Visual perception [1 ed.] 0121897508

Table of contents :
I. Introduction
II. The experiment of Hecht, Schlaer, and Pirenne
III. The physics of light
IV. Quantal fluctuations
V. The action of light on rod pigments
VI. The excitation of rods
VII. Cones and cone pigment
VIII. Color vision I - discriminations among wavelength mixtures
IX. Color vision II - retinal color systems
X. Color vision III - the perception of color
XI. The psychophysiology of brightness - I spatial interaction in the visual system
XII. The psychophysiology of brightness - II modulation transfer functions
XIII. Brightness and color constancy
XIV. Temporal properties of the visual system
XV. Stimulus Generalization
XVI. Speculations on "higher processes"

Citation preview

'

PERCEPTiON

VISUAL

N.

TOM S[anlord

Research

(4

CORNSWEET Institute

PRESS

ACADEMIC New

San Francisco

York

A Subsidiary of

Harcourt

rl-1141)t.(,r>(,1: I

"

'--

Brace

London Jovanovich, Publishers

Contents

Preface

I.

INTRODUCTION Information

II.

THE

EXPERIMENT

OF

SCHLAER,

HECHT,

PIRENNE

The General

Design

of the Experiment

The State of the Subject-Dark Location

Adaptation Field

of the Test Flash in the Visual Summation

Size of the Test Flash - Spatial of the Test Flash -Temporal Duration Color

of the Test Flash -The

The Experiment

Itself

Spectral

Summation Sensitivity

Curve

AND

vi

Contents

The Interptetation

of Results

Problems

Ill.

THE

PHYSICS

A Definition Light

OF

LIGHT

of "Seeing"

27

Sources

29

Lenses and Refraction The Intensity Depth

31

of an Image

42

of Focus

The Stimulus

in the Hecht

Collimated Sources

45 Experiment

46

Light

53

of Imperfection

Measurements

of the Retinal

of the Real Retinal

Image

56

Image

60

Problems

IV.

67

QUANTAL

FLUCTUATIONS

Quantal

Fluctuations

The Relationship Subject's

in the Stimulus

between

68

Quantal

Fluctuation

and the

Variability

Sources

of Subject

Quantal

Fluctuations

72

Variability

78

at Suprathreshold

Light

Levels

81

Problems

V.

THE

88

ACTION

Changes

OF

LIGHT

in Rhodopsin

ON

Molecules

ROD

in the Light

PIGMENTS

and in Darkness

The Characteristics

and Perceptual

Correlates

of State a

The Characteristics

and Perceptual

Correlates

of States

b, c, and d Problem

Vl.

THE

EXCITATION

The Fundamentals The Excitation Adaptation

CONES Histological Individual The Nature The Kinetics Problem

118 as a Consequence

of Quanta

AND

124

PIGMENT

between

Differences of Cone of Cone

131

of Rods and Cones

Distinctions

of

127

Adaptation

CONE

Properties

Psychophysical

Activity

Structures

and Rod Excitation

The Early Stage of Dark

Vll.

RODS

of Neural

of Retinal

the Absorption Dark

OF

Rods and Cones

135 139 149

Pigments Pigments

149 150 154

vii

Contents

AMONG

I-DISCRIMINATIONS

VISION

COLOR

Vlll.

MIXTURES

WAVELENGTH

55

Names

Color

56

Mon .'@)

40

'fflal

y

3

30

& e

20 Fig

TO

3 I

Spectral

sten at 2750oK,

o

temperature

200

400

600

800

1000 1200 1400 1600 1800 2000

Wavelength

(nm)

of a very

emission a typical

and 3500"K, bright

photoflood

curves

for tung-

household

lamp

the temperature lamp.

Refraction

and

Lenses

31

3.2

hg

'l 00

Emissionspectrumofatypical

represent

The spikes

atmosphere.

atoms.

gaps in mercury

energy

of one

at a pressure

arc lamp

mercury

60 40

jl

20

o

.1 200

Wavelength

li

i

i

400

8CO

600 (nm)

arc

lamp

around

the

mercury orbits

ferent

because

kinds

of atoms

of light

kind

is

be

diftwo

the

for

are different.

called

band

narrow

a relatively

within

quanta

emitting

of the diode,

crystal

the

within

levels

energy

among

jump

charges

this

through

is passed

current

an electric

When

diode.

or

source,

electroluminescent

state,

a solid

new

of a relatively

spectrum

emission

is the

source

electric

structure

mercury will

orbits

electron

the

of

levels

energy

the

the

When

wavelengths

emitted

the

gas,

primarily jump between and these orbits exist at

levels.

energy

of discrete

3.3a

light-emitting unit,

of mercury,

in Fig.

curve

The

nuclei

atomic

a different

with

replaced

the electrons

number

a small

only

(see Fig. 3.2),

of wavelengths.

the

AND

REFRACTION

All

travel

lengths, per

second) when

duced

quanta. uum

that

The

However,

a line

through

the

lines

velocity

the effect

by one third

any

of light of air on

in air light

of a quantum or more.

velocity their

and

is so close may

their

wave-

(186,000

miles

of

are

velocities

of the

the wavelengths

in a vac-

to its velocity

be ignored

for the

re-

in velocity

the reduction

medium,

of the medium

to print.

regardless

However,

on

laser

representing

narrow

be too

line

the

because

correctly

and at the same space.

empty

nature

laser

radiation,

pass through

they

poses. The velocity reduced

would

scale

in straight

upon

depending

wide.

electromagnetic

of

quanta

adjusted

horizontal

on this

light

LENSES

is too

graph

a properly

represen-

is not a good

in Fig. 3.3b

spectrum

band

wavelength

narrow

most

from

light

of the

tation

emission

The

laser.

is the

of the

light

provides

that

source

The

present

in water or glass, howeve5

pur-

may be

32

The Physics

of Light

TOO

Fig. 3.3

Emission spectra of relatively

sources.

(a) The spectrum

phosphide

electroluminescent

Note that the horizontal (,))

compared

ah

figures.

new

of a gallium crystal.

scale is expanded

with those in the preceding

(b) The spectrum

of a heliurn-

neon laser.

500

520

540

560

580

Wavelength

600

620

640

(nm)

TOO

8 80 #.

i

(b)

r:io

20

n 500

111111

520

I

540

560

580

Wavelength

600

620

640

(nm)

Consider

a single

As the quantum

quantum

enters

reduced

velocity.

tum will

be reflected

ing path. flected

the glass,

(There from

by the path

labeled

the surface

than

2, its direction

velocity angle

of incidence as it enters

of refraction,

of the quantum has an angle

and the process

is called

understanding

of visual

CBN

by which (Note

of zero,

and it will

the laws of refraction

on

be changed

it

when

depends

upon

and its change

in Fig. 3.4 is called the glass bends

in

the

the path in path

then necessarily

The theoretical

the

as indicated

that the quantum

may be deduced

processes,

is incident

in direction

of the quantum

refraction.

of zero as well.)

will

its incom-

that are not re-

to the surface,

of this change ABN)

back along

those quanta

of motion

path at a

O.04 that the quan-

if a quantum

the glass. The angle

of incidence

angle of refraction which

(angle

and travel

perpendicular

1 in Fig. 3.4.

in its original

of about

only

However,

enters the glass. The amount the angle

it continues

discussion,

be considered.)

glass at an angle other

the path labeled

is a probability

For the present

will

following

considerations

are not necessary

1

have an

from for the

at least at the level of this book.

It is

33

Lenses and Refraction

to understand

sufficient

both

depends

(which

locity

in turn depends

bility."

upon

and upon

the kind

of a quantum

its change

of refracting

systems,

in general,

In the present

obey

example,

what

is called

means

this

that,

in ve-

material

of the quantum).

the wavelength Optical

of incidence

its angle

upon

of the path

that the refraction

the "law

and

of reversi-

if a quantum

origi-

the surface along, say, path the glass and traveled toward be BA. In that infrom the glass would CB, its path upon emerging the lain the diagram would be that stance, the only change required that was be reversed. That is, the angle bels for the two angles should would now be called the angle called the angle of incidence formerly and vice versa. of refraction

nated inside

Image

Formation

the quantum

Consider when

it enters

A in Fig. 3.5. The path is refracted leaves the bent again as the quantum

path labeled

the glass,

and

glass. Now

consider

B. The angles

of the surfaces

of the glass have

been

will be bent just far enough that so that this path of a quantum similarly point /. The glass in path C is it will intersect the path A at to theline of the glass are perpendicular chosen. Here the two surfaces are zero. angles of refraction from the source to /, so that the

chosen

Air

Line

perpendicular

to air-g,lass N

Angle incide

Fig. 3.4

Paths traveled

light incident air-glass

upon an

interface.

by

of

surface

B

34

Fig

3.5

glass with that

Three

pieces

faces

the three

angled

light

The

Physics

of Light

of Glass

so

paths,

A, B, and C all intersect atpointf

Source

This process each with nitely,

of putting

its surface

more

and more

angles properly

and the end result

of such a series

glass, as in Fig. 3.6. The surfaces that any quantum refracted

just

happens

inset at the bottom

hit the

lens, and within

centered

smooth

S, that strikes

were

indefipiece

of

of glass, or lens, are such

point

the lens will

/, regardless

placed

of this figure

would

would

form

of reversibility,

be

of where

in the plane

it

of /, the

be seen. The outer

the optic

necessarily

evident source

will

from

re-

tion will

to be radiated pletely

undeflected.

thequanta the optic

along

the optic

that pass through

in

source.

at /, the lens

this figure

axis

meet

Therefore,

axis will

is formed

converge,

that

leaves

the surfaces its angle

All quanta

pass through

since the image

at all,

for this should

A quantum

will

lies on the

axis of any lens, it

of the source

of zero.

the lens

line in Fig. 3.6, is

axis. The reason

not be deflected.

optic

Then,

placed

the optic

on

of Fig. 3.6.

will the

source

if an image

an angle of incidence also be zero-it

were

a bright

of the

at point S.

lies

source

an examination along

disk with

the image

of the lens, the broken

also lie on the optic

and travels

glass with

is called

axis of the lens. The be true that,

be a dark

if the source

the center

axis of the lens. If a

that image

point

an image of the source

The line through called

this area would

in it. The bright

By the principle

will

is a single

of the screen would be lighted evenly by the quanta that did not

3ions

optic

to pass through

of glass into the path,

can be continued

of this piece

by the source,

to hit the lens. If a screen

pattern

point

emitted

enough

pieces

chosen,

is the point

the

of the

of refrac-

that happen

the

lens com-

upon

the image

be

which

mustfall

all on

axis of the lens.

The source and its image are redrawn as SI and /1, respectively, in Fig. 3.7. Now suppose a second source, 52, is introduced, about the same distance

from the lens as S,. Consider

radiated from 52 along

the

path

indicated.

the behavior It will

of a quantum

be deflected

very

35

Lenses and Refraction

it will be the glass, but if the lens is symmetric, upon leavthrough the same angle in the opposite direction deflected and leaving the lens will therefore ing the glass, and its paths entering of the path is very small, so long be parallel. The actual net deflection and may be as the lens is thin relative to the other distances involved, There is no path is unique. This particular ignored for the moment. which the quanta leaving 52 are undeflected. This path upon

slightly

entering

other path for intersects

axis (which

the optic

is the only

path of zero deflection

for a

path source at SI) at a point inside the lens, and the one undeflected this same from any source (for example, 53) will always pass through point. that they form

an image

of SI, they will also form images of any other sources about

the same

the surfaces

When

away

distance about

from

of a lens are so designed

the

the same distance

lens,

on the other

of 52 and 53 must be located Given

where

the fact that a path through the location

and given

source

any other

the

and

all

be formed

at

side of the lens. Thus, the images in the diagram.

are shown

they

the center

of any one source

in the same plane

will

images

of a lens is undeflected,

and its image,

the image

of

is determined.l

For example, for any real, simple lens, the images are small errors in most of this discussion. upon Iheir offfrom the lens, depending distances different slightly at formed are of off-axis sources more exact where except approximaNons to first-order axis angles. This discussion will be confined 'There

descriptions

are relevant

to visual perception.

Glass Optic

lens

axis Screen

I Source

/

I

Bright

point

(image of source)

Dark an

Frg. 1.6 A lens forming

image 1, of a light source, S. The inset at the bottom represents

the distribution

oflightfallingon

asseen when the direction axis.

thescreen, viewed

along

of the optic

Dim

illumination

36

Fig. 3 7 A lens forming

The Physics of Light

an

image of a set of three sources, all equally

distant

from the lens. The plane containing called

the sources is

the object

plane (the

set of sources can be called an object) containing

and the plane the images

S,

X

is called the image plane.

I Object

m a He plane

plane

Ordinarily,

point

usually

concerned

optical

purposes,

tion

of point

flecting

from

discussed

may

illustrated

in

of light

images

however,

sources

light

thumb

sources with

some

Fig.

is known,

3.8.

not of much

ofilluminated

any object

of light,

If the

the

source.

to locate

images

of the

contains

the

object

the image

other

We

of any

of the

image

points

may

For

as a collec-

is glowing the

are

objects.

be considered

Therefore,

location

interest.

or luminous

may

whether

other

be used

are

or

is re-

principles

planar

just

object,

of the

end

be found

as is of the

by simple

geometry. The plane

Focal

Length

plane that

that contains

The diagram

in Fig. 3.6

source

is moved

angles

that

image

will

very

long

farther

the paths be formed

distance

the lens will closer

the

away

to the

lens.

the

to the

the paths

be essentially

parallel,

Let us call

the

the

the

object

image

plane.

in Fig. 3.9a.

from

with

closer

is called

is called

is redrawn

form

away,

object

image

the

lens,

Suppose,

as in Fig.

lens surfaces lens.

will

If the point

of quanta

distance

now, 3.9b.

source from

will

between

gram

in Fig.

The distance lens, and To find some

light

3.9c dl,

represents

case

of the

the

is moved

a

it that strike

be formed

source

new

that

dl.

even

and the

The dia-

of infinity.

in this special case, is called the focal length of the

is a very

useful

the focal from

the special

The

the object

lens do and the distance between the image and the lens

The

thatthe

be such

radiated

and the image

plane.

length

an object

parameter of any fairly

of the lens. lens,

simply

far away

hold

(say

it up in the path

a tree

through

of

a win-

37

Lenses and Refraction

A lens forming

Frg. 3 8 an object.

Each straight

an image of line is the

ray from a path of the undeviated the point in the object, through optical

center

corresponding

of the lens, to the in the image.

point

Image Source X

Fig. 3.9

A lens forming

an

As rmage of a point SOLirCe. the source moves away

from the

lens, the image

moves closer.

In (c), the

source ts at infinity

the image distance

and

is at the focal of the lens.

that excitation and inhibition in neurons under normal conditions may sometimes, or in some places, be produced by direct ion flow instead of by the ion flow resulting indirectly from the action of chemical transmitter substances. As yet, there is no evidence of such electrical excitation in normal mammallian neurons. However, there is evidence of electrical transmission in the nervous systems of some fishes, and it is quite possible that electrical transmission may naturally occur in some of the neural

The Neurons

in the

There

Human

Retina

guished

are several

types of neurons

of neurons

self. At the time scribe

retina,

but recent

about

In the (probably be consistent assumption, every

kinds

THE

OF

changes

OF

ABSORPTION OF

QUANTA

accomplished, Somehow, tion

Figure

a real

in Dowl-

explosion

of cell

may

of these

known

it would

as a working

be connected

connections

that were

of

to occur.

is completed, to accept,

in the

may

with

be either

drawing

to be present

of the in the

this book was written.

of retinal

concerning

the

it is probably

pigment

NEURONS.

While

nature which

the occurrence tissue.

of visual

there

process

will

be described

of the isomerization,

molecule,

Figure

of the

molecules

true that isomerization

processes,

of the rhodopsin

of neural

work

6.5 is a semischematic

the isomerization

that was discussed

type

to try to de-

elements

known

in

nerve it-

these units is about

that work

is presently

that each

premature

microscopy

among

every

to the optic

that

distin-

cells are the last

all of the neural

suggests

before

and connections

one of two general changes

and

in the activity

AS A cal evidence

CONSEQUENCE

what

retina when

In some way,

STRUCTURES THE

type,

EXCITATION RETINAL

interim

or inhibitory.

of cells

primate

Hopkins

the idea that

other

excitatory

with

the receptors

electron

the interactions short)

The ganglion

among

superb

at Johns

the types being

it is probably

connections

laboratory

knowledge

from

of this writing,

the specific

human

running

retina.

in the retina,

by their shapes and locations.

the chain

ing's

tissue of the human

is nO unequivoby which

excites

again,

V. A pocket

this

neurons

is by

below. or the subsequent

must cause a change

6.6 shows,

in Chapter

produces

the model

in the excitaof rhodopsin

has been drawn

in this

rig-

125

Fig. 6.5

The Excitation of Retinal Structures

Semischematic

diagramof theconnections among neuralelements in the primate

ihatwereidenti-

retina

Ijed as of 1966.R,rod; (, COnei MB, midget bipolar nerVe cell; RB, rod bipolar; FB,flat bipolar; H, horizontal II.

A .imacrine

Cell;

diffuse gangwhere cells are contiguous : synapses. [From mling and Boycott 166). CopyrigM, 1966, the American Asso-

OA.,h

?b

(Q

l DG,

). iaa*..;aa' -.,',: a J!ei a . eh. &a.

n. The regions

+inn

for the Advance-

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OMB '€ FB 4 $

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socket into which the retinal moleculefits. When the system is in state a this pocket is buttoned, but when it isomerizesto b, the pocket is unbuttoned and begins to open up. According to this model, then, the isomerization of the pigment moleculeopens a path between the inside of the pocket and the surroundingmedia. There are two ways in which such an occurrencemight result in the activation of any nearby neural tissue. This site and the millions like it in each rod are imbedded in a folded membrane,and the membraneis almost certainly semipermeable. It might, in fact, be similar or identical to the membranes surrounding neuronal cell bodies. If this is true, the pocket could act as a hole in the membrane, permitting ion flow as ure

beneath

the

126

of Rods

The Excitation

{From Walde+al

long as well

diagram

Semischematic

b.b

rig.

it

of the

of a rod

states

pigment

molecule.

kl9631.}

flow

The ions that would

is open.

pass across

gration,

(d)

(C)

(b)

ia)

sensitive

neighboring

neural

these neighboring

depolarizing

through

the hole

membranes

neurons.

might

on their rr)i

If the neurons

or the

the depolariof propagating of the rod itself were capable had been absorbed would thus that a quantum zation, the information way through a chain of away from the rod, and begin its be transmitted membrane

neurons There

to the brain. is another

vate subsequent

way in which neurons.

the opening

Suppose

of the pocket

that the pocket

encloses

could

acti-

an active

an excitand that the active site generates site on the protein molecule, The substance might be generated substance. atory neural transmitter or when the pocket is unbuttoned, in the pocket and then be released of the site with the surrounding it might be formed by the interaction If either of only while the site is exposed. media, and thus generated substance could find its the excitatory these processes were to occur, neural tissue, causing its depolarizaexcitable way to any neighboring the of an impulse or impulses along tion and the eventual transmission that the no reason to believe, a priori, optic nerve. (Of course, there is of neurons. It is possible produces excitation of a quantum absorption the reducing substance, releases inhibitory pocket that an opened the reduction in activity s GNATS

level of some steady activity, and that

the presence Within

of the light.)

each of the models

mentioned

above,

there are several

pos-

basicallY or theories in detail, and many models modifications might also be proposeddescribed from the ones already different upon whiCh iO is so little evidence Since, at the present time, there it would nOf and their modifications, base a choice among the models

sible

1 27

Dark Adaptation and Rod Excitation

some

how

examine

EXCITATION

in detail

here.

