Vision Science 748
Central Visual Mechanisms II
Norton’s Part: Measuring vision; intensity
discrimination; acuity; spatial vision; temporal
factors
Loop: Color; Suprathreshold
Liu: Binocular Vision; Depth Perception;
Binocular rivalry
Class (mostly) – Mon – Fri. 1:00 - 2:50
No class May 7 -11 (ARVO)
Exam #1 May 14 (Monday), 9:30 a.m.
Worrell Conference Room
Exam #1 (80 pts) on Norton’s material (quizzes
included in the 80 points total)
Exam #2 Fri. May 25th (80 pts)
Lab
May 4 1 – 3? Or 4? p.m.
You will measure your thresholds and
plot them
Three main purposes of this course:
1) Learn how visual function is measured (in single cells & whole
animals/humans)
2) Learn basic facts about visual function (what is normal?)
3) Relate what you have learned about the neural basis of visual
function to measures of vision (Why does the visual system
respond as it does?)
You’ve been learning neural function - YOU STILL ARE!!
What causes visual behavior? NEURONS!
Apply what you know about CNS function to what we study now.
The answers on exams often should include a description of what
neurons are doing to cause the visually-guided behavior!
The neurons in the visual pathway
respond to physical stimuli (light)
and produce visual function which
produces visually-guided behavior
Textbook: Norton’s part
The Psychophysical Measurement of Visual Function
Norton*, Corliss*, Bailey
Richmond Products, Inc. 2006
You have what is needed.
In Norton’s part:
Some or all of 5 Chapters + appendix
Ch 1. Principles of Psychophysical Measurement
Ch. 9, (5 pages)
Chapter 2 – absolute threshold of vision
Appendix – Measuring light
Ch 3. Intensity Discrimination
Ch 5. Spatial Acuity
Ch 6. Spatial Vision
Ch 7. Temporal Factors in Vision
Specific chapter assignments were given earlier
Overview
At the beginning of each chapter.
Contains a summary of the content of the chapter.
Declarative section headings
summarize the section they
precede
“In the Method of Constant Stimuli the examiner
randomly presents a set of stimuli with fixed,
predetermined values”
“Correct for guessing by incorporating catch trials”
Study Guide
Questions at the end of each chapter intended to help you
clarify your knowledge (not as useful as I had hoped)
Lecture overlaps with the book a lot (on purpose!)
That is why I would prefer to not lecture, but to
1) Answer your questions
2) Ask you questions if you don’t ask me
Both require that you read the material before class
Glossary – intended to help you know
what terms mean for exam
Definitions given in the text – it helps
to learn them verbatim
Equations – to be a complete answer,
must tell what the variables mean
Equations – must tell what the
variables mean
Y k F
a
where Y (psi) is the sensory
magnitude, k (kappa) is an arbitrary
constant determining the scale
unit, F (phi) is the stimulus
magnitude, and a (alpha) is an
exponent that is characteristic of
the stimulus used.
Graphs – The hardest part of this class
(because they tend to all look alike)
… but important because they show the
relationship between stimuli and
responses
Graphs – can be confusing
What is on the X-axis? (& approx. scale)
Usual arrangement:
Physical Stimulus on X-axis (Independent Variable)
Graphs – can be confusing
What is on the X-axis? (& approx. scale)
What is on the Y-axis? (& approx. scale)
Usual arrangement:
Response on Y-axis
(Dependent Variable)
Physical Stimulus on X-axis (Independent Variable)
Graphs – can be confusing
What is on the X-axis? (& approx. scale)
What is on the Y-axis? (& approx. scale)
How plot a data point?
Usual arrangement:
Response on Y-axis
(Dependent Variable)
Physical Stimulus on X-axis
(Independent Variable)
Graphs
What is different in each graph in a
“family” of curves?
Log Threshold
Luminance
(quanta/s/deg2)
Log Background Intensity
7.83
5.94
4.96
3.65
No Background
9
8
7
6
5
4
Stimulus area = 0.011 deg2
0.001
0.01
0.1
1
Flash Duration (s)
10
100
Chapter 1
Principles of Psychophysical
Measurement
Measuring visual function in humans
occurs in clinical settings & in
laboratory settings.
Measuring visual function in neurons
uses the same tools Applies to neurons
as well as whole creatures (animals;
humans)
The “Natural Science of the Soul”

Psychophysics (from the Greek psyche
[soul] and the Latin physica [natural
science]) has been developed as a way to
measure the internal sensory and perceptual
responses to external stimuli.
Definition:
Psychophysics is the study
of the relationship
between physical stimuli
and perceptual responses
We study here visual psychophysics, but
there also is auditory psychophysics,
somatosensory psychophysics, etc.
Two basic types
of psychophysical measures
1) Threshold measures (Do you see it”)
Determine the boundary between values that
are seen (above threshold) and values that
are too small to be seen (below threshold)
2) Sensory Magnitude measures
(“What does it look like”)
Relationship between a Stimulus and
a Response



The stimulus is always a physical entity that can
be measured directly with instruments.
The response can be the number of action
potentials produced per second by a neuron
(“firing rate”), or it can be a criterion behavior,
such as an animal pressing a lever. With humans,
it can be a verbal response (“I see it.”)
In all cases, the perception that occurs between the
stimulus and response is inferred.
– We are not interested in “perception” in this course but
in the relationship between the physical stimuli and the
response.
Threshold measure:
Psychophysics is the study of the relationship
between physical stimuli and perceptual responses
Example: Do you see the light?
Physical stimulus – light intensity
Perceptual response – Seeing the light
Neural Example – threshold for
detecting a flashed light.
0.0
0.5
1.0
1.5
Time (s)
2.0
Responses of a neuron in the lateral geniculate nucleus of
an anesthetized cat to three separate presentations of a
near-threshold visual stimulus. Each small vertical line
represents an action potential produced by the neuron.
Each row shows the responses of the neuron in a 3 s
period. From 0 until 2.5 s a background luminance was
present. The stimulus (a light) was turned on at 2.5 s and
turned off at 3.0 s, so the stimulus was on for only 0.5 s.
(Unpublished data from D. W. Godwin and T. T. Norton,.)
2.5
On
3.0
Off
Another Threshold measure:
Psychophysics is the study of the relationship
between physical stimuli and perceptual responses
Example #2: How far down an eye chart
can you read?
Physical stimulus – Letter size
Perceptual response – Identifying letters
How you measure vision changes
the results you get!! So, learn the
rules for measuring vision.







Which chart to use?
How many letters per line?
How far apart are the
letters and lines?
How much smaller are the
letters on the next line?
Which letters to use?
How far down the chart
must the patient try to
read?
How score the result?
Could also determine the threshold
concentration of an antibody
needed to produce a visible reaction
on tissue
A dose-response curve is a
threshold measurement
The LD50 is also a threshold
measurement
(the concentration of a drug needed
to kill half of a group of animals or
people)
Psychophysical measurements are
fundamental in many laboratory
settings
Need to know the scientific basis for
measuring vision
The results you get depend
on the way you measure
vision – a single neuron or
in a whole visual system
Visual thresholds are the most common
psychophysical measurement
Why are we interested in knowing
threshold? It gives useful information.
Does the threshold of neurons in V1 match the
threshold of the monkey or bird or person? Is
the neuronal threshold the reason for the
“owner’s” threshold?
In a patient with retinal degeneration, which
neurons are responsible for loss of vision?
Threshold - Definition
Threshold is defined as the minimum value of a
stimulus required to elicit a perceptual response or an
altered perceptual response.
Two types of threshold measurement:
absolute threshold (in vision) is the minimum value of
a stimulus required to detect the presence of light
under ideal conditions.
A difference (or increment) threshold is defined as
the minimum change in stimulus value that must be
added or subtracted to a stimulus to elicit an altered
perceptual response.
The task required of a patient or subject during threshold
measurements varies in complexity
detection task – (in vision) does the subject (or neuron) see
something?
discrimination task – (in vision) distinguishing between two
stimuli with regard to some stimulus characteristic when each
stimulus is visible by itself. (does a neuron respond more strongly
to stimulus 1 or stimulus 2?)
recognition task. – providing a name or category of a test object
that is visible (hard for a neuron to do, but a whole animal could
do a matching task to show recognition)
The distinctions among these various types of tasks are not sharp,
but are hierarchical.
Threshold Determination Methods
Method of Constant Stimuli
Method of Limits
-Staircase
-Tracking
Method of Adjustment
Important Stimulus Dimensions
intensity
wavelength
size
exposure duration
frequency
shape
relative locations of elements of the stimulus
cognitive meaning
In addition,(NOT stimulus Dimensions!)
location on the subject’s retina
light adaptation of the subject’s visual system
Key in measuring thresholds: Try to
keep all dimensions unchanged except
the one being measured
Stimulus configurations
(Oversimplified for illustration)
Spot on an adapting field (increment thresholds)
Bipartite field
Bipartite field with an adapting field
Spatially separated stimuli (difference thresholds)
(Also could use letters on a chart)
A
B
L
T
= L + L
LT
L
L
T
= L - L
LT
L T= L +  L
L u m in a n c e
+ L
L
- L
L T = L-  L
0
L
There are many possible values of ΔL,
But only 1 value (theoretically) for
threshold ΔL
Definition (again)
Threshold is defined as the minimum value of a
stimulus required to elicit a perceptual response or an
altered perceptual response.
Definition
Threshold is defined as the minimum value of a stimulus
required to elicit a perceptual response or an altered
perceptual response.
But threshold can vary over time (somewhat)
Psychophysically measured threshold values vary
because of
fluctuations in the stimulus
fluctuations in neural activity
fluctuations in alertness or attention
psychological bias
Action potentials recorded from a
single LGN neuron
0.0
0.5
1.0
1.5
Time (s)
2.0
Responses of a neuron in the lateral geniculate nucleus of
an anesthetized cat to three separate presentations of a
near-threshold visual stimulus. Each small vertical line
represents an action potential produced by the neuron.
Each row shows the responses of the neuron in a 3 s
period. From 0 until 2.5 s a background luminance was
present. The stimulus (a light) was turned on at 2.5 s and
turned off at 3.0 s, so the stimulus was on for only 0.5 s.
(Unpublished data from D. W. Godwin and T. T. Norton,.)
2.5
On
3.0
Off
Graded potentials
(in the retina,
before ganglion
cells)
Action potentials
(“spikes”) – from
ganglion cells and from
LGN and cortex (and
superior colliculus, etc.
Action potentials recorded from a
single LGN neuron
0.0
0.5
1.0
1.5
Time (s)
2.0
2.5
On
Responses of a neuron in the lateral geniculate nucleus of
an anesthetized cat to three separate presentations of a
near-threshold visual stimulus. Each small vertical line
represents an action potential produced by the neuron.
Each row shows the responses of the neuron in a 3 s
period. From 0 until 2.5 s a background luminance was
present. The stimulus (a light) was turned on at 2.5 s and
turned off at 3.0 s, so the stimulus was on for only 0.5 s.
(Unpublished data from D. W. Godwin and T. T. Norton,.)
Neural fluctuations: the neuron sometimes responds
more, sometimes less, to the same stimulus.
Also, the neuron has variable background
(“maintained”) activity that makes it hard for the neuron
to detect when the stimulus is present.
3.0
Off
Psychophysically measured threshold values vary
because of
fluctuations in the stimulus
fluctuations in neural activity
fluctuations in alertness or attention
psychological bias
Because of variability, threshold isn’t always easy to determine
Threshold Determination Methods
Method of Constant Stimuli
Method of Limits
-Staircase
-Tracking
Method of Adjustment
Assignment for Monday
In your own area of research, think of a threshold
measurement you have to make.
Write a brief description (1 or 2 paragraphs) of how
that threshold is measured and which of the three main
Threshold Determination Methods is used.
In the Method of Constant Stimuli the examiner
randomly presents a set of stimuli with fixed,
predetermined values
Percent "YES"
responses
100
75
50
25
Background Field Intensity
L = 0 units
0
0
1
2
3
4
5
6
7
8
9
10
Test Field Intensity, LT (arbitrary units)
Figure 1-4. Idealized psychometric function for a threshold detection task using
the Method of Constant Stimuli. The threshold stimulus value is obtained by
drawing a horizontal line from the 50% value on the response axis to the
psychometric function and then dropping a vertical line from the function to the
test field intensity axis.
In Class Demo
Rule: Plot straight lines
between data points
“Silliest Plotting Error”
Plot data points from left to right
“Silliest Plotting Error”
Plot data points from left to right
“Most Interesting Curves”
Percent "YES"
responses
100
75
50
25
Background Field Intensity
L = 0 units
0
0
1
2
3
4
5
6
7
8
9
10
Test Field Intensity, LT (arbitrary units)
Figure 1-4. Idealized psychometric function for a threshold detection task using
the Method of Constant Stimuli. The threshold stimulus value is obtained by
drawing a horizontal line from the 50% value on the response axis to the
psychometric function and then dropping a vertical line from the function to the
test field intensity axis.
Fraction of "Yes" Responses
Graduate Class, 2009
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
1
2
3
4
5
6
Stim ulus Value
7
8
9
10
Fraction of "Yes" Responses
Graduate Class, 2004
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
1
2
3
4
5
6
Stim ulus Value
7
8
9
10
Fraction of "Yes" Responses
Graduate Class, 2005
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
1
2
3
4
5
6
Stim ulus Value
7
8
9
10
Fraction of "Yes" Responses
Graduate Class, 2006
Note that the steeper the
slope of the psychometric
function, the more
accurately defined the
Note that the steeper the
threshold is (assuming
slope of the psychometric
the x-axis remains the
function, the more
same.)
accurately defined the
threshold is (assuming
the x-axis remains the
same.)
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
1
2
3
4
5
6
Stim ulus Value
7
8
9
10
The Method of Constant Stimuli is the most precise
method for determining threshold (the “Gold
Standard”).
But, this method is cumbersome and time-consuming
because there are many trials where the stimulus value
is not close to threshold.
Threshold Determination Methods
Method of Constant Stimuli
Method of Limits
-Staircase
-Tracking
Other newer ones, like “QUEST”
Method of Adjustment
In the Method of Limits the examiner sequentially
presents a set of stimuli with fixed values
Stimulus Value
1
2
3
4
5
6
7
8
9
10
Transition
1
(Ascending)
N
N
Y
N
N
Y
Y
5.5
Trial Number (Stimulus Presentation Direction)
2
3
4
(Descending)
(Ascending)
(Descending)
N
N
N
N
N
Y
Y
N
Y
Y
N
Y
Y
Y
N
Y
Y
Y
Y
3.5
3.5
5.5
Table 1- 1. Example of subject’s responses over five trials using the
method of limits.
5
(Ascending)
N
N
Y
Y
2.5
Average
4.1
In Class Demo
The Method of Limits is more efficient than the
Method of Constant Stimuli because fewer trials are
presented.
Two potential problems:
anticipation
perseveration
Staircase procedure.
Developed during WWII to test bomb detonators
Staircase procedure.
Trial Number
Stimulus
Value
1
1
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
16
17
N
N
N
N
Y
Y
N
N
Y
N
Y
Y
Y
Table 1- 2. Example of a subject’s responses over 17 trials
using the staircase variation on the Method of Limits.
N
N
Y
Y
Staircase procedure.
Staircase procedure.
Trial Number
Stimulus
Value
1
1
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
16
17
N
N
N
N
Y
Y
N
N
Y
N
Y
Y
Y
Table 1- 2. Example of a subject’s responses over 17 trials
using the staircase variation on the Method of Limits.
N
N
Y
Y
The number of reversals can be small, yet give a good estimate of
threshold if the step sizes are adjusted to an optimal size
error correct
error
correct
correct
correct
error
error
When you correctly identify the side the stimulus is on, the contrast
decreases. The first time you are incorrect is a “reversal”. The contrast
then is increased until you are “correct.” That is a second “reversal.”
Contrast then decreases until you are wrong again, the third reversal,
and then increases until you are correct again (4th reversal). Threshold
contrast is the average of the four reversal values.
Tracking procedure
High-contrast
Sample of grating
Contrast
See grating, pressing button
3
1
2
0
"Beep-Beep"
Time
"Beep-Beep"
"Beep"
5
6
4
Grating not visible, release button
7
8
Threshold Determination Methods
Method of Constant Stimuli
Method of Limits
-Staircase
-Tracking
Method of Adjustment
In the Method of Adjustment
the subject controls the stimulus values
A
B
L
T
= L + L
LT
L
L
T
= L - L
LT
L T= L +  L
L u m in a n c e
+ L
L
- L
L T = L-  L
0
L
Probabilitywith
of which LT is
Frequency
seeing
L
seen as equal
to L
T
as equal to L
-0.68 SD Mean +0.68 SD
-3
-2
LT<L
-1
0
1
Intensity Difference, LT-L (arbitrary units)
2
3
LT>L
The distribution of values of LT that a subject decides are equal to L
forms a normal distribution if enough trials are used. The mean of
the distribution will be very close to L. The threshold is taken as the
value of LT that, when added to or subtracted from L gives an LT
that is detectable on 50% of the trials. This occurs 0.68 standard
deviations above and below the mean.
The Method of Adjustment is most easily used when
the stimulus can be changed in a continuous manner,
rather than in steps.
Subjects generally enjoy the Method of Adjustment
because they actively participate.
Boredom and inattention are less of a problem with the
Method of Adjustment than with the other methods.
Potential problem with the Method of Adjustment
subjects may use the position of the dial as a cue to
where threshold "ought" to be.
This strategy can by foiled by using a dial that has no
numbers and has a variable amount of slip.
Controlling response bias and guessing
Correct for guessing by incorporating “catch” trials
Establish the guessing rate by forcing the subject to
make choices (“forced choice” technique)
What do you do if the psychometric function doesn’t drop down
to 0% “Yes” responses for low stimulus values?
Assume subject/patient has a bias to guess “Yes.”
Percent "YES"
Responses
100
Uncorrected for guessing
Corrected for Guessing
75
50
25
Background Field Intensity
L = 0 units
0
0
1
2
3
4
5
6
7
Test Field Intensity, LT (arbitrary units)
8
9
10
Correct for guessing by incorporating “catch” trials
where the stimulus is not presented at all. This gives the
guessing rate.
Correct for guessing by incorporating “catch” trials
Percent "YES"
Responses
100
Uncorrected for guessing
Corrected for Guessing
75
50
25
Background Field Intensity
L = 0 units
0
0
1
2
3
4
5
6
7
8
Test Field Intensity, LT (arbitrary units)
Frequency of seeing curves before (upper curve) and after (lower curve) correction for
guessing. Note that the amount of correction decreases as the stimulus value
increases.
9
10
The correction factor is:
True Percent of YES Responses 
Observed Fraction of YES Responses Guessing Rate
X 100
1  Guessing Rate
This equation corrects less at higher stimulus values
Stimulus value 0, 0% = (0.3 – 0.3)/0.7 *100
Stimulus value 4, 29% = (0.5 – 0.3)/0.7 *100
Stimulus value 10, 100% = (1.0 – 0.3)/0.7 *100
The way it is really done is to establish the
guessing rate by forcing the subject to make
choices
The Forced Choice technique
Most frequently used: “two-alternative-forced choice”
In Class Demo
For a two-alternative forced-choice procedure,
the correction factor is 0.5 (chance is 50:50):
True Percent of YES Responses 
Observed Fraction of YES Responses  0.5
X 100
1  0.5
Two-alternative Forced-choice in-class Demo
Grad class - 2005
100
Percent Correct Responses
90
80
70
60
50
Obtained percent correct
40
"True" percent correct
30
20
10
0
-10
1
2
3
-20
Stimulus
4
Threshold comes
out the same either
way & it is simpler to
use uncorrected with
75% as threshold
Two-alternative Forced-choice in-class Demo
Grad class - 2006
100
Percent Correct Responses
90
80
70
60
Obtained percent correct
50
"True" percent correct
40
30
20
10
0
1
2
3
Stimulus
4
Threshold comes
out the same either
way & it is simpler to
use uncorrected with
75% as threshold
Two-alternative Forced-choice in-class Demo
Grad class - 2008
Percent Correct Responses
100
90
80
70
60
Obtained percent correct
50
"True" percent correct
40
30
20
10
0
1
2
3
Stimulus
4
Two-alternative Forced-choice in-class Demo
Grad class - 2009
Percent Correct Responses
100
90
80
70
60
50
40
Obtained percent correct
"True" percent correct
30
20
10
0
-10
-20
1
2
3
4
5
4
3
2
Stimulus
Percent Correct Responses
Two-alternative Forced-choice in-class Demo
2009
Grad class - 2010
100
90
90
80
80
70
60
70
50
60
40
30
50
20
40
10
30
0
-10
20
-20
10
-30
-40
0
-50
-10
-60
-20
-70
Obtained percent correct
"True" percent correct
1
2
3
4
1
2
3
4
5
4
3
2
Stimulus
With TAFC, usually, don’t apply the correction; just
make threshold be at 75%, chance at 50%
Observer's
Percent
Correct
100
Kate at 12 weeks
Threshold
75
50
Chance
25
0
12.0
6.0
3.0
1.5
0.8
0.4
1.6
1.9
Stripe Width (cycles/deg)
0.4
0.7
1.0
1.3
LogMAR
Information from Chapter 9
Sometimes a new or modified method is
needed: the Forced-choice Preferential
Looking technique (Davida Teller)
For thousands of years, people thought infants couldn’t
see more than light and dark.
“just a bundle of organs and nerves during the first
month”
The “blooming, buzzing confusion of infancy”
In the 1960’s people began to realize infants could do
more than had been thought, like this newborn imitating
his father.
To learn what infants can see required devising
psychophysical techniques that would work with infants.
