Ebook: Two-Dimensional Digital Signal Processing II. Transforms and Median Filters

Springer, 1981. — 228 p.Activities in digital image processing have been increasing rapidly in the past decade. This is not surprising when one realizes that in a broad sense image processing means the processing of multidimensional signals and that most signals in the real world are multidimensional. In fact, the one-dimensional signals we work with are often collapsed versions of multidimensional signals. For example, speech is often considered as a one-dimensional signal, viz., a function of a single variable (time). However, speech originally exists in space and therefore is a function of 4 variables (3 spatial variables and time).
There are analog (optical, electro-optical) as well as digital techniques for image processing. Because of the inherent advantages in digital techniques (flexibility, accuracy), and because of the rapid progress in computer and related technologies, such as LSI, and VLSI, it is fair to say that except for some specialized problems, digital techniques are usually preferred.
The purpose of this book and its companion Two-Dimensional Digital Signal Processing I: Linear Filters (/file/1787582/) is to provide in-depth treatments of three of the most important classes of digital techniques for solving image processing problems: Linear filters, transforms, and median filtering. These two books are related but can be used independently.
In the earlier volume 6 of this series, Picture Processing and Digital Filtering (/file/1787580/), selected topics in two-dimensional digital signal processing including transforms, filter design, and image restoration, were treated in depth. Since then, a tremendous amount of progress has been made in these areas. In 1978 when we were planning on a second edition of that book (published in 1979), a decision was made not to make significant revisions but only to add a brief new chapter surveying the more recent results. And we projected that in-depth treatments of some of the important new results would appear in future volumes of the Springer physics program.
These two present books on two-dimensional digital signal processing represent the first two of these projected volumes. The material is divided into three parts. In the first part on linear filters, which is contained in the companion volume, major recent results in the design of two-dimensional non-recursive and recursive filters, stability testing, and Kalman filtering (with applications to image enhancement and restoration) are presented. Among the highlights are the discussions on the design and stability testing of half-plane recursive filters, a topic of great current interest.Introduction.
Efficient Matrix Transposition.
Two-Dimensional Convolution and DFT Computation.
Winograd's Discrete Fourier Transform Algorithm.
Median Filtering: Statistical Properties.
Median Filtering: Deterministic Properties.