Multidimensional Signal and Color Image Processing Using Lattices

3Discrete‐Domain Signals and Systems

3.1 Introduction

Although the original images projected on a sensor and the final images presented to a viewer's visual system are continuous in space and time, a discrete intermediate representation is required in order to carry out digital image and video processing operations. Thus images must be sampled in space and time for processing and eventually converted back to continuous form for presentation to the viewer. In this chapter we introduce discrete‐space and discrete‐space‐time signals and systems under the general name of discrete‐domain signals and systems.

For the sampling of one‐dimensional signals, all that needs to be specified is the sampling period (or equivalently, the sampling frequency), and possibly the sampling phase. In two, three, or more dimensions, the situation is more complicated. We have to specify how the samples are arranged in space and time. The simplest arrangement is to lay out the samples on a rectangular grid, and this is the approach taken in most discussions of digital image processing. However, there are many important applications where this is not the case. For example, in standard broadcast television, the interlaced scanning method is used; scanning lines in each vertical pass of the image are midway between the scanning lines of the previous vertical pass. It follows that any scheme for sampling standard TV signals will lead to nonrectangular sampling in 3D space‐time. Another important example of ...