P3D Stereo Nomenclature (part 3[b] of 3)

[Bruce Springsteen <bsspringsteen@xxxxxxxxx>]

Why I dislike the "Viewing Base = Recording Base" condition, and the First
Deformation of classic ortho-stereoscopy:

1. RECORDING vs VIEWING.  I prefer a definition of orthostereo that
pertains only to viewing.  To place any burden for orthoscopy on the taker
of a picture, other than the necessary stereo recording conditions I have
laid out in Definition I, seems unfair to the viewmaker and inconsistent
with the rest of the classic "deformations", all but one of which are
viewing errors, and that one not really stereo by Definition I.  How is
the viewmaker to know what the interpupillary of some hypothetical
observer will be?  He cannot.  If his IPD is 70mm and he records at that
"ortho" base, are we to accept a theory that says his recording is
suddenly non-ortho if some 60mm fellow looks at his views?  What if he
records at 65mm which matches neither his "reality" nor his customer's? 
Nodding to this absurdity, we usually offer the solace that the normal
"range" of human eyespacings will not yield *perceptible* scale
differences if an "average" recording value is selected (6.5 cm? 6.2
cm?...).  But that's a fuzzy ex post facto practicality, not the stuff of
fundamental principle, and only points up the vagueness of this basic
stereo rule.  I suggest that, once the terms of my Definition I have been
met, any stereogram has been duly "encoded", and the burden of "decoding"
it accurately in terms of ortho is solely the responsibility of the
viewer.  There is no orthostereo recording.

2.  INTENT vs ACCIDENT.  While all of the other non-ortho "deformations"
are inadvertent and undesirable effects (at best we say that they are
often unnoticeable until a certain threshold is reached), the effects of
scaling/base changes are almost always intentional and specifically for
exploitation of the effect.  It seems conceptually inconsistent and unfair
to place a usually deliberate recording choice at the head of a list of
usually accidental distortions.  Hypo- and hyper-stereo deserve better
company.  I can't accept that David Lee's scenic hypers, or Pat
Whitehouse's nature hypos, belong in a category with deformations like
stretch, squash, frustum, and skew that are nearly always a side-effect of
vicissitudes in viewing.

3.  RESIZING vs DISTORTING.  The difference between the uniform scaling
effect of stereobase and the uneven distortions of the other classic
non-ortho circumstances seems qualitatively significant to me, and worthy
of better distinction.  By way of analogy, there is an important
difference between a globe, which projects the earth's landforms in a way
that is free of distortion but at reduced size, and a flat map which
always deforms/distorts the "real" shapes of things.  The globe deserves
to be called a "real" representation, at least when compared to the flat
maps.  (No need to quibble that the earth is really oblate, fellows. ;-) )
 Similarly, the creation of hypers and hypos does not "distort" anything,
it merely scales space in a way that a Gulliver could easily navigate as
he did the "real" earth, once he assumed the proper scale.

4.  OBJECTIVE vs SUBJECTIVE.  The proportions of shapes in space are an
intrinsic quality that they have, regardless of the presence or shape of
an observer.  They are absolute, not defined by any anthropocentric
standards like IPD or shoe size or mood.  Shape has an objective reality
that cares not for you or me.  But scaling of  stereo space, its apparent
size and distance from an observer, is utterly relative and subjective - a
result of perception by a particular individual, not a part of external
"reality" in the sense that volumetric shape is.  Classic "ortho"
definitions appeal to this private notion of "reality", indeed make it the
purpose and meaning of the term.  But it is a fraud!  When Boris Starosta
makes a computer-generated image of a pixie in a cattail-filled pool, he
selects a virtual stereo-base in a size that he feels will present good
parallax and relative size between the virtual photographer and his
subject - but what is that size if he wants to call it "ortho"?  How big
is a pixie?  Five feet tall?  Twenty feet?  Four inches with the cattails
in a correspondingly small world?  Does "ortho-reality" exist in a fantasy
image?  If I make three drawn anaglyphs of a great stellated dodecahedron,
each with a different base in proportion to the object, which drawing is
"ortho?"  Our classic ortho-standard is half geometry and half ego - a
strange brew!   If we make "average" man the measure of all things ortho,
then why do we not include color in the ortho requirements, as most men
have color vision?  (Herbert McKay supported this idea.)  Why do we not
exclude taking lenses with a field of view less than that of the human
eye?   Better to subsume all these subjective things in their own
category, "anthropostereo" or "idiostereo" perhaps.  The recording base
condition is too arbitrary and idiosyncratic to be a basic requirement for
"right-viewing", IMO.  

