Variational models with elastica energies: a comparison, a new model and new algorithms

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dc.contributor Zhu, Wei
dc.contributor Hadji, Layachi
dc.contributor Hu, Fei
dc.contributor Sun, Min
dc.contributor Zhao, Shan
dc.contributor.advisor Zhu, Wei He, Xuan 2018-07-11T16:49:08Z 2018-07-11T16:49:08Z 2018
dc.identifier.other u0015_0000001_0002941
dc.identifier.other He_alatus_0004D_13447
dc.description Electronic Thesis or Dissertation
dc.description.abstract This work comprises two parts. In the first part, we propose novel ALM based algorithms for the ECV-L1 and ECV-L2 segmentation models in order to compare their performance. By imposing one extra constraint, we develop novel augmented Lagrangian functionals that ensure the segmentation level set function to be signed distance func- tions, which avoids the reinitialization of segmentation function during the iterative process. With the proposed algorithm and with the same initial contours, we compare the performance of these two high-order segmentation models and numerically verify the different properties of the two models. Following our previous work, in the second part, we propose a new denoising model with L1 Elastica as the regularizer with corner preserving property. We develop a novel ADMM based algorithm with every subproblem being solved in a closed form. The numerical results on synthetic and real-life images verify the theoretical analysis and show that the model outperforms ROF in preserving contrast. They also show that the new algorithm has fast convergence rate.
dc.format.extent 84 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.title Variational models with elastica energies: a comparison, a new model and new algorithms
dc.type thesis
dc.type text University of Alabama. Dept. of Mathematics Mathematics The University of Alabama doctoral Ph.D.

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