Image Projections for Extreme Wide Angle Animations.
With a standard rectilinear image projection it is not practical to use a wider FOV than 120°. Beyond this the rectilinear distortion at the edges confines most of the image to a small central portion of the image. It is possible to use different image projections that will expand the range of usable FOVs including Omnimax (about 180°x82°) and even "spherical" video.
Image Projections
Each image projection has it's own characteristics which must be taken into consideration when deciding on which one to use.
Equirectangular
This image projection is normally used for spherical panoramas. The clue to this image is in it's name. As you can see from the sample below, there is an even spacing between each 10° increment across the entire image. Equal distances (horizontally and vertically) in the image are equivalent to equal angles in the original scene.
Vertical straight lines will remain straight, but horizontal straight lines will become curved. If you are standing in the centre of a circle then the perimeter of the circle will be a straight line in this image projection (e.g. the horizon).
To be viewed correctly this image must be wrapped around a sphere.
Rectilinear / Normal
Most
photographers work with lenses that produce rectilinear images. These
stretch the image so that vertical, horizontal and diagonal lines that we
perceive as being straight are reproduced as straight lines. Rectilinear
images are restricted to a field of view of less than 180° in both the
horizontal and vertical directions.
Because the image is optically stretched towards the corners rectilinear lenses tend to suffer from light fall off, where the corners of the image are darker than the centre.
Cylindrical
No prizes for guessing that this image is meant to be viewed wrapped around a cylinder. In this image projection you will see that the distances for each 10° increment gets bigger as you move vertically from the centre of the image. It is restricted to vertical fields of view less than 180°. This image projection is used in the original QTVR format. Most swing lens/rotating panoramic cameras produce this type of image
Circular Fisheye
![[ sample image ]](images/circ_fisheye.jpg)
Circular
fisheye images usually have fields of view around 180° or greater. No
attempt is made to "correct" straight lines. Only straight lines passing through the
centre of the image will remain straight.
This image projection is effectively a hemispherical image, like looking at a tennis ball cut in half.
Full Frame Fisheye
![[ sample image ]](images/ff_fisheye.jpg)
Full
frame fish eye lenses are optically very similar to circular fisheye lenses.
The image projection is effectively the same but the field of view is
smaller, with the edge of the frame obscuring the rest of the image.
Summary
| Projection | Straight Lines | Notes | ||
|---|---|---|---|---|
| Vertical | Horizontal* | Diagonal | ||
| Rectilinear | Yes | Yes | Yes | Normal image projection, useful for FOV <120° |
| Cylindrical | Yes | No | Yes | Closest projection to rectilinear that is suitable for FOV >120° but vertical FOV should be restricted to <120°. |
| Equirectangular | Yes | No | No | Widest possible range of FOVs. Restrict vertical FOV to <160° to avoid excessive distortion at top and bottom of image. |
| Fisheye** | No | No | No | Suitable for any FOV. |
* Excluding the horizon
** Excluding lines passing through the centre of the image
Further Reading
For those wanting to know more of the mathematics of projections try this pages as a starter. <http//mathworld.wolfram.com/topics/MapProjections.html>