However,

it is instructive

of these

models

might

be related

to two

to

perceptual

of brightness.

and the perception

adaptation

dark

phenomena,

ADAPTATION ROD AND

them

to discuss

be fruitful

In the precedingchapter,the relationshipbetweenthe amount of unbleachedvisual pigment and the visual thresholdwas discussed,and evidencewas presentedthat the number of quanta that must be ab-

if a molecule

that,

quanta

follows

that the more

cules

are in state d. The visual

for these

accounts

it incorporates

from

of which

is debatable.

time

to permit

a sensible

here

cussed

in

way

which

this presentation, reader,

theory

alternative

but alternatives may

begin

dark-adapted

the isomerization

doing

will

by stating subject of about

research the

dictates such

kinds

workers

kind

in this of

here.

is known

about

what will nine

At each

dark

visual

pigment

stage

it results

molecules,

in

to the

adaptation.

when

as and

occur

may

say he sees a flash or more

that

as well

psychophysical

perform.

not be discussed

area,

dis-

one

the

of theorizing

or theories

assumptions

at the present

theories;

many the

theories,

or assumptions,

evidence

little

is chosen

theory

subtheories

to illustrate

that

experiments

physiological

among

choice

of workers

the thinking

guides

is too

There

theory

one

of possible

number

specific

many

merely

is chosen

a large

among

a great

each

totally

if they are

This

adaptation.

dark

about

facts

arbitrarily

somewhat

We

differently

in which

the way

illustrate

will

discussion

The following

the

to sense the

state.

in that

and

it behaves

are in state d, since

molecules

fact that

way,

in some

seems,

system

mole-

if more

its threshold

to exceed

substance)

excitatory

(e.g.,

It

quanta. stimulation

a stronger

requires

system

rest of the visual

a

half

the

then the nine

than

effect

greater

a much

have

will

million

sub-

of excitatory

molecules,

other

of the

state

the same

roughly

have

rea-

the

accept

If we

amount

same

the

release

regard-

it isomerizes,

will

an isomerization

of the

regardless

stance)

molecules.

example,

(for

effect

local

pigment

other

that

assumption

sonable

a quantum,

of the

state

less of the

in state a absorbs

It is known

to be seen.

for a flash

are in state a, in order

that

molecules

by the

be absorbed

must

quanta

half a million

approximately

however,

d,

is in state

of the pigment

25%

When

to be seen.

a flash

for

sorbed

be ab-

must

quanta

nine

about

zero,

d is virtually

in state

pigment

of

propor'aon

the

so that

adapted,

dark

is completely

eye

the

when

For example,

increases.

state

bleached

in the

of pigment

proportion

the

as

to see increases

in order

molecules

pigment

by visual

sorbed

A in and

128

The Excitation

of Rods

will sayhedoesnot if fewerisomerizations occur.Therewill be On(4 isomerizationin each of about nine rods,and the flash will be seerl 1( the rods are relatively close to each other spatiallyand the isomeriz,) tions are close to each other temporally. If someof the pigmentis j(l the bleachedstate,a greaternumberof isomerizationsare required for the same response.

The basic element in the theory under considerationis the follow

ing: We will hypothesizethat the site at the bottom of the pocket in Fig. 6.6 is one that generates chemical mediator substancewhether Or that this generation is a simple cherr)jcal reaction, in that the rate at which the substance is generated is re duced when the concentration of the substance in the neighborhood of the site of generation is increased. Also assume that when the molecule is in state a, the pocket is securely buttoned, so that none ofthe mediatorcan leakout. Given thoseassumptions, itfollowsthatwhilea not the pocket

pocket

is open.

Assume

is in state a, it fills up with

been buttoned :omes

for a long time,

so great that the generation

Then when contents

the molecule

in a burst.

immediately

the mediator finally

will

Furthermore,

"no"

if fewer

remains

again.

))B

ceases.

releasing open,

its

the site

mediator substance (since the concentra-

We will

assume,

further,

away or deactivated

in this discussion,

and

the molecule

that released

the variability

That is, when

if nine or more

reduced),

media-

by some other agent.

and his dark-adapted

absorptions.

say "yes"

as the pocket

opens,

to leak out at a low rate until

can be neglected

always

the pocket

continue

is diffused

as nine quantal

effectively

to the site has been greatly

For convenience subject

and, after it has

of the substance

adjacent

regenerates

tor substance

substance,

of new substance

is isomerized,

will again begin to 3enerate tion

mediator

the concentration

inherent

threshold

in the

will

be taken

he is dark-adapted,

he will

isomerizations

occur,

and always

say

than that occur.

The theory

is summarized

by the

schematic

diagram

in Fig. 6.7-

molecules, and mediator substance flows out of the pockets (Stage 1). NOW a crucial assumption will be made, namely thatthe excitation resulting from this chemical mediator is a negatively accelerated function ofthe Some of the quanta

amount

of mediator,

incident

on the receptors

as shown

isomerize

pigment

in Stage 2 of the figure.

In other

Warder

proportional to tYPe of relation shown in the plot in Fig. 6.7. (Without some nonlinear relationship somewhere in the visual system, no theory could possibly be the output

of the excited

the amount

of mediator

consistent

with

part of each cell is not directly

substance

but follows

the general

the data of dark adaptation.)

Stage 3 in the diagram stage, thatis,

present,

in Fig. 6.7

one that adds the outputs

is simply

a spatial

from a number

51317)111,ition

of different

rods.

129

Dark

and Rod Excitation

Adaptation

of a modDiagram visualsystemto in 3ccount for thechange dark-adapthreshold during in igtion. It is explained

17

5;g, 6.7 el of

the

6,)'

(quanta)

Light

Ql

"il 01

(JJ)l Stage

Input 0, Rods

1

(O,)

Output,

Stage

/

2

(O,)

OutpuI +

Stage

Summation

3

102

(03)

Output,,

+

it Steady-state Stage

4

suppression

(o,. )

Output, II

Stage

( ,)

a

+

Decision

5

Output, = "yes" if 04 4 threshold Output, = "no" if 04 < threshold

"Yes"J L"No"+ special

that is also a critical

part of theories

ena. Stage 4 gives an output only if the input is steady, or changing put,

greater

be its output.

will

occur

this property structure discussed

small

a very

or only

as well

in a number

when only

(There

profound

of other places

the

input

evidence

in the nervous perceptual

the typical two

"yes"

the

that stages with system,

and their will

stage. It simply amount

than that. This stage corresponds the subject experiment, dark-adaptation categories,

is changing,

be

in this book.)

is smaller

response

That is,

give no out-

consequences

decision The last stage in this model is called a fixed if the input to it is greater than some "yes" the input

it will

very slowly,

and

phenom-

perceptual

the input to it changes.

is excellent

places

by this theory

required

of many other

The faster

one.

in various as their

thatis

property

Stage 4 has another

and "no."

says

and "no"

if

to the fact that, in is only

permitted

130

The

Excitation

o € Rods

Now let us examine the properties of this theory as a whole. eye is completely

dark-adapted,

and then a flash is delivered

If th(

of suffi-

cient intensity that nine quanta are absorbed by the visual pigment contained in the rods feeding Stage 3, each rod will contribute a ((i7tain output to the summation stage. Since this is a change (from 1§( zero output before the flash), it will be transmitted

through Stage 4 t(i

the decision stage, and from the Hecht et a/. experiment

and the

B5

sumptions set forth above, we know that the input to the decision stage will be great enough that its output will be "yes." Let us arbitrarily call thatinput level to Stage 5 (that is, the threshold level for Stage 5), nine units

of excitation.

the eye is light-adapted

Now

until 1000

of the pigment

molecules

are in the bleached state, and then the adapting light is turned off. A few seconds later, almost all of the 1000 molecules will still be in the bleached state (since

regeneration

is relatively

slow),

but

bleached sites will have been unbuttoned their initial bursts of chemical mediator

will

have

sume,

that

the

that

has been

merely

per unit

for the

of time

awhile

is, say,

unbuttoned.

sake

leaking one

Then

the

of discussion,

of that

total

of the visual

as compared

the nine

flash

was

presented

such

a large

stimulation "yes"

However,

the

open

signal

pockets

most

and the decision Now the

suppose

bleached

result

in the

cules.

(ThiS

lent flash

that

state,

only

there

a test flash

output

substance.

shown

mediator

(as the pigment no output

conditions,

eye,

stage will

in

say

of chemical

with

regener-

from

that

1000

Stage 4,

resulting

nine been

in the on

there

However,

than has

since

the

intense

pigment

are slightly

the

redrawn

(nine

in

input

Fig.

eye,

6.8.

the

units).

mole-

fewer

mole-

release

a

de-

to the

for the following

dark-adapted

to

the equiva-

will

resulting

in

enough

than

isomerizations

units,

figure

molecules

is intense

more

cision

change

would

to state a).

by regenerated

6.7

that

in strong

stage

quanta

of transmitter

Fig.

expect

regenerate

slightly

burst

occurred

in

the threshold

result

a flash

be smaller

present

might

of nine

require

in

leakage

is delivered

in state a.) Each of the nine

curve

We

the decision

slowly

it is first

or 50 units,

when

would

be virtually

these

cules

The

very

will

for the dark-adapted

isomerizations

the

when

for

say "no."

under

absorption will

from

changes

stage will

and

of mediator

be 1000/20,

eye.

gs-

unbuttoned

out

present

of the molecules

resulting

ates). As a consequence,

will

that

Now

mediator

substance

of the rest of the system, (until

pours

were

dark-adapted

of excitatory

continuously

from

that

time

subsided. amount

of chemical

pigment

units

to the

amount

which

amount

the neighborhood with

for a long enough

out of any pocket

twentieth

all of those

reaSOn. When

result However,

was

nine

the after

131

Hypotheticalcurve of the relationshipbetween of ihe input and the output Stage 2 in Fig. 6.7. The CurVe representsany negatively acceleratedrelationFig. 6.8

The Early Stage of Dark Adaptation

.p c

z

6o 50

of by theabsorption

Changeproduced. r. i nme quanta when light-adapted = 4 h

40

f

301-

-

---------%

'-"}-

ship-

'

/iiichangeinoutputlrequires F"'

/'

to produce a threshold

I '%,L,

I

/

. j.

/. I II

I

I

:

30

40

50

I

TO

'I

:

20

j i

I

il

change in Output.2 = 24

70

60

I

I

I

80

90

100

)

dark-adapted

when

nine quanta

when

the response

are in the bleached

order

that the resulting

"yes."

