MATC20 Image Analysis, 7.5 credits, is an optional course at upper basic level available for students enrolled in the Bachelor´s or Master´s Programme in Mathematics at the Faculty of Science. The course is given by the Department of Mathematics at the Faculty of Engineering (with the course code FMAN20). The course is given in English at half study pace during the first half of the autumn semester.

Course Content
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.

The course covers

Basic mathematical concepts: image transforms, Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT).
Image enhancement: grey level transformation, filtering.
Image restoration: filtering, inverse methods.
Scale-space theory: continuous versus discrete theory, interpolation.
Feature extraction: filtering, edge and corner detection.
Segmentation: graph methods, active contours, mathematical morphology.
Bayesian image processing: MAP (Maximum A Posteriori) estimation, simulation.
Pattern recognition: classification, Support Vector Machine (SVM), Principal Component Analysis (PCA), learning.
Registration: transformation, e.g. using rescaling or rotation and different images in a coordinate system so that equivalent points on the object end up over each other.
Machine learning: learning, testing, generalisation, hypothesis spaces.

Teaching
The teaching consists of lectures and computer laboratory sessions.

Assessment
The course is assessed through written assignments during the course and possibly a written take-home examination and an associated oral examination. To be awarded a pass with distinction (or grade 4-5), the candidate must pass the take-home examination and an oral examination with distinction.

Course Literature
The material in the course is covered by the lectures with notes. For additional information please see

Official Course Description

Syllabus in English
Kursplan på svenska

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science