Bildanalys för doktorander

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

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

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.

*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.

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.

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.

**Types of instruction:** Lectures, project

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

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

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