Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
One-Dimensional Regularization with Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Using Dynamic Programming for Solving Variational Problems in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
The theory and practice of Bayesian image labeling
International Journal of Computer Vision
The complexity of multiway cuts (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical models for machine learning and digital communication
Graphical models for machine learning and digital communication
A revolution: belief propagation in graphs with cycles
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Inference in Bayesian networks using nested junction trees
Learning in graphical models
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: modeling, learning, sampling and computing, Part I
Approximation algorithms
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
An MRF-Based Approach to Generation of Super-Resolution Images from Blurred Observations
Journal of Mathematical Imaging and Vision
Example-Based Super-Resolution
IEEE Computer Graphics and Applications
Multimodal Estimation of Discontinuous Optical Flow using Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
Interactive Organ Segmentation Using Graph Cuts
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Multi-camera Scene Reconstruction via Graph Cuts
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Discrete Applied Mathematics
Understanding belief propagation and its generalizations
Exploring artificial intelligence in the new millennium
Segmentation by Grouping Junctions
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Markov Random Fields with Efficient Approximations
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Stereo Matching Using Belief Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
MRF Solutions for Probabilistic Optical Flow Formulations
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Comparison of Graph Cuts with Belief Propagation for Stereo, using Identical MRF Parameters
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tree consistency and bounds on the performance of the max-product algorithm and its generalizations
Statistics and Computing
Convex Optimization
"GrabCut": interactive foreground extraction using iterated graph cuts
ACM SIGGRAPH 2004 Papers
Pictorial Structures for Object Recognition
International Journal of Computer Vision
Visual Hand Tracking Using Nonparametric Belief Propagation
CVPRW '04 Proceedings of the 2004 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'04) Volume 12 - Volume 12
Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)
Spatial Priors for Part-Based Recognition Using Statistical Models
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Discriminative Learning of Markov Random Fields for Segmentation of 3D Scan Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Fields of Experts: A Framework for Learning Image Priors
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Energy Minimization via Graph Cuts: Settling What is Possible
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Effciently Solving Dynamic Markov Random Fields Using Graph Cuts
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
International Journal of Computer Vision
Efficient Belief Propagation for Early Vision
International Journal of Computer Vision
Graph Cuts and Efficient N-D Image Segmentation
International Journal of Computer Vision
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Measure Locally, Reason Globally: Occlusion-sensitive Articulated Pose Estimation
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Linear Programming Relaxations and Belief Propagation -- An Empirical Study
The Journal of Machine Learning Research
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimizing Nonsubmodular Functions with Graph Cuts-A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Spatial Statistics of Optical Flow
International Journal of Computer Vision
Approximate Labeling via Graph Cuts Based on Linear Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Representation and Matching of Pictorial Structures
IEEE Transactions on Computers
Dynamic Graph Cuts for Efficient Inference in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiview Stereo via Volumetric Graph-Cuts and Occlusion Robust Photo-Consistency
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simultaneous Segmentation and Pose Estimation of Humans Using Dynamic Graph Cuts
International Journal of Computer Vision
Training structural SVMs when exact inference is intractable
Proceedings of the 25th international conference on Machine learning
On partial optimality in multi-label MRFs
Proceedings of the 25th international conference on Machine learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient MRF deformation model for non-rigid image matching
Computer Vision and Image Understanding
Computer Vision and Image Understanding
Measuring uncertainty in graph cut solutions
Computer Vision and Image Understanding
Efficient belief propagation for higher-order cliques using linear constraint nodes
Computer Vision and Image Understanding
Fast Generalized Belief Propagation for MAP Estimation on 2D and 3D Grid-Like Markov Random Fields
Proceedings of the 30th DAGM symposium on Pattern Recognition
Semiautomatic segmentation with compact shape prior
Image and Vision Computing
Optimizing Binary MRFs with Higher Order Cliques
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Star Shape Prior for Graph-Cut Image Segmentation
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Beyond Loose LP-Relaxations: Optimizing MRFs by Repairing Cycles
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Nonrigid Image Registration Using Dynamic Higher-Order MRF Model
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Learning CRFs Using Graph Cuts
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
Feature Correspondence Via Graph Matching: Models and Global Optimization
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
International Journal of Computer Vision
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
International Journal of Computer Vision
Robust Higher Order Potentials for Enforcing Label Consistency
International Journal of Computer Vision
Markov Random Field Modeling in Image Analysis
Markov Random Field Modeling in Image Analysis
Learning structural SVMs with latent variables
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
An Analysis of Convex Relaxations for MAP Estimation of Discrete MRFs
The Journal of Machine Learning Research
P³ & Beyond: Move Making Algorithms for Solving Higher Order Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Dense Registration with Deformation Priors
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Thin junction tree filters for simultaneous localization and mapping
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Global Stereo Reconstruction under Second-Order Smoothness Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Learning 3D mesh segmentation and labeling
ACM SIGGRAPH 2010 papers
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
Fusion Moves for Markov Random Field Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Order-Preserving Moves for Graph-Cut-Based Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonparametric belief propagation
Communications of the ACM
Object Detection with Discriminatively Trained Part-Based Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dynamic Hybrid Algorithms for MAP Inference in Discrete MRFs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal contour closure by superpixel grouping
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Towards more efficient and effective LP-based algorithms for MRF optimization
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
What, where and how many? combining object detectors and CRFs
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Superpixels and supervoxels in an energy optimization framework
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Graph cut based inference with co-occurrence statistics
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Multiscale conditional random fields for image labeling
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
3D knowledge-based segmentation using pose-invariant higher-order graphs
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
TriangleFlow: optical flow with triangulation-based higher-order likelihoods
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
MRF inference by k-fan decomposition and tight Lagrangian relaxation
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
MRF Energy Minