This course focuses on the processing technologies for multi-dimensional information. Topics include sampling and quantization of multi-dimensional information, compression coding (entropy coding, quantization error analysis, orthogonal transform, Karhunen-Loeve transform (KLT), and Discrete Cosine Transform (DCT)), recent advances in image processing (image segmentation, colorization, image editing, and image retargeting), and image restoration via convex optimization (convex function/set, convex programming algorithms and regularization methods for image processing). The course enables students to understand the mathematical tools widely applicable to solve the real-world information processing problems.
By the end of this course, students will:
1. Understand the fundamental of image coding methods.
2. Explain how to extract the essential and mathematical problems from real-world image processing problems.
3. Acquire the fundamentals of convex optimization
4. Apply mathematical tools for wide variety of multi-dimensional information processing problems.
Signal processing, image processing, convex optimization
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
To allow students to get a good understanding of the course contents, all course materials are provided on the lecturer's web-site. The additonal description is provided at the lecture.
Course schedule | Required learning | |
---|---|---|
Class 1 | Guidance | Understand the course objectives. |
Class 2 | Quantization, sampling, sampling theorem | Understand the sampling theorem |
Class 3 | Entropy, source coding theorem | Undestand the fundamental of compression coding. |
Class 4 | Quantization, analysis of quantization error | Understand the statistical analysis of quantization error. |
Class 5 | Orthogonal transform,KLT (Karhunen-Loeve transform) | Understand the optimality of KLT |
Class 6 | From KLT to DCT (Discrete Cosine Transform) | Understand the relationship between DCT and KLT. |
Class 7 | Application of eigenvalue problem,Locally linear embedding, Normalized cuts | Understand the applications of eigenvalue problem. |
Class 8 | Colorization using optimization, Poisson image editing | Understand that the simple system of linear equations can be used for solving the image processing problems. |
Class 9 | Image retargetting,Seam carving, Bidirectional similarity | Understand the difficulties of image retargeting problem and how to solve them. |
Class 10 | Image recovery via convex optimization 1, Least square method,Tikhonov regularization | Understand the regulazaition technique and its necesity. |
Class 11 | Image recovery via convex optimization 2, convex function, convex set, gradient descent | Understand the fundamentals of convex optimization |
Class 12 | Image recovery via convex optimization 3, TV regularization,norm,Legendre-Fenchel transform | Understand the complex regularization term. |
Class 13 | Image recovery via convex optimization 4, mixed-norm ,Chambolle's algorithm | Understand the numerical algorithms of convex optimization |
Class 14 | Image mosaicing and homography | Understand the basic 3D image transform. |
Class 15 | Presentation | Acquire presentation and communication skills |
Not specified
All course materials are provided on the lecturer's web-site.
Overall learning achievement is evaluated based on written report on the recent advances in image processing (100%).
Not specified.
In 2009, this course is given as 5 days intensive lectures from 1st to 6th classes on August 19, August 20, August 21, September 18 and September 19 during the summer vacation.