Spatially adaptive detection of local disturbances in time series and stochastic processes on the integer lattice Z2

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 three parts of texture analysis which are going to be studied here, i.e., image smoothing, texture synthesis and defect detection. In the image smoothing, we shall develop a two dimensional kernel smoothing method with correlated error. Two approaches are used in synthesising texture. The first is by 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 texture synthesis. We treat defect detection as multihypothesis testing problem with the null hypothesis representing the absence of defects and the other hypothesis representing various types of defects.