Most photographers who know what cylindrical, Mercator, Panini,... projections are just think of them in the context of stitching (merging several captures that cover a very large field of view). But there is no reason why single images cannot benefit from reprojection. In particular UWA images covering a large FOV, in some situations can be improved by reprojecting them from the pinhole camera model (usually called 'perspective' projection in computer vision) to any other projection.
The pinhole projection that most camera and lenses work with has a unique and valuable property: it's the only one that projects ALL straight lines found in the scene as straight lines on the projected 2D image. But it has a drawback: when the FOV is large, important distortion occurs in those subjects far from the image centre. It's not a problem of the optics, in fact it is not a photographic issue but just a mathematical consequence of the linear projection.
I have been playing with the following (re)projections and applying them to different UWA captures:
Gemini Pro wrote the functions in C++ for me, but these reprojections can also be done on any serious stitching software such as
PTGui, and probably you can even cheat
Photoshop by duplicating your input image and use its rudimentary stitching module to perform the reprojection.
I practised on four use cases where the reprojection enhanced in some way the original UWA capture:
Cylindrical projection for landscapesA cylindrical projection can be used in landscape photography to eliminate the distortion that appears near the lateral edges of an ultra-wide-angle image, making geographical features appear at a scale and with proportions closer to what the photographer actually saw. Applied to the following panoramic-format photograph by Javier Camacho Gimeno, captured from a single 18 mm full-frame equivalent exposure, the projection makes the Cervino, located at the centre of the image, more prominent while removing the characteristic edge stretching and restoring more realistic shapes to the peaks near the sides of the frame (click on link to view at higher resolution):
http://guillermoluijk.com/datosimagensonido/cervino18mm.gif
Stereographic projection to restore spherical shapesA stereographic projection can restore the circular appearance of spherical objects in the original scene, which the camera projection rendered as ellipses that are difficult to interpret. A Mercator projection would also provide a good correction, although both projections introduce curvature into straight lines in the scene (click on link to view at higher resolution):
http://guillermoluijk.com/datosimagensonido/spheres12mm.gif
Panini projection in urban scenesA Panini projection is well suited to urban scenes, where it counteracts the distortion caused by a very wide angle of view. The result is a more natural-looking image, with the appearance of having been taken using a longer focal length while preserving the full horizontal field of view. This correction works particularly well when the scene contains a central vanishing point toward which all perspective lines converge. Another urban example can be found
here (click on link to view at higher resolution):
http://guillermoluijk.com/datosimagensonido/street12mm.gif
Panini projection in 3D video gamesThis may sound exotic but a Panini projection can also be applied to 3D video games (e.g. Mordhau), preserving the wide horizontal field of view needed for better situational awareness while ensuring that characters near the edges of the screen do not appear distorted. At the same time, distant subjects are brought visually closer, making them easier to identify (click on link to view at higher resolution):
http://guillermoluijk.com/datosimagensonido/mordhau.gif
Full article here (pick English translation top right if you don't speak Spanish):
UWA image enhancement through reprojectionRegards!