Thus this theory

tion"

OF DARK ADAPTATION

alighted

must

chapter,

in

for the fact that

for a flash to be seen in(This "explana-

increases.

pigment

be explained.

themselves

model

must

For exam-

in Stage 2?)

relationship

field for a long time,

mole-

1000

the response

to yield

explanation

steadily

a subject

that when

it was explained

in

be isomerized

Each of the stages in this

the nonlinear

causes

In the preceding views

a possible

which

of substages,

ple, what

provides

incomplete.

is obviously

consist

be large enough

of bleached

as the amount

creases

units,

results

stage,

must

change

that must be absorbed

of quanta

of four

Fig. 6.8 that when

24 new ones

state,

this

to the decision

the system

It can be seen from

"no."

cules

the number

IE EARLY STAGE

through

transmitted

accelerated,

A change

units.

four

of only

change

in an output

results

is negatively

the curve

substance

in mediator

a change

produced

because

50 to 59, and

from

9

=

the flash

light-adaptation,

of

absorption

from

resulting

Change

is established

an equilibrium

in his

of visual

and regeneration such that the rates of isomerization has been lookpigment are constant and equal. Suppose that a subject for and his threshold ing at such an adapting field, then it is turned off,

retina,

a flash of light

is measured

very

shortly

after the offset

of the adapting

light. According

to the theory should

lowing

events

newly

isomerized

stance,

and since

lease of mediator

occur:

molecule

outlined While

the adapting

contributes

the rate of isomerization substance

will

light

its supply

be constant.

the fol-

section,

in the preceding

is still

on, each

of mediator

is constant, The theory

sub-

the rate of realso assumes

132

Fig

[i

9 Hypothetical

of active substance

chemical during

of Rods

The Excitation

amount mediator light

and

dark adaptation.

o(f

light

Adapting Time

that

a substance

that

the

rium

such

equal

the

after

4 in Fig. 6.7

Stage

not

The

fact

under

these

circumstances

should

not

be taken

as will

be explained

in detail

in Chapter

The amount

of mediator

substance

present

theory,

diator)

tO a lower

mined

by the

and

and then

level,

of pigment.

regeneration

present

progression

of the

excitation

of me-

at a rate deter-

to fall slowly This

newly

any newly

the rate of deactivation

continue

if

Now,

of mediator

the rate at which

ref(ects

its contents,

dumps

pocket

opened

that

out of

by

contribution

the amount

and

cease,

a speed

(with

rapidly

drop

will

will

molecules

isomerized

contributed leaking

slowly

the

off,

turned

is suddenly

light

adapting

light

adapting

the

when

not yet regenerated.

and

opened

previously

have

that

pockets

XI.)

amount

the

and

subject

of the

as a refutation

of the amount

be the sum

will

molecules

isomerized

by newly

the

time

on for a long

has been

the

see the field

he does

that

field.

see the adapting

should

and

output,

resulting

the

block

should

to the theory,

(According

be present.

will

substance

mediator

of active

amount

a constant

time,

on for a long

has been

light

the adapting

Therefore,

away).

(or diffused

it is inactivated

at which

rate

will

is released

substance

mediator

at which

rate

the

that

equilib-

in a second

result

wil(

This

away.

diffuses

mediator

or

is present,

mediator

chemical

the

inactivates

that

in

is plotted

Fig. 6.9. One

of the

is that

discussion pends

when the

from an

gradual

the

light

This

results

reduction

that

light

is first

usually

the threshold

turned

called

off, dark

and

should then

adaptation.

present

dedLlr-

2 in Fig. 6.7.

of Stage

the nonlinearity

then,

the theory,

adapting

from

to be seen

substance

mediator

under

theory

for a flash

required

intensity of chemicaJ

the amount

upon

ing the flash. follows

consequences

essential

drop

should

It

sharply undergO

133

The Early Stage of Dark

What These

actually plots

predicted. different

happens

all show

the

just

rise, a new

at the

feature the

absolute

value

output

to demonstrate

alternative

in the retina actually

begin

light,

begins more slowly

be delivered

test flash

is ample

before

may nevertheless

Adapting

when

OCCLIT

field

4 may

be

off.

perception

is as follows:

made

lightis

is extinguished.

Although

less intense of the neural

resulting

of the adapting

(trolands) 984 311 98.4 31 .1

Fig. 6. TO Threshold flash

3.11

during

adaptation, U U.j

I

light

Absolute

Time

after

1 .0

extinction

1.5 of

adapting

2.0 field

(Trolands

old

all curves

finally

(t953).]

of

are units of

The value that

minutes

of dark

intensities

threshold,

that

of a short

stages

several

illumination.)

the bottom 0.6

intensity early

absolute

forty

threshold

for

adaptation.

retinal 0.0]1

the

of the

is, the threshreach

after

in the dark, is shown near of the figure.

this

lFrom

than stages

the test flash may

the neural change

of the extinction

the

added

part, there are several

is less intense. Thus, although

effect

this For

to

a stage

that the activity

extinguished,

after the neural

and

on the subject's

evidence

are

for

proportional

as

in the

discussion."

The test flash is considerably

physiological the stimulus

curves

is a rise

under

light

phase,

To account

of its input,

the adapting

the

there

to the model

before

the adapting

intensities,

goes

in Fig. 6.10.

by a slow

in that

light

of extrasensory

The simplest

and there

adapting

of change

slightly

is shown

followed

prediction

stage

rate

the action

explanations.

the adapting

higher

be added

of

of the

adaptation

drop

adapting

must

rises in tmeshold

appears

the

dark

rapid

theoretical

when

example,

during

an early

However, from

threshold

'The

Adaptation

Baker

from the ligm.

134

The

Excitation

of Rods

between

Stages 4 and 5 that has the simple

negatively

accelerated

in Stage when After

the the

the early zero.

2. These

flash

additions

adapting

light

adapting

light

A test flash this

would

is extinguished,

steady, occurs

would

presented the

would

be signaled

very input

close that

by the offset of the adapting be smaller

be superimposed

than

before

it would

curred

near the time

of offset

would

consequently

be increased.

the output

been

light

is ex-

to Stage 4,

to the new large

input

if ;1 light nonpro-

of the flash would,

had the flash light,

of

Stage 4 is thus

the adapting

the very

The effect

of the adapting

H

reaSOnS;

Stage 4. However, when

contribute

upon have

time, from

in the input

through

light.

is

rise in threshold

the adapting

increase

it would

duced

therefore,

a long

to the time

stage

for the

and the output

well

that its output

just like the nonlinearity

for the following

on for

a certain

linear

would

account

has been

produce

change

were

that

property

of the input,

is extinguished,

stages becomes

tinguished and

function

not oc-

and the threshold

Vll

O(K>

CONES

preceding

THE

STOLOGICAL

discussion

in

chapter,

the

In this

rod

vision.

will

be described,

perties

of cones

Figure

7.1

and and

CONES

is, ones

(that the

cones

cones shapes.

735

cone

in

cannot

away

found the

fovea

always

rods

between

relationships

and

cones pro-

the

treat

will

book

of the

with

exclusively

dealt

has

book

vision.

a typical

of

more

this

remainder

the

is a drawing

OPERTIES OF the rods are shaped AND

PIGMENT

CONE

AND

or less like from look

rods,

the fovea) as rodlike

be distinguished

and

rod

typical

two

and

the

peripheral

are cone-shaped. as rods on

the

do. basis

cones.

All

cones

However,

Thus, of their

rods

and

general

136

Fig fAlker

7 I

Receptors

C,reeff

in the

human

and

Cones

Pigment

Cone

of

Direction

retina.

light

incident

N(

(1900).]

'

'-.z.'l'a

-o"%-

',0

,

;j2aQ"I-;'W': %\

:;gll

+>

%

*'?y"",xXx2i"'aiv "%0s oa

5Q

!;

g N!EK

(a)

(b) Position

Contrastand Constancy

The

phenomenon

monly

called

experienced

example

gion does not depend colored eye

paper

under

between source.

that

any

ordinary

the actual

upon

light

if the

background

when

held

oflight light

in front

silhouetted

darker

it was normally

reflected is bright

enough,

when

they are strongly

reflected

from them

be seen when

they are against

it up at arm's

of a re-

one

length,

sky or a large

when

light

it is in front of the even though

is the same.

paper

experience backlighted,

is more than ample

a dark background.

com-

Look at it with

illuminated, the

very

Find a piece of gray or

from the paper

of it. It is common

light actually

hold

a

brightness

and the bright

looks much

than it did when amount

then

is

the

to be opaque.

and

have chosen

that

its intensity.

enough

Note that the paper

contrast

of the fact

simply

is thick

the eye you

light source

people

simultaneous

will

look

In fact, black

to see objects

or

even when

the

to allow

them to

Fig

I I 6 Mach

bands

produced

on a color

wheel.

279

Brightness

Fig.

is not a Simple

TT 7 An example

identical

intensities,

on backgrounds

Function

of Intensity

of simultaneous but their

that differ

much

less strongly,in

identical,

grounds

contrast of

in the

constancy.

papers

any

intensity,

may

same

Heinemann

experiments. isks (a0 inI lm) were er, while

the

:ontaining imeter.

lb) (The

te left and xation point

:, but that l here.) 'in (}955).]

of the small squares because

reflects

as they

black

their

are

back-

had

reflects

only

still looks darker that will

made

how the brightness

indoors.

the

O.90 X 1

an important

into

direct light

have

about

Furthermore,

the

black

units ofintensity

and

paper

study

in some

of a patch oflight

When

reflected

0.9 units;

=

about

still

relative

than the white

be described

aboutlO%.

illumination

therefore

large

brightness

reflects

paper

yet the papers

=100

despite

is called

reflects

room

and

phenomenon;

constant

white

paper

ordinary

O.10 X 1000

inside

fairly

a piece of ordinary

from

to another

on it. This

by 1000-fold;

(1955)

and constancy

remains

illumination,

increase

paper

paper outside

to measure

incident

related

that falls

light, while

brightnesses

paper outside the white

object

are moved

the

'

be seen, although

can

are different

is very closely

For example,

sunlight,

the

all have

they lie

contrast,

The intensities

brightnesses

illumination

90% of theincident these

because

are ofdifferentintensities.

brightness

changes

brightness

Fig. 11.7.

but their

Brightness the

The small squares

are different

in intensitv.

This same phenomenon,

all

contrast.

brightnesses

but the black

inside.

of brightness detail

here.

contrast

He wanted

was influenced

by the

280

Spatial

in the Visual

Interaction

System

of its background.

intensity

the subject

that presented

To do this, with

a view

an apparatus

he constructed

in Fig. 11,8,

like that illustrated

of the "test" disk /t and ask the su5 IB at some predetermined levels and then the background disk lm until its brightness of the matching ject to adjust the intensity equal

appeared

was to set the intensities

procedure

His general

to the test disk.

at some value, say 100 intensity units, and two disks match, for a series then had the subject adjust /m to make the of measurements are shown in of values of /t,. The results of such a set match when /t = 100 (except Fig. 11.9. When lb is zero, the two disks set /t

First, Heinemann

effects

to the

in relation

are very small

Then as the intensity of the background IB j5 value lm also rises slightly. This indj raised, the matching measured).

being

gradually

which

errors,"

"constant

for so-called

brightness

cates

that

the

when

the

intensity

"contrast"

of the

of its background

is raised.

slightly

increases

test disk

left-hand

It is the opposite

of a

effect.

