algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of mathematical concepts, their problem-solving abilities
, 1 Introduction
The purpose of this chapter is to present suggested guidelines for teaching material from
this book at the senior and first-year graduate level. We also discuss use of the book
web site. Although the book is totally self-contained, 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.
ExamsWhile business, law, and mathematics exams differ significantly in content and structure, there are some overlapping features in the way they test students:Critical Thinking: Each field requires students to think critically—whether it's
analyzing a business case, interpreting legal issues, or solving a complex mathematical problem.Application of Knowledge: All three fields require students to apply knowledge to practical scenarios. Business and law exams often feature case
studies or problem-based questionsalgebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of mathematical
concepts, their problem-solving abilities, key differences emerge in the nature of the assessments. Business exams often blend theory with practical decision-making, law exams rely on legal reasoning and precedent, and mathematics exams
emphasize problem-solving and technical skills.________________________________________ConclusionExams in business, law, and mathematics each test different skill sets, from analytical reasoning to problem-solving and theoretical
application. Business exams challenge students to apply their knowledge to real-world situations, law exams require detailed analysis of legal principles and cases, and mathematics exams focus on the mastery of concepts and the ability to solve
complex problems. While each discipline has its own unique approach to assessment, all aim to prepare students for professional success in their respective fields. By understanding the structure and focus of these exams, students can better prepare
for their academic and professional journeys.5. The Role of Exams in Business, Law, and Mathematics EducationExams in business, law, and
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 one-semester senior
course, a one-semester graduate course, and a full-year course of study covering two
semesters. We assume a 15-week program per semester with three lectures per week.
In order to provide flexibility for exams and review sessions, the guidelines discussed
in the following sections are based on forty, 50-minute lectures per semester. The back-
ground assumed on the part of the student is senior-level 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.
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 on-line 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.
ExamsWhile business, law, and mathematics exams differ significantly in content and structure, there are some overlapping features in the way they test students:Critical Thinking: Each field requires students to think critically—whether it's
analyzing a business case, interpreting legal issues, or solving a algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students'
understanding of mathematical concepts, their problem-solving abilitiesand technical skills.________________________________________ConclusionExams in business, law, and mathematics each test different skill sets, from analytical
reasoning to problem-solving and theoretical application. Business exams challenge students to apply their knowledge to real-world situations, law exams require detailed analysis of legal principles and cases, and mathematics exams focus on the
mastery of concepts and the ability to solve complex problems. While each discipline has its own unique approach to assessment, all aim to prepare students for professional success in their respective fields. By understanding the structure and
focus of these exams, students can better prepare for their academic and professional journeys.5. The Role of Exams in Business, Law, and Mathematics EducationExams in business, law, and
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.
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 3.2.2; Section 3.3.1; Section 3.4; Section 3.5; Section 3.6; 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 frequency-domain point of view. The
instructor has significant flexibility 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 frequency-domain 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 ―flavor‖ 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. (5.8-3) 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
ExamsWhile business, law, and mathematics exams differ algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding
of mathematical concepts, their problem-solving abilitiesand technical skills.________________________________________ConclusionExams in business, law, and mathematics each test different skill sets, from analytical reasoning to problem-
solving and theoretical application. Business exams challenge students to apply their knowledge to real-world situations, law exams require detailed analysis of legal principles and cases, and mathematics exams focus on the mastery of concepts
and the ability to solve complex problems. While each discipline has its own unique approach to assessment, all aim to prepare students for professional success in their respective fields. By understanding the structure and focus of these exams,
students can better prepare for their academic and professional journeys.5. The Role of Exams in Business, Law, and Mathematics EducationExams in business, law, and
chapter also can be brief at the senior level by focusing on enough material to give the
student a foundation on the physics of color (Section 6.1), two basic color models (RGB
and CMY/CMYK), and then concluding with a brief coverage of pseudocolor processing
(Section 6.3).
We typically conclude a senior course by covering some of the basic aspects of image
compression (Chapter 8). Interest on this topic has increased significantly as a result of
the heavy use of images and graphics over the Internet, and students usually are easily
motivated by the topic. Minimum coverage of this material includes Sections 8.1.1 and
8.1.2, Section 8.2, and Section 8.4.1. In this limited scope, it is worthwhile spending
one-half of a lecture period filling in any gaps that may arise by skipping earlier parts of
the chapter.
One Semester Graduate Course (No Background in DIP)
The main difference between a senior and a first-year graduate course in which neither
group has formal background in image processing is mostly in the scope of material
covered, in the sense that we simply go faster in a graduate course, and feel much freer
in assigning independent reading. In addition to the material discussed in the previous
section, we add the following material in a graduate course.
Coverage of histogram matching (Section 3.3.2) is added. Sections 4.3, 4.4, and 4.5
are covered in full. Section 4.6 is touched upon briefly regarding the fact that imple-
mentation of discrete Fourier transform techniques requires non-intuitive concepts such
as function padding. The separability of the Fourier transform should be covered, and
mention of the advantages of the FFT should be made. In Chapter 5 we add Sections 5.5
through 5.8. In Chapter 6 we add the HSI model (Section 6.3.2) , Section 6.4, and Sec-
tion 6.6. A nice introduction to wavelets (Chapter 7) can be achieved by a combination
, 1 Introduction
The purpose of this chapter is to present suggested guidelines for teaching material from
this book at the senior and first-year graduate level. We also discuss use of the book
web site. Although the book is totally self-contained, 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.
