Bildanalys

**Valid from:** Autumn 2013**Decided by:** FN1/Anders Gustafsson**Date of establishment:** 2014-01-31

**Division:** Mathematics**Course type:** Course given jointly for second and third cycle**The course is also given at second-cycle level with course code:** FMA170**Teaching language:** English

The aim of the course is to give necessary knowledge of digital image analysis for further research within the area and to be able to use digital image analysis within other research areas such as computer graphics, image coding, video coding and industrial image processing problems. The aim is also to prepare the 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 (Discrete Fourier Transform), FFT (Fast Fourier Transform). Image enhancement: Grey level transforms, filtering. Image restoration: Filterings, inverse methods. Scale space theory: Continuous versus discrete theory, interpolation. Extraction of special features: Filtering, edge and corner detection. Segmentation: graph-methods, active contours, mathematical morphology. Bayesian image handling: MAP(Maximum Aposteriori) estimations, simulation. Pattern recognition: Classification, SVM (Support Vector Machines), PCA (Principal Component Analysis), learning. 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, laboratory exercises, exercises

**Examination format:** Written assignments**Grading scale:** Failed, pass**Examiner:**

**Course coordinator:** Karl Åström `<karl.astrom@math.lth.se>`