10,000

1000

TOO

10 Frg

The effect

l T.9

upon

ness of a disk of varying of its background. actually

1

l,,, background

TOO intensity

(arbitrary

1000 units)

10,000

axis is

of the matching matched

'the

its brightness

brightness

of the test spot. Thus, it is a of the brightness

spot. [A(ter TO

The vertical

the intensity

spot when

measure

1

the bright-

the intensity

EC,H.J

Hernemann

of the test (1959,

Subject

281

Brightness

is not a Simple

Function

As /1, continues

of Intensity

to increase,

the test disk

brightness

begins

to drop

until, when /b is about 110 units, the subject sets /m at zero,indicating that the test disk looks as dark as the dark background. This entire

curve

is a measure

region

were

would

be a horizontal

of brightness

independent

of the intensity line.

of a very strong contrast The entire

curve

contrast:

If the brightness

of its surroundings,

The curve

actually

indicates

of a

the curve the presence

effect.

in Fig. 11.9 was measured

with

test disk 11 set at a fixed level (100). Heinemann

the intensity

repeated

of the

these

same

measurements for a number of different /t settings, and the results are shown

in Fig. 11.10.

the one there

Note

in Fig. 10.9.

is a small

proaches

the

that all the curves

As the background

increase

intensity

in brightness,

intensity

of the disk,

are essentially increases

but when the

similar

to

from

zero,

the background

ap-

brightness

of the

disk

drops

sharply." The

curves

brightness

in Fig. 11.10

contrast,

In order

to understand

tion

tends

falling

of patches

that

The

piece

of gray

let us reexamine

constant,

despite

is often

used

paper,

subject

A subject

ranging

is also

paper,

out, from from

shown

at some

trial

The

to trial,

and its surroundings

lighted,

'FO( each curve,

tried this. The subjects

mann added a lighted

could

from

will

reported

constancy

that

of an array

to white. constant

is simply and

The at all

another

he is asked

to

of him, the one that looks the

intensity

of the test patch

of illumination

conditions,

can be

on the test

almost

in!ensity intensity

always

room

choose

that drives the brightness were increased

drsk as well.

so

that

is

a matching

beyond

of the test disk this level? Hei-

darker than a patch with

They were only able to make the match

to the marching, be matched.

and in particular

in an ordinary

that the test disk looked

not make a match.

disk, and they could

black

is held

him,

shade

are performed

if the background

background

from

a test patch

particular

there is a value of background

it, and they therefore an unlighted

of

may also be varied.

the subject

happen

brightness

papers

distance

and the

as the measurements

just to zero. What would nemann

con-

in the illumina-

is seated in front

in shade

the series of grays in front

as the test patch.

normally

just what

changes

to measure

So long as there are no extraordinary long

set of measure-

refers to the fact that the brightness

on this set of "matching"

times.

patch

point,

it more precisely.

of gray

illumination

varied

an extensive

of

on it.

helps to define

pick

this

constancy

to remain

A procedure

same

description

constancy.

is. In general,

an object

a quantitative

but they also contain

ments of brightness

stancy

represent

Then both disks looked

nO light in

when

Heine-

darker

than

282

System

in the Visual

Interaction

Spatial

T0,000

of different

Fig. ? '1.9, for a number

[From

units).

gives 1, (in arbitrary

each curve

1000 "

below

The number

test disk intensities.

Subiect

(1955),

I-lememanri

in

like that

L-ig I I 10 A set of curves

EGH ]

100

r

TO (Z'

'10

3

TOO

31

nO

0 I //

TO,COO

IOOO

TO

OT

3100

1000

I,, (arbitrary units)

gray

light,

he will

flects

50%

say that

the subject's

When

falling that

reporting

light on the

of the amount

of the

retinal

when

lighter

hand,

other

the

that

raised,

from

so long also falls

choices

images

falling

on the matching

the

shade

of gray

oflight

falling

of the

test

of on

patch

and

independent

are completely

indicate

if it looks

to be exhibit-

he is said

that

constancy.

perfect

to be exhibiting

increases,

its illumination

test

the

less than

he is showing darker

when

the

subjects

show

only

looks

patch

perfect

illumination

iS

is "over-constancy."

ordinary

Under

he is said

if his

or "under-constancy,"

kind,

are of this

If his judgments

leve(,

illumination

of the

choices

constancy.

ing brightness

tures

that

also re-

overlOOO-fold).

vary

On

intensities

the

though

it (even

than

regardless

stays the same

the test patch

ifthe

is essentially

subject

The

patches.

even

that

patch

like the matching

do this

greater

times

is 1000

patch

He will

light.

of the

most

it looks

incident

of the

50%

reflects

that

For

as the test gray.

the same

or nearly

is a gray

if the test patch

example,

test

the same

is physically

that

perfect

as the

light

conditions, constancy; from

on the regions

the

most

in particular, source

surrounding

that

perfect

constancy

is illuminating

the test patch.

minor

the

However,

deparOBTAINS

test patCh

ifthe !I-

283

Brightness

is not

lumination of light

a Simple

Function

is confined exactly

then

upon

falling

the light

The

Heinemann's

already

the

points

intensity

point

is, the

Now

labeled

and

which

would

have

on a lighter

gray

increased

patch

under

the way

in fact

in which

constitute

as well

on a patch

a set of

as contrast.

and

We

its background

just

two

points

on the set of curves

(a) and

units

and

(a) and both

(b). the

background

(b) is that

looking

the

conditions

are very

the

subject

and

the

at a gray

in

(a), the units.

120.

For That

Now,

on the

same

as that

piece

of paper

on the entire

of the

brightness

similar

(i.e.,

is, indeed,

the

of the test

by ten.

illumination

His judgments

12

intensities

(a) to (b) is exactly

and

Thus

was

the

have

labeled

are 100

multiplied

if he was

to

For the point

values

been

from

background

two

do

at some

consider

change

same).

discussed

continues

by ten-fold.

the

be

patch

occurred

those

are almost

entirely

the

have

the

depends

to the

and

between

retina,

on

occurs

10

its surround

subject's

it spills

a spot

is shown.

constancy

(b), the corresponding

difference

of

to explain

thelightfalling

labeled

was

by projecting

patch

will

in Fig. 11.10,

of brightness

when

test

no constancy

it is sufficient

shown

that

of the

(e.g., none

phenomenon

Here,

constancy

Fig. 11.10,

was

Xlll

brightness.

test spot

this

alone

so that

brightness

of

data,

know

test patch

on it, and

measures

is changed,

spot

the

in Chapter

quantitative

the

the

significance

length

same

to the test patch

onto

background),

of Intensity

scene

of the test

the values

showing

of /,,

brightness

constancy. The

points

points

for

constant

which

and

the

subjects

mination"

fact

was

constancy that

down

over

began

others

does

context of the present the brightness ing

on

the

among

the intensities

All

of the phenomena

any point

in the visual

of that

within just field

by more

than

even

than

general

some

the

intensities

in Chapter

five-

the "illuhand,if

the

background,

significance

conditions

in detail

in some

about

when

On the other

in a

of the

and

breaks

Xlll.

In the

it is given as an example of the fact that

depends

image

The

under

be discussed

chapte5

as the

less intense

are

of points

So long

oflOOO:1.

the set of

its surround

constancy,

down.

occur

of an object retinal

a range

among

groups

not differ

or much

to break

will

such

good

from

and

discovery. did

very

more

constancy

under

of test spot

important

showed

much

chosen

examined

its surround

was varied

test spot then

a very

and

arbitrarily

intensities

Heinemann

made

of the test spot fold,

the

ratio.

detail,

(b) were

(a) and

not point,

the overall described is not always

upon

the

but

rather

intensity upon

oflight the

fall-

relations

image. illustrate

that

monotonically

the

brightness related

at

to the

Spatial

284

System

Visual

in the

Interaction

do, however,

corresponding receptors. All of these demonstrations lustrate

that the brightness

among

the intensities

by the intensity

is determined

at each point

brightness

That is, in every

field.

il-

on the relationships

at any point depends

in the visual

of ttl( of th(3

is the strength of excitation

in the field

at any point

brightness

correlate

that the physiological

the hypothesis

strations disprove

that recep-

then these demon-

related to intensity,

is monotonically

tor excitation

namely

is accepted,

of this chapter

cussed at the beginning

dis-

assumption

physiological

If the reasonable

at that point.

intensity

case th(>

distribution

jll

the point in question and also includes some of area. The excitatory effects of intensities at neighbl'the surrounding interact with each other, and the physiological ing points evidently @{ correlate of the brightness at each point must be some function a region

that includes

excitations.

postinteraction

the resulting

studies of the nature

physiological

of excellent

There are a number

systems of animals, and these of the perception of studies are highly relevant to an understanding evidence about spatial interacphysiological brightness. Therefore, tions in the visual system will be discussed now, and after that, we will return to a more detailed analysis of the related perceptual phenomena in the visual

interactions

of spatial

EVIDENCE THE

CONCERNING

IN

THE VISUAL

properties

States, and

eyes of this

lateral

OF analysis,

SPATJAL INTERACTION

United

Fig.

in

shown

animal

of the The

PHYSIOLOGICAL NATURE

The

and since

71.11

preliminary

of this eye are similar

ing humans,

it has been studied

has been carried

SYSTEM the Johnson

out

is found

is called

animal

the

on

the eastern

horseshoe

lend

themselves

studies

indicated

very extensively.

in Philadelphia

shores

crab, Limulus. tO physiological

that many animals,

to those of higher

in the laboratories

Foundation

for the physiological

hypothesis

an adequate

in an attempt to develop correlate of brightness.

of the includ-

Most of this work

of H. K. Hartline, and more

recently

first at at the

in New York. While it may seem that studUniversity The Limugus Rockefeller an animal are unlikely to produce INSIGHTS!nfO ies of so primitive these studies have, in fact, had an enormOuS human perception, upon current theories of the processes of human brigFlfinfluence obvious it seems perfectly while Furthermore, ness perception.

285

The Physiology of Spatial Interaction

that human visual processes are much more complicated the Limulus,

there

tive differences nas

in the functioning

that are relevant

most certainly motion

differences

in the perception

tive properties

Limuli

of visual

are usually

ment

is to be run, one of them

from

the eye,

eye

a circle

Then the optic eye, with

stimulation,

while

then

centimeters

centimeters

mounted

be inserted

the

neural

system

of the field

on a mosaic

an amount

of light

flected

from

particular

Limulus,

there

in each facet forms the receptors

shape of the facet, light from

in each facet, somewhat

circular

facets

so that each

to the amount of the field.

system

for optic may

that forms

an

receptor

re-

radiated

or re-

In the faceted

eye of

for each facet,

and the lens

a very poor one) in the plane of

of the visual

receive

of the Limulus

receptor

human.

lap because

out. The

ofthe

pigment

light

from

lens, the

are such that pigment

overlapping

but

fields.

each facet

a region

and the

Electrodes

area of the field falls on the visual

we can consider

from

moist.

in the facet. The characteristics

the optics

in the

region optical

and adjacent

displaced

Comparing

of receptors,

and the location

a roughly

is kept

is lifted

is available

(the lens and cornea)

an image (although

contained

out of the shell.

