title: Nonsmooth Convex Variational Approaches to Image Analysis
creator: Lellmann, Jan
subject: ddc-510
subject: 510 Mathematics
description: Variational models constitute a foundation for the formulation and understanding of models in many areas of image processing and analysis. In this work, we consider a generic variational framework for convex relaxations of multiclass labeling problems, formulated on continuous domains. We propose several relaxations for length-based regularizers, with varying expressiveness and computational cost. In contrast to graph-based, combinatorial approaches, we rely on a geometric measure theory-based formulation, which avoids artifacts caused by an early discretization in theory as well as in practice. We investigate and compare numerical first-order approaches for solving the associated nonsmooth discretized problem, based on controlled smoothing and operator splitting. In order to obtain integral solutions, we propose a randomized rounding technique formulated in the spatially continuous setting, and prove that it allows to obtain solutions with an a priori optimality bound. Furthermore, we present a method for introducing more advanced prior shape knowledge into labeling problems, based on the sparse representation framework.
date: 2011
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/12505/1/lellmann_thesis.pdf
identifier: DOI:10.11588/heidok.00012505
identifier: urn:nbn:de:bsz:16-opus-125056
identifier:   Lellmann, Jan  (2011) Nonsmooth Convex Variational Approaches to Image Analysis.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/12505/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng