Syllabus academic year 2007/2008
COMPUTER VISIONFMA270

Higher education credits: 6. Grading scale: TH. Level: A (Second level). Language of instruction: The course might be given in English. FMA270 overlap following cours/es: FMA271 och FMA271. Optional for: C4, D4, D4bg, E4bg, F4, F4tmb, Pi4. Course coordinator: Director of Studies Lars-Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Recommended prerequisits: FMA037 Complex Analysis, FMA036 Linear Analysis, Image 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: http://www.maths.lth.se/matematiklth/vision/datorseende/datorseende.html.

Aim
The aim of the course is to give an overview of the theory and practically useful methods in computer vision, with applications within e.g. vision systems, non-invasive measurements and augmented reality. In addition the aim is to make the student develop his or her ability in problem solving, with and without a computer, using mathematical tools taken from many areas of the mathematical sciences, in particular geometry, optimisation, mathematical statistics, invariant theory and transform theory.

Knowledge and understanding
For a passing grade the student must

be able to clearly explain and to use basic concepts in computer vision, in particular regarding projective geometry, camera modeling, stereo vision, recognition and structure and motion problems.

be able to describe and give an informal explanation of the mathematical theory behind some central algorithms in computer vision (the least squares method, Newton based optimization and stochastic methods).

Skills and abilities
For a passing grade the student must

in an engineering manner be able to use computer packages independently to solve problems in computer vision.

be able to show good ability independently to identify problems which can be solved with methods from computer vision, and be able to choose an appropriate method.

be able independently to apply basic methods in computer vision 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 computer vision.

Contents
Projective geometry. Geometric transformations. Modelling cameras. Stereo vision. Photogrammetry. Recognition. 3D-modeling. Geometry of surfaces and their silhouettes. Visualisation.

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