Digital Image Processing Solutions Assignment

Digital Image Processing Solutions Assignment Words: 2875

The notation used throughout this annual corresponds to the notation used in the text. The decision of what material to cover in a course rests with the instructor, and it depends 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 trine frames indicated when the course is being taught in an electrical engineering or computer science curriculum. In each case, no prior exposure to image processing is assumed. We give suggested guidelines for one. Semester courses at the senior and @rest-heartedly levels.

It is possible to cover most of he book in a two-semester 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 better teaching aid. To this end, the instructor Will the new organization to be much more -expiable and better illustrated. Although the book is sell contained, we recommend use to the companion web site, where the student will and detailed solutions to the problems marked with a star in the text, review material, suggested projects, and images from the book.

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One of the principal reasons for creating the web site was to free the instructor room having to prepare materials and handouts beyond what is required to teach from the book. Computer projects such as those described in the ebb site are an important part of a course on image processing. These projects give the student hands-on 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 irreconcilableness multi-user or personal computer having a hard copy output device.

Introduction The purpose of this chapter is to present suggested guidelines for teaching eternal from this book at the senior and @rest-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, 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 material. In the following discussion eve 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 -explicitly for exams and review sessions, the guidelines discussed in the following sections are based on forty, So-minute lectures per semester.

The background 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 resented 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 [email protected] 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, UT it is an option that often is attractive in programs that place little emphasis on the signal processing aspects of the geld and prefer to focus more on the implementation of spatial techniques. Chapter I Introduction The companion web site Venn:Incompressibility. Com is a valuable teaching aid, in the sense that it includes material that previously was covered 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 period 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 to 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. Chapter 2 should be covered in its entirety.

Some of the material (such as parts of Sections 21 and 23) 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 significant appeal to the beginning student) and it introduces a host of basic spatial processing tools used throughout the book. For a senior course, eve recommend coverage of Sections 3. 21 through 3. 2. U Section 3. 3. LU Section 3. U Section 3. U Section 3_u Section 3. 7. I , 3_7. 2 (through Example 3. 1), and 3. 7 3. Section 3. 8 can be assigned as independent reading, depending on time. Chapter 4 also discusses enhancement, but from a frequency-domain point Of view. The instructor has [email protected] -explicitly here. As mentioned earlier, is possible to skip the chapter altogether, but this Will typically preclude meaningful coverage of other areas based on the Fourier transform (such as @altering 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 Altering examples (say, low- and highways @altering using Buttonholer @alters, as discussed in Sections 4. 3. 2 and 4. 4. 2). At the discretion to the instructor, additional material can include full coverage of Sections 4. And 44, It is seldom possible to go beyond this point in a senior course. Chapter S can be covered as a continuation of Chapter 4. Section 5. Makes this an easy approach. Then, it is possible give the student a I-favor} 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 @alters in Section 53. 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 ND restoration are the same thing when it comes to noise reduction by spatial Altering.

A good way to keep it brief and conclude coverage Of restoration is to jump at this point to inverse @altering (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 @altering, it is possible to introduce the interactive} form of the Wiener @alter in CEQ. (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 4 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 (ERG and COM/CACM), and then concluding with a brief coverage of pseudopodia processing (Section 6. 3), We typically conclude a senior course by covering some of the basic aspects of image compression (Chapter 81 Interest on this topic has increased [email protected] as a result of the heavy use of images and graphics over the Internet, and dents usually are easily motivated by the topic Minimum coverage of this material includes Sections 8. . 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 @ling 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 @rest-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, ND 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 43, 4. 4, and 4. 5 are covered in full. Section 46 is touched upon brie-y regarding the fact that implementation of discrete Fourier transform techniques requires non-intuitive concepts such as function padding. The capability of the Fourier transform should be covered, and mention of the advantages of the FT should be made. In Chapter 5 we add Sections 5. Through 5. . In Chapter ewe add the HIS model (Section 6. 3,2) Section 6,4, and Section 6. 6. A nice introduction to wavelets (Chapter 7) can be achieved by a combination of classroom discussions and independent reading. The minimum number of sections in that chapter are 7. 1, 7. 2, 7. 3, and 7. 5, with appropriate (but brief) mention of the existence of fast wavelet transforms. Finally, in Chapter 8 we add coverage of Sections 8_3, 8. 4,2, 8. 51 (through Example 8. 16), Section 8. 5. 2 (through Example 8. 20) and Section 8. 53.

If additional time is available, a natural topic to cover next is morphological image recessing (Chapter g). The material in this chapter begins a transition from methods whose inputs and outputs are images to methods in which the inputs are images, but the outputs are attributes about those images, in the sense [email protected] in Section 1. 1. We One Semester Graduate Course (with Background in DIP) recommend coverage of Sections 9. 1 through 9. 4, and some of the algorithms in section 9. 5. Some programs have an undergraduate course in image processing as a prerequisite to a graduate course on the subject.

