TABLE OF CONTENTS This chapter centers around the question of how to represent the information contained in images. Together with the next two chapters it lays the mathematical foundations for low-level image processing. Two key points are emphasized in this chapter.
First, the information contained in images can be represented in entirely different ways. The most important are the spatial representation (Section 2.2) and wave number representation (Section 2.3). These representations just look at spatial data from different points of view. Since the various representations are complete and equivalent, they can be converted into each other. The conversion between the spatial and wave number representation is the well-known Fourier transform. This transform is an example of a more general class of operations, the unitary transforms (Section 2.4).
Second, we discuss how these representations can be handled with digital computers. How are images represented by arrays of digital numbers in an adequate way? How are these data handled efficiently? Can fast algorithms be devised to convert one representation into another? A key example is the fast Fourier transform, discussed in Section 2.5.
Images constitute a spatial distribution of the irradiance at a plane. Mathematically speaking, the spatial irradiance distribution can be described as a continuous function of two spatial variables:
| (2.1) |  |
Computers cannot handle continuous images but only arrays of digital numbers. Thus it is required to represent images as two-dimensional arrays of points. A point on the...
