[photo-3d] Re: Algorithm Wanted

["Bruce Springsteen" <bsspringsteen@xxxxxxxxx>]

Dr. T, who helps beginners, said to Bruce S., who hinders experts:

> Bruce, sorry... I had assumed that you could digitize
> the pictures and were looking for a numerical algorithm
> or the principle on how to solve the problem via a
> computer.

Don't be sorry!  I love that answer and am framing it in gold. You
tackled the non-practical version of my question, entirely within
the rules.  Remember, I admitted both the pure mathematical
and the practical kinds of answers.  But is there any way to 
implement your general solution if I can't digitize the pictures and
harness the computer?  A nice analog approach to your algorithm
would be clever.
 
> You asked if any three points would do it.  These
> points must be in different depth levels.  If you could
> pick foreground, middle ground and background, that
> would be ideal, but you don't know what these are.
> If the pictures are digitized then you could pick
> a lot of points and run some kind of optimization
> routine.

Wow, sounds kind of difficult!  Yes, this is where the basic problem
has not really been solved.  The star-field version I stated for Ken
is a good example I think - perhaps not as far fetched as it may
seem - imaging having the two halves of a random-dot stereogram
and needing to orient them without any clues besides the
dots themselves. 

> Now, in practical terms this problem has hunted me too.
> Quite a few hyperstereos from Grand Canyon had a small 
> rotation and shift. I was rotating one chip trying to 
> see if this made things better and had hard time figuring 
> it out.  That's because with small rotations the vertical 
> displacements are very small.
> 
> Anyone who has tried to align such slightly misalignment
> pairs will, no doubt, sympathize with me :)

I do, and this is how the problem first occurred to me some months
ago, with a pair of prints that seemed to both have "roll" from my
hand held shifting, and unevenly trimmed prints that apparently
were not run level through the processor.  The methods in my 3D
books and online for checking rotation problems were not getting
me quickly to an answer, and I began to realize how tricky the
problem can be.  At least in that case I had some idea of "up",
and of the depths of various parts of the scene.  Even then, it was
a pain.

I still think there must be a general solution that can be
accomplished with regular common equipment, excluding computers.
I have vague visions of something with a pin or two, and rotating
transparent grids of some sort, but my rotten intuition freezes
at that point.

Anybody else have some ideas - don't let George's summed vectors
scare you off!  We need someone with dirt under their fingernails
to cut the Gordian Knot!

Bruce