In this case, is possible to cover material from the ;Rest eleven chapters of the book. Sing the undergraduate guidelines described above, we add the following material to form a teaching outline for a one semester graduate course that has that undergraduate material as prerequisite. Given that students have the appropriate background on the subject, independent reading assignments can be used to control the schedule. Coverage of histogram matching (Section is added Sections 43, 4. 4, 4. 5, and 4. 6 are added. This strengthens the student’s background in frequency- domain concepts.

A more extensive coverage of Chapter S is possible by adding sections 5. 2. 3, 5. 3. 3, 5. 4. 3, 5. , 5. 6, and 5. 8. In Chapter 6 we add full-color image processing (Sections 6. 4 through 6. 7). Chapters 7 and 8 are covered as in the previous section. As noted in the previous section, Chapter 9 begins a transition from methods whose inputs and outputs are images to methods in Which the inputs are images, but the outputs are attributes about those images. As a minimum, we recommend coverage Of binary morphology: Sections gull through 9. 4, and some of the algorithms in Section 9. . Mention should be made about possible extensions to gray-scale images, but coverage of this material may not e possible, depending on the schedule. In Chapter 10, we recommend Sections 10. 1, 10-2. 1 and 10. 22, 103. 1 through 103. 4, 10. 4, and 10. 5. In Chapter lee typically cover Sections 11. 1 through 11. 4. Two Semester Graduate Course (No Background in DIP) A full-year graduate course consists to the material covered in the one semester undergraduate course, the material outlined in the previous section, and sections 12. 1, 12. 2, 123. 1, and 123. 2.

Projects One of the most interesting aspects of a course in digital image processing is the pictorial Chapter 1 Introduction nature Of the subject. It has been our experience that students truly enjoy and Bennett from judicious use of computer projects to complement the material covered in class. Since computer projects are in addition to course work and homework assignments, we try to keep the formal project reporting as brief as possible. In order to facilitate grading, we try to achieve uniformity in the way project reports are prepared. A useful report format is as follows: Page 1: Cover page. Reject title C Project number Course number C Student’s name C Date due C Date handed in C Abstract (not to exceed 1/2 page) Page 2: One to two pages (Max) of technical discussion. Page 3 (or 4): Discussion of results, One to two pages (Max), Results: Image results (printed typically on a laser or inkiest printer). All images must contain a number and title referred to in the discussion of results Appendix: Program listings, focused on any original code prepared by the student. For brevity, functions and routines provided to the student are referred to by name, but the code is not included.

Layout: The entire report must be on a standard sheet size (e. G. , E II inches), stapled with three or more staples on the left margin to form a booklet, or bound sing clear plastic standard binding products. Project resources available in the book web site include a sample project, a list of suggested projects from Which the instructor can select, book and Other images, and MUTUAL functions. Instructors who do not wish to use MUTUAL will end additional software suggestions in the Support/Software section Of the web site. Problem Solutions Problem 2. The diameter, x, of the retinal image corresponding to the dot is obtained from similar triangles, as shown in Fig. UP. 1. That is, 0:014 which gives x = 0:add. From the discussion in Section 2. 1. 1, and taking some berries of interpretation, we can think of the fovea as a square sensor array having on the order of 337,000 elements, which translates into an array of size 580 E 580 elements. Assuming equal spacing between elements, this gives 580 elements and 579 spaces on a line 1. 5 mm long. The size of each element and each space is then s = 159] = E CICS m.

If the size (on the fovea) of the imaged dot is less than the size off single resolution element, we assume that the dot Will be invisible to the eye. In Other words, the eye Will not detect a dot if its diameter, d, is such that Because interest lies only on the boundary shape and not on other spectral characteristics of the specimens, a single illumination source in the far ultraviolet (wavelength of . 001 microns or less) Will be able to detect all Objects. A far-ultraviolet camera sensor would be needed to image the specimens. B) No answer required since the answer to (a) is [email protected] Problem 2. 5 From the geometry of Fig. 2. 3, mm=mm= z=mm, orzo = 100 mm. So the target size is 100 mm on the side. We have a total of 1024 elements per line, so the resolution of 1 line is 10 elements,’mm.

For line pairs we divide by 2, giving an answer of 5 Ip/mm. Problem 2. 6 One possible solution is to equip a monochrome camera with a mechanical device that sequentially places a red, a green, and a blue pass utter in Toronto of the lens, The strongest camera response determines the color, If all three responses are approximately equal, the object is white. A faster system would utilize three different cameras, each equipped with an individual @alter. The analysis would be then based on polling the response of each camera.

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