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Full-Text Articles in Physical Sciences and Mathematics
Texture Analysis Using Partially Ordered Markov Models, Jennifer Davidson, Ashit Talukder, Noel A. Cressie
Texture Analysis Using Partially Ordered Markov Models, Jennifer Davidson, Ashit Talukder, Noel A. Cressie
Professor Noel Cressie
Texture is a phenomenon in image data that continues to receive wide-spread interest due to its broad range of applications. The paper focuses on but one of several ways to model textures, namely, the class of stochastic texture models. the authors introduce a new spatial stochastic model called partially ordered Markov models, or POMMs. They show how POMMs are a generalization of a class of models called Markov mesh models, or MMMs, that allow an explicit closed form of the joint probability, just as do MMMs. While POMMs are a type of Markov random field model (MRF), the general MRFs …
Mine Boundary Detection Using Partially Ordered Markov Models, Xia Hua, Jennifer Davidson, Noel A. Cressie
Mine Boundary Detection Using Partially Ordered Markov Models, Xia Hua, Jennifer Davidson, Noel A. Cressie
Professor Noel Cressie
Detection of objects in images in an automated fashion is necessary for many applications, including automated target recognition. In this paper, we present results of an automated boundary detection procedure using a new subclass of Markov random fields (MRFs), called partially ordered Markov models (POMMs). POMMs offer computational advantages over general MRFs. We show how a POMM can model the boundaries in an image. Our algorithm for boundary detection uses a Bayesian approach to build a posterior boundary model that locates edges of objects having a closed loop boundary. We apply our method to images of mines with very good …
Asymptotic Properties Of Maximum (Composite) Likelihood Estimators For Partially Ordered Markov Models, Hsin-Cheng Huang, Noel A. Cressie
Asymptotic Properties Of Maximum (Composite) Likelihood Estimators For Partially Ordered Markov Models, Hsin-Cheng Huang, Noel A. Cressie
Professor Noel Cressie
Partially ordered Markov models (POMMs) are Markov random fields (MRFs) with neighborhood structures derivable from an associated partially ordered set. The most attractive feature of POMMs is that their joint distributions can be written in closed and product form. Therefore, simulation and maximum likelihood estimation for the models is quite straightforward, which is not the case in general for MRF models. In practice, one often has to modify the likelihood to account for edge components; the resulting composite likelihood for POMMs is similarly straightforward to maximize. In this article, we use a martingale approach to derive the asymptotic properties of …