## MATH4336 Intro to Math of Image Processing (3 credits)

- Description:
- This course introduces digital image processing principles and concepts, tools, and techniques with emphasis on their mathematical foundations. Key topics include image representation, image geomety, image transforms, image enhancement, restoration and segmentation, descriptors, and morphology. The course also discusses the implementation of these algorithms using image processing software.
- Prerequisites: MATH2011/2021/2023 and 2111/2121/2131 and 2351/2352, or MATH2011/2021/2023 and 2350.
- Exclusions: COMP4221 and ELEC4130

- Instructor: Shingyu Leung
- Email: masyleung @ ust.hk
- Office: 3491
- Office hours:
- Class webpage: http://www.math.ust.hk/~masyleung/4336.13s.html
- Class blog: http://math4336-2013s.blogspot.com/

- TA: Ms. Xing Zhang
- Email: xzhangap

- Lectures: Room 4505, TuTh 10:30AM - 11:50AM
- Textbook: Digital Image Processing - Gonzales & Woods + some lecture notes
- http://www.imageprocessingplace.com/DIP-3E/dip3e_main_page.htm
- Chapter 1, 2: http://www.imageprocessingplace.com/DIP-3E/dip3e_sample_book_material.htm
- Errata Sheet: http://www.imageprocessingplace.com/DIP-3E/dip3e_errata_sheet.htm
- Midterm: TBA in class
- Final: TBA

## Intended Learning Outcomes

- Upon sucessful completion of this course, students should
- 1. Be equipped with theoretical knowledge, principles and techniques to image processing problems.
- 2. Acquire a good appreciation of roles of mathematics in image processing.
- 3. Be able to implement image processing algorithms on computers.
- 4. Be able to apply computer algorithms to real-life problems.
- 5. Be able to [resent numerical output from a computer code in a systematical way.

## Announcement

## Notes

## Grading Scheme

- 15% Homework
- 15% Project
- 30% Midterm
- 40% Final
- More information will be given in the lecture prior to the exams.
- No make-up exams.

## Homeworks and Solutions

## Topics

(*) if time permits- Introduction to digital image processing
- Origins and fundamental steps in digital image processing
- Introduction to MATLAB
- Image as Matrix
- Tools: Linear Algebra. Singular value decomposition
- Applications: Histogram processing for image enhancement. Filtering for image enhancement and restoration. Linear signal/image compression. Image segmentation.
- Topics: Image sampling and quantization
- Image in the Frequency Space
- Tools: Fourier transform. FFT.
- Applications: Image enhancement.
- Topics: Fourier series. Fourier transform. (*) Distribution theory.
- Image as Function
- Tools: Calculus of variation. Partial differential equations
- Applications: Image restoration. Image segmentation.
- Topics: Linear diffusion. Nonlinear diffusion (Perona-Malik, ROF). Snake model for segmentation. (*) Geodesic active contour. (*) Chan-Vese mode.