Design for Embedded Image Processing on FPGAs, 2nd Edition

10Geometric 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 include zooming, rotating, and perspective transformation. Such transformations are typically used to correct spatial distortions resulting from the imaging process, to register an image to a predefined coordinate system (for example registering an aerial image to a particular map projection, or rectifying a stereo pair of images so that the rows corresponds to epipolar lines), or to register one image with another.

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 and using random access processing. It is usually quite difficult to implement geometric transformations 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 10.1. The forward mapping defines the output pixel coordinates, , as a function, , of the input coordinates:

(10.1)

Since the mapping is specified in terms of input pixel locations, ...