(as the eye of the fly). In the human

proportional

is a separate

to remove

tissue.

is faceted

image

nerve runs

Therefore,

attached,

The

itself (see Fig.

to it. The optic

brain.

nerve

tissue

they

an experi-

as near to the brain as possible,

of optic

optical

where

When

the eye is first sawed

ceives

some

as very primi-

part of the shell

to the

into the neural

is a single

of in-

out and an eye removed.

in such a way that the front

The eye of the Limulus eye, there

are al-

the processes

room,

sand.

are attached

nerve is severed

a few

reti-

to the perception

however,

moistened

is a transparent

surrounding

eye is then

(There

can be considered

is fished

structures

a few

regard

in a refrigerated

in the sea-water

of the cornea

the

with

kept in a sandbox

and the retinal

and the Limulus

systems.)

themselves

equivalent

of any qualita-

perception.

Perhaps,

of brightness

bury

11.11)

brightness

for example.

than those of

evidence

of the human

to human

important

and color,

volved

The Preparation

is, as yet, no unequivocal

of the field; of diffraction,

in Limulus

Each facet the fields

eye to the opticsof to be the rough and

each

of different

aberrations

and

receptor human

scattered

human

analog

eye,

of each

receive receptors light,

light over-

and

the

286

Spatial Interaction in the Visual System

Lateral eye

287

The Physiology

of Spatial

Fig. } 1. I T The arthropod

Interaction

Limulus, commonly

the left are top and bottom

fields their

of different

skill

single

;ingle Facets

any

If the

whole

eye

like

those

fiber

aEach facet contains is evidence

When

device,

nerve

the angular

of the

the two

may

is illuminated,

of their

that

angles

between

fields."

it is possible and is then

are connected

to tease

to drape placed

anywhere

to an amplifier

are conducted

a

the fiber

and

down

that

and recorded.

a series

in Fig. 11.12.

within

as if each facet Were an eye containing being recorded

electrode

the

of nerve suppose,

impulses now,

will

that

be re-

instead

of

several anatomically

that these structures,

io be discussed

extents

impulses

be observed

because

of Limulus,

electrodes nerve

crab. At

eye is shown above.

microscope,

nerve

another

shown

the horseshoe

overlap

a dissecting

and

optic

corded

out

called

of the lateral

facets

than

using

fiber

an electrode.

recording

from

and

nerve

on the eye,

yrdings

Limulus

axes are smaller

With

over

views; a close-up

here, each facet will

separate structures that contain visual pigment, and there one facet, may be able to act with a degree ofindependence, a lens and several receptors. However, under the conditions

aCt aS a single

from, and the facet is uniformly

reCeptOr. That is, only one output

illuminated.

"channel"

is

System

in the Visual

(nteraction

Spatial

288

l-*-*-&'-"'*-l

a

s

of light

Extinction Onset

of light FrB lower

from

light

prevent

one

particular

that

neighboring

that

facet

will

fiber

is taken

care

and

will

fiber

the nerve

re-

facets

If the

is illuminated.

facets,

at a time.

facet

the nerve

illuminated,

are

of a facet

size

the

one

only

found

among

scattering

(1932).]

than

smaller

lighting

eye,

particular

one

when

only

spond

of light

it is always

conditions,

these

Under

the

over

about

moved

were

a spot

eye,

the entire

lighting

of

lower

of a few seconds and Graham

Har+line

on. lFrom

remained

the light

which

an interval

represents

The gap in each record

record.

of the

of ten for each successively

by a factor

was reduced

light

stimulating

the eye of

from

deflections

O.2 sec. The intensity

every

occurring

line are time markers

white

during

and the regular

The spikes are nerve impulses

Limulus.

fiber

of a single

activity

of the electrical

12 Record

ft

to

not re-

excited bY among faconly a single facet, and that there is no spatial summation on a were performed experiment that if the analogous ets. (Remember of any of a stimulation retina, to rods in the human fiber connected

spond.

group

tions

produced

they

have

by many

reached

If a different

followed,

be illuminated

fiber it will

in order

recorded

in the firing

rods all add together,

the ganglion

nerve

being

the fiber

result

would

of rods

large

procedure

that

it appears

Thus

of the

is

from

axon.

The eXC!(aby

or summate,

the time

cells.)

is placed always

to produce

over be found activity

the electrode that

and

a different

in the

fiber.

the Same

mus' Tha[ !Sr eaCh faCei

289

The Physiology

fiber

of Spatial

Interaction

in the optic

nerve appears (and it is also true that virtually nerve fiber). Now,

recording

from

a single

to be connected every fiber,

facet

to a different

is connected

facet

to an optic

a series of experiments

may be of the activity recorded from such a preparation for a number of different levels of intensity of the illumination, and Fig.l1.l3 shows plots of these results. Figurell.14 shows a series of measurements of the dark adaptation of a single facet of the Limulus eye. Although the time course of adaptation is different from human rods and cones, the general characteristics are clearly similar. performed.

Figure

1L12

is an example

In general,

every facet of the Limulus eye, when stimulated alone, in the way that one would expect from a general knowledge of human vision. However, the topic of interest in this chapter is the nature of the interactions that occur between receptors or facets. The fact that no spatial summation in exhibited in the eye of Limulus has already been pointed out. However, inhjbitory interaction among facets is a conspicuous feature of the action of the Limulus eye. For example, suppose that any facet, call it A, is illuminated steadily so that it is firing at a rate of 100 impulses per second. If, then, the light falling on A is unchanged, but light is added to a neighboring facet, B, the frequency of firing of A will decrease. That is, adding light to a responds

A

Fig. 11 13 A plot of the records 11.12

(plus one more

point

in Fig.

represent-

ing an intensity

ten times greater than in Fig. 11.1 2). The curve A is the rate of firing during

the greatest labeled the initial I 10

1000 Relative

intensity

I T0,000

librium

burst

and B is the final

rate of firing.

and Graham(19321.]

lAf[er

Har[Hne

equi-

290

Spatial

Interaction

in the Visual

System

Fig. ) l 14 Dark-adaptation

-3.0

of the Lrmulus represents

of a facet

eye. The vertical

the logarithm

sity of a flash just strong -4.0

axis

of the intenenough

to

cause the nerve fiber

to fire one im-

pulse.

and McDonald

[From

HarLline

(1947).1

o

Time

in dark

(min)

neighboring hibiting

facet will

reduce

A. In fact, the only

be observed any single ways

40

30

20

10

in the optic facet

either

nerve

if illuminated

remain

if the ifluminated

facets

illuminating

When studied

or decrease to which

when

interactions

of ways.

were

For example,

on a neighboring

group

tion of the distance

between

gion,

and as a function

(Fig. ll.15b),

interaction.

its activity

light

When

on a single facet was measured

falling

from,

the activity

apart.

facets that can

is inhibitory

they

If al-

to any

is smaller

are widely

sepa-

of the other.

first discovered,

they

the magnitude as a function

were

of the inhibiof the intensity

of facets (Fig. ll.l5a),

the measured

will

is added

is reduced

one has no effect upon the activity

in a number

oflight

between

of Limulus

are farther

these inhibitory

tory effect

in A; B may be said to be in-

of interaction and recorded

the same

other single facet. The extent rated,

the activity

form

as a func-

facet and the inhibiting

of the area of theinhibiting

repatch

(Fig. l1.15c).6 The curves of these

in Fig. 11.15

studies

were

to an understanding inhibitory the

spatial

somehow other

interaction

be determined

Individual

among

Facets

To clarify following dissected

"The strength

They

and the results

do not lead directly

However,

in the Limulus

it is clear that eye, and, since

of each

are remarkably

with

each

of and that study revealed

and much

was undertaken,

facet

must

more

direct,

study

simple.

facets, (he procedure was followed: A single optic nerve fiber WaS out and placed on an electrode. The e'y'e WaS then explored the nature

ofinhibihon

ing its rate of firing, firing,

a different,

processes

shapes,

facets, the shapes of these curves

by the interactions

of the interactions

that the underlying

involved.

is present

of separate

one. For this reason,

the nature

Interactions

very hard to interpret. of the processes

is composed

eye

do not have simple

of the inhibitory

is usually

then adding

and subtractmg

measured

interactions

by illuminating

light to a neighboring

the second rate from the first.

(inhibiting)

among

the facet being recorded region,

agam noting the

from,notnewrateof

Fig

I T 15 The effecK

ables upon

in the eye of Lrmulus. inhibition

by which

inhibiting

decreases

rate of the inhibited

mately

boring

fiber. varies

logarithmically

with

falling

the facet

inhibitory

effect

inhibitory

light

io

u

effect

and the lower level)

inhibition tance

o 0

1

2

Log of intensity

falling

on

3

inhibiting

(b)

and

inhibited

facets

(C)

1

2

3

4

with

region.

varies

5

of

the dis-

the facet recorded illuminated

from (This

in different

In (c), the inhibitory

direc-

effect

in-

the area of a spot of light

on facets

recorded

inhibiting

inhibitory

parts of the eye and in different tions.

spot

falling

between

The upper

one, the equi-

strongly

function

the

on, and

In (b), the strength

between

creases with

Distance

level.

the initial

varies

and the other particular

(The

when

is first turned

represents

neigh-

from.

is greatest

curve

librium

o

approxithe inten-

on a region recorded

then falls to a steady

B

of the

the firing In (a), the

of inhibition

sity of light

of

axes) is the

the presence

activity

strength

(a'

of inhibition The strength

(on the vertical

amount

30

of three vari-

the strength

from.

neighboring lFrom

(1')56);

curve

scribed

by Har[line

the one

Hartline

et al.

(b) is from the data deon p

664.1

292

Spatial

Interaction

in the Visual

System

Light

Fig

JJ

with

I ) )6 Schematic

of the procedure two

a small

nated

by

another

spot oflight

itself, optic

(i.e.,

one

a second

fibers

caused nerve

such

that

fired

the

that

when

fiber

Next,

vihile

their

intensities.

was

were

was

illumi-

made

from

(two)

is represented

When

both

facets

for facet

illuminated).

taken

corresponding

This

when

to a neighboring

facet

recordings

which,

a search

connected

a neighboring

from

facets simultaneously.

was found

to fire. was

was found,

at various

neighboring

the facet

fiber

fiber

simultaneously,

minated

until

representation

for recording

of the

were

schematically

illu-

in Fig.

