Spatially adaptive detection of local disturbances in time series and stochastic processes on the integer lattice Z_1hn2 [Elektronische Ressource] / Siana Halim

.Spatially adaptive detection of localdisturbances in time series and stochastic2processes on the integer lattice ZSiana HalimVom Fachbereich Mathematikder Universit at Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum Naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. Jurgen Franke2.hter: Prof. Dr. J. S. MarronVollzug der Promotion: 16 September 2005D386AbstractIn modern textile manufacturing industries, the function of human eyes to detect distur-bances in the production processes which yield defective products is switched to cameras.The camera images are analyzed with various methods to detect these disturbances au-tomatically.There are three parts of texture analysis which are going to be studied here, i.e., imagesmoothing, texture synthesis and defect detection.In the image smoothing, we shall develop a two dimensional kernel smoothing methodwith correlated error. Two approaches are used in synthesising texture. The rst isby constructing a generalized Ising energy function in the Markov Random Field setup,and for the second, we use two dimensional bootstrap methods for semi regular texturesynthesis.We treat defect detection as multihypothesis testing problem with the null hypothesisrepresenting the absence of defects and the other hypothesis representing various types ofdefects.iAcknowledgementBut where shall I nd courage? asked Frodo. That is what I chie y need.