Hi Hoover,
Many people asked for me to post back the numbers I received.
Could you please send out the message below?
Thanks,
brian wandell
---------------
Hello,
Thank you all for sending me your useful numbers. And your jokes.
And your helpful suggestions about how I might be a better person.
Many of you have asked that I post the responses back to the net.
Here they are. Geoff Boynton and I edited them only slightly by
removing mail headers, carriage returns and an occasional word here or
there. The entries are more or less in the order I received them.
(Sorry if we screwed up your message.)
We are in the process of checking some of these numbers ourselves, and
we make no promises. As one of you wrote in a fair criticism of my
original submission:
As a suggestion for your endevour (sic): it would probably be most helpful if
there were more specific identification of the application of such
values. For example, you mentioned the number of cones per degree ---
should one assume that the number refers to the fovea? Would it perhaps
be a good idea to indicate the limits (e.g., +/- X deg.)? Similarly, you
mention that the human "lens" provides about 60 diopters of optical
power. Actually, the cornea provides about 40 diopters, while the lens
itself provides a variable amount (from 20-32 D), assuming that I am
remembering correctly. And, of course, again, one should specify that
this would only be correct for a young eye.
It will take me longer to add my own numbers and to edit the list into
a single, brief summary page. When I have finished it will appear in
two places. First, I will post it as part of our world-wide web home
page at Stanford (http://white.stanford.edu). Second, I hope to be
able to make the list clear and precise enough so that it can be
placed in the endpapers of a textbook I am writing that is nearing
completion, entitled Foundations of Vision (Sinauer, hopefully this
Spring).
Thank you all for your help and good humor.
Brian Wandell
-------
David Burr
One obvious number is that the slope of the psychometric function for
almost anything (on log co-ords) is 3. (Weibull function) or a sigma
of about 4 dBs for a cummulative Gaussian. I guess Pelli showed this
for contrast, but it seems to work for orientation, signal-to-noise
measures, vernier or whatever, provided you taker logs, although I
don't know if it's been formally documented.
--------
Charles H. Anderson
Not sure you remember me, but here are two factors that play a major
role in my thinking about human visual performance. The first deals
with how visual acuity changes with eccentricity, the second with the
spatial extent of the window of visual attention.
The resolution, dE, at the retinal ganglion cell level, primarily
Parvo, changes with eccentricity according to the equation, with all
units in degrees.
dE ~ a(E+E0) ~ 0.01(E+1.3)
These numbers are for the macaque monkey. My guess for human values is
that a~0.006-0.008, and E0 is somewhere between 1.0 and 1.5 for both
monkey and humans. Visual acuity drops by a factor of 2 at and
eccentricity of E0~1.0 degrees. The linear fall off in resolution
reflects the underlying scale invariance of the system. The
anisotropy with angle around the fovea is small except along the
horizontal meridian toward the blind spot, where the resolution could
be a factor of 2 smaller in size, i.e. higher acuity.
As I recall this is quite good out to 40 to 50 degrees.
One has to be careful not to confuse this equation with grating
threshold sensitivity since the Magno system, more specifically the
non-linear subpopulation of the Magno system, can respond to higher
spatial frequencies, especially in the periphery. This response
however is only to the power, all phase information is lost. I have
estimated that information carried in the optic nerve as "dynamic
texture", i.e. the power of high temporal-spatial frequencies, exceeds
that of color. This information is used in manner similar as color is
for both searching for targets as well as aiding in recognition. It
also bypasses the cognitive system altogether and is used to initiate
protective reflexes against in coming objects. Another interesting
numberical factor is the sampling spacing of the Magno system is about
a factor of 3 larger than that of the Parvo system at all
eccentrities. There is some data, which Van Essen believes, that
suggests this rises to about 5 in the center of the fovea.
Reference:
Van Essen, D.C. and Anderson, C.H., ``Information processing
strategies and pathways in the primate retina and visual cortex'', in
Introduction to Neural and Electronic Networks , eds. S.F. Zornetzer,
J.L. Davis, and C. Lau, Academic Press, Orlando, Florida, 1990.
