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

[Bruce Springsteen <bsspringsteen@xxxxxxxxx>]

Bruce's Heterodoxy Finally Exposed:

Definition I:  I define "stereoscopic recording" as making two perspective
projections (arbitrarily called "left" and "right") of a real or imagined
scene, photographed, drawn or otherwise produced, taken from two station
points separated by any distance with their optical axes parallel and
directed at the same point in infinity, and perpendicular to the line
which includes both station points, the visual cones of both projections
taking in the same angle of view.

Definition II:  I define "stereoscopic viewing" as two projections "left"
and "right" made as in Definition I, presented directly or indirectly to
the corresponding eyes of an observer, such that a "cyclopean image" is
formed in the mind, wherein disparities between the two images are
interpreted as a single three dimensional scene viewed binocularly.

Definition III:  I define "orthostereoscopic viewing" as two projections,
viewed according to Definition II, such that all pairs of points in each
image shall subtend the same angle at the eye, in the same orientation on
the retina as would have been received at the recording station points. 
This means that orthostereo viewing will reproduce the *proportions* of
the recorded space and all objects in it accurately, but not necessarily
at the size and distance that the observer would perceive them in viewing
the actual scene.  [This is, in effect, the traditional definition of
orthosteroscopy, but with the "recording base condition" removed.]

Definition IV:  I define a "deformation" in stereoscopic viewing as an
alteration in the relative proportions of the viewed space and the objects
in it, the three coordinate dimensions no longer having the same geometric
relationship to one another as in the recorded space.  A "distortion" is
the same thing.  A scene that exhibits deformations may meet the
requirements of Definition II (for stereo viewing) but will not satisfy
Definition III (for ortho-stereo viewing), and any viewing that violates
Definition III requirements will have deformations.

Definition V:  I define a "disturbance" as the effects seen when
attempting to stereoscopically view images not made in accordance with
Definition I, or when viewing correctly-made images in a way that causes
deformations or retinal rivalries that severely impair - or prevent - the
formation of a cyclopean image.

Why am I so uncomfortable with the classic definition of "orthostereoscopy
(Recording Base = Viewing Base while Recording Focal Length = Viewing
Focal Length)?  I've never felt it quite "hangs together" and I've been
trying to decide exactly why for some time.

The obvious omission in my Definition III above is the ortho-requirement
that the "taking" or "recording" base be (nearly) the same as that of a
hypothetical human's interpupillary distance - which is meant to reproduce
an entire scene in the same apparent size and distance, relative to this
"average" observer, as it would have in "reality".  Ferwerda, after
Berssenbrugge, calls the failure to meet this condition a "deformation"
(distortion) of the stereo image, resulting in either "lilliputism" or
"gigantism".  It is number one on the deformation list.  George Themelis
described this ortho requirement as B = Bv.  For comparison, the other
traditional non-ortho deformations are, in order:

2. Distance (or loosely "focal length") deformation.  A failure in
VIEWING. Each stereo image in the pair must be viewed from an *effective*
distance such that it subtends the same angle at the eye as the actual
scene would. The practical meaning of this *in viewing transparencies,
which are not enlarged* is that the focal length of the viewer must match
the focal length of the taking lens.  (I would call this focal length
matching a "secondary" requirement of ortho, related to a particular
method of recording and viewing, and not applicable in all forms of
stereo.) This is George's F = Fv.  The deformation appears as "stretch' or
"squash/squeeze" in the z-dimension.

3. Convergence, or frustum deformation.  A failure in VIEWING.  This was
the subject of Abram Klooswyk's recent multi-part posting, in which he
coined the description C = Cv.  It requires that the effective infinity
separation (distance between homologous infinity points) in viewing not be
greater or less than the interpupillary distance of the observer, thereby
preserving the convergence angles (C) seen in "reality".  Failure to meet
this condition distorts objects in the stereo image in all three
dimensions.

4. Oblique, or parallelogram deformation.  A failure in VIEWING.  This is
the result of viewing a stereo pair from one side or the other of the
"ortho" position, off the central axis of the scene.  This situation is
encountered most often in projection, or in viewing printed anaglyphs. 
Objects in front of (nearer than) the image plane seem to follow the
observer left or right, while those behind the plane skew in the opposite
direction.  This also occurs vertically if the center of the scene is
shifted above or below the plane of eye-level in viewing, though the
deformations will not be *exactly* as in the horizontal case.

5. Pseudoscopic deformation.  Another VIEWING failure.  It is the
presentation of the left image to the right eye, right image to left eye,
creating a "quasi-inversion" of depth in the stereo scene.  This is a
violation of my Definition II, the conditions of stereo viewing, whether
ortho or not.

6. Bulge deformation.  A failure of RECORDING.  This is a consequence of
"toeing-in" the axes of the lenses, which is a violation of the conditions
for making ANY stereo pair, by my Definition II.  Consequently I am not
convinced this should be included as a deformation of ortho-space, but
rather seen as non-stereo recording, akin to taking the left and right
views tilted in different vertical directions, or with diverging axes. 

Something about that first deformation seems odd and out of place with the
rest.  Let me try to explain...

(continued)



































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