,
although the trend in these curves
suggests it would be very poor.)
Next 3 lectures:
14.) noise (and how it affects thresholds for various tasks:
e.g. contrast, motion, 'slant from texture')
insert midterm 2 here (covers lectures 7-12 i.e. not today)
15.) probability (maximum likelihood methods
how to combine different depth cues? )
16.) Bayesian methods ( what priors assumptions do
vision systems make, and why ?)
Again I have exagerrated the
amplitude.
That is the end of vision lectures. A few days after that,
you
will need to tell me which paper you want for your Oral
Presentation.