vision science 748 central visual mechanisms ii

Vision Science 748Central 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)

LabMay 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 partThe 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 + appendixCh 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 meBoth 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

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.

Y Fk a

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 confusingWhat is on the X-axis? (& approx. scale)

Physical Stimulus on X-axis (Independent Variable)

Usual arrangement:

Graphs – can be confusingWhat is on the X-axis? (& approx. scale)What is on the Y-axis? (& approx. scale)

Response on Y-axis(Dependent Variable)

Usual arrangement:

Physical Stimulus on X-axis (Independent Variable)

Graphs – can be confusingWhat is on the X-axis? (& approx. scale)What is on the Y-axis? (& approx. scale)How plot a data point?

Physical Stimulus on X-axis(Independent Variable)

Response on Y-axis(Dependent Variable)

Usual arrangement:

GraphsWhat is different in each graph in a

“family” of curves?

Flash Duration (s)

0.001 0.01 0.1 1 10 100

4

5

6

7

8

9

Log Threshold Luminance(quanta/s/deg2)

Stimulus area = 0.011 deg2

Log Background Intensity7.83 5.94 4.96 3.65 No Background

Chapter 1Principles 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 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )

R e s p o n s e s o f a n e u r o n i n t h e l a t e r a l g e n i c u l a t e n u c l e u s o f a n a n e s t h e t i z e d c a t t o t h r e e s e p a r a t e p r e s e n t a t i o n s o f a n e a r - t h r e s h o l d v i s u a l s t i m u l u s . E a c h s m a l l v e r t i c a l l i n e r e p r e s e n t s a n a c t i o n p o t e n t i a l p r o d u c e d b y t h e n e u r o n . E a c h r o w s h o w s t h e r e s p o n s e s o f t h e n e u r o n i n a 3 s p e r i o d . F r o m 0 u n t i l 2 . 5 s a b a c k g r o u n d l u m i n a n c e w a s p r e s e n t . T h e s t i m u l u s ( a l i g h t ) w a s t u r n e d o n a t 2 . 5 s a n d t u r n e d o f f a t 3 . 0 s , s o t h e s t i m u l u s w a s o n f o r o n l y 0 . 5 s . ( U n p u b l i s h e d d a t a f r o m D . W . G o d w i n a n d T . T . N o r t o n , . )

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

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?

How you measure vision changes the results you get!! So, learn the rules for measuring vision.

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)

LLTLLT

L T = L + L L T = L - L

L

LT=L+L

LT=L-L

+L

-L

0

A B

Luminance

There are many possible values of ΔL,

But only 1 value (theoretically) for

threshold ΔL

Definition

Threshold is defined as the minimum value of a

stimulus required to elicit a perceptual response or an

altered perceptual response.

(again)

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

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )


Action potentials recorded from a single LGN neuron

Graded potentials (in the retina, before ganglion cells)

Action potentials

(“spikes”) – from ganglion cells and from LGN and cortex (and superior colliculus, etc.

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )


Action potentials recorded from a single LGN neuron

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.

Psychophysically measured threshold values vary

because of

fluctuations in the stimulus

fluctuations in neural activity

fluctuations in alertness or attention

psychological bias



Method of Limits

-Staircase

-Tracking


Because of variability, threshold isn’t always easy to determine

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

Test Field Intensity, LT (arbitrary units)

0 1 2 3 4 5 6 7 8 9 10

Percent "YES" responses

0

25

50

75

100

Background Field IntensityL = 0 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

“Most Interesting Curves”


0 1 2 3 4 5 6 7 8 9 10

Percent "YES" responses

0

25

50

75

100


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.

Graduate Class, 2009

0.000.100.200.300.400.500.600.700.800.901.00

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Frac

tion

of "

Yes"

Res

pons

es


0.000.100.200.300.400.500.600.700.800.901.00

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Frac

tion

of "

Yes"

Res

pons

es

Note that the steeper the slope of the psychometric function, the more accurately defined the threshold is (assuming the x-axis remains the same.)