The second factor is that the relative spatial extent of the window of
visual attention spans a diameter of about 30 nodes, where the
absolute spatial size of the nodes depends on the scale at which
covert attention is set. I first settled on this factor using the
observation that grating sensitivity increases with the number of
cycles displayed up to about 10-15 cycles. To first order this is
independent of spatial frequency. Using the Nyquist limit, this means
the number of samples involved in the analysis is about 20-30. This is
much smaller than the number of cycles you can actually perceive. The
equation above would suggest that the number of resolvable points
would be = 2*E/dE ~ 200!
Since then I have found many examples that show there is something
special about a spatial extent of 30 nodes. George Sperling has shown
that sign language can be perceived with better than 90% accuracy
using a display 28 by 20 pixels in size. Note that this holds
irrespective of the distance between the viewer and the screen. We
have summarized some of the supporting experiments in
Van Essen, D.C., Olshausen, B., Anderson, C.H. and Gallant, J.L.,
``Pattern recognition, attention, and information bottlenecks in the
primate visual system.'' In: Proc. SPIE Conf. on Visual Information
Processing: From Neurons to Chips, vol. 1473, 17-28, 1991.
The machine vision project I initiated at the David Sarnoff Labs back
in 1983 was inspired by these observations. The neurobiological
circuitry for processing visual information using a window of
attention that can be translated and zoomed in scale have been
reported in.
Olshausen, B., Anderson, C. and Van Essen D., ``A neurobiological
model of visual attention and invariant pattern recognition based on
dynamic routing of information''}, J. Neuroscience, {\bf
13},pp. 4700-4719, 1993.
A second more detailed paper has been accepted for publication in the
Journal of Computational Neuroscience.
"A Multiscale Dynamic Routing Circuit for Forming Size- and
Position-Invariant Object Representations" Bruno A. Olshausen, Charles
H. Anderson, and David C. Van Essen
I believe there will also be a paper appearing in Science shortly by
Ed Conner, Van Essen, and Gallant on experiments showing cells in area
V4 encode information in a local coordinate frame that moves with
covert attention.
---------
Irving Biederman
A number that I have found useful--and an important constraint
in trying to understand models of visual recognition--is 100 msec. It
is the exposure duration, followed by a mask, required to recognize an
object or scene. This value is not noticeablly increased (if at all)
if RSVP presentations are employed rather than single trial
presentations. Also, in RSVP a negative detection task ("Press the
key if you see a picture that is NOT a mode of transportation") is not
much more difficult than positively specified basic level classes
(e.g., "Hit the key if you see a chair").
While we are in the temporal domain, another result that I find useful
is that cells in the anterior reaches of IT show tuned responding
e.g., if a face cell to a picture of a face) in under 100 msec from
the presentation of the picture. Though these cells will continue to
fire for about 400 msec, much of their information (as estimated from
a population code of face cells) is in the first 50 msec.
As for a non-temporal constant: Only two or three simple parts (in
their appropriate relation) rather than the whole object are almost
always sufficient for basic level
--------
Davida Teller
Brian -- I don't know if this qualifies, but here is my favorite "Rule
of Thumb": your thumbnail at arm's length is a bout a degree of visual
angle! Also, the sun and the moon each subtend about 1/2 degree. In
another area, by behavioral testing, an infant's acuity in
cycles/degree is roughly numerically equal to its age in months (5
months, 5 c/d, etc). dt
---------
Brian Brown
Undergraduates (and postgraduates) often have trouble estimating
angular subtenses.... the 'Rule of thumb'.. is that the thumbnail at
arms length covers about 1.25 degrees (or at least mine does), and can
be used then to estimate angular sizes and distances in the real world
for any object that can be aligned with the thumb. And of course 1cm
at 57 cm is 1 degree.
Corneal radius: about 7.8 mm
Corneal power: about 42D (as you see, leaving only 18D for the lens and effectivity of the corneal power and lens power)
Corneal diameter: 12 mm
Axial length: about 25 mm
Change in refractive power: about 3D/mm change in axial length
Time taken for a saccadic eye movement in ms: 20 + twice the amplitude in degrees,
so that a 10 deg saccade takes about 40 ms.
