Archive for March, 2007

Opaque Sphere vs. Transparent Sphere

Opaque Sphere Thumbnail
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Click here for an 1800×1800 image of the above thumbnail.

Transparent Sphere Thumbnail
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Click here for an 1800×1800 image of the above thumbnail.

Transparent Sphere 2x Deviation Thumbnail
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Click here for an 1800×1800 image of the above thumbnail.

View the images with red/cyan glasses (red on the left).
This demonstrates the phenomenon of an opaque sphere and a transparent sphere (the top and middle images), with the same deviation, looking “perfectly spherical”.
Both of those spheres have very close to 3% deviation, which is just a bit less than the “optimum” of 3.3% (40 deg FOV), so view these spheres with something close to 35 to 40 deg field of view (did I mention I hate math? ;-) for “optimum viewing” of these images (one or the other won’t matter a huge amount. ;-)
If you create the transparent sphere (the bottom image) with “twice as much deviation” (i.e. close to 6 to 6.6% deviation), assuming that it needs to be “twice as deep”, it will simply demonstrate “excessive deviation”.
6.6% deviation, BTW, is getting very close to “stereoscopic failure” (inability to stereoscopically fuse the imagery), as you can see in this demo.

0% deviation is “totally flat” (no stereoscopic image)
3.3% deviation is “optimum” (exactly in the middle of the range)
6.6% deviation is the “upper limit” (very close to stereoscopic failure)

Deviation is a “constant” factor in stereoscopy.

— I’m getting a few comments coming in about this and some people are reporting that they are not having any problems “looking at” the bottom sphere.
Are people who are *not* having problems fusing the
bottom sphere looking at it with the “proper FOV” of something close
to 38 deg (or so)? Just the sphere, now… don’t include the white
space around it.
If I stand back a couple of feet farther away from my monitor than
that, I have much less of a problem (I know, that seems weird, too, as
that should actually exaggerate the z-axis).
Close to 38 deg (or so), it’s “no cigar” for me… a very confusing,
“difficult to view” image. My wife said the exact same thing as I
did… and I made sure she saw it with “close to” a 38 deg FOV.
I’ve been viewing stereo 3D for years, and when I get up around 7%
deviation with a 40 deg FOV, my eyes literally “hurt” when I try to
look at the image. 10% dev (40 deg FOV) and it’s hopeless for me… I
absolutely cannot do it without severe pain.

Closer To Stereoscopic Truth

First of all, I will repeat myself just a bit (for an introductory
statement):
Our circle of confusion (our eye’s “version” of depth of field)
defines our range of depth that is in clear focus. I can _see_ this
with my own eyes… consistently. (trust me… I am doing many tests
in all lighting conditions and lighting affects are not significant
until you reach the point of not being able to see anything - too dark
or too light, i.e. “blinded”)
This amount of depth that is in clear focus will increase in relative
amounts as the “far point” gets farther away, but the “deviation
amount”, which is defined as the _horizontal_ measurement between the
nearest point and the farthest point in our field of view, will stay
relatively constant (the same). What happens is when the far object
gets farther and farther away, the converging lines of sight, from our
eyes to the far point, lengthens. That point of “start of focus” (the
point in depth where the clear focus _begins_), also then moves
farther away in progressive amounts, and the angle widens, relative to
the face (eyes). It is a good idea to look at the graphic again, now,
before I say anything more, and I probably should make a new graphic
that shows this variable:
http://www.puppetkites.net/stereo3dtutgraphics/optimumdeviationeyes.gif
Next, the place where deviation is measured (see the graphic) moves
farther away from the face (it is the same point of the starting point
of focus), but when you then re-measure it, it is still the same
width!… always. When the far point is at infinity, that point will
be .89m (about 3 feet) away from your face. As the far point gets
closer, that point of “beginning of focus” or the point where
deviation is measured, gets close and closer to the face, the angle
narrows, and the deviation measurement stays exactly the same, with
the exception of ambient lighting, which is only affecting the
measurements by less than 1% or so… not much at all…. so small it
is difficult to measure a difference.
Now, as far as on screen deviation is concerned, this “theory” will
still hold true “on the screen”, but in a different way (same basic
visual results, though). The “best seat” for the image with 3.3%
deviation would be the one that has a 40 deg FOV (per Imre’s
correction). With an image with 3.3% deviation, a “correct volume of
character” would be experienced, as long as there were no “errors” in
the stereoscopic composition (again, there is a long list of possible
errors in addition to “wrong deviation”, e.g. keystoning, barrel
distortion, cardboarding). As you get progressively closer to the
screen, your FOV increases, and you start to see the z-compression
(apparent flattening). At a certain point, it will become “severe” but
the FOV can then also be defined as relatively “severe”. As you get
progressively farther away from the seat that has 40 deg FOV, your FOV
decreases, and you start to see z-exaggeration (apparent stretching).
at a certain point, it will become “severe”, but the FOV can then also
be defined as “severe”.
This scenario creates a “range”, where “optimum” deviation and FOV
are exactly in the middle (half way). As you offset this “range” in
any way, it will push the variables off to one side of the spectrum or
the other, i.e. an image with more than 3.3% deviation would
demonstrate z-compression (flattening) in a larger range and images
with less than 3.3% deviation would demonstrate more z-exaggeration in
a larger range, in progressive amounts, as you get more and more or
less and less.
0% deviation is totally flat (no depth) throughout the entire range.
6% deviation is extremely deep throughout the entire range, and
somewhere around 8% or so, stereoscopic failure occurs (the ability to
fuse or merge the images).
This is the basic idea… there are a long list of variables after
this…

The 3.3% (1/30) and 33.3% (1/3) Stereoscopic Connection

Attn: My recent revision of the theory will have an affect on the numbers in this post!
See:
http://www.puppetkites.net/blog/archives/33

If you look at my “deviation guide” (the piece of paper with “Some Text” written on it and a black vertical bar that is 3.3% of the paper width wide),
http://www.puppetkites.net/blog/archives/31
you will notice that when you move it out to the point where it “just becomes in focus” (per instructions), which defines your stereoscopic depth of field/circle of confusion _and_ 3.3% of your eyes’ stereoscopic field of view (”optimum deviation”) via any one point on that paper, the borders of the paper will then equal 33.3% of your eyes’ stereoscopic field of view. I “knew” what I was seeing, then, and even mentioned it, but just now figured out “why” I was seeing it.
The “correct” eyes’ stereoscopic field of view is 120 deg (not 140). 33.3% of 120 deg is 40 deg. The borders of the paper will (at that point) be 33.3% (1/3) of your eyes’ stereoscopic field of view, i.e. “optimum field of view” for viewing a stereo graphic with 3.3% deviation “on” that piece of paper.
Believe it… or not. :-)

The 3.3% Deviation of the Human Eyes Theory

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Click here for a larger image of on the thumbnail above.
Updated and animated May 16, 2007.

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Click here for a larger image of on the thumbnail above.

Updates, with comments, are here:
http://www.puppetkites.net/blog/archives/42

DOF/COC/Optimum Deviation/Optimum FOV

DOF = Depth of Field
COC = Circle of Confusion
FOV = Field of View
deg = degrees

I overlooked something remarkably simple… (doh! sorry, I missed this)
If you make a stereoscopic deviation “gauge” on a piece of paper, and determine what our natural optimum stereoscopic deviation is (1/30th or 3.3% of 140 deg), which is strictly defined, by nature, via our eyes’ version of DOF (which is COC), as I show you how to do, here, the _edges_ of the paper, then, will also strictly define the viewing FOV:
http://www.puppetkites.net/blog/archives/31
It’s that simple! Mathematicians can tell us precisely what that FOV is, in deg. Obviously, it must be somewhere very near 30 to 36 deg, which is (not coincidentally, I’m quite sure) the recommended FOV for home theaters and last row seats for a movie theater.