First off - I am absolutely not a hoax believer...
That was apparent in your first post. I'm sorry that it seems you're being asked to account for another's claims. Unfortunately many first-time posters arrive here "just asking questions" as a way to put critics off guard.
Since I am not a photography expert or good at discussions I just thought if I throw the question in this forum I might get some answers that I can bounce back at him on the swedish forum.
Sure, I'm glad my answer helped. In general it's cumbersome to discuss here something that's happening in other forums, but if you find our answers useful then I'm willing to keep helping.
Referring again to http://www.aulis.com/stereoparallax.htm
Step 3 of the proposed process mentions applying transformations in image space, such as perspective distortions, independent x- and y-axis scaling, and rotations. First, some of these would not be projection-preserving, and thus are invalid in rectification. Second, there is no mention made of how the parameters for these transformations are derived. Hence they amount to manual processing and therefore cannot be scientifically reproducible.
The proposed antiprojection, La = Lb b/a
, is linear. Most lenses do not implement a linear projection model, and the Zeiss Biogon explicitly does not. Hence the mathematical framework is simplistic and incorrect.
Fig. 7 purports to show a parallax difference between two Apollo photos that include a distant background. The author believes that because a geometric change is apparent in the blink-comparator, this should be attributed to parallax. In fact the method fails.
- No values are given for any rotations, distortions, or other transformations applied to the photograph(s). The results are therefore irreproducible and scientifically invalid.
- A simple contrast expansion of the "difference" image shows misalignment in the ridge lines consistent with a rotation between raster images roughly coincident with the original line of sight. The author has misapplied his broken method and thus interprets the difference in rotation (and possibly subsequent distortive attempts to correct it) as parallax.
Figs. 10 and 11 are similar. The author applies uncontrolled, arbitrary image-space manipulations that are not projection-preserving, then proceeds to attribute resulting misalignment of the raster to parallax. And again, no method is shown for deterministically deriving the distortion parameters; it is purely subjective and therefore irreproducible.
The author then imagines that the effects he introduces through non projective-preserving manipulations are explicable in affine space by a sort of concave screen. This is pure fantasy: a much simpler explanation exists, that of the ineptitude of the author's image-space manipulation and his fundamental misunderstanding of the actual projective geometry at work here. He has proven absolutely nothing other than his ability to produce in one instance a distortion map that corrects for the distortion he previously applied in another instance. There is absolutely nothing here that is valid or proven to be a method for determining the authenticity of photographs.