Two-alternative Forced-choice
Preferential Looking (FPL)
Children prefer to look at something, over
nothing (Fantz)
Stimuli of greater complexity are preferred over
very simple stimuli
In FPL the child is presented with two
stimuli. An observer watches the child and
must report which side the child looked
toward. (Davida Teller and students)
Two-alternative Forced-choice
Preferential Looking (FPL)
The observer must (is “forced” to) decide that
the child looked to one side or the other.
The observer’s judgment is recorded and the
observer is given feedback (“the side you
chose was/was not the side the stimulus was
presented on”).
When the observer is 100% correct, the child
must have looked at the stimulus 100% of the
time.
The Acuity Card Procedure
Forced-choice Preferential
Looking
Infant’s WILL look!
low frequency grating
observer’s view of infant
looking
What do YOU think?
Where is the stimulus?
Take a guess?
Can the infant see the stripes?
YES!
NO?
Advantages of Acuity Cards
simple apparatus
observer-infant
interaction
Two-alternative Forced-choice
Preferential Looking (FPL)
The observer must (is “forced” to) decide that
the child looked to one side or the other.
The observer’s judgment is recorded and the
observer is given feedback (the side you
chose was/was not the side the stimulus was
presented on).
When the observer is 100% correct, the child
must have looked at the stimulus 100% of the
time.
Two-alternative Forced-choice
Preferential Looking (FPL)
As the stimulus is changed so it is closer
to threshold, the child (and, therefore,
the observer) will make mistakes.
When the observer’s responses are 50%
correct, the child must not see the
stimulus well enough to look at it.
Creates a psychometric function with
threshold at 75% correct.
Observer's
Percent
Correct
100
Kate at 12 weeks
Threshold
75
50
Chance
25
0
12.0
6.0
3.0
1.5
0.8
0.4
1.6
1.9
Stripe Width (cycles/deg)
0.4
0.7
1.0
1.3
LogMAR
Fraction of "Yes" Responses
Graduate Class, 2008
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
1
2
3
4
5
6
Stim ulus Value
7
8
9
10
Two-alternative Forced-choice in-class Demo
Grad class - 2008
Percent Correct Responses
100
90
80
70
60
Obtained percent correct
50
"True" percent correct
40
30
20
10
0
1
2
3
Stimulus
4
New Topic
Detecting the response to a visual stimulus
against the “noise” of ongoing neural activity
Using Signal Detection Theory to Understand
Threshold Variability
Near threshold, there always is overlap between the
neural response when the stimulus is present
(“Signal”) and the neural response when the stimulus
is absent (“Noise”) so there is not one criterion one
can use to decide accurately whether a stimulus is
present. If the criterion fluctuates over time, the
measured threshold will change.
At threshold, neurons must “decide” whether a
stimulus is present against a background of
“noise”
0.0
0.5
1.0
1.5
Time (s)
2.0
Responses of a neuron in the lateral geniculate nucleus of an
anesthetized cat to three presentations of a near-threshold visual
stimulus. Each small vertical line represents an action potential
produced by the neuron. Each row shows the responses of the
neuron in a 3 s period. From 0 until 2.5 s a background luminance
was present. The stimulus (a light) was turned on at 2.5 s and turned
off at 3.0 s, so the stimulus was on for only 0.5 s. (Unpublished data
from D. W. Godwin and T. T. Norton,.)
2.5
On
3.0
Off
0.0
0.5
Number
50 msec noise “bin”
1.0 of APs during1.5
2.0
Time
(s)
0 occurs 1 time
1 occurs 0 time
Responses of a neuron in 2the
lateral
geniculate nucleus of an
occurs
1 times
anesthetized cat to three presentations of a near-threshold visual
3 occurs 0 times
stimulus. Each small vertical line represents an action potential
This is forproduced
3 rows.
Now 4 occurs
times the responses of the
by the neuron. Each
row0 shows
1 time
in a 3 s period.
until 2.5
s a background luminance
expand toneuron
30 rows
(30 From50occurs
was present. The stimulus (a light)
was0 times
turned on at 2.5 s and turned
6 occurs
stimulus and
noise
off at 3.0 s, so the stimulus was
on for0 only
7 occurs
times0.5 s. (Unpublished data
pairings) from D. W. Godwin and T. T. Norton,.)