0.000.100.200.300.400.500.600.700.800.901.00

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Frac

tion

of "

Yes"

Res

pons

es

Note that the steeper the slope of the psychometric function, the more accurately defined the threshold is (assuming the x-axis remains the same.)

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.



Method of Limits

-Staircase

-Tracking


Other newer ones, like “QUEST”

In the Method of Limits the examiner sequentially

presents a set of stimuli with fixed valuesTrial Number (Stimulus Presentation Direction)

Stimulus Value 1(Ascending)

2(Descending)

3(Ascending)

4(Descending)

5(Ascending)

1 N N N2 N N N N3 Y N N Y4 N Y Y N Y5 N Y Y N6 Y Y Y7 Y Y N8 Y Y9 Y10 Y Average

Transition 5.5 3.5 3.5 5.5 2.5 4.1

Table 1- 1. Example of subject’s responses over five trials using themethod of limits.

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


Stimulus Value

Trial Number

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16 17

1 2 N 3 N N N 4 N Y N N 5 Y Y N Y 6 N Y 7 Y 8 Y 9 Y

Table 1- 2. Example of a subject’s responses over 17 trials using the staircase variation on the Method of Limits.

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.

error error

correct correcterror

errorcorrect

correct

The number of reversals can be small, yet give a good estimate of threshold if the step sizes are adjusted to an optimal size

T r a c k i n g p r o c e d u r e

"Beep-Beep"

"Beep-Beep""Beep"

1

2

3

4

5

6

7

8

Con

tras

t

0

See grating, pressing button

Grating not visible, release button

High-contrast Sample of grating

Time



Method of Limits

-Staircase

-Tracking


In the Method of Adjustment

the subject controls the stimulus values

LLTLLT

L T = L + L L T = L - L

L

LT=L+L

LT=L-L

+L

-L

0

A B

Luminance

LT<L Intensity Difference, LT-L (arbitrary units) LT>L

-3 -2 -1 0 1 2 3

Probability of seeing LT

as equal to L +0.68 SDMean-0.68 SD

The distribution of values of LT that a subject decides are equal to Lforms a normal distribution if enough trials are used. The mean ofthe distribution will be very close to L. The threshold is taken as thevalue of LT that, when added to or subtracted from L gives an LTthat is detectable on 50% of the trials. This occurs 0.68 standarddeviations above and below the mean.

Frequency with which LT is seen as equal to L

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)


0 1 2 3 4 5 6 7 8 9 10

Percent "YES"Responses

0

25

50

75

100Uncorrected for guessingCorrected for Guessing


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.”

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.

Correct for guessing by incorporating “catch” trials where the stimulus is not presented at all. This gives the

guessing rate.


0 1 2 3 4 5 6 7 8 9 10

Percent "YES"Responses

0

25

50

75

100Uncorrected for guessingCorrected for Guessing


Correct for guessing by incorporating “catch” trials

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.

T h e c o r r e c t i o n f a c t o r i s :

100Rate Guessing1

Rate GuessingResponses YES ofFraction ObservedResponses YES ofPercent True X

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

This equation corrects less at higher stimulus values

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):

1000.51

0.5Responses YES ofFraction ObservedResponses YES ofPercent True X

Two-alternative Forced-choice in-class Demo Grad class - 2005

-20

-10

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4

Stimulus

Perc

ent C

orre

ct R

espo

nses

Obtained percent correct

"True" percent correct

Threshold comes out the same either way & it is simpler to use uncorrected with 75% as threshold


0

10

20

30

40

50

60

70

80

90

100

1 2 3 4

Stimulus

Perc

ent C

orre

ct R

espo

nses



Threshold comes out the same either way & it is simpler to use uncorrected with 75% as threshold


