P3D Stereo Nomenclature (part 2 of 3)

[Bruce Springsteen <bsspringsteen@xxxxxxxxx>]

In presenting us with an excellent description of the third deformation,
the frustum or convergence deformation, Abram Klooswyk added some
important insights to George Themelis' description of classic
orthostereoscopy.  We are always reminded that ortho requires the "taking"
base to match the "viewing" base, and "taking" perspective (or focal
length at a given subject distance) to match the effective "viewing"
perspective (usually by matching focal length of viewer to that of the
camera lenses).

This clearly establishes ortho as a condition of *viewing* a stereo pair
in a way that preserves the scene as it would appear *in person*, on the
occasion of *taking*.  Traditionally, this includes the expectation that
the taking base will be near the average human interpupillary, since
changing the distance (Bv) between your eyes while viewing is, as George
observed, not so easy to do!  He used the following notation to describe
this pair of classic requirements:
 
B = Bv  (taking base = viewing base)
F = Fv  (taking focal length = viewing focal length)

He also added a "taking" variable I, the distance from the near subject,
which influences both B's and F's.

Here is where Abram noticed a lack of symmetry between 3 taking factors
and 2 viewing factors.  Something seemed not quite right in this, and he
reminded us that those two conditions so often repeated in the literature
are merely necessary, not sufficient, for orthostereo.  If left and right
images are presented in viewing with their infinity separation shifted
inward or outward from direct alignment with the eyes, then all
separations between homologous points are increased by a fixed amount, and
that changes all convergence angles and brings about the deformation known
as "frustum". This may be described as either a "stretch" in depth with
enlargement of more remote parts of the scene, or a "squash" in depth with
enlargement of nearer parts, depending on whether you have increased or
decreased the left and right image separation.

In viewing systems with a stereo "window" at a fixed distance, this
deformation may often occur, when objects photographed are nearer than the
system will allow.  Beginners are told to move the chips away from each
other, to "push" the entire scene back behind the mask window where it
belongs.  In mounting prints, "mounting for the window" will usually cause
separations that are greater or less than "ortho", regardless of "taking"
base and focal lengths that have been matched - I myself have often done
this.  In every such instance, frustum deformation is the result.

[In my ongoing endorsements of the View Magic over/under stereoscope as a
learning tool, I should note that I used mine, with some prints of a large
open cube I had seen on campus, to watch the frustum deformations occur as
I moved the right view from side to side.  Then I placed two identical
pairs but with different separations together and compared the
differences. This was after drawing all the angles on scratch paper to see
the geometry involved.  Abram's pearls constantly send me back to the
drawing board!]

So what does all this have to do with (English) stereo nomenclature, the
specialized language we use here to explain stereo concepts to each other?
Only that this seems to be an example of the confusion we can get into
when our words are sometimes precise and sometimes general.  I had gotten
used to narrowly defining stereo "stretch" as distortion in the
z-dimension only, without expansion in x and y, thus unique to focal
length mismatches. This was how I had construed Ferwerda's usage, it
appears wrongly so.  Abram and George consider stretch to refer to any
elongation in z-space, in the company of x and y distortions or not - as
long as it's not a uniform scale enlargement in hypostereo.  That's a
slightly more liberal application of the term.  There may be
stereoscopists who feel no qualms about calling any increase in a
dimension, proportional or not with others, a "stretch".  I have no
logical basis to argue against such a view, only whatever precedent and
sense of order I might appeal to.

Still, terms like convergence, parallax, distortion, deformation,
deviation, stereopticon, viewable, have all at one time or another been
identified here as words with different senses to different users.  To
make matters more treacherous, people like me have the habit of inventing
our own usages when the old ones seem inadequate or inelegant.

As an example, I plan next to propose my own slight re-interpretation of
the term "orthostereoscopic".  I don't expect it to be a popular proposal,
but at least it may be stimulating.  It will air out some discomfort with
the orthodox ortho that I have felt for some time.  The variables
discussed by Abram and George made me decide to try.  Next week, part 3.

Bruce (Did I say Avenging Angel?  I meant Diverging Angle!) Springsteen



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