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/4336.12s.html
Class blog: http://math4336-2012s.blogspot.com/

TA: Mr. Zhang Zhen
Email: jackzz

Lectures: Room 2463, Monday 1500-1620, Friday 1030-1150
Tutorial: Friday 1600-1650
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: 19 March (Mon) in class
Final: 21 May (Mon) 1230-1430 Room 2463

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

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Notes

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Grading Scheme

15% Homework:
15% Tutorial Worksheet:
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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Topics

(*) if time permits
Introduction to digital image processing
Origins and fundamental steps in digital image processing
Introduction to MATLAB
Digital image fundamentals
Image sampling and quantization
Introduction to mathematical tolls in digital image processing
Intensity transformations
Background and basic intensity transformation functions
Spatial averaging
Gaussian filtering
Histogram processing
Smoothing and sharpening spatial filters
*Singular value decomposition (SVD) and image compression
Fourier transform and its applications in image processing
Fourier series
Fourier transform
*Distribution theory
Discret Fourier transform
Image smoothing and sharpening using frequency domain filters
Image restoration
Noise models
Image degradation models
Restoration using inverse and Wiener filterings
*Image segmentation
Region representation
Boundary-based approach
Region-based approach
Variational methods for image processing
Calculus of variation
Linear diffusion
Nonlinear diffusion using the Perona-Malik model and the ROF model
*Variational methods for image segmentation

Actual Schedule of Lectures

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