0

10

20

30

40

50

60

70

80

90

100

1 2 3 4

Stimulus

Perc

ent C

orre

ct R

espo

nses




-20-10

0102030405060708090

100

1 2 3 4

Stimulus

Perc

ent C

orre

ct R

espo

nses



5 4 3 2


-20-10

0102030405060708090

100

1 2 3 4

Stimulus

Perc

ent C

orre

ct R

espo

nses



5 4 3 2


-70-60-50-40-30-20-10

0102030405060708090

100

1 2 3 4

Stimulus

Perc

ent C

orre

ct R

espo

nses



With TAFC, usually, don’t apply the correction; just make threshold be at 75%, chance at 50%

Stripe Width (cycles/deg)

12.0 6.0 3.0 1.5 0.8 0.4

Observer'sPercentCorrect

0

25

50

75

100

Chance

LogMAR

0.4 0.7 1.0 1.3 1.6 1.9

Threshold

Kate at 12 weeks

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”

Information from Chapter 9Sometimes a new or modified method is

needed: the Forced-choice Preferential Looking technique (Davida Teller)

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 stimuliIn 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)


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


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.


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.

Stripe Width (cycles/deg)

12.0 6.0 3.0 1.5 0.8 0.4

Observer'sPercentCorrect

0

25

50

75

100

Chance

LogMAR

0.4 0.7 1.0 1.3 1.6 1.9

Threshold

Kate at 12 weeks


0.000.100.200.300.400.500.600.700.800.901.00

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Frac

tion

of "

Yes"

Res

pons

es


0

10

20

30

40

50

60

70

80

90

100

1 2 3 4

Stimulus

Perc

ent C

orre

ct R

espo

nses



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 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )

R e s p o n s e s o f a n e u r o n i n t h e l a t e r a l g e n i c u l a t e n u c l e u s o f a na n e s t h e t i z e d c a t t o t h r e e p r e s e n t a t i o n s o f a n e a r - t h r e s h o l d v i s u a ls t i m u l u s . E a c h s m a l l v e r t i c a l l i n e r e p r e s e n t s a n a c t i o n p o t e n t i a lp r o d u c e d b y t h e n e u r o n . E a c h r o w s h o w s t h e r e s p o n s e s o f t h en e u r o n i n a 3 s p e r i o d . F r o m 0 u n t i l 2 . 5 s a b a c k g r o u n d l u m i n a n c ew a s p r e s e n t . T h e s t i m u l u s ( a l i g h t ) w a s t u r n e d o n a t 2 . 5 s a n d t u r n e do ff a t 3 . 0 s , s o t h e s t i m u l u s w a s o n f o r o n l y 0 . 5 s . ( U n p u b l i s h e d d a t af r o m D . W . G o d w i n a n d T . T . N o r t o n , . )

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )

R e s p o n s e s o f a n e u r o n i n t h e l a t e r a l g e n i c u l a t e n u c l e u s o f a na n e s t h e t i z e d c a t t o t h r e e p r e s e n t a t i o n s o f a n e a r - t h r e s h o l d v i s u a ls t i m u l u s . E a c h s m a l l v e r t i c a l l i n e r e p r e s e n t s a n a c t i o n p o t e n t i a lp r o d u c e d b y t h e n e u r o n . E a c h r o w s h o w s t h e r e s p o n s e s o f t h en e u r o n i n a 3 s p e r i o d . F r o m 0 u n t i l 2 . 5 s a b a c k g r o u n d l u m i n a n c ew a s p r e s e n t . T h e s t i m u l u s ( a l i g h t ) w a s t u r n e d o n a t 2 . 5 s a n d t u r n e do ff a t 3 . 0 s , s o t h e s t i m u l u s w a s o n f o r o n l y 0 . 5 s . ( U n p u b l i s h e d d a t af r o m D . W . G o d w i n a n d T . T . N o r t o n , . )

