TeachingSs08EvolvingContoursHauptseminar

 Chair for Computer Aided Medical Procedures & Augmented Reality Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality

 MICCAI 2015Munich, Germany MEDICON 2013Sevilla, Spain MICCAI-STENT 2013Nagoya, Japan IPCAI 2013Heidelberg, Germany

# Hauptseminar: Evolving Contours for Medical Image Analysis

Figure 1: Evolving level set with topology change, Source: Wikipedia

2 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.

## Abstract

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: [3]

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.

## Schein requirements

As usual:

• attendance of the Hauptseminar meeting
• active class participation (discussions)
• handout (8 - 16 pages) in LaTeX
• presentation (approximately 45 minutes + discussion) in Powerpoint or PDF format

## Timeline

• 4-6 weeks before presentation: Outline
• 2 weeks before presentation: Handout
• 1 week before presentation: Presentation Slides

## Topics & Schedule (preliminary)

Date Time Topic Student Handout/Slides Supervisor
May 21, 2008 13.30 Introduction to Level Set Methods and Their Implementation Aliaksei Maistrou   Andreas Keil
June 4, 2008 16:00 Introduction to Statistical Shape and Appearance Models for Segmentation Nika Razansky handout slides Stefanie Demirci
June 23, 2008 13:30 Hybrid Medical Image Segmentation: Combining Level Sets and Statistical Models Martin Lehner   Stefanie Demirci

## Topic Definitions and Material

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

Topic Definition:
• 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)
• J.A. Sethian's excellent web resource
• 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

Topic Definition:
• 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

TeachingForm
Title: Evolving Contours for Medical Image Analysis
Professor: Prof. Dr. Nassir Navab
Tutors: Andreas Keil, Stefanie Demirci
Type: Hauptseminar
Information: 2 SWS, 4 ECTS
Term: 2008SoSe
Abstract:

Edit | Attach | Refresh | Diffs | More | Revision r1.21 - 22 Jun 2008 - 21:03 - StefanieDemirci

Lehrstuhl für Computer Aided Medical Procedures & Augmented Reality