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
Occlusions, Discontinuities, and Epipolar Lines in Stereo
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Markov Random Fields with Efficient Approximations
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
An iterative image registration technique with an application to stereo vision
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 2
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tight convex relaxations for vector-valued labeling problems
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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We propose an extension of the well-known LP relaxation for Markov random fields to explicitly allow continuous label spaces. Unlike conventional continuous formulations of labelling problems which assume that the unary and pairwise potentials are convex, our formulation allows them to be general piecewise convex functions with continuous domains. Furthermore, we present the extension of the widely used efficient scheme for handling L1 smoothness priors over discrete ordered label sets to continuous label spaces. We provide a theoretical analysis of the proposed model, and empirically demonstrate that labelling problems with huge or continuous label spaces can benefit from our discrete-continuous representation.