Multidimensional Signal, Image, and Video Processing and Coding, 2nd Edition

Chapter 10

Three-Dimensional and Spatiotemporal Processing

In Chapter 2 we looked at 2-D signals and systems. Here, we look at the 3-D case, where often the application is to spatiotemporal processing, i.e., two spatial dimensions and one time dimension. Of course, 3-D more commonly refers to the three orthogonal spatial dimensions. Here, we will be mostly concerned with convolution and filtering, and so need a regular grid for our signal processing. While regular grids are commonplace in spatiotemporal 3-D, they are often missing in spatial 3-D applications. In any event, the theory developed in this section can apply to any 3-D signals on a regular grid. In many cases, when a regular grid is missing or not dense enough (often the case in ...