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  4. Image segmentation methods and an application to brain images
 
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Image segmentation methods and an application to brain images

Citation Link: https://doi.org/10.15480/882.2180
Publikationstyp
Master Thesis
Date Issued
2019
Sprache
English
Author(s)
Nicolai, Christoph  orcid-logo
Advisor
Lindner, Marko  orcid-logo
Referee
Guillemard, Mijail  
Title Granting Institution
Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2018-07-04
Institut
Mathematik E-10  
TORE-DOI
10.15480/882.2180
TORE-URI
http://hdl.handle.net/11420/2305
In this master thesis, a class of methods for image segmentation is discussed. Image segmentation is the decomposition of an image in separate objects. An example for such a decomposition is the separation of individual persons and the background in a photograph. The focus of this thesis is medical image processing. An exemplary task is the segmentation of two- or three-dimensional images of the human brain, where the different objects could be white matter, grey matter, the corpus callosum and the background. Changes over time in the structure of the brain can then not only be subjectively assessed by a physician, but also be automatically quantified and observed.

Basic methods compute such a segmentation by so-called thresholding. Here, image pixels are assigned to a region only by their brightness. For images with soft transitions between the different brightness levels, this yields many small segments along the object borders. The topic of this master thesis is the analytical derivation and efficient implementation of an alternative approach, the minimization of the so-called Mumford-Shah functional. The method discussed in this thesis also considers the brightness of the image pixels, but avoids the subdivision in too many small objects.
Subjects
Image processing
Image segmentation
Mumford–Shah functional
Magnetic resonance imaging
Primal-dual optimization
DDC Class
510: Mathematik
Lizenz
http://rightsstatements.org/vocab/InC/1.0/
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