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New Convex Relaxations and Global Optimality in Variational Imaging

Swoboda, Paul

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Abstract

Variational methods constitute the basic building blocks for solving many image analysis tasks, be it segmentation, depth estimation, optical flow, object detection etc. Many of these problems can be expressed in the framework of Markov Random Fields (MRF) or as continuous labelling problems. Finding the Maximum A-Posteriori (MAP) solutions of suitably constructed MRFs or the optimizers of the labelling problems give solutions to the aforementioned tasks. In either case, the associated optimization problem amounts to solving structured energy minimization problems. In this thesis we study novel extensions applicable to Markov Random Fields and continuous labelling problems through which we are able to incorporate statistical global constraints. To this end, we devise tractable relaxations of the resulting energy minimization problem and efficient algorithms to tackle them. Second, we propose a general mechanism to find partial optimal solutions to the problem of finding a MAP-solution of an MRF, utilizing only standard relxations.

Item Type: Dissertation
Supervisor: Schnörr, Prof. Dr. Christoph
Date of thesis defense: 1 August 2016
Date Deposited: 10 Oct 2017 11:45
Date: 2016
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 004 Data processing Computer science
510 Mathematics
Controlled Keywords: Bildverarbeitung, Maschinelles Sehen info, Optimierung
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