Big Ben's Panorama Tutorials

Image Projections 

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Index
A Brief History
Image Projections
Creating Panoramas

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Introduction
Software
Photography
Background Info
Script Parameters
Control Points
Lens Calibration
Stitching
Technical Considerations
Alternative Uses
PTViewer
FAQ

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.

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

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.

Circular Fisheye

Circular 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

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.

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.

Summary

* 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>

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