Image Analysis for PhD Students
Bildanalys för doktorander

FMA105F, 7.5 credits

Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-04-22

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English

Aim

The main aim of the course is to give a basic introduction to theory and mathematical methods used in image analysis, to an extent that will allow research and industrial image processing problems to be handled. In addition the aim is to help the doctoral student develop his or her ability in problem solving, both with or without a computer. Furthermore, the aim is to prepare the postgraduate student for further studies in e.g. computer vision, multispectral image analysis and statistical image analysis.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to explain clearly, and to independently use, basic mathematical concepts in image analysis, in particular regarding transform theory (in space as well as in the frequency domain), image enhancement methods, image compression and pattern recognition.
• be able to describe and give an informal explanation of the mathematical theory behind some central image processing algorithms (both deterministic and stochastic).
• have an understanding of the statistical principles used in machine learning

Competences and Skills

For a passing grade the doctoral student must

• in an engineering manner be able to use computer packages to solve problems in image analysis.
• be able to show good capability to independently identify problems which can be solved with methods from image analysis, and be able to choose an appropriate method.
• be able to independently apply basic methods in image processing to problems which are relevant in industrial applications or research.
• with proper terminology, in a well structured way and with clear logic be able to explain the solution to a problem in image analysis.

Course Contents

Basic mathematical concepts: Image transforms, DFT, FFT. Image enhancement: Grey level transforms, filtering. Image restoration: Filterings, inverse methods. Sampling and Interpolation: Continuous versus discrete theory, interpolation. Extraction of special features: Filtering, edge and corner detection. Segmentation: graph-methods, active contours, mathematical morphology. Registration. Machine Learning: Training, testing, generalization, hypothesis spaces.

Course Literature

Szeliski, R.: Computer Vision: Algorithms and Applications. Springer, 2010. ISBN 9781848829343.
It is possible to pass the course without owning the book, using material available through the course home page.

Instruction Details

Types of instruction: Lectures, project

Examination Details

Examination formats: Written report, seminars given by participants
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: Basic calculus and linear algebra. Higher skills in experimentation, in project work and in programming.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page: http://www.maths.lu.se/english/phd-studies/