5.  TOO MANY "BASE" CONDITIONS.  Classic ortho viewing requires that B =
Bv. Since the interpupillary distance of an observer (Bv) is not subject
to change, that throws the burden of this rule on the recording base (B). 
But wait!  It IS possible to change the observer's interpupillary
*relative* to the recorded scene.  When we shift the left and right images
horizontally out of alignment with the viewer's eyes, as in projector
adjustments or in my View Magic prints, we are *effectively* changing Bv! 
Abram K chose to describe this situation with the additional terms C = Cv
for "preservation of convergence angles".  But I add things up this way:

Cv = Cr.  The Viewing Center (axis of vision of each eye) must be in line
with the Recording Center (center of perspective of each image in the
pair, as set when recording).  To move Cv and Cr out of horizontal
alignment in viewing is to try to change the parallax and convergence
angles *after* they have been fixed in the image, and it will not work. 
This is faulty decoding of the stereo scene encoded in the image pair. 
The "key" to ortho decoding lies at one particular point, relative to the
image, and deviation from that point garbles the "message" to a greater or
lesser degree.  Cv = Cr is the requirement for preserving parallax - the
true "base" condition, to replace the one we discarded.  To this I'll add:

Av = Ar.  The effective Angles (angular position relative to each eye's
axis of vision) of all points in each view, and thus of the entire view,
must be the same as would be seen from the station point in recording. 
This includes the traditional statement that the scene must subtend the
same angle at the eye as in recording, but with the additional benefit of
including orientation (up/down, left/right) of the images and, in fact,
can stand alone without Cv = Cr, as that is also implied.  But this
condition preserves perspective and orientation as set at recording.  To
try to view from an effective position that changes Av is to try to change
the perspective of the view after it is set in recording, and that won't
work.

This is the same condition as viewing a single 2D photograph from the
"correct" perspective with one eye.  We are just doing it with two images.
 Note that base expressed as an absolute distance (so many centimeters) is
gone, and we now refer to parallax/convergence preservation in terms of an
alignment.  The actual distance between left and right images is not a
fundamental issue - the left view could be in one room and the right in
another, with mirrors and lenses directing the images to their correct
effective position before the eyes.  The interpupillary distance can also
be ignored in this pure description - one eye could be in one room with
its image and the other eye in the other room (with some creative anatomy
involving long optic nerves on stereo-viewing space aliens, or some such).

Also absent is any reference to focal length of camera or viewer.  Those
terms relate to a specific method of stereoscopy, hand-viewed
transparencies, and so are inappropriate in a general definition of
orthostereo.   Av = Ar will be free to imply different practical
requirements in different forms of stereo - anaglyphic, projected, print -
favoring no one method by speaking in its peculiar terms.   Too often we
express the rules of stereoscopy in terms of secondary, not primary
requirements, related to some specific practical necessity - leaving the
impression that we have defined a primary requirement.   (This is the
opposite concern from worrying that theoretical facts will be assumed
relevant in practice, when often they are not.  McKay's dictum "If you
can't see it, it isn't there" and the P3D motto "Don't worry, shoot
happy!")

That's all.  Submitted with trepidation for your amusement.

Bruce (The Apostate) Springsteen  














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