P3D The double-nail illusion

[abram klooswyk <abram.klooswyk@xxxxxx>]

Gabriel Jacob, p3d 3773, 07 Mar 2000, has sent us three 
stereograms. Because I ran out of virtual mounts, I have put 
them together in one mount: 
              _____________________ _____________________ 
             |                     |                     |
1            |         o           |           o         | 
2            |           o         |         o           |
3            |         o o         |         o o         |
             |_____________________|_____________________|

(Again fixed pitch font required)

Gabriel asks us to figure out why in the third (lower) 
stereogram the balls appear both at the window.
Top view schemes:
----------------------------------
fig A:
                     O

Window plane   ---        ---      

                     O

             __            __
          _/   \__      _/    \_  
         /        \    /        \ 
Eyes    |    L     |  |    R     |
         \        /    \        /   
           \____/        \____/     

------------------------------------
fig B:

Window plane ---    O  O   --- 



             __            __
          _/   \__      _/    \_  
         /        \    /        \ 
Eyes    |    L     |  |    R     |
         \        /    \        /   
           \____/        \____/     

-------------------------------------
The combination of stereogram 1 and 2 should give a percept as 
in fig. A, actually the percept is as in fig. B. This may seem 
a trivial question, but it is related to basic questions of 
binocular depth perception: how does the visual system manage 
to construct distances and surfaces from essentially ambiguous 
information. Since Bela Julesz constructed his first random 
dot stereograms (RDS) the studies and published theories have 
been numerous. I didn't read much of them, but trying a few is 
enough to understand how vast and complicated the field is.
It also goes back to the so-called Wheatstone-Panum limiting
case.

One perplexing demonstration by Julesz is a RDS which portrays 
a transparent 3D surface (like lace) and another surface 
behind it. This all from a seemingly random dot distribution. 
How does the brain know which dots belong together to form a 
surface? One theory says that adjacent dots "attract" each 
other to form a contiguous surface, at the same time 
suppressing other percepts.

An interesting real objects-demonstration does the same as the 
stereograms above, it is the double-nail illusion, first 
published by Jodi D Krol and Wim A van de Grind, Perception 
1980 (9), 651-669. After that paper many variations were tried, 
leading to a Phd thesis by Jodi Krol in 1982 (I was present 
when he defended this thesis at the University of Amsterdam).

The basic demonstration is introduced about as follows: 
Take two identical nails and prick them exactly vertical in a 
lath, about 25 mm (one inch) apart. Hold the lath horizontal 
at eye level and in the midsagittal plane (the symmetry plane 
of the head, aligned with the nose). Successively close the 
left and the right eye and adjust the lath to make the 
apparent (monocular) distances between the nails equal. Then 
fig. A (without window) depicts the situation. It is also 
essential to see the nails at exactly the same height. It 
helps when the feet of the nails is obscured by some object 
to hide the points where they stick in the lath.

Now, looking with both eyes, the nails will appear side by 
side at the same distance from the eyes, as shown in fig. B. 

An even simpler way to see this illusion is to hold a thin 
object, e.g. a match, at a distance of about 1 cm before a 
mirror, again aligning it to get symmetrical views of the 
match and its mirror image. After some forth and back looking 
between real and mirror image again two matches side by side 
are seen.

Abram Klooswyk