Brian Brown
References:
There are a number of them scattered from 1901 to the 70's that I have
looked at... the best is probably Robinson's classic paper Robinson
DA. The mechanics of human saccadic eye movement. J Physiol 180,
569-590, 1964. There is a little Handbook of Ophthalmic Optics,
published by the Carl Zeiss Co 7082 Oberkochen West Germany which I
got free through my optometry connections which has a whole range of
useful terminology, anatomy, optical constants, stuff about spectacle
lenses, photometry, luminances, pupil sizes etc, etc. The version I
have was revised by Dr Helmut Goersch, and it's dated 1983, and it's a
very good source for this kind of stuff. If Stanford has a connection
to Zeiss (I guess you guys buy microscopes and other imaging systems),
it would be worth asking about. A very handy reference for this kind
of stuff.
--------
Jeffrey B. Mulligan
candelas per m^2 x area of pupil in mm^2 = photopic trolands
approximate relative luminous efficiencies of typical rgb monitor:
R:G:B = 3:6:1
----
ken britten
10^6 fibers/optic nerve.
30 cortical areas for vision
approx 1 degree spatial scale for "short-range" motion, centrally. (Braddick)
V1 RF size = .1 * eccentricity
MT RF size = .8 * eccentricity (Maunsell & Van Essen)
-----
Peter A Howarth
2 Diopters ....... the approximate amount of longitudinal chromatic
aberration of the human eye over the visible spectrum The reference I
like is Howarth and Bradley, Vision Research 26, 361-366, 1986 but
probably a better one is Wald and Griffin 1947, JOSA, 37, 321-336
----
Mike Shadlen
120,000 neurons per mm^3 in monkey striate cortex or 200,000 under 1
mm^2 of cortical surface. (O'Kusky and Colonnier, J Comp Neurol 1982,
210:278) (see also, Peters' chapter in Cerebral cortex, Vol 6, Joes
and Peters eds. 1987, New York, Plenum)
This one's sort of obscure, but I think about it a lot: 150 neurons in
a microcolumn of cortex defined by a cylinder the diameter of a layer
5 pyramidal cell's dendritic tree. The real numbers are 143 for
monkey and 203 for cat. (Peters and Yilmaz, Cerebral Cortex 1993,
3:49-68) (Peters and Sethares, J Comp Neurol 1991, 306:1-23)
--------
jeremy wolfe
My favorite number these days is 50 msec/item as an estimate of the
rate at which serial attention moves from item to item in visual
search. There are various theoretical complications surrounding this
but it does useful work for me.
--------
Dan kersten
I don't know if this really satisfies the "usefulness" criteria as
well as #cones/deg. You may be familiar with Cherniak's article below
that was stimulated by the discrepancies he noted in the literature
citations regarding how big the human cortex is (area estimates
differed by a factor of 10, I believe...again this discrepancy
probably has more to do with "who really cares", than any inherent
difficult in making the estimates more precise.)
If you plan on publishing any of these, they should probably be
double-checked. I just pulled them off of an old spreadsheet I filled
out when I first read Cherniak's article.
If one assumes 40% of the connections carry visual information (a
visual scientist estimate, linguists probably put it closer to 1%),
one can calculate that there are 1,990 miles of visual connections--a
number neither very useful or very believable--but may be fun to
quote. Cherniak, J. of Cog. Neurosc., 1990, vol 2., pp 58-68
Area of cortex 160000 mm^2
Thickness of cortex 2 mm
Volume of cortex = 320000 mm^3 0.32 liters
Cortex synapse density 4000 synapse/neuron
Cortex connectivity 200000000 synapses/mm^3
connectivity/neuron 5 mm
connection length/mm^3 25000 mm
neuron density in cortex 50000 neurons/mm^3
Total brain volume 1.4 liters
Total neurons in cortex 1.60E+10
--------
Anthony Adams
Incidently 60D is about the power of the human EYE- not the human lens
(which is only about 9-11D IN the eye.
Optic nerve head is 5x7degrees angle (Vertical=7)
20/200 letter ('the big E") is just under one degree angular subtense (50 min exactly)
---------
William Levick
B = dE (approximate, for relatively small E)
where: B (radians)is the angular diameter of out-of-focus blur circle
d (meters) is the diameter of the entrance pupil
E (diopters) is the out-of focus error of the eye.
