MA4009: Mathematical Principles of Image Processing
| School | Cardiff School of Mathematics |
| Department Code | MATHS |
| Module Code | MA4009 |
| External Subject Code | G100 |
| Number of Credits | 20 |
| Level | L7 |
| Language of Delivery | English |
| Module Leader | Professor Alexander Balinsky |
| Semester | Spring Semester |
| Academic Year | 2014/5 |
Outline Description of Module
At no other time in human history have the influence and impact of image processing on modern society, science, and technology been so explosive. Image processing has become a critical component in contemporary science and technology and has many important applications. This module provides an introduction to the basic ideas and concepts of mathematical image processing. In this course, we will consider the following problems: image denoising and enhancement, image restoration/reconstruction, image segmentation, texture models, machine learning and pattern analysis.
On completion of the module a student should be able to
- Know and understand digitized images and its properties.
- Know and understand image pre-processing.
- Know and understand some modern image analysis tools.
- Understand main principles of pattern analysis and machine learning.
How the module will be delivered
30 one hour lectures
Some handouts will be provided in hard copy or via Learning Central, but students will be expected to take notes of lectures.
Students are also expected to undertake at least 120 hours private study including preparation of worked solutions for problem classes.
Skills that will be practised and developed
Skills:
The ability to understand and apply mathematical tools for image analysis in many contemporary applications.
Transferable Skills:
Ability to recognize, formulate and solve mathematical problems in an interdisciplinary environment.
How the module will be assessed
Formative assessment is carried out in the problem classes. Feedback to students on their solutions and their progress towards learning outcomes is provided during these classes.
The in-course element of summative assessment is based on a class test (taken under examination conditions) similar in form to the tutorial exercises.
The major component of summative assessment is the written examination at the end of the module. This gives students the opportunity to demonstrate their overall achievement of learning outcomes. It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.
The examination paper has a choice of four from five equally weighted questions.
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Spring Semester | 85 | Mathematical Principles Of Image Processing | 3 |
| Class Test | 15 | Class Test | N/A |
Syllabus content
- The digitized images and its properties.
- Image modeling and representation.
- Image denoising and deblurring.
- Image segmentation and inpaiting.
- General pattern theory.
- The mathematics of machine learning.
- Applications in medical image processing.
Essential Reading and Resource List
Please see Background Reading List for an indicative list.
Background Reading and Resource List
Image Processing, Analysis, and Machine Vision, Sonka, M., Hlavac, V., & Boyle, R.
Geometrical Partial Differential Equations and Image Analysis, Sapiro, G.
Image Processing and Analysis: Variational, PDE, Wavelets, and Stochastic Methods, Chan, T. F., & Shen, J.