■ Preface xvii

material is an intuitive derivation of the sampling theorem and its implica-

tions.The 1-D material is then extended to 2-D, where we give a number of ex-

amples to illustrate the effects of sampling on digital images, including aliasing

and moiré patterns. The 2-D discrete Fourier transform is then illustrated and

a number of important properties are derived and summarized. These con-

cepts are then used as the basis for filtering in the frequency domain. Finally,

we discuss implementation issues such as transform decomposition and the

derivation of a fast Fourier transform algorithm.At the end of this chapter, the

reader will have progressed from sampling of 1-D functions through a clear

derivation of the foundation of the discrete Fourier transform and some of its

most important uses in digital image processing.

Chapter 5: The major revision in this chapter was the addition of a section

dealing with image reconstruction from projections, with a focus on computed

tomography (CT). Coverage of CT starts with an intuitive example of the un-

derlying principles of image reconstruction from projections and the various

imaging modalities used in practice. We then derive the Radon transform and

the Fourier slice theorem and use them as the basis for formulating the con-

cept of filtered backprojections. Both parallel- and fan-beam reconstruction

are discussed and illustrated using several examples. Inclusion of this material

was long overdue and represents an important addition to the book.

Chapter 6: Revisions to this chapter were limited to clarifications and a few

corrections in notation. No new concepts were added.

Chapter 7: We received numerous comments regarding the fact that the

transition from previous chapters into wavelets was proving difficult for be-

ginners. Several of the foundation sections were rewritten in an effort to make

the material clearer.

Chapter 8: This chapter was rewritten completely to bring it up to date. New

coding techniques, expanded coverage of video, a revision of the section on

standards, and an introduction to image watermarking are among the major

changes. The new organization will make it easier for beginning students to

follow the material.

Chapter 9: The major changes in this chapter are the inclusion of a new sec-

tion on morphological reconstruction and a complete revision of the section

on gray-scale morphology. The inclusion of morphological reconstruction for

both binary and gray-scale images made it possible to develop more complex

and useful morphological algorithms than before.

Chapter 10: This chapter also underwent a major revision. The organization

is as before, but the new material includes greater emphasis on basic principles

as well as discussion of more advanced segmentation techniques. Edge models

are discussed and illustrated in more detail, as are properties of the gradient.

The Marr-Hildreth and Canny edge detectors are included to illustrate more

advanced edge detection techniques.The section on thresholding was rewritten

also to include Otsu’s method, an optimum thresholding technique whose pop-

ularity has increased significantly over the past few years. We introduced this

approach in favor of optimum thresholding based on the Bayes classifica-

tion rule, not only because it is easier to understand and implement, but also