Spatially adaptive detection of local disturbances in time series and stochastic processes on the integer lattice Z ^2

  • In modern textile manufacturing industries, the function of human eyes to detect disturbances in the production processes which yield defective products is switched to cameras. The camera images are analyzed with various methods to detect these disturbances automatically. There are, however, still problems with in particular semi-regular textures which are typical for weaving patterns. We study three parts of that problem of automatic texture analysis: image smoothing, texture synthesis and defect detection. In image smoothing, we develop a two dimensional kernel smoothing method with locally and directionally adaptive bandwidths allowing correlation in the errors. Two approaches are used in synthesising texture. The first is based on constructing a generalized Ising energy function in the Markov Random Field setup, and for the second, we use two-dimensional periodic bootstrap methods for semi-regular texture synthesis. We treat defect detection as multihypothesis testing problem with the null hypothesis representing the absence of defects and the other hypotheses representing various types of defects. We develop a test based on a nonparametric regression setup, and we use the bootstrap for approximating the distribution of our test statistic.
  • Räumliche adaptive Erkennung von Störungen in Zeitreihen und stochastischen Prozessen auf Gitter Z^2

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Author:Siana Halim
Advisor:Jürgen Franke
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2005
Year of Publication:2005
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2005/09/16
Date of the Publication (Server):2005/09/20
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011