On Mon, 14 Sep 1998 09:54:39 +0200, Helmut Dersch wrote:
>Neuman-Ruether wrote

>> >A fisheye image does not create
>> >this effect as long as it is flat (and normal prints as well as slide
>> >projection screens are flat). This is the distortion, which is completely
>> >independent of the viewer's eyes.

>> I think you are saying that the rectangular view is right because
>> rectangularity follows the rules of rectangular perspective - a bit of
>> a circular argument, I suppose...;-) I could as well say that if the
>> subject is viewed from a point in the center of the flat side of a
>> hemisphere and the image is projected onto that hemisphere, which
>> is then flattened for convenience (giving a fisheye image), that that
>> "proves" we see in spherical perspective... While this model would
>> better fit wide-angle views than the rectangular model (which falls
>> apart as the angle of view becomes extreme, and cannot support views
>> approaching 180 degrees, let alone those exceeding it [spherical
>> perspective can, as does our vision...]), it would still not prove
>> that this is a correct model, only that it is equally reasonable
>> within itself (though it does happen to offer fewer difficulties at
>> wide angles of view than the rectangular model...;-).

>Ok, now we're in semantics. I have used the word "correct" to
>mean a flat image, which creates an indistinguishable view of the
>real world (for _any_ viewer). This definition clearly applies
>to rectilinear images, but not to fisheye images. It is possible
>to extract corrected views from fisheye images (my software
>"Panorama Tools is doing that). I agree that
>the projection of fisheye lenses is a lot more appropriate
>to capture the information of a wide angle scene. This doesn't mean
>that it is also useful for displaying it.
>
>And I suppose that more people would agree with my definition
>than with a definition coupling correctness with storage-
>convenience.

We appear to be in agreement on everything above, except, maybe
the conclusion about display... (see more below).

>> No, you are right, but the little rectangles we are used to looking
>> at also do not look natural, especially when the view shown in the
>> image exceeds maybe 80-90 degrees... BTW, I think the argument that
>> is successful in all of this (rather conclusive, actually, that we
>> see straight lines off axis as curved [though not necessarily in
>> strict spherical perspective...;-]) is the fact that we can actually
>> see that straight lines off axis of our center of vision are
>> curved...! ;-) One easy example is available at a seashore. Look
>> sharply up, while paying attention to the bottom area of your field
>> of vision (while facing the water horizon), and you can clearly see
>> that the horizon line curves strongly...
>> (Sometimes it takes a lot to point out the obvious...;-)

>You are mixing up "seeing straight lines" and "seeing rectangles as
>rectangles" with the rectilinear perspective Suppose you have a
>150 degree-view rectilinear image (print). View this from
>the correct distance, and it creates the same illusion in your
>brain as the real 3D-world does, _including_ curved instead of straight
>lines, and _including_ those deformed off-axis rectangles. A 150-degree
>fisheye image does not look natural, and any viewer (human or non-human)
>can easily distinguish it from the real-world view (unless you
>bend the print into some complicated sphere-like, but not identical, shape,
>and stick your head into it).

Again, we agree on the technicalities, but not on the conclusion...
To restate: a flat rectangular-perspective image can be "seen-through"
to view the original subject and there will be complete perspective
agreement between the subject and the object (though the eye-system
will be applying its own additional curvature to both the subject
and its representation...); a hemispherical image properly viewed will
do the same thing; a flattened hemispherical image (fisheye photo), or
a "dished" rectangular image, for that matter, will not "correctly"
(in that "reality-recovery" is directly possible...) render the
subject in the image. BUT, as extremely wide angles of coverage are
approached (and certainly as one reaches or exceeds 180 degrees), the
rectangular image type suffers serious technical problems, and also
aesthetically appears to most people to be FAR from an accurate
representation of most subjects. Here, I think, the curvature of the
fisheye view (though it cannot easily be used to recover "reality"
when viewed on a flat plane - though it works fine projected into a
hemisphere), better represents very wide angle views to most people
(since spherical perspective better approximates the familiar [if
unrecognized...] characteristics of the eye-view perspective - which,
oddly enough, most people incorrectly assume to approximate
rectangular perspective). Given two photographs of people and other
rounded objects (many near the edge of coverage) of a very wide area
of coverage (say, about 120 degrees horizontal...) taken with a
rectangular-perspective lens, and another taken with a
spherical-perspective lens (both taken from the same "normal"
reasonably distant viewpoint), I think most people would find the
fisheye rendition of the subject "more natural looking". Given the
same conditions, but substituting buildings as subject matter, and the
choice could go either way, depending on preference for the lesser of
the two ills...;-) (BTW, one of my favorite WA lenses for people in
urban environments is a 16mm full-frame fisheye mounted on a 1.4X
teleconverter. It is "kind" to both people and buildings... [it
"squashes" people less, shows less "front-to-back" perspective
stretching, and introduces less building "tilt-convergence" than a
rectangular-type lens of similar width of coverage.) I think an ideal
super wide angle lens would be one of about 150 degrees coverage, and
which would have strong and smooth barrel distortion roughly halfway
between none and that of the fisheye - this, I think, would produce
images (for a super-wide lens...) that would look the best and seem
the most reasonable and familiar in its image characteristics (and it
would perhaps most nearly approximate the perspective characteristics
of our own vision...).

>Btw, this is not to bash fisheye-lenses I am doing 90% of my
>photographing with them, and they are the ideal tools to capture
>the information of wide-angle scenes, but, as I said, not to
>display them.

We should be arguing each other's preference, since I enjoy the weird
characteristics of super-wide rectangular lenses - see this, from my
web page:
http://www.fcinet.com/ruether/web_photos/phun_fotoz/people/ba17.jpg
and you appear to enjoy the weird characteristics of fisheyes - see
this, from your web page:
http://www.fh-furtwangen.de/~dersch/Marburg/Schlcirc.JPG
(though I know that your images are intended as the means to a further
end...;-). This has been an interesting discussion - thanks!