Chapter 9

Geometric Transformations

The next class of operations to be considered is that of geometric transformations. These redefine the geometric arrangement of the pixels within an image (Wolberg, 1990). Examples of geometric transformations include zooming, rotating and perspective transformation. Such transformations are typically used to correct spatial distortions resulting from the imaging process, or to normalise an image by registering it to a predefined coordinate system (for example, registering an aerial image to a particular map projection or warping a stereo pair of images so that the rows corresponds to epipolar lines).

Unlike point operations and local filters, the output pixel does not, in general, come from the same input pixel location. This means that some form of buffering is required to manage the delays resulting from the changed geometry. The simplest approach is to hold the input image or the output image (or both) in a frame buffer. Most geometric transformations cannot easily be implemented with streaming for both the input and output.

The mapping between input and output pixels may be defined in two different ways, as illustrated in Figure 9.1. The forward mapping defines the output pixel coordinates, , as a function, , of the input coordinates:

(9.1) ...