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Joint methods in imaging based on diffuse image representations

dc.contributor.advisorRumpf, Martin
dc.contributor.authorBerkels, Benjamin
dc.description.abstractThis thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics.
Simultaneous edge detection and registration of two images:
The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped.
Detection of grain boundaries from atomic scale images of metals or metal alloys:
This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese.
Joint motion estimation and restoration of motion-blurred video:
A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model.
Convexification of the binary Mumford-Shah segmentation model:
After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed.
dc.rightsIn Copyright
dc.subjectFunktion von beschränkter Variation
dc.subjectGlobale Optimierung
dc.subjectKonvexe Optimierung
dc.subjectRegistrierung (Bildverarbeitung)
dc.subjectMumford-Shah functional
dc.subjectlevel set method
dc.subjectFinite Element method
dc.subjectgradient flow
dc.subjectfunctions of bounded variation
dc.subjectglobal optimization
dc.subjectconvex optimization
dc.subjectimage processing
dc.subjectimage registration
dc.subjectcrystalline structure
dc.subjectmotion blur
dc.subject.ddc510 Mathematik
dc.titleJoint methods in imaging based on diffuse image representations
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeBartels, Sören

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