title: Variational Approaches for Image Labeling on the Assignment Manifold
creator: Savarino, Fabrizio
subject: ddc-510
subject: 510 Mathematics
description: The image labeling problem refers to the task of assigning to each pixel a single element from a finite predefined set of labels. In classical approaches the labeling task is formulated as a minimization problem of specifically structured objective functions.  Assignment flows for contextual image labeling are a recently proposed alternative formulation via spatially coupled replicator equations.   In this work, the classical and dynamical viewpoint of image labeling are combined into a variational formulation. This is accomplished by following the induced Riemannian gradient descent flow on an elementary statistical manifold with respect to the underlying information geometry.  Convergence and stability behavior of this approach are investigated using the log-barrier method. A novel parameterization of the assignment flow by its dominant component is derived, revealing a Riemannian gradient flow structure that clearly identifies the two governing processes of the flow: spatial regularization of assignments and gradual enforcement of unambiguous label decisions. Also, a continuous-domain formulation of the corresponding potential is presented and well-posedness of the related optimization problem is established. Furthermore, an alternative smooth variational approach to maximum a-posteriori inference based on discrete graphical models is derived by utilizing local Wasserstein distances. Following the resulting Riemannian gradient flow leads to an inference process which always satisfies the local marginalization constraints and incorporates a smooth rounding mechanism towards unambiguous assignments.
date: 2020
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/28522/1/Thesis.pdf
identifier: DOI:10.11588/heidok.00028522
identifier: urn:nbn:de:bsz:16-heidok-285225
identifier:   Savarino, Fabrizio  (2020) Variational Approaches for Image Labeling on the Assignment Manifold.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/28522/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng