Weakly differentiable functions
Weakly differentiable functions
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
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to Linear Optimization
Introduction to Linear Optimization
Segmentation by Grouping Junctions
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (Mps-Siam Series on Optimization 6)
A Convex Formulation of Continuous Multi-label Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
An Experimental Comparison of Discrete and Continuous Shape Optimization Methods
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
New algorithms for convex cost tension problem with application to computer vision
Discrete Optimization
Optimality bounds for a variational relaxation of the image partitioning problem
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Robust trajectory-space TV-L1 optical flow for non-rigid sequences
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
A fully implicit framework for Sobolev active contours and surfaces
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
Robust classification using l2,1-norm based regression model
Pattern Recognition
Efficient minimization of the non-local potts model
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Completely Convex Formulation of the Chan-Vese Image Segmentation Model
International Journal of Computer Vision
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Approximate envelope minimization for curvature regularity
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Uzawa block relaxation methods for color image restoration
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume 2
Remote sensing image object extraction using convex geometric active contour model
Proceedings of the Fifth International Conference on Internet Multimedia Computing and Service
A Combined First and Second Order Variational Approach for Image Reconstruction
Journal of Mathematical Imaging and Vision
A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models
Journal of Mathematical Imaging and Vision
Total Cyclic Variation and Generalizations
Journal of Mathematical Imaging and Vision
Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem
Journal of Mathematical Imaging and Vision
Convex Relaxation of a Class of Vertex Penalizing Functionals
Journal of Mathematical Imaging and Vision
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We propose an algorithmic framework for computing global solutions of variational models with convex regularity terms that permit quite arbitrary data terms. While the minimization of variational problems with convex data and regularity terms is straightforward (using, for example, gradient descent), this is no longer trivial for functionals with nonconvex data terms. Using the theoretical framework of calibrations, the original variational problem can be written as the maximum flux of a particular vector field going through the boundary of the subgraph of the unknown function. Upon relaxation this formulation turns the problem into a convex problem, although in a higher dimension. In order to solve this problem, we propose a fast primal-dual algorithm which significantly outperforms existing algorithms. In experimental results we show the application of our method to outlier filtering of range images and disparity estimation in stereo images using a variety of convex regularity terms.