Using Dynamic Programming for Solving Variational Problems in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Stereo Without Epipolar Lines: A Maximum-Flow Formulation
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
SIAM Journal on Numerical Analysis
Watersnakes: Energy-Driven Watershed Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A property of the minimum vectors of a regularizing functionaldefined by means of the absolute norm
IEEE Transactions on Signal Processing
Nonlinear evolution equations as fast and exact solvers of estimation problems
IEEE Transactions on Signal Processing
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing
International Journal of Computer Vision
Discrete regularization on weighted graphs for image and mesh filtering
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Total variation minimization and graph cuts for moving objects segmentation
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
An Upwind Finite-Difference Method for Total Variation-Based Image Smoothing
SIAM Journal on Imaging Sciences
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Constrained total variation minimization and application in computerized tomography
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
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This paper deals with the total variation minimization problem when the fidelity is either the L2-norm or the L1-norm. We propose an algorithm which computes the exact solution of these two problems after discretization. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems associated with each level set. Exact solutions of these binary problems are found thanks to minimum-cut techniques. We prove that these binary solutions are increasing and thus allow to reconstruct the solution of the original problems.