8 occurs 0 times
9 occurs 0 times
Average, 2.33 spikes per bin
50 spikes/s means 2.5 spikes/50 msec, average over 30 rows
(30 stimulus and noise pairings); 200 on the y-axis means 10/50
msec
Number of APs during
50 msec signal “bin”
2.5
On
0 occurs 0 3.0
times
1 occurs 0 Off
times
2 occurs 0 times
3 occurs 0 times
4 occurs 0 times
5 occurs 1 time
6 occurs 0 times
7 occurs 0 times
8 occurs 2 times
9 occurs 0 times
Average, 7
spikes per bin
This is for 30 presentation of stimulus and noise
Frequency of
Occurence
7
Mean of Noise
A
6
5
Maintained Discharge (Noise)
Distribution
4
3
2
1
0
Overlap: Possible
Confusion
Mean of Noise + Signal
7
B
6
5
Maintained Discharge (Noise) +
Response to Flash (Signal)
Distribution
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of Action Potentials in 50 msec Period
13
14
15
There is no single “optimal” criterion number of action
potentials that the nervous system should use to
decide whether to respond as though a stimulus was
present, or to respond as though a stimulus was not
present.
One can try various criteria –
Changing the criterion (the threshold
one adopts) affects the pattern of hits,
misses, false alarms and correct
rejections
“The saga of the snake in the grass”
Decide that 6 or more action potentials means “snake”
Frequency of
Occurence
7
Mean of Noise
A
6
5
Maintained Discharge (Noise)
Distribution
4
3
2
1
0
Overlap: Possible
Confusion
Mean of Noise + Signal
7
B
6
5
Maintained Discharge (Noise) +
Response to Flash (Signal)
Distribution
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of Action Potentials in 50 msec Period
13
14
15
Out of the four possible outcomes there are two ways
to be correct:
by deciding the stimulus is there when it is present (a
Hit)
and by deciding that it is not there when it is absent (a
Correct Rejection).
There are also two ways to be wrong:
by deciding the stimulus is present when it is absent (a
False Alarm)
and by deciding it is not present when it is (a Miss).
A. Criterion for “seeing” = 6 action potentials
Response
“I see it”
“I don’t see it.”
Stimulus Present
Stimulus Absent
Hits (H)
n = 30
False Alarms (FA)
n = 11
Misses (M)
n=0
Correct Rejections (CR)
n = 19
Hit Rate = H/(H+M)
= 30/(30+0) = 1.00
False Alarm Rate = FA/(FA+CR)
= 11/(11+19) = 0.37
Miss Rate = M/(H+M)
= 0/(30+0) = 0
Correct Rejection Rate = CR/(FA+CR)
= 19/(11+19) = 0.63
B. Criterion for “seeing” =10
9 action potentials
Response
“I see it”
“I don’t see it.”
Low threshold: No misses; will
Stimulus Present
Stimulus
Absentfalse
always
avoid snake,
but
Hits (H) will restrictFalse
Alarms (FA)
alarms
food
access
n = 19
n=0
Misses (M)
n = 11
Correct Rejections (CR)
n = 30
Hit Rate = H/(H+M)
= 19/(19+11) = 0.63
False Alarm Rate = FA/(FA+CR)
= 0/(0+30) = 0.00
Miss Rate = M/(H+M)
= 11/(19+11) = 0.37
Correct Rejection Rate = CR/(FA+CR)
= 30/(0+30) = 1.00
Frequency of
Occurence
7
Mean of Noise
A
6
5
Maintained Discharge (Noise)
Distribution
4
3
2
1
0
Overlap: Possible
Confusion
Mean of Noise + Signal
7
B
6
5
Maintained Discharge (Noise) +
Response to Flash (Signal)
Distribution
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of Action Potentials in 50 msec Period
13
14
15
Decide that 10 or more action potentials means “snake”
Frequency of
Occurence
7
Mean of Noise
A
6
5
Maintained Discharge (Noise)
Distribution
4
3
2
1
0
Overlap: Possible
Confusion
Mean of Noise + Signal
7
B
6
5
Maintained Discharge (Noise) +
Response to Flash (Signal)
Distribution
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of Action Potentials in 50 msec Period
13
14
15
A. Criterion for “seeing” = 6 action potentials
Response
Stimulus Present
Stimulus Absent
Hit Rate = H/(H+M)
= 30/(30+0) = 1.00
False Alarm Rate = FA/(FA+CR)
= 11/(11+19) = 0.37
Miss Rate = M/(H+M)
= 0/(30+0) = 0
Correct Rejection Rate = CR/(FA+CR)
= 19/(11+19) = 0.63
High threshold:
No false
alarms,
Hits (H)
False Alarms (FA)
= 30
n = 11
so foodn access
is high, but
“I don’t see it.”misses
Misses
(M)
Rejections (CR)
mean
that theCorrect
mouse
n=0
n = 19
may be eaten
“I see it”
B. Criterion for “seeing” =10
9 action potentials
Response
“I see it”
“I don’t see it.”
