Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: This thesis provides an introduction to the statistical modeling technique known as graphical
models. Since graph theory and probability theory are the two legs of graphical models, these
two topics are presented, and then combined to produce two examples of graphical models:
Bayesian Networks and Markov Random Fields. Furthermore, the max-sum, sum-product
and junction tree algorithms are discussed. The graphical modeling technique is then applied
to the specific problem of finding coplanar points in stereo images, taken with an uncalibrated
camera. Although it is discovered that graphical models might not be the best method, in
terms of speed, to use for this appliation, it does illustrate how to apply this technique in a
real-life problem. / AFRIKAANSE OPSOMMING: Hierdie tesis stel die leser voor aan die statistiese modelerings-tegniek genoemd grafiese modelle.
Aangesien grafiek teorie en waarskynlikheidsleer die twee bene van grafiese modelle is,
word hierdie areas aangespreek en dan gekombineer om twee voorbeelde van grafiese modelle
te vind: Bayesian Netwerke en Markov Lukrake Liggaam. Die maks-som, som-produk en
aansluitboom algoritmes word ook bestudeer. Nadat die teorie van grafiese modelle en hierdie
drie algoritmes afgehandel is, word grafiese modelle dan toegepas op ’n spesifieke probleem—
om punte op ’n gemeenskaplike vlak in stereo beelde te vind, wat met ’n ongekalibreerde
kamera geneem is. Alhoewel gevind is dat grafiese modelle nie die optimale metode is om
punte op ’n gemeenskaplike vlak te vind, in terme van spoed, word die gebruik van grafiese
modelle wel ten toongestel met hierdie praktiese voorbeeld. / National Research Foundation (South Africa)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/4094 |
| Date | 03 1900 |
| Creators | Roux, Jeanne-Marie |
| Contributors | Hunter, K. M., Herbst, B. M., University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. |
| Publisher | Stellenbosch : University of Stellenbosch, Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 87 p. : ill. |
| Rights | University of Stellenbosch |
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