Stochastic image models for algorithm design
Abstract
In this work two different stochastic image models are proposed for use in two different areas of image processing. First, we develop both a theory and specific methods for performing optimal transform coding of multispectral and multilayer images. The theory is based on the assumption that the image may be modeled as a set of jointly stationary Gaussian random processes. Although we do not assume the autocorrelation has a separable form, we show that the optimal transform for coding has a partially separable structure. Three different algorithms are shown to be asymptotically optimal under different data constraints. The proposed coding techniques are implemented using subband filtering methods, and the various algorithms are tested on multispectral images to determine their relative performance characteristics. We also develop a novel multiscale stochastic image model to describe the appearance of a complex three-dimensional object in a two-dimensional monochrome image. This formal image model is used in conjunction with Bayesian estimation techniques to perform automated inspection. The model is based on a stochastic tree structure in which each node is an important subassembly of the three-dimensional object. The data associated with each node or subassembly is modeled in a wavelet domain. We use a fast multiscale search technique to compute the sequential MAP (SMAP) estimate of the unknown position, scale factor, and 2-D rotation for each subassembly. The search is carried out in a manner similar to a sequential likelihood ratio test, where the process advances in scale rather than time. The results of this search determine whether or not the object passes inspection. A similar search is used in conjunction with the EM algorithm to estimate the model parameters for a given object from a set of training images. The performance of the algorithm is demonstrated on two different real assemblies.
Degree
Ph.D.
Advisors
Bouman, Purdue University.
Subject Area
Electrical engineering
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