Stimulus Present
Stimulus Absent
Hits (H)
n = 19
False Alarms (FA)
n=0
Misses (M)
n = 11
Correct Rejections (CR)
n = 30
Hit Rate = H/(H+M)
= 19/(19+11) = 0.63
False Alarm Rate = FA/(FA+CR)
= 0/(0+30) = 0.00
Miss Rate = M/(H+M)
= 11/(19+11) = 0.37
Correct Rejection Rate = CR/(FA+CR)
= 30/(0+30) = 1.00
Can calculate hit rate and false alarm rate for ANY criterion
Frequency of
Occurence
7
Mean of Noise
A
6
5
Maintained Discharge (Noise)
Distribution
4
3
2
1
0
Overlap: Possible
Confusion
Mean of Noise + Signal
7
B
6
5
Maintained Discharge (Noise) +
Response to Flash (Signal)
Distribution
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of Action Potentials in 50 msec Period
13
14
15
An ROC curve summarizes the Hits and False Alarms
for all possible thresholds
Hit Rate
1.0
6
7
0.9
5
4
321
8
9
0.8
0.7
10
0.6
0.5
11
0.4
0.3
12
0.2
13
0.1
14
15
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
False Alarm Rate
Receiver Operating Characteristic (ROC) curve for the responses shown in the previous figure. If the threshold is
set at 15 action potentials, there are 0 Hits and 0 False Alarms. If it is set at 14, there will be a few Hits, but 0 False
Alarms. As the threshold is decreased further, the P(Hit) increases but the P(False Alarm) remains at 0 until the
threshold reaches 9, at which point False Alarms begin to increase. As the threshold is further lowered, through
the overlap region in the previous figure, the probability of both Hits and False Alarms increase. For thresholds
below 6, there is no further increase in hit rate, but the false alarm rate climbs toward 1.0.
Frequency of
Occurence
7
Mean of Noise
A
6
5
Maintained Discharge (Noise)
Distribution
4
3
2
1
0
Overlap: Possible
Confusion
Mean of Noise + Signal
7
B
6
5
Maintained Discharge (Noise) +
Response to Flash (Signal)
Distribution
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of Action Potentials in 50 msec Period
13
14
15
Signal Detection Theory also applies to human
perceptual responses
Criterion Value
Frequency
Stimulus Absent
Correct Rejections
False Alarms
0.0
d'
Stimulus Present
Misses
Hits
0.0
-3
-2
-1
0
1
2
3
Magnitude of Sensation (arbitrary units)
Distribution of hypothetical “perceptual response” in a human subject over many trials
when the stimulus was absent (top) and when the stimulus was present (bottom). The
criterion value (vertical line) indicates the criterion a subject would adopt if Hits, Misses,
False Alarms and Correct Rejections had the rewards and costs listed in another figure.
Hit Rate
ROC Curve
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
False Alarm Rate
0.8
1.0
d’ (“d prime”) is a measure of the separation of two normal
distributions.
d’ = the difference between the means of the “noise” and
“signal plus noise” distributions divided by the common
standard deviation of the two distributions.
d’ quantifies the detectability of the signal (small d’ =
signal is hard to detect)
d'=1.5
A
d'=1.0
B
d'=0.5
C
Srimulus Absent
Stimulus Present
ROC Curve
In the LGN, changed
the detectability of a
stimulus by
increasing the
transfer ratio using
bicuculline to block
GABAa inhibition
Using Signal Detection Theory to Understand
Threshold Variability
Near threshold, there always is overlap between the
neural response when the stimulus is present
(“Signal”) and the neural response when the stimulus
is absent (“Noise”) so there is not one criterion one
can use to decide accurately whether a stimulus is
present. If the criterion fluctuates over time, the
measured threshold will change.
You will hear clinicians talk about the
“sensitivity” and “specificity” of diagnostic
techniques.
Sensitivity is the hit rate
Specificity is the absence of false alarms
So plot (1 – specificity) on an ROC curve
Want a diagnostic tool that has high
sensitivity and high specificity
Visual thresholds are the most common
psychophysical measurement
“Do you see it?”