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dc.contributor.authorNi, Kaien_US
dc.date.accessioned2013-06-15T02:58:21Z
dc.date.available2013-06-15T02:58:21Z
dc.date.issued2013-04-08en_US
dc.identifier.urihttp://hdl.handle.net/1853/47683
dc.description.abstractThis thesis is devoted to the detectability of an inhomogeneous region possibly embedded in a noisy environment. It presents models and algorithms using the theory of the longest significant run and percolation. We analyze the computational results based on simulation. We consider the length of the significant nodes in a chain with good continuation in a square lattice of independent nodes. Inspired by the percolation theory, we first analyze the problem in a tree based model. We give the critical probability and find the decay rate of the probability of having a significant run with length k starting at the origin. We find that the asymptotic rate of the length of the significant run can be powerfully applied in the area of image detection. Examples are detection of filamentary structures in a background of uniform random points and target tracking problems. We set the threshold for the rejection region in these problems so that the false positives diminish quickly as we have more samples. Inspired by the convex set detection, we also give a fast and near optimal algorithm to detect a possibly inhomogeneous chain with good continuation in an image of pixels with white noise. We analyze the length of the longest significant chain after thresholding each pixel and consider the statistics over all significant chains. Such a strategy significantly reduces the complexity of the algorithm. The false positives are eliminated as the number of pixels increases. This extends the existing detection method related to the detection of inhomogeneous line segment in the literature.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectFilamentary detectionen_US
dc.subjectLongest significant chainen_US
dc.subjectAsymptotically powerful testen_US
dc.subjectImage detectionen_US
dc.subject.lcshImage analysis
dc.subject.lcshImage processing Statistical methods
dc.titleThe asymptotic rate of the length of the longest significant chain with good continuation in Bernoulli net and its applications in filamentary detectionen_US
dc.typeDissertationen_US
dc.description.degreePhDen_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Koltchinskii, Vladimir; Committee Co-Chair: Huo, Xiaoming; Committee Member: Lounici, Karim; Committee Member: Mei, Yajun; Committee Member: Peng, Liangen_US


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