Cylindrical perspective is a form of distortion caused by fisheye

Fisheye lens

In photography, a fisheye lens is a wide-angle lens that takes in a broad, panoramic and hemispherical image. Originally developed for use in meteorology to study cloud formation and called "whole-sky lenses", fisheye lenses quickly became popular in general photography for their unique, distorted...

 and panoramic lenses which reproduce straight horizontal lines above and below the lens axis level as curved while reproducing straight horizontal lines on lens axis level as straight. This is also a common feature of wide-angle anamorphic lenses of less than 40mm focal length in cinematography

Cinematography

Cinematography is the making of lighting and camera choices when recording photographic images for cinema. It is closely related to the art of still photography...

.

Essentially it is just barrel distortion

Barrel distortion

In geometric optics and cathode ray tube displays, distortion is a deviation from rectilinear projection, a projection in which straight lines in a scene remain straight in an image...

 but only in the horizontal plane. It is an artifact of the squeezing process that anamorphic lenses do to fit widescreen images onto standard-width film.

See also

• Distortion (optics)
• Stretch-o-Vision
  Stretch-o-Vision
  Stretch-o-Vision is a neologism used to describe the practice of upconverting video from a standard aspect ratio to a widescreen aspect ratio. HDTV programming is broadcast in the 16:9 aspect ratio, a widescreen image. However, most SDTV programming is usually broadcast in the 4:3 aspect ratio....