It is probably well known but I was not aware of a citation when I
presented it in: Levick, W.R. (1972). Receptive fields of retinal
ganglion cells. Pp. 531-566 in: Handbook of Sensory Physiology, Vol
VII/2. Physiology of Photoreceptor Organs, ed. by M.G.F. Fuortes.
Springer Verlag: Berlin. A simplified form, together with other data
is given on pp. 538-539.
--------
Robert P. O'Shea
O'Shea, R. P. (1991). Thumb's rule tested: Visual angle of thumb's
width is about 2 deg. Perception, 20, 415-418.
----------
Stan Schein
A number that is related to 120 cones/deg of visual angle is foveal
retinal magnification, which is about 290 um/deg in human and 210
um/deg in macaque monkey. (I specify foveal, because the distance
from the posterior nodal point to the retina declines with
eccentricity, so retinal magnification does proportionately.
-----
Ben Backus
The stereoscopic threshold for a step in depth on a surface is 3 sec
of arc. The threshold for detecting that points are not coplanar is
30 sec. [Stevenson, S. B., Cormack, L. K., & Schor,
C. M. (1989). Hyperacuity, superresolution and gap resolution in human
stereopsis. Vision Res, 29(11), 1597-605.]
The eyes are 6 cm apart
Best contrast sensitivity is at 3
cycles/deg. [Van Nes, F.L., & Bouman, M.A. (1967). Spatial modulation
tranfer in the human eye. Journal of the Optical Society of America,
57(3), 401-406.]
Max spatial resolution is 60 cycles/deg [Campbell & Green, 1965?]
Visible spectrum runs 400-700 nm
Other useful numbers:
A 1 cm wide object at 57 cm distance subtends 1 degree of visual
angle; the width of one's thumb in cm is its angular subtense in
degrees at arm's length.
Luminance in cd/m^2 of starlight is 10^-3, moonlight is 10^-1,
indoor lighting is 10^2, and sunlight is 10^5. [Hood & Finkelstein,
Ch. 5 in some book from which I have an unlabeled reprint. Maybe
it's: Handbook of perception and human performance / editors, Kenneth
R. Boff, Lloyd Kaufman, James P. Thomas. New York : Wiley, c1986.]
Useful numbers I don't remember but hope will be in your collection:
The field of view for both eyes together
The binocular region's field of view
Axial length of eyeball
Rod and cone integration times
Easy way to remember how much light a troland is
Wavelength of peak sensitivities of L, M, and S cones
Fastest simple RT for flash detection; Typical V1 neuron's RT to a flash of light.
Size of a V1 foveal hypercolumn in deg visual angle
Number of different V1 hypercolumns used to tile retinotopic visual space
----------
Thomy Nilsson
Here is a less common "fact". The minimum interval at which two
brief (1 ms), small (30') pulses of light can be discriminated from a
single equal energy pulse is about 15- 20 ms and at photpic luminance
seems not to vary with luminance. (Vision Res '79, ARVO '92).
When it come to solid angles, here is what I've found to be a good
approximation for that elusive unite the steradian: Hold your arm
straight out infront of you; bend the elbow 90 degrees; now rotate the
bent portion as much as possible about the axis of the straight
portion. The resulting area that would be swept by a 180 sweep with a
center at the mid point of the bent forearm equal about 1 steradian.
Surprizingly big. Smaller or larger people's portions of arm lengths
seem to maintain this principle.
------
Lawrence K. Cormack
I constantly find myself using : 360/(2*PI) approx. 57.3
------
J.D. Moreland
The use of age-matched controls is good practice in many clinical
studies but is not appropriate for diabetes since lens absorbance
changes are accelerated. Ideally, lens absorbance should be matched
individually but, where the required facilities for this are not
available, simple formulae may be utilised to define lens-equivalent
age controls.
Thus:
E = A + 2.54T - 3.8 for 20 <= E <= 60
E = 0.30A + 0.76T + 40.9 for 60 < E < 80
where E is the age of a normal lens having the same absorbance
spectrum as that of a diabetic patient of age A and with a diabetes
duration T > 1.5. For T up to 1.5, E = A.
