Convex Relaxation of a Class of Vertex Penalizing Functionals

Authors:
Kristian Bredies;Thomas Pock;Benedikt Wirth
Affiliations:
Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria 8010;Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria 8010;Courant Institute of Mathematical Sciences, New York University, New York, USA 10012
Venue:
Journal of Mathematical Imaging and Vision
Year:
2013

Citing 18
Cited 0

Visual reconstruction

Visual reconstruction
Nonlinear total variation based noise removal algorithms

Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators

Mathematical Programming: Series A and B
Filtering, Segmentation, and Depth

Filtering, Segmentation, and Depth
A Convolution-Thresholding Approximation of Generalized Curvature Flows

SIAM Journal on Numerical Analysis
A Cortical Based Model of Perceptual Completion in the Roto-Translation Space

Journal of Mathematical Imaging and Vision
Total Generalized Variation

SIAM Journal on Imaging Sciences
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

Journal of Mathematical Imaging and Vision
Global Solutions of Variational Models with Convex Regularization

SIAM Journal on Imaging Sciences
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method

SIAM Journal on Imaging Sciences
Total variation for cyclic structures: Convex relaxation and efficient minimization

CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Framework for Region-Based Image Segmentation and Inpainting Involving Curvature Penalization

International Journal of Computer Vision
Filling-in by joint interpolation of vector fields and gray levels

IEEE Transactions on Image Processing
The Elastic Ratio: Introducing Curvature Into Ratio-Based Image Segmentation

IEEE Transactions on Image Processing
Continuous Multiclass Labeling Approaches and Algorithms

SIAM Journal on Imaging Sciences
Introducing total curvature for image processing

ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Diagonal preconditioning for first order primal-dual algorithms in convex optimization

ICCV '11 Proceedings of the 2011 International Conference on Computer Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate a class of variational problems that incorporate in some sense curvature information of the level lines. The functionals we consider incorporate metrics defined on the orientations of pairs of line segments that meet in the vertices of the level lines. We discuss two particular instances: One instance that minimizes the total number of vertices of the level lines and another instance that minimizes the total sum of the absolute exterior angles between the line segments. In case of smooth level lines, the latter corresponds to the total absolute curvature. We show that these problems can be solved approximately by means of a tractable convex relaxation in higher dimensions. In our numerical experiments we present preliminary results for image segmentation, image denoising and image inpainting.