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National Taiwan Normal University Course Outline Spring , 2022 |
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| I.Course information |
| Serial No. | 2718 | Course Level | Undergraduate / Master |
| Course Code | MAC9023 | Chinese Course Name | 影像處理與分析（二） |
| Course Name | Image Processing and Analysis (II) | ||
| Department | Department of Mathematics | ||
| Two/one semester | 1 | Req. / Sel. | Sel. |
| Credits | 3.0 | Lecturing hours | Lecture hours: 3 |
| Prerequisite Course | ◎1. This is a cross-level course and is available for junior and senior undergraduate students, master's students and PhD students. 2. If the listed course is a doctroal level course, it is only available for master's students and PhD students. | ||
| Comment | |||
| Course Description | |||
| Time / Location | Thur. 2-4 Gongguan MA-210 | ||
| Curriculum Goals | Corresponding to the Departmental Core Goal | ||
| 1. Promote the professional skills in mathematics |
College: 1-1 Equipped with professional mathematics competences 1-2 Being able to reason and induct with mathematical logic Master: 1-1 Equipped with professional mathematics competences 1-2 Being able to reason and induct with mathematical logic |
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| 2. Develop problem-solving skills with applied mathematics in Image Processes and Analysis. |
College: 2-2 Possessing the competences of transferring and contextualizing theories in mathematics and mathematics education 3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity Master: 2-2 Possessing the competences of transferring and contextualizing theories in mathematics and mathematics education 3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity |
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| 3. Raise the level of mathematical abstract thinking |
College: 3-4 Having insights, intuitions, and senses of mathematics Master: 3-4 Having insights, intuitions, and senses of mathematics |
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| 4. Interpreting the connection between mathematics and other disciplines from a high point of view |
College: 1-5 Being able to use mathematics as tools to learn other subjects 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 2-1 Being able to communicate and express mathematically 4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning Master: 1-5 Being able to use mathematics as tools to learn other subjects 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 2-1 Being able to communicate and express mathematically 4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning |
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| II. General Syllabus |
| Instructor(s) | CHERN, Jann-Long/ 陳建隆 | ||
| Schedule | |||
This is a course for dealing with problems of image inpainting and image segmentation. Some classical methods and the related mathematical models will be introduced in this course. It is expected to set up a one-year special course on image processing and analysis for students in the Department of Mathematics. We plan to propose and understand the topics of image processing from the perspective of building models, and provide a cross-domain course to expose students to cross-domain application knowledge. There are many important problems and skills in the field of image processing, such as denoising, deblurring, image enhancement, and image cutting. At the beginning of the course, students will learn the basic knowledges of image processing and the mathematical theory behind them. After completing the basic imaging skills, various image processing problems and topics will be introduced. Students will report in groups the related algorithms and computer programs for each selected topic. Through this learning mode, students can also use their understanding contents of image processing to apply mathematical skills for solving topic problems. Some basic knowledges of calculus and matrix calculations will be used in this course. The followings are the plan of studing schedule: 1. Geometry of Curves and Surfaces 2. Deterministic Image Models 3. Topic I: Algorithm and Implementation 4. Interpolation Schemes for Image Inpainting 5. Partial Differential Equation Inpainting Method 6. Topic II: Algorithm and Implementation 7. Active Contours for Image Segmentation 8. Students' Midterm Reports 9. Functions with Bounded Variations 10. Variational Methods for Image Inpainting 11. Topic III: Algorithm and Implementation 12. Variational Methods for Image Segmentation 13. Topic IV: Algorithm and Implementation 14. Students' Final Reports |
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| Instructional Approach | |||
| Methods | Notes | ||
| Formal lecture | In this image processing and analysis course, we will teach the basic principles and applications of related mathematical algorithms with examples. | ||
| Group discussion | The key points of the related studying topics are discussed in groups by students. | ||
| Lab/Studio | The students of the course will discuss in groups the related algorithms and computer programs of image processing learned in the classroom. | ||
| Case studies | The students of the course will report in groups the related algorithms and computer programs for each selected topics of image processe and analysis. | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Assignments | 30 % | The students will need to do the home works of image processes and analysis. This part will take 30% of final score. | |
| Class discussion involvement | 10 % | We will discuss the related topics together in the class. This part will take 10% of final score. | |
| Attendances | 10 % | The students will study the course lectures in the class or on-line class. This part will take 10% of final score. | |
| Presentation | 30 % | For each group students will read and give a report of selected exercises for image processes. This part will take 30% of final score. | |
| Case study reports | 20 % | For each group students will read, report and analysis each respective topics of selected topics for image processes. This part will 20% of final score. | |
| Required and Recommended Texts/Readings with References | The References of this course are the following: 1. Related Lectures References 2. Tony Chan, Jianhong Shen, Image Processing And Analysis, Societyfor Industrial and Applied Mathematics, 2005. 3. Per Christian Hansen, James G. Nagy, and Dianne P.O’Leary, Deblurring Images: Matrices,Spectra, and Filtering, Society for Industrial and Applied Mathematics,2006. 4. Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing, Prentice-Hall,2008 5. Gilles Aubert and Pierre Kornprobst, Mathematical Problems in Image Processing, Partial Differential Equations andthe Calculus of Variations, 2nd Edit." |
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