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Algorithms for fields and an application to a problem in computer vision [Elektronische Ressource] / Anna Katharina Binder

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179 Pages
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Published 01 January 2009
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TECHNISCHE UNIVERSITAT MUNCHEN
Zentrum Mathematik
Algorithms for Fields and an Application to a
Problem in Computer Vision
Anna Katharina Binder TECHNISCHE UNIVERSITAT MUNCHEN
Zentrum Mathematik
Algorithms for Fields and an Application to a
Problem in Computer Vision
Anna Katharina Binder
Vollstandiger Abdruck der von der Fakultat fur Mathematik der Technischen Universitat
Munchen zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr. Peter Rentrop
Prufer der Dissertation: 1. Univ.-Prof. Dr. Gregor Kemper
2. Univ.-Prof. Dr. Dr. Jurgen Richter-Gebert
3. Univ.-Prof. Dr. Peter Muller
Julius-Maximilians-Universitat Wurzburg
Die Dissertation wurde am 26. 03. 2009 bei der Technischen Universitat eingereicht und
durch die Fakultat fur Mathematik am 13. 07. 2009 angenommen. FürmeineEltern.Abstract
This thesis is composed of several di erent parts. We start with an investigation of an
important problem in computer vision. An appropriate mathematical modeling of this
problem motivates a problem in invariant theory, the examination of the natural action of
m nthe group PGL S on the set ofn-point con gurations ( P ) (for some in nite eldm+1 n K
K and some m;n2N).
This in turn leads to an investigation of algorithms for elds. We develop an algorithm
for the intersection of elds (in special cases) and a method for testing whether a eld is
algebraically closed in another eld. Moreover, we give an algorithm for testing simpleness
of a eld extension as well as nding { if applicable { a generating element. The latter
leads to a new proof of a generalized version of the Theorem of Luroth.
Another approach to solve problems in