E, A and T are all in years.
See: J D Moreland. "Lens-equivalent age controls for diabetics". Invest Ophthalmol Vis Sci 1993, 34, 281-282. (Letter to the Editor)
--------
Michael Bach
I like the simple equation: at 57cm distance (e.g. to your stimulus)
one degree visual angle covers 1 centimeter.
--------
Al Ahumada
Modal # of eyes per subject: 2
--------
Roger Tootell
A conversion factor that I use alot, and which does not seem to be as
widely known as it should be, is: One diopter refracts light by 0.57
degrees. Useful when calculating the effect of various lenses and
prisms.
Another handy factoid known to most physiologists is that at 57 cm,
one degree is one centimeter wide; at 57 inches one degree is one inch
wide, etc.
--------
Reading
My favorite one involves the enhancement of visual performance gained
by going binocular. It applies to absolute light detection
thresholds, brightness discrimination, critical flicker frequency, and
visual acuity. The gain in sensitivity is always [more or less] equal
to the square root of 2! You can arrive at this result through
sampling theory, probability summation, or areal summation [an
adaptation of Piper's law to binocular vision]. One of the
implications of this approach is that a three eyed individual should
enjoy an enhancement equal to the square root of three! [as suggested
by the late Fergus Campbell}
--------
John S. Werner
Lothar Spillmann
Gullstrand's schematic eye puts the refractive power of the human
cornea at 43.05 dptrs and that of the lens at 20.28 (unaccommodated)
and 30.13 dptrs (fully accommodated), respectively. The result of
accommodation is to change the EQUIVALENT power of the eye as a whole
from 59.60 dptrs to 68.22 dptrs, a difference of 8.62 dptrs. Source:
Davson, H. (Ed.): The Eye, vol. 4, page 105 (1962), Academic Press,
New York-London.
---------
Jay M. Enoch
In studies where the Stiles-Crawford effect is of importance, or in
ocular ray tracing, a simple relationship relating displacement in the
entrance pupil of the eye to change in the angle of incidence at the
retina is as follows:
1.0 mm in the entrance pupil of the eye = 2.5 degrees change in the angle of incidence.
I first encountered this derivation (based on the emmetropized Gullstrand eye) in a monograph produced for the Air Force by Brian O'Brien and Norma Miller (post 2nd World War). I have separately derived it an reported it in many papers (including my book on Vertebrate Photoreceptor Optics). Interestingly, I pursued the issue using the Pommerantzef Schematic Eye derived for wide angle fundus photography. This same relationship holds for the peripheral retina as well for at least 30 degrees eccentricity (i.e., it may vary slightly, but only by a few tenths of a degree per mm displacement).
----------
Patrick Cavanagh
Size of giant squid's eye: 19 feet
Percent of all receptors in body which are on the retinae: 70%
Number of moons which will tile the sky: 100,000
Hyperacuity equivalent to: seeing an eye movement at a distance of one mile
Number of neurons in the brain in 1974: 10 billion
Number of neurons in the brain in 1994: 100 billion
Reason mirrors reverse left-right, not up-down: left-right symmetry of body
Earliest subjective contour: 4000 BC
Number of seizures induced by TMS: 2
Number of seizures induced by research fMRI: 0
Duration of Hess positive rod afterimage: 1 minute
Percent of submitted articles which never get published: 0%
Movie image rate: 24 per second
Movie frame rate: 72 per second (each shown 3 times)
Earliest motion model: Al-Haytham, 1024AD
Earliest pop-out model: Al-Haytham, 1024AD
--------
G.M. Boynton
One quantum is sufficient to activate a rod. (Cornsweet, Hecht et al)
Average saccade size is about 10' of arc. (Ratliff, F., and
Riggs. L.A. (1950) Involuntary motions of the eye during monocular
fixation. J Exptl. Psychol 40 687-701
Pupil size ranges from 3mm under 2.5 log cd/mm^2 to 8mm in darkness
(Wyszeki & Stiles, Color science. New York: Wiley, 1982)
There are 11 basic color names (Boynton, Robert M. Olson, Conrad
X. Vision Research. 1990 Vol 30(9) 1311-1317.)