Stereogram Tutorial
Júlio M. Otuyama
Introduction
Stereograms are illusions of 3D surfaces. This tutorial shows
how it works, with a simple "do it by yourself" approach. The
random dot stereogram is very easy to understand, although not a
trivial concept. Unlike holograms that requires laser beams,
stereograms can be created, printed and visualized with computers.
But it may be not an easy task to see its 3D surfaces.
Stereo Pairs / Stereograms
Stereo Pairs / stereograms work because the brain can detect
small differences between the images seen by each eye. Stereo pairs
have been studied since a long time - Leonardo da Vinci almost
discovered the concepts of stereo pair visualization. But only
Wheatstone correctly described this concepts. Random dot
stereograms is a very new discover, developed by Bela Julezs,
during 1970's. Random Dot Stereograms give us a deep impact because
there is an invisible hidden surface.
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random dot stereogram
Hidden surface: square
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Visualization
The visualization of a stereogram requires an unusual skill:
each eye must be targeted to distinct places on the image. This is
unusual to our brains. That is the reason some people hardly (or
can not) see stereograms.
There are two ways to visualize stereograms:
- divergent view
- convergent view
The target of each eye (left and right) is shown:
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| regular visualization - no stereogram |
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| divergent visualization of a stereogram |
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| convergent visualization of a stereogram (cross) |
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Once one gets the divergent or convergent visualization, he/she
has a clear view of 3D surfaces.
Helper to visualization:
- divergent:
- Eyes relax (infinite focus)
- Transparent media (stereogram on a plastic film)
- convergent:
- Reference point between the eyes and stereogram (put a pen in
the half way from your eyes to the stereogram)
Random Dot Stereogram
Our brain is able to perceive the environment 3D information.
The main reason for that are small differences between each eye
images. Both images are captured with a small difference (the
distance between our eyes). This results in very small shifts on
each retina projection image, hard to notice. But although small,
those differences give us the 3D sensation.
Creating a Random Dot Stereogram
The easiest way to learn how a stereogram works is to create
one. Next, the recipe to generate a random dot stereogram (adapted
from Bella Julesz article). There is also a second approach, based
on "ASCII Stereogram". With the ASCII Stereogram, it is easier to
understand the disparity shifts. You can see both as stereograms,
if you have skill enough.
| Steps to generate a stereogram: |
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| (a) Create a random dot image |
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ABCDEFGHI
JKLMNOPQR
STUVWXYZ0
123456789
0ZYXWVUTS
RQPONMLKJ
IHGFEDCBA
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| (b) Duplicate the image and put side by side |
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ABCDEFGHI ABCDEFGHI
JKLMNOPQR JKLMNOPQR
STUVWXYZ0 STUVWXYZ0
123456789 123456789
0ZYXWVUTS 0ZYXWVUTS
RQPONMLKJ RQPONMLKJ
IHGFEDCBA IHGFEDCBA
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| (c) Select a piece of one image |
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ABCDEFGHI ABCDEFGHI
JKLMNOPQR JKLMNOPQR
STUVWXYZ0 STUVWXYZ0
123456789 123456789
0ZYXWVUTS 0ZYXWVUTS
RQPONMLKJ RQPONMLKJ
IHGFEDCBA IHGFEDCBA
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| (d) Lateral shift of this piece of image |
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ABCDEFGHI ABCDEFGHI
JKLMNOPQR JKLMNOPQR
STUVWXYZ0 STVWXXYZ0
123456789 124566789
0ZYXWVUTS 0ZXWVVUTS
RQPONMLKJ RQPONMLKJ
IHGFEDCBA IHGFEDCBA
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| The hidden image is the piece shifted |
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ABCDEFGHI ABCDEFGHI
JKLMNOPQR JKLMNOPQR
STUVWXYZ0 STVWXXYZ0
123456789 124566789
0ZYXWVUTS 0ZXWVVUTS
RQPONMLKJ RQPONMLKJ
IHGFEDCBA IHGFEDCBA
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Convergent/Divergent view and disparity
With divergent view, the shifted square appears as
floating (nearer than everything else). With convergent
view the shifted square appears as a hole (farther than
everything else).
Disparity is the concept that explain why we get the 3D perception
of the nearer and the farther distance. This concept can be
explained with "ASCII Stereogram". Let's call disparity as the
number of letters to to go from a letter in the left pair to its
counterpart at the right pair. For instance, from the first letter
"A" of the left pair takes 10 letters of disparity
to reach its counterpart in the right pair:
ABCDEFGHI A
^123456789^
On the (b) step, all the letters have the same disparity (it is
only a flat surface).
The shift on step (d) changes the disparity. For instance, the
letter "V" now takes 9 letters of disparity
to reach its counterpart in the right pair:
VWXYZ0 STV
^12345678^
With divergent view this means that our eyes have to "move a
little" to perceive this as the same letter by both eyes. The
"movement" required is the right eye to move a little toward left,
just like we were seeing things nearer. That is why this letter is
perceived as nearer than the background. As a matter of fact, our
eyes don't move, but the image projected on the retina causes this
effect, and our brain is able to detect this.
Now we can make a relationship of shifts and disparity:
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Left Pair |
Right Pair |
| Increase Disparity |
Shift to Left |
Shift to Right |
| Decrease Disparity |
Shift to Right |
Shift to Left |
And a relationship of disparity and divergent/convergent
view:
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Smaller Disparity
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Larger Disparity
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Divergent View
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Float Near
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Float Far
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Convergent View
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Float Far
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Float Near
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The disparity causes inverse effects with divergent versus
convergent view because of the cross in the convergent view.
Try it (MS Windows 3.x/95/98/me/NT/2000/XP/2003/Vista...)!
This lab can be done on you computer in a few moments. No extra
software is required.
This description is based on MS Windows / IE, but it's easy to
adapt to Apple Mac, Linux, etc.
| Steps to generate a Stereogram: |
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| Save this image on your computer: |
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Open the image with an image edition tool (Paint, Paintbrush,
Photoshop, etc)
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Select a small piece of one image with the selection tool
(usually the dotted square)
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| Shift the selection (lateral shift only) |
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The resulting image is a random dot stereogram made by
you!
Hint: you can select any kind of shape, even letters (yes, your
name!). But the shape must be large enough for our brain to detect
it.
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SIRDS - Single Image Random Dot Stereogram
The Random Dot Stereogram is a scientific proof (see below), but
what made this concept widely know was the illustrations called
SIRDS (books like Magic Eye, CG Stereogram, etc). To create a
SIRDS, you have to put not two, but a repeating pattern of random
dots, and make shifts to get the desired effect. Instead of black
and white random dot patterns, you can use a colored pattern to
fill the repetition. To create complex surfaces there are computer
algorithms that copy the pattern side by side based on grayscale
disparity maps.
Grayscale disparity maps
The easiest way to create stereograms with complex surfaces is
to use grayscale disparity maps. The grayscale disparity map is a
representation of some surface with each gray tone associated to a
distance. For instance, you could create a background black
disparity map, with a floating square near, represented by a white
square. To create a random dot stereogram based on this disparity
map, you have to copy (or copy and shift) the random dot pattern
based on the corresponding coordinate content color in the
disparity map. When the color is black, just copy the pixel to the
other image. If the color is white, copy the pixel to the other
image and shift it. The figure below illustrate this procedure.
This is almost the same random dot stereogram presented
previously.
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Grayscale disparity map (only one cycle)
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The disparity map associates gray tones to distances:
- black - background distance
- gray and white - floating squares at different distances
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Copy the pixel based on the corresponding coordinate content
color of disparity map:
- copy pixel with no shift if the disparity map content is
black
- copy pixel with small shift if the disparity map content is
gray
- copy pixel with large shift if the disparity map content is
white
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Result: Random Dot Stereogram
- black: background
- gray square: small disparity
- white square: large disparity
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Creating a SIRDS
Now we can create a generic SIRDS with a (not so) complex
surface. There are many cycles to compose the SIRDS because one
cycle requires the pattern from the previous cycle. That is the
reason SIRDS requires computer programs to generate. It is a
difficult task to copy the pattern based on the disparity map, and
this copy requires data only available after the computation of
each cycle. Sometimes there are holes with no pattern after cycle
copy, that requires artificial filling with extra patterns.
Sometimes the same pattern is copied many times at very close
pixels, creating an (undesirable) visual clue of the hidden
surface. As a matter of fact, a computer program don't need to
implement the cycles, just copy a non transparent pixel to another
pixel as many times it is required. The cycle is just a consequence
of the procedure.
This procedure shows a black (no shift) and white (shift) copy.
With a general gray scale disparity map, the shift can be small or
big, based on how black or white the gray tone is. Usually the
image is processed with higher resolution than the original, to
achieve a sub pixel shift accuracy.
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Grayscale disparity map
(many cycles)
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Someone could think to move the whole white selection with just
one shift, avoiding the cycles. It wouldn't work because the
disparity of the background and the whole selection is the
same.
There is another approach to generate SIRDS, with an
algorithm based on ray tracing concepts. The result is almost
the same, with no visible differences, but it takes a lot more computer resources.
Yes, I did implement a ray tracing algorithm to create stereograms
- because at that time there was no information of how stereograms
worked, and I had no idea who developed those illustrations (there
was no stereogram books yet; I could only get a copy from an
anonymous copy (of a copy) of a one page stereogram illustration).
Everybody was amazed with that illusion. I was learning C
programming language during my under graduation, so the ray tracing
stereogram program was a good exercise. Later I found information
about Bela Julesz and random dot stereograms.
An interesting illusion
The random dot stereogram is described in "Foundations of
Cyclopean Perception" article of Bela Julesz. This article is not
about entertainment, but a scientific procedure to show how our
brain works. In this article Bela Julesz shows that with the random
dot stereogram:
- Random dot stereogram pair conveys information that is lost
with only one image presentation.
- Each image does not have any clue about 3D information (shape
from shade, contours, etc);
- Our brain is able to extract the 3D information from a random
dot stereogram (you just need to visualize it).
So, this shows that:
- There is 3D information detection from the lateral shifts
(brain stereopsys skill);
- This 3D information can not be detected at retina stage;
- Detection happens somewhere that receives information from both
eyes (binocular stage).
Books
Foundations of Cyclopean Perception - Bela Julesz
There is also the book Eye, Brain and Vision
(EBV) from David Hubel. That is the best introduction to human
vision from a neuro scientist. Although it is a scientific book, it
is very clear and easy to read.
Some Stereograms
Images: Brazilian Flag, 3 Rings, Wine Glass, Pigeons, Birds, Half Sphere, Helicoid, USP Stereogram
Flash animation: Hanabi Stereogram
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