TY  - GEN
N2  - 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.
A1  - Lellmann, Jan
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/12505/
ID  - heidok12505
KW  - Konvexe Relaxation 
KW  -  Sattelpunktproblem 
KW  -  Coarea-FormelImage Segmentation 
KW  -  Continuous Cut 
KW  -  Saddle Point Problem 
KW  -  Convex Relaxation 
KW  -  Coarea Formula
AV  - public
TI  - Nonsmooth Convex Variational Approaches to Image Analysis
Y1  - 2011///
ER  -