Hauptseminar: Evolving Contours for Medical Image Analysis
Figure 1: Evolving level set with topology change, Source: Wikipedia
by Andreas Keil, Stefanie Demirci, and Prof. Dr. Nassir Navab2 SWS 4 ECTS Time & Location:MI 03.13.010, time to be announced, probably block-wise
The seminar language is English.
If you are interested in the seminar please send a short . Please include last and first name, e-mail address, current semester, discipline (major/minor field of study), and a desired topic.
March 14th, 2008 will be the last date to withdraw your registration. Not withdrawing before this date will result in a 5.0 grade for unacceptable or incomplete work.
The task of segmenting medical image data often can be carried out by using basic algorithms like region growing, e.g.
There are, however, clinical questions which give rise to advanced segmentation problems.
In order to solve those problems, more sophisticated algorithmic approaches have to be applied.
One of them is called "Level Sets" and provides the programmer with a lot of options to define his segmentation goals.
The segmentation is achieved by adjusting region boundaries.
These adjustments are driven by user-defined energies and forces.
Minimizing those energies leads to partial differential equations which – in the end – have to be solved using finite differences.
Figure 2: Narrow band around some boundary, Source: 
The boundaries are represented implicitely, defining them as the zero level set (hence the name) of some function :
(In contrast, "Snakes" are explicitely defined curves or surfaces using splines or other basis functions.)
A boundary's movement over time can then be modeled as evolution of the defining level set function :
Those PDEs are discretized using finite differences and solved with usual schemes thereafter. So-called "Narrow Band Methods", which operate on a local band around border pixels only, can be applied, thereby reducing the workload dramatically (see Figure 2).
This seminar is about understanding level set methods as well as their numerical implementation from the first talk. Further topics at the end of the semester will cover applications from segmentation and image reconstruction.
The literature given below will be provided, but you are of course encouraged to look for more ;-). Google Scholar does an excellent job in finding journal papers and articles from conference proceedings.
Introduction to Level Set Methods and Their Implementation
Introduction to and illustration of level sets
Mathematical derivation of level set equation
Outline of numerical solution
Literature / Material:
J.A. Sethian: Level Set Methods and Fast Marching Methods. Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, 2nd edition, 1999 (Chapters 1 and 2; download of introduction, chapter 1, and bibliography)
S. Osher and R.P. Fedkiw: Level set methods: An overview and some recent results. J. Computational Physics, 169(2):463-502, 2001
C. Li, C. Xu, C. Gui, and M.D. Fox: Level set evolution without re-initialization: A new variational formulation. In Proc. IEEE Conf. Comp. Vis. and Pattern Recog. (CVPR), volume 1, pages 430-436. 2005
S. Osher and N. Paragios: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, 2003. (Chapter 1)
T.F. Chan and L.A. Vese: Active contours without edges. IEEE Trans. Image Process., 10(2):266-277, 2001
J.A. Sethian: Theory, algorithms, and applications of level set methods for propagating interfaces. Acta Numerica, pp. 309-395, 1996
Applications for Level Set Methods in Image Segmentation and 3D Reconstruction
Presentation of an application of level set methods in either segmentation or reconstruction
Explanation of the energy functional chosen for this specific application
Deriving the update equation from the energy functional
Literature / Material:
will be provided, depending on the exact subject chosen by the student