ExamsWhile business, law, and mathematics exams differ significantly in content and structure, there are some overlapping features in the way they test students:Critical Thinking: Each field requires students to think critically—whether it's
analyzing a business case, interpreting legal issues, or solving a complex mathematical problem.Application of Knowledge: All three fields require students to apply knowledge to practical scenarios. Business and law exams often feature case
studies or problem-based questionsalgebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of mathematical
concepts, their problem-solving abilities, key differences emerge in the nature of the assessments. Business exams often blend theory with practical decision-making, law exams rely on legal reasoning and precedent, and mathematics exams
emphasize problem-solving and technical skills.________________________________________ConclusionExams in business, law, and mathematics each test different skill sets, from analytical reasoning to problem-solving and theoretical
application. Business exams challenge students to apply their knowledge to real-world situations, law exams require detailed analysis of legal principles and cases, and mathematics exams focus on the mastery of concepts and the ability to solve
complex problems. While each discipline has its own unique approach to assessment, all aim to prepare students for professional success in their respective fields. By understanding the structure and focus of these exams, students can better prepare
for their academic and professional journeys.5. The Role of Exams in Business, Law, and Mathematics EducationExams in business, law, and
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 one-semester senior
course, a one-semester graduate course, and a full-year course of study covering two
semesters. We assume a 15-week program per semester with three lectures per week.
In order to provide flexibility for exams and review sessions, the guidelines discussed
in the following sections are based on forty, 50-minute lectures per semester. The back-
ground assumed on the part of the student is senior-level 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.
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 on-line 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.
ExamsWhile business, law, and mathematics exams differ significantly in content and structure, there are some overlapping features in the way they test students:Critical Thinking: Each field requires students to think critically—whether it's
analyzing a business case, interpreting legal issues, or solving a algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students'
understanding of mathematical concepts, their problem-solving abilitiesand technical skills.________________________________________ConclusionExams in business, law, and mathematics each test different skill sets, from analytical
reasoning to problem-solving and theoretical application. Business exams challenge students to apply their knowledge to real-world situations, law exams require detailed analysis of legal principles and cases, and mathematics exams focus on the
mastery of concepts and the ability to solve complex problems. While each discipline has its own unique approach to assessment, all aim to prepare students for professional success in their respective fields. By understanding the structure and
focus of these exams, students can better prepare for their academic and professional journeys.5. The Role of Exams in Business, Law, and Mathematics EducationExams in business, law, and
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.
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 3.2.2; Section 3.3.1; Section 3.4; Section 3.5; Section 3.6; 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 frequency-domain point of view. The
instructor has significant flexibility 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 frequency-domain 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 ―flavor‖ 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. (5.8-3) 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
ExamsWhile business, law, and mathematics exams differ algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding
of mathematical concepts, their problem-solving abilitiesand technical skills.________________________________________ConclusionExams in business, law, and mathematics each test different skill sets, from analytical reasoning to problem-
solving and theoretical application. Business exams challenge students to apply their knowledge to real-world situations, law exams require detailed analysis of legal principles and cases, and mathematics exams focus on the mastery of concepts
and the ability to solve complex problems. While each discipline has its own unique approach to assessment, all aim to prepare students for professional success in their respective fields. By understanding the structure and focus of these exams,
students can better prepare for their academic and professional journeys.5. The Role of Exams in Business, Law, and Mathematics EducationExams in business, law, and
chapter also can be brief at the senior level by focusing on enough material to give the
student a foundation on the physics of color (Section 6.1), two basic color models (RGB
and CMY/CMYK), and then concluding with a brief coverage of pseudocolor processing
(Section 6.3).
We typically conclude a senior course by covering some of the basic aspects of image
compression (Chapter 8). Interest on this topic has increased significantly as a result of
the heavy use of images and graphics over the Internet, and students usually are easily
motivated by the topic. Minimum coverage of this material includes Sections 8.1.1 and
8.1.2, Section 8.2, and Section 8.4.1. In this limited scope, it is worthwhile spending
one-half of a lecture period filling in any gaps that may arise by skipping earlier parts of
the chapter.
One Semester Graduate Course (No Background in DIP)
The main difference between a senior and a first-year graduate course in which neither
group has formal background in image processing is mostly in the scope of material
covered, in the sense that we simply go faster in a graduate course, and feel much freer
in assigning independent reading. In addition to the material discussed in the previous
section, we add the following material in a graduate course.
Coverage of histogram matching (Section 3.3.2) is added. Sections 4.3, 4.4, and 4.5
are covered in full. Section 4.6 is touched upon briefly regarding the fact that imple-
mentation of discrete Fourier transform techniques requires non-intuitive concepts such
as function padding. The separability of the Fourier transform should be covered, and
mention of the advantages of the FFT should be made. In Chapter 5 we add Sections 5.5
through 5.8. In Chapter 6 we add the HSI model (Section 6.3.2) , Section 6.4, and Sec-
tion 6.6. A nice introduction to wavelets (Chapter 7) can be achieved by a combination
