Course syllabus

# Bildanalys

Image Analysis

## FMAN20, 7,5 credits, A (Second Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Image Analysis

Valid for: 2018/19

Decided by: PLED F/Pi

Date of Decision: 2018-03-23

Elective for: BME4-sbh, BME4-br, C5, D4-bg, E4-mt, E4-bg, F4, F4-bg, F4-bm, L5-gi, Pi4-bg, Pi4-biek

Language of instruction: The course will be given in English on demand

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 the student to handle industrial image processing problems. In addition the aim is to help the student develop his or her ability in problem solving, both with or without a computer. A further 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 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 student must

- in an engineering manner be able to use computer packages to solve problems in image analysis.
- 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 manner and with clear logic be able to explain the solution to a problem in image analysis.

*Basic mathematical concepts*: Image transforms, Discrete
Fourier Transform, 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:* Maximum A Posterori (MAP)
estimations, simulation.

*Pattern recognition:* Classification, SVM (Support
Vector Machine), Principal Component Analysis (PCA), learning.

*Registration*

*Machine Learning:* Training, testing, generalization,
hypothesis spaces.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Compulsory computer exercises and assignments. Approved results on these are enough to pass the course. To get a higher grade, a written and an oral test are required.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Required prior knowledge: FMAF05 Systems and Transforms, or similar (for example FMAF10 Applied Mathematics - Linear Systems).

The number of participants is limited to: No

The course overlaps following course/s: FMA170, FMA172, MATC20

- 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.

Director of studies: Anders Holst, studierektor@math.lth.se

Course coordinator: Kalle Åström, kalle@maths.lth.se

Course administrator: Studerandeexpeditionen, expedition@math.lth.se

Course homepage: http://www.ctr.maths.lu.se/course/newimagean/