Image Processing Reference

In-Depth Information

Fig. 10.4
Bilinear

interpolation. The final pixel

value becomes a weighted

sum of the four nearest pixel

values

10.3 Homography

Geometric transformation can also be used to correct errors in images. Imagine

a telescope capturing an image of a star constellation. The image is likely to be

distorted by the fact that light is bent in space due to the gravitational forces of the

stars and also by the changing conditions in the Earth's atmosphere. Since the nature

of these phenomena is known, the transformation they enforced on the image can

be compensated for by applying the inverse transformation.

Another, and perhaps more relevant, error that can be corrected by a geomet-

ric transformation is
keystoning
. A keystone is the top-most block in an arch, i.e.,

an arch-shaped doorway. Since the keystone is wedge-shaped it is used to describe

wedge-shaped images. Such an image is obtained when capturing a square using a

tilted camera or when projecting an image onto a tilted plane, see Fig.
10.5
. Since

this is a common phenomenon, most video projectors have a built-in geometric map-

ping function, which can correct for keystoning.

Let us investigate the correction of keystoning in more depth by looking at a con-

crete example. Imagine you are designing a simple game where a projector projects

circles onto a table and a camera captures your finger when touching the table. The

Fig. 10.5
Keystoning