MATH4336 Intro to Math of Image Processing (3 credits)

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 @
Office: 3491
Office hours:
Class webpage:
Class blog:

TA: Ms. Xing Zhang
Email: xzhangap

Lectures: Room 4505, TuTh 10:30AM - 11:50AM
Textbook: Digital Image Processing - Gonzales & Woods + some lecture notes
Chapter 1, 2:
Errata Sheet:
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.


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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

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(*) 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.

Actual Schedule of Lectures

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