11')6. The curve

in Fig. 11.17

is a curvilinear,

and

ofinhibition light

exerted

falling

other

way

However,

on the

inhibiting

the

a very The

illuminated

is a linear

is illuminated hibition beled

amount

very

facet.

results

of B is greater

threshold" than

logarithm

is used

is strongly on

emerges.

it is firing

by the

region

in the figure).

this threshold

frequency,

There

the strength

of the intensity

experiment

the firing

the results.

between

the

horizontal

are

plotted

Such

a plot

very

of Firing slowly,

to the As soon

ofthe

curved

the axis.)

somewhat is shown

in

when

B iS

of A is reduced

of the frequency

so that

on A (as represented "inhibitory

of the

relationship by which

of plotting

(The function

scale

function

dimly,

way

relationship

and the

intensity

simple

Fig. 11.l8a.

one

simple,

on a fiber

if a linear when

differently,

shows

not very

of B. When it exerts

left of the

B

no in-

point

la-

as the rate of firing

the activity

in B results

in

293

The Physiology

of Spatial

a reduction fire

Interaction

in the frequency

if B were

rate well

dark.

above

tional A.

In this

above

the frequency

from

B, as shown

cally

inhibit

plot,

of the

10%

threshold

are

Let

an equation

and it will

prove

fired

by B over

by and

B is effectively

subtract-

A is subtracting

impulses

the two facets recipro-

linear way.

that describes

the relationship

plotted

useful to do so.

FB

bethefrequencyoffiringofB bethefrequencyatwhichAwouldfireifAalonewere (i.e.,

B dark)

quency

might

and will

be so referred

be called

the

(This level

"uninhibited" of excitation

freof A,

to, hence the letter "e.")

be the excitation level of B be the coefficient representing the strength of the inhibition

that A exerts on B

Fig. 11.17 between

Plot of the relationship the intensity

on one facet it inhibits from curve curve on

of the addi-

impulses.

eg

"'ab

it

A's

bethefrequencyoffiringofA

eb

intensity

from

Fg

illuminated

Log relative

fired

at a

the inhibi-

the impulses

impulses

other words,

in a simple

proportion

subtracted

and firing,

in Fig. 1l.18b.ln

B is firing of inhibition

of B. Once

from

A, but at the same time,

It is easy to write in Fig. 11.18,

of firing

subtracted

each other

A. When

the amount

it is as if some fixed

both facets are illuminated from

the level that A would

to inhibit

threshold,

by B were

inhibitory

impulses

ing

fired

particular

the

When

with

is exceeded,

impulses

of A below

That is, B begins

the inhibitory

exerts on A is linear tory threshold

of firing

inhibiting

facet

of light

and the extent

its neighbor.

falling to which

lCalcula+ed

B in Fig. } }.13 and the

in Fig. 11.18.]

294

Spatial

Interaction

in the Visual

System

4.0

Fig

I I IB The relationship

the freque(icy

o€ firing

its inhibitory

3.0

fiber. (a)

both

effect

When

ties of light, as shown 1.0

Har[line

and

upon a neighboring

two facets

illuminated

between

of a fiber

with

A and B are varying

each inhibits

intensi-

the other,

by these two graphs.

lFrom

and RakNrl (1957).1

o o

30

20

TO Frequency

of firing

of fiber

40

B

5.0

40

.,

F,,

j:)

(b)

3.0

a)

i, o (5

2.0

1 .0

o o

20

TO Frequency

40

30

of firing

of fiber

A

KBg

bethecoefficientofinhibitionthat8exertsonA

OgB

be the threshold of inhibition

oba be the inhibitory

of A on B

threshold of B on A

Then : Fa o ea

-

Kba (Fb

-

gbo)

Pa o '-a

when

F5

05a,

(1)

When

F,, < qbai

(2)

when

Fg

->

0ab,

(3)

when

Fg




and Fti a eb Fb Equation equals

(1)

"

-

xab (Fa

may

be

the frequency

some

6).5)

eb read that

minus a fixed proportion above

-

threshold

as follows:

A would ("ba)

level.

fire

The

frequency

if it alone

Were

of the rate at which This

equation

only

of firing illuminated

(4) Of

A

(ea)

B is firing over and the SYS'em

describes

295

The Physiology

of Spatial

Interaction

correctly so long as the inhibiting

facet

that is, when the frequency of firing of

Fl, >- Ol)a,

equals

or exceeds

the inhibitory

threshold.

When the frequency of B is lower than the inhibitory threshold (F5 < oba)i the term Kba(FB - gba) in Eq. (1)is negative, and therefore,if Eq. (1) held, Fa would increase as F5 decreased from the inhibitory threshold to zero. However, from the data in Fig. 11.18, it is clear that this does not happen. Instead, when F, Equations

(3) and

that the facets

are reversed

It is probably

easier

of the

additional

matic

diagram

neurons

that

to behave.

Light

to output

tional

to the

optic brain,

nerve

fiber

but they

be presented,

in the same of the

of the

also

impulses

branch

and

except

intensity).

This

travel

they

operates nerve

Whenever the fiber

along

to the fiber

through

(f)

((

Fig. l 1. }9 Schematic

Excitation

(e11)

behave

synapse

as the retina

of a

that would

in Lrmulus

does.

Light falls on the facets that contain photosensitive the light

synapse

diagram

connections

-Klia

(Fh -

Output

level e, which

"ha)

frequency -

xah (Fa

-

('till)

excites

synaptic

threshold

impulses

from

down Fh 'o eh

pigment.

is to produce

the optic

off and inhibit with

a strength

strength

The effect

of

an excitation a synapse

if the

is exceeded.

Output

the synapse travel nerve,

but also branch

the neighboring proportional

of the output

threshold

value.

metrical;

each unit

minus

The system inhibits

fian

a collateral

the neighbor

set of neural

the

propor-

excitation

down

back

inhibit

causing

in the optic

threshold.

of

eye seems

is roughly

firing

the synaptic

off and

system

in a facet,

e (which

sense

to the sche-

as the Limulus

are propagated

where

to make

of a simple

structures

to produce

exceeds

region,

way

level

light

synapse

fires,

way,

by referring

is a diagram

excitation

the excitation

same

the equations,

This

acts on some a certain

to the neighboring

Light

will

behave

logarithm

the

in role.

that

an excitatory

bers when

in exactly

to understand

data

as stated in Eq. (2).

< "'bar Fa = ea,

be read

in Fig. 11.19. would

facet

through

(4) can

cell to the some is sym-

the other.

an

296

Spatial

in the Visual

Interaction

System

inhibitory synapse. If we assume that the synapses behave in a simple linear way, that is, that their outputs are proportional to the difference between the excitatory and inhibitory inputs, then each facet will in of its own output. hibit the other by a fixed proportion It is This model manifests lateral, reciprocal, recurrent inhibition. lateral because it operates between regions that are separated spatially on the eye. It is reciprocal because each facetinfluences the other @11(4, It is recurrent because the site where inhibition acts is earlier in the chain than the site from which it arises. That is, the inhibition, in addition to traveling laterally, also travels back toward the input end ofthe system. Such a recurrent arrangement is also called a negative feed back

system."

The line labeled B in Fig. 1'].21 represents the inhibitory effect of a unit A on another unit B. If the same experiment is repeated when the inhibited unit C is farther from A, the plot changes as shown in Fig, 11.21. The farther apart are the two units being examined, the smaller coefficient), and the is the slope (that is, the smaller is the inhibitory greater is the inhibitory threshold, until, beyond a certain distance, one unit

has no effect

on the other.

It might be expected that the inhibitory effect of A on B, (Kab) would be exactly the same as the inhibitory effect of B on A (Kb.a) and, similarthe equations and data to be in Fig. l 'l T9is merely offered as an aid to remembennB the data in here. It is certainly not the only plausible model that fits the data For example, Data to 1T.20). (Fig. nonrecurrent is inhibition Fig. H. T8 can also be fitted by a model in which the oy by more than One of inhibition stage recunen+ by a single either fitted can be later be presented the other. The evidence strongly suggests that there is only one stages, one following nonrecunent 'The

model

presented

sysinhibitory lateral reciprocal I l 20 A nonrecurrent acts at a site iater in the chain than the Thus the strength of inhibition site from which it originated. of firing of the inhibiting not to the frequency is proportional Fig

tem. The inhibition

unit,

but rather

to its excitation

level.

In the hueye, and that it therefore probably manifests recunen+ inhibition. butthe recunent inhibitotY Il'l(ideli between these possibilities, man, there aTe nO data to discrimmate Staged, will be used Set of nonrecurrem the appropriate being simpler tlian the model containing (((lHrent j,[:b:here. It should also be pointed out that there are many altemative ways ot modeling It is not convenient. and is simple it because chosen merely tion. Again, the model in Fig. lT.T9is eye. the Lmiulus of physiology actual the represent intended to =stage= in the Limulus

297

The Physiology

of Spatial

Interaction

Fig. I 1.2 l The inhibitory

V 9!

fiber

ffl E ao h,

1.5

when ABC

,0

"-, ? ! -f

€

u>

,5

E

3

,t N c 4

*

ytronger

LLLJ

1 .0

3.0

fibers,

from

of a B and C.

A than B is. The

the facets are, the

is the inhibiting

the lower

effect

is the inhibitory

K and

threshold

O.

mm

lFrom Ra[Nff and Har[line

(1959}.}

B

o.s

D

-,

C is farther

closer together

()@

0--

effect

A upon two other

C

()/"a

o 0

Fiber

5 A (inhibiting

0 10

15

fiber)

20

frequency

25

(impulses

per sec)

ly, that the inhibitory thresholds, there

is some

facets

that

time, cal

causes

if

However,

variation these

a large

as they almost variations

values

of the interconnections

to differ

group

of receptors

always

are under

are effectively

made by considering that simplify

and "ba) would be equal. In fact,

(f)ah

in the nature

normal

KaB = KBg

-

So far, we have seen that, by an amount

and that the strength property

ofthe

system,

all ofthe

features

of great

importance

many

sion, can be explained. hibitory

influences

To determine corded

from

eye, each facet

inhibits

frequency

only

one

curvesin

property

its

of firing,

facets decreases

Given

of the Limulus

combinations.

illumination

of the chart

(6)

as the

more

simple

Fig. 11.15,

to the understanding

pose line

Fa = egg.

between

The missing

this property

it will

when

complicated

the three facets arein

stimulated,

(5)

and

of human

vi-

in which

in-

is the way

add together.

in various

the

Fb:egbi

increases.

case in which that

is

Therefore, we can

"ba-

to its own

of the interaction the facets

error

when

in the Limulus

proportional

between

=

these statisti-

no serious

one set of subscripts:

bah)

distance

and

of facets.

at the same

conditions,

out,

and "ab

raeaxab(rbab) Fb = eb - "'ab('a

pair

are all operating

averaged

Eqs. (1) and (3) by eliminating

neighbors

for any given

between

fire 100

Consider aline

in Fig. 11.22.