0 occurs 1 time1 occurs 0 time

2 occurs 1 times3 occurs 0 times

4 occurs 0 times

5 occurs 1 time6 occurs 0 times

7 occurs 0 times

8 occurs 0 times

9 occurs 0 times

0 occurs 0 times

1 occurs 0 times

2 occurs 0 times

3 occurs 0 times

4 occurs 0 times

5 occurs 1 time6 occurs 0 times

7 occurs 0 times

8 occurs 2 times9 occurs 0 times

Number of APs during 50 msec noise “bin”

Number of APs during 50 msec signal “bin”

This is for 3 rows. Now expand to 30 rows (30 stimulus and noise pairings)

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

Average, 2.33 spikes per bin Average, 7 spikes per bin

Frequency ofOccurence

0

1

2

3

4

5

6

7

Mean of Noise

Number of Action Potentials in 50 msec Period

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7

Mean of Noise + Signal

Overlap: PossibleConfusion

Maintained Discharge (Noise)Distribution

Maintained Discharge (Noise) +Response to Flash (Signal)

Distribution

A

B

This is for 30 presentation of stimulus and noise

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”


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B

Decide that 6 or more action potentials means “snake”

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 Stimulus Present Stimulus Absent

“I see it” Hits (H) n = 30

False Alarms (FA) n = 11

“I don’t see it.” 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” = 9 action potentials






Hit Rate = H/(H+M) = 19/(19+11) = 0.63


Miss Rate = M/(H+M) = 11/(19+11) = 0.37


10Low threshold: No misses; will always avoid snake, but false alarms will restrict food access


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B

Decide that 10 or more action potentials means “snake”

A. Criterion for “seeing” = 6 action potentials






Hit Rate = H/(H+M) = 30/(30+0) = 1.00


Miss Rate = M/(H+M) = 0/(30+0) = 0


B. Criterion for “seeing” = 9 action potentials






Hit Rate = H/(H+M) = 19/(19+11) = 0.63


Miss Rate = M/(H+M) = 11/(19+11) = 0.37


10

High threshold: No false alarms, so food access is high, but misses mean that the mouse may be eaten


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B

Can calculate hit rate and false alarm rate for ANY criterion

Receiver Operating Characteristic (ROC) curve for the responses shown in the previous figure. If the threshold isset 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 FalseAlarms. As the threshold is decreased further, the P(Hit) increases but the P(False Alarm) remains at 0 until thethreshold reaches 9, at which point False Alarms begin to increase. As the threshold is further lowered, throughthe overlap region in the previous figure, the probability of both Hits and False Alarms increase. For thresholdsbelow 6, there is no further increase in hit rate, but the false alarm rate climbs toward 1.0.

False Alarm Rate

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Hit Rate

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

14

13

12

11

10

9

87 6 5 4 321

15

An ROC curve summarizes the Hits and False Alarms for all possible thresholds


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B

Signal Detection Theory also applies to human

perceptual responses

Distribution of hypothetical “perceptual response” in a human subject over many trialswhen the stimulus was absent (top) and when the stimulus was present (bottom). Thecriterion 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.

Magnitude of Sensation (arbitrary units)

-3 -2 -1 0 1 2 3

Frequency

0.0

0.0

Criterion Value

d'

False Alarms

Hits

Correct Rejections

Misses

Stimulus Absent

Stimulus Present

False Alarm Rate

0.0 0.2 0.4 0.6 0.8 1.0

Hit Rate

0.0

0.2

0.4

0.6

0.8

1.0 ROC Curve

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)

Srimulus AbsentStimulus Present

d'=1.5d'=1.0d'=0.5

A

B

C

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 rateSpecificity is the absence of false alarmsSo plot (1 – specificity) on an ROC curve

Want a diagnostic tool that has high sensitivity and high specificity

“Do you see it?”

Visual thresholds are the most common psychophysical measurement

vision science 748 central visual mechanisms ii

Documents