Part of the confusion that many people have with Panorama Tools is
working out what type of image they have. To illustrate the different
types I have overlayed a 10° grid over an image and remapped it to
different image projections.
Equirectangular / psphere
This is the image projection 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.
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
Rectilinear / Normal
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.
fisheye images usually have fields of view around 180° or greater. No
attempt is made to "correct" straight lines and since there is
no image stretching the illumination across the entire image is very even.
This is a great benefit for image stitching. Straight lines passing
through the centre of the image will remain straight.
This image projection is effective a hemispherical image, like looking
at a tennis ball cut in half.
The only lines that remain straight in this type of image are those
passing through the centre of the image.
Full Frame Fisheye
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.
The diagonal field of view is usually around 180°. At this stage I
should emphasise that the type of image a lens produces is NOT related to
its focal length. You can get either a 15mm rectilinear lens OR a
15mm fisheye lens. It is important to know what type of image your lens
produces when attempting to stitch images together.
* Excluding the horizon
** Excluding lines passing through the centre of the image
For those wanting to know more of the mathematics of projections try
this pages as a starter. <http://mathworld.wolfram.com/topics/MapProjections.html>