A is also

are resimple

in Fig. 11.22.

so that when

per second,

When

facets

the relatively

as shown

on B is adjusted impulses

eye, three

as shown

Sup-

it alone

is

on the first

illuminated

arbitrary level, it will inhibit B. In this example, assume that

at some KaB =

0.1

298

B

A

Interaction

C

Fig. 11.22 An example

add. When

rates

Firing A

Stimulus

0

B alone

amounts

B

C

100

0

A and

B

80

92

0

C and

B

0

88

60

A and

B and

80

80

60

C

by which

amount

be inhibited

it would

by which

B

the sum of the

is simply

is inhibited

facets

facets are illumi-

all three

the total

nated,

of the fact that of different

effects

the inhibitory

o

o

o

System

in the Visual

Spatial

alone.

by A and by C each acting

and that 0ab = 0. Then, if A is illuminated strongly will

per

second, Now

11.22).

and

then C will

per second,

B will

second, (line

4,

facet

that

is, simply

Fig.

'1'l.22).

the sum of the

of 20 effects

inhibitory

per

of A and C

exerted

inhibition

of all of the separate

the sum

impulses on

inhibitory

any

in-

on the facet.

fluences

Fa a ea -

Fb "

i'f

Fli5(9'iBaridFc':OH(Hr Kab(Fa

if

Fa -> (9ab

if

-

-

Kac(Fa -

Fa

-> "'ac

(The equations

that hold when

tory thresholds

will

ber ofinteracting

t9ob)- Kac(Fc -

Kab(Fb-

e5-

Fc " ec

of firing

of three

units are":

stimulated

simultaneously

the frequencies

describe

that

Thus the equations

i'h unit

3 of Fig,

and the intensities

inhibition

the total

In general,

simply

is always

a total

undergo

B will

(line

so that they fire 80 and 60 impulses,

of lights on A and C are adjusted respectively,

inhibit

are illuminated

facets

to

enough

B by 12impulses

per second

88 impulses

fire

all three

when

we assume

strongly

that "'cb = 0.2 and '9cb = 0, and C is illuminated fire, say, 60 impulses

in Fig,

2 of the chart

and B and C areilli,iminated.lf

Then A is darkened

11.22).

(line

per second

by 8 impulses

be inhibited

is, B

That

per second.

to 92 impulses

drop

B will

per second,

pulses

to fire 80 im-

enough

be omitted

"'ab)

Kbc(Fc -

eac)

Obc)

and Fc -> 05c, "ac) - Kbc(Fb - 6'bc) and F1,, -> "be .

frequencies for simplicity.)

of firing

are below

In general,

inhibi-

for an)/ num-

units, the expression for the frequency of firin3 ofthe

is:

oAgainassumingthatKah =

Klla,

etc.

299

The Physiology

of Spatial

Interaction

J =

Fi" ei That

is, the frequency

of any

sum of all inhibitory Now

let

us examine

typical

tions:

(1) the inhibitory

and

the

conditions.

K,,a.)

equals

we will

coefficients

in which

with

threshold;

that

approximation

the equations

use two

between

F >

minus

for two

units

the

-

F5 = eb

-

K K

for any number

series

are always

interactions

simplifying

(2) we

of firing we

reduce

Fa = ea

Fi o ei

under

approxima-

will only

are high

will

(e.g.,

The figures

in the

therefore

make

=

(8)

Fb, Fa.

(9) is:

It

KijFj

j=0

of conditions

(10)

'

described

strongly

in Fig. 11.23.

enough

that,

when

chart

are those shown

(ea = e5)

calculated

in the figure.

from Since

The

illumi-

and since theirinhibitory

Eq. (8) and the two

00 Frequency of Firing Stimulus

K

A

B

A alone B alone A and B

O.1 O.1 O.1

TOO 0 91

0 100 91

A and B

O.3

77

77

A and B

O.9

52.6

52.6

F, = e, - KFb F, -= eb -

KF,

solving for Fa Fa = ea r

K(eb -

KFa)

ea-KXe5 i K2

a

therefore, when K = O.I

"'

TOO-TO

=i

= "'

Fh = TOO- 0.1 X 91 F,

=

91

ea =

(9), as

units

are

coefficients have

AB

The rates of io facets that c other with fficients. As the :oefficient K ine rates of firing n this example, :ets are illumiintensities such 'xcitation levels,

the

to:

of units

X

-

illuminated

calculation

equally stimulated

con-

compared

nated alone, each would fire 100 impulses per second. That is, 100 and e5 =100. in the sample

the

0.

=

equation

examine

level

any pair of receptors

0, and

j

facets

of these

the frequencies

is, where

that 0

The general

two

the excitation

are equal (as discussed above), and

examples

Now

a

consequences

First,

sider

Then

unit

(7)

eii)

Kii (j-

j=0

influences.

some

KaB

11

X

e, = eli = 100

in the

Interaction

Spatial

300

Visual

System

to be equal (Ka5 = Kha), it is obvious that their outputs must also be equal. Note from the chartin Fig. 11.23 that iftheinhibiincreases, the frequencies of firing decrease, as migll1 tory coefficient been assumed

be expected. the case, illustrated

Now consider

when

Further,

inhibition.

no

be, for example,

greater (as it would

be ifthere

is g,reater than it would coefficient

inhibitory

the

the tyy0

of the inhibitory

is greater than it would

and also the ratio of outputs

were no inhibition, be with

in outputs

the difference

interaction,

Here, as a consequence

excited.

units are not equally

in which

in Fig. 11.24,

is

ifthe two units were closer togeth-

between their firing rates increases. In fact, when th(3 is O.5 or greater, the output of the less strongly coefficient

er), the difference inhibitory

to zero, and the other unit is thus uninhib-

unit is reduced

illuminated

ited. This kind of interaction, then, can be said to be a contrast amplifier, in that the contrast between the two outputs is greater with inhibiWe will

inhibition.

be without

tion than it would

return to this point

later. Suppose that the characteristics known

as a result,

and

investigated,

oughly

of a particular

eye have been thor-

the following

properties

:

between

the relationship

(1)

the intensity

of the stimulating

and the excitation level (e) of each recepto5 coefficients (K) that obtain between (2) the inhibitory receptors, or the value of K as a function of the distance the value of the inhibitory

(3)

cussion.)

AB

00 B

Stimulus

K

A alone

O.1

B alone

O.1

0

O.1

40.5

Fig

Firing

I I 24

facets

inhibitory

The

illuminated.

A and A and

B B

O.3

A and

B

O.4

A and

B->0.5

0

50 100

96 93.4 92.4 TOO

increases

the

rates of two

hibitory

coefficient of the

output

nated strongly hibited.

facet

falls

illuminated

interaction

inhibitory

their

between

difference

Furthermore,

mutually

are unequally

that

outputs.

the

each pair of between

re-

when

the

in-

is O.5 or greater, illumi-

less strongly to zero one

and

threshold

(6)) as a function

of the dis-

(That value is assumed to be zero for this dis-

receptors.

tance between

rates

light

and

ceptors,

Firing

are

the

is thus

more unin-

301

The Physiology

of Spatial

Given

Interaction

those

frequencies

can

parameters,

the

be calculated

for

tion,

and so long as the values

tions

will

ways.

differ

from

For example,

tors were

equations

Fig. 11.23). oflight,

in two

If five

with

any pattern,

800

equations

distribu-

very

unknowns

(as in the

sample

areilluminated may

the output

with

entire

distribution

unknowns,

there

calculation

by solving

Limulus

eye

are

recepby solv-

arbitrary

can be found

since

two

found

any

be calculated

the

interesting

and 11.24, were

When

in 800

the output

in some

in Figs. 11.23

output distribu-

frequencies

distribution

unknowns.

of

intensity

the output

receptors

the output in five

input

distributions

charts

and

distribution

given

of K are not all zero,

input

in the

illuminated,

ing two

tions

the

spatial any

in

pattern five

equa-

is illuminated

by solving

about

800

about

facets

in

the eye. Obviously,

finding

extraordinarily resulting that

distribution

underlie

simple.

not

curves

very

Some

themselves

However,

a knowledge

the

of

plots

Eq. (7)

of the

the

interactions

for the understanding the

sented

Limulus

eye.

That

sible

to predict

ing the tively

the action 11.25. line.

correctly

prediction

of the

If there

were

receptor.

In general,

Now

by the open consider

level, the

facet1

output

in the

levels

in Limulus perception. is pre-

as the

dashed

is virtually without

aetually

pattern,

a general

it would

examination

of the facets

"T'

by the fire

by the open

solv-

a qualita-

labeled

indicated

impos-

of in Fig.

dashed

at some

fre-

above

the

circle would

be those

in Fig. 11.25.

again.

frequency

eye,

predicted

in Fig. 11.5

the facet

represented

excitation

circles

facets

particular

at an intensity

spatial

coefficients,

is redrawn

from

Consider

no inhibition

the excitation

the actual

system.

been

of human

distribution for this

be made

illuminated

quency,

plotted

can

visual

It is being

but

and

in the eye.

distributions,it

the output

equations,

have

distribution

distribution

For mostintensity

necessary correct

intensity

represpatial

of the

inhibitory

between

that

plots

complicated, nature

the

very

in various

relationships

implications

in Fig. 11.25.

the

could

and

suppose

to the

These

of facets

For example,

line

obvious

results

processes

the

are themselves

about

and stimulation-to-excitation of the

but

are moderately

information

is

and

examples.

numbers

by algebra

it one-eyed),

complicated,

are good

large

clear

in the eye. from

thresholds,

have

in Fig. 11.15

The

interaction

quite

equations

does

transformations

of stimulating

provide

exactly

look

many

Limulus

complicated

The curves

distributions.

for that

(although may

these

sent the results

do

the solution

tedious

Becauseinhibition

of that

facet

will

is presentin be lower

than

the eye, the dotted

line (FI < el), that is, it is inhibited by its neighbors (which are allfiring at some

low

level).

(Assume,

for convenience,

that

the pattern

extends

302

Spatial

Fig. l I 25 The rectangles along

the horizontal

represent

the intensity shown

8

/

_

7

/O

on the eye,

the activity

levels of the would

be as inm,

dicated

by the open circles

if there

were

no inhibition;

inhibition,

_

3

----------/O

S-

will

the shape represented

'

7

-

-

-

-

-

-

k

-

-

00 000

Frequency of firingz

()

o

O

-

a a

a

JL

1

JL4

JL

_

S _

f f f f f f f f -

/O /O

0000000000o

lateral

the output

tern of activity

/ 0

4