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| BIL7170 | Mathematical Models in Image and Video Proc. | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of COMPUTER ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Bekir DİZDAROĞLU | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Show constrained and unconstrained regularization methods for greyscale and color images by using partial differential equations. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | understand a general notion of PDE-based methods. | 1,8 | 1,3 | | PO - 2 : | understand regularization methods by using PDE. | 1,8 | 1,3 | | PO - 3 : | understand image modeling methods. | 1,8 | 1,3 | | PO - 4 : | understand the application of multivalued and constrained PDE methods. | 1,8 | 1,3 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Image reconstruction. Diffusion filters. Total variation image restoration. PDE-based image inpainting and magnification. Theories and applications of graph cuts in vision and graphics. Minimal paths and fast marching methods for image analysis. Motion analysis, optical flow and tracking. Optical flow estimation. Image alignment and stitching. Visual tracking. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | General Context and Notations: PDE's and Computer Vision, Mathematical notations | | | Week 2 | Image Restoration: Image Degradation, The Energy Method | | | Week 3 | PDE-Based Methods: Smoothing PDE's, Enhancing PDE's | | | Week 4 | More PDE-Based Methods: Neigbourhood filters and PDE's | | | Week 5 | The Segmentation Problem: Definition ve Objectives | | | Week 6 | The Segmentation Problem: The Mumford and Shah Functional | | | Week 7 | The Segmentation Problem: The Level-Set Method | | | Week 8 | The Image Inpainting Methods: Variational Models, PDE-Based Approaches
| | | Week 9 | Mid-term exam | | | Week 10 | Decompositon an Image into Geometry and Texture: Meyer's Model | | | Week 11 | Image Sequence Analysis: Optical Flow Methods | | | Week 12 | Image Sequence Analysis: Sequence Segmentation and Restoration | | | Week 13 | Quizzes and homeworks | | | Week 14 | Image Sequence Analysis: The Level-Set Approach and The Variational Model | | | Week 15 | Multivalued Images: An Extended Notion of Gradient | | | Week 16 | End-of-term exam | | | |
| 1 | Aubert, G., Kornprobst, P. 2006; Mathematical Problems in Image Processing, Berlin, Springer, 377 p.
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| 1 | Suri, J.S., Laxminarayan, S. 2002; PDE and Level Sets: Algorithmic Approaches to Static and Motion Imagery, Kluwer Academic Publishers, 455 p. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 03/04/2024 | 2 | 50 | | End-of-term exam | 17 | 30/05/2024 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Ödev | 10 | 1 | 10 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 151 |
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