Deutsch: Zimmer gerade fotografiert und in die winkeltreue Projektion umgerechnet.
links: großes Bildfeld
rechts: Hemisphäre (üblicher Bildwinkel)
${\displaystyle \varphi }$, ${\displaystyle \theta }$ sind Kugelkoordinaten (Objekt) und ${\displaystyle r}$, ${\displaystyle \phi }$ Polarkoordinaten (Bild).

English: Photo of room straightly taken and remapped into stereographic projection.
left: large image field
right: hemisphere (usual angle of view)
${\displaystyle \varphi }$, ${\displaystyle \theta }$ are spherical coordinates (object) and ${\displaystyle r}$, ${\displaystyle \phi }$ polar coordinates (image).

${\displaystyle r=2f\tan {\frac {\theta }{2}}}$
${\displaystyle \phi =\varphi }$

f = 795.3 pixel

You can crop lossless with JPEGTRAN or JPEGCROP. The parameter format is WIDTHxHEIGHT+LEFT+TOP.