Mathematical Sciences

Lund University

Image Analysis for PhD Students

The main goal of the course is to give a basic introduction to theory and mathematical methods used in image analysis, to an extent that will allow image processing problems to be developed and evaluated. In addition the aim is to help the PhD student develop his or her ability in problem solving, both with and without a computer. Furthermore, the aim is to prepare the student for further studies in computer vision, multispectral image analysis, machine learning and statistical image analysis.

The course consists of 10 lectures (mondays 10-12 and thursdays 10-12). During the lectures we will present material from seven modules (described below). Each participant works on his/her own material during the course and presents the results on wednesday 11/12. It is assumed that each student participates actively during the course. Use your individual material and data and try to implement methods from the lectures, examplifying such methods with your data. In order to make progress on your projects there are also project supervision on wednesdays 10-12, where you can get help on material, programming, etc from the lecturers and computer vision PhD students.

Module 1 - Introduction to images and to image analysis systems. Linear algebra for images. The convolution operator and the Fourier transform and their relation to each other. Detection. Understanding of filter types (low-pass, high-pass, band-pass and band-reject), definition of image quality and strategies for image optimization. Module 2 - Discretization of continuous signals, and associated errors. Image interpolation. The discrete Fourier transform. Multimodality image registration, Applications Module 3 - Image segmentation and voxel classification in general. Thresholding. Segmentation using energy methods, Segmentation using snakes. Level set methods. Tracking. Applications. Module 4 - Visualization and screen representation, color coding, alpha channel, contrast, transparency, histogram equalization, Applications. Module 5 - Image reconstruction of 3D volumes from 2D projections. Analytical methods, Iterative Methods. Noise models. Applications. Module 6 - Image system development and evaluation. Monte Carlo simulations of imaging systems, Observer studies. Applications. Module 7 - Machine learning for image classification and clustering. Methods includes neural networks, support vector machines, random forests and self-organizing feature maps. Applications

Lectures: (date, time, lecturer, room, lecture content) 4/11 10-12 KÅ Andromeda, material from Module 1

7/11 10-12 KÅ Andromeda, material from Module 1

11/11 10-12 KÅ Andromeda, material from Module 3

14/11 10-12 KÅ Andromeda, material from Module 3

18/11 10-12 KSG Cassiopeia, material from Module 2

21/11 10-12 KSG Andromeda, material from Module 2

25/11 10-12 ML Cassiopeia, material from Module 4, 5, 6

28/11 10-12 ML Andromeda, material from Module 4, 5, 6

2/12 10-12 MO Cassiopeia, material from Module 7

5/12 10-12 MO Andromeda, material from Module 7

Project supervision: (date, time, room)

6/11 10-12 Andromeda

13/11 10-12 Cassiopeia

20/11 10-12 Andromeda

27/11 10-12 Andromeda

4/12 10-12 Andromeda

Project presentations: (date, time, room)

11/12 10-15 MH:210B

All presentations are in the library of the math building. The library is on the second floor of the building. The room is in the south part of the library (MH:210b).

Programme for presentations

Wednesday December 11th

Pre-Lunch presentation:

10:30 Regina Schmitt "Image based tracking of silicon beads"

Post-Lunch presentations:

13:15 Christian Bierlich "Finding Higgs particles using Image analysis techniques"

13.35 Erik Mårsell "Detecting oscilating patterns"

13:55 Linus Ludvigsson "Automated analysis of TEM/SEM image of atomic lattices"

14:15 Henrik Persson "Neuron weight measurement

14:35 Niklas Olén "Assessing vegetation growth from images using registration and classification"


Course Material

Lecture 3
Notes by Gunnar Sparr on Linear algebra, convolution, fouriertransform (in swedish)
Lecture 4 extra
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 9
Lecture 10
Exercises machine learning
Material for exercises on machine learning

Course Start

Introductory Meeting:
2013-11-04, 11:15
Astronome: Andromeda

Start date:

Reading periods:
Autumn, second half