Syllabus academic year 2007/2008

Higher education credits: 6. Grading scale: TH. Level: A (Second level). Language of instruction: The course might be given in English. FMA170 overlap following cours/es: FMA172 och FMA172. Optional for: C4, D4, D4bg, E4mt, F4, F4mt, F4tmb, L4gi, L3XTG, Pi4bm, Pi4sbs. Course coordinator: Director of Studies, Lars-Christer Böiers,, Matematik. Recommended prerequisits: Linear Analysis. Assessment: Compulsory computer exercises and assignments. Approved results on these are enough to pass the course. To get a higher grade a written or oral test is requied. Home page:

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 industrial image processing problems to be handled. In addition the aim is to help the student develop his or her ability in problem solving, with or without a computer. Furthermore, the aim is 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 student must

be able to explain clearly and 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).

Skills and abilities
For a passing grade the student must

in an engineering manner be able to use computer packages to solve problems in image analysis.

be able to show good capability independently to identify problems which can be solved with methods from image analysis, and be able to choose an appropriate method.

be able independently to 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 concepts of mathematics: Image transforms, DFT, FFT.

Image enhancement: Grey level transforms, filtering.

Image restoration: Filtering, the Wiener filter.

Scale space theory: Continuous versus discrete theory, interpolation.

Extraction of special features: Filtering, edge and corner detection.

Segmentation: Split and merge algorithms, mathematical morphology.

Bayesian image handling: MAP estimations, simulation.

Image compression: JPEG, wavelets, fractals, PCA.

Forsyth, Ponce, Computer Vision: A Modern Approach, Prentice-Hall 2003, ISBN: 0131911937.