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Digital Image Processing Second Edition Instructorzs Manual Rafael C. Gonzalez Richard E. Woods Prentice Hall Upper Saddle River, NJ 07458 www.prenhall.com/gonzalezwoods or www.imageprocessingbook.com

ii Revision history 10 9 8 7 6 5 4 3 2 1 Copyright c°19922002 by Rafael C. Gonzalez and Richard E. Woods

Preface This manual contains detailed solutions to all problems in Digital Image Processing, 2nd Edition. We also include a suggested set of guidelines for using the book, and discuss the use of computer projects designed to promote a deeper understanding of the subject matter. The notation used throughout this manual corresponds to the notation used in the text. The decision of what material to cover in a course rests with the instructor, and it de pends on the purpose of the course and the background of the students. We have found that the course outlines suggested here can be covered comfortably in the time frames indicated when the course is being taught in an electrical engineering or computer sci ence curriculum. In each case, no prior exposure to image processing is assumed. We give suggested guidelines for onesemester courses at the senior and ﬁrstyear graduate levels. It is possible to cover most of the book in a twosemester graduate sequence. The book was completely revised in this edition, with the purpose not only of updating the material, but just as important, making the book a better teaching aid. To this end, the instructor will ﬁnd the new organization to be much more ›exible and better illustrated. Although the book is self contained, we recommend use of the companion web site, where the student will ﬁnd detailed solutions to the problems marked with a star in the text, review material, suggested projects, and images from the book. One of the principal reasons for creating the web site was to free the instructor from having to prepare materials and handouts beyond what is required to teach from the book. Computer projects such as those described in the web site are an important part of a course on image processing. These projects give the student handson experience with algorithm implementation and reinforce the material covered in the classroom. The projects suggested at the web site can be implemented on almost any reasonably equipped multiuser or personal computer having a hard copy output device.

1 Introduction The purpose of this chapter is to present suggested guidelines for teaching material from this book at the senior and ﬁrstyear graduate level. We also discuss use of the book web site. Although the book is totally selfcontained, the web site offers, among other things, complementary review material and computer projects that can be assigned in conjunction with classroom work. Detailed solutions to all problems in the book also are included in the remaining chapters of this manual. Teaching Features of the Book Undergraduate programs that offer digital image processing typically limit coverage to one semester. Graduate programs vary, and can include one or two semesters of the ma terial. In the following discussion we give general guidelines for a onesemester senior course, a onesemester graduate course, and a fullyear course of study covering two semesters. We assume a 15week program per semester with three lectures per week. In order to provide ›exibility for exams and review sessions, the guidelines discussed in the following sections are based on forty, 50minute lectures per semester. The back ground assumed on the part of the student is seniorlevel preparation in mathematical analysis, matrix theory, probability, and computer programming. The suggested teaching guidelines are presented in terms of general objectives, and not as time schedules. There is so much variety in the way image processing material is taught that it makes little sense to attempt a breakdown of the material by class period. In particular, the organization of the present edition of the book is such that it makes it much easier than before to adopt signiﬁcantly different teaching strategies, depending on course objectives and student background. For example, it is possible with the new organization to offer a course that emphasizes spatial techniques and covers little or no transform material. This is not something we recommend, but it is an option that often is attractive in programs that place little emphasis on the signal processing aspects of the ﬁeld and prefer to focus more on the implementation of spatial techniques.

2 Chapter 1 Introduction The companion web site www:prenhall:com=gonzalezwoods or www:imageprocessingbook:com is a valuable teaching aid, in the sense that it includes material that previously was cov ered in class. In particular, the review material on probability, matrices, vectors, and linear systems, was prepared using the same notation as in the book, and is focused on areas that are directly relevant to discussions in the text. This allows the instructor to assign the material as independent reading, and spend no more than one total lecture pe riod reviewing those subjects. Another major feature is the set of solutions to problems marked with a star in the book. These solutions are quite detailed, and were prepared with the idea of using them as teaching support. The online availability of projects and digital images frees the instructor from having to prepare experiments, data, and handouts for students. The fact that most of the images in the book are available for downloading further enhances the value of the web site as a teaching resource. One Semester Senior Course A basic strategy in teaching a senior course is to focus on aspects of image processing in which both the inputs and outputs of those processes are images. In the scope of a senior course, this usually means the material contained in Chapters 1 through 6. Depending on instructor preferences, wavelets (Chapter 7) usually are beyond the scope of coverage in a typical senior curriculum). However, we recommend covering at least some material on image compression (Chapter 8) as outlined below. We have found in more than two decades of teaching this material to seniors in electrical engineering, computer science, and other technical disciplines, that one of the keys to success is to spend at least one lecture on motivation and the equivalent of one lecture on review of background material, as the need arises. The motivational material is provided in the numerous application areas discussed in Chapter 1. This chapter was totally rewritten with this objective in mind. Some of this material can be covered in class and the rest assigned as independent reading. Background review should cover probability theory (of one random variable) before histogram processing (Section 3.3). A brief review of vectors and matrices may be required later, depending on the material covered. The review material included in the book web site was designed for just this purpose.

One Semester Senior Course 3 Chapter 2 should be covered in its entirety. Some of the material (such as parts of Sections 2.1 and 2.3) can be assigned as independent reading, but a detailed explanation of Sections 2.4 through 2.6 is time well spent. Chapter 3 serves two principal purposes. It covers image enhancement (a topic of signif icant appeal to the beginning student) and it introduces a host of basic spatial processing tools used throughout the book. For a senior course, we recommend coverage of Sec tions 3.2.1 through 3.2.2u Section 3.3.1u Section 3.4u Section 3.5u Section 3.6u Section 3.7.1, 3.7.2 (through Example 3.11), and 3.7.3. Section 3.8 can be assigned as indepen dent reading, depending on time. Chapter 4 also discusses enhancement, but from a frequencydomain point of view. The instructor has signiﬁcant ›exibility here. As mentioned earlier, it is possible to skip the chapter altogether, but this will typically preclude meaningful coverage of other areas based on the Fourier transform (such as ﬁltering and restoration). The key in covering the frequency domain is to get to the convolution theorem and thus develop a tie between the frequency and spatial domains. All this material is presented in very readable form in Section 4.2. |Light} coverage of frequencydomain concepts can be based on discussing all the material through this section and then selecting a few simple ﬁltering examples (say, low and highpass ﬁltering using Butterworth ﬁlters, as discussed in Sections 4.3.2 and 4.4.2). At the discretion of the instructor, additional material can include full coverage of Sections 4.3 and 4.4. It is seldom possible to go beyond this point in a senior course. Chapter 5 can be covered as a continuation of Chapter 4. Section 5.1 makes this an easy approach. Then, it is possible give the student a |›avor} of what restoration is (and still keep the discussion brief) by covering only Gaussian and impulse noise in Section 5.2.1, and a couple of spatial ﬁlters in Section 5.3. This latter section is a frequent source of confusion to the student who, based on discussions earlier in the chapter, is expecting to see a more objective approach. It is worthwhile to emphasize at this point that spatial enhancement and restoration are the same thing when it comes to noise reduction by spatial ﬁltering. A good way to keep it brief and conclude coverage of restoration is to jump at this point to inverse ﬁltering (which follows directly from the model in Section 5.1) and show the problems with this approach. Then, with a brief explanation regarding the fact that much of restoration centers around the instabilities inherent in inverse ﬁltering, it is possible to introduce the |interactive} form of the Wiener ﬁlter in Eq. (5.83) and conclude the chapter with Examples 5.12 and 5.13. Chapter 6 on color image processing is a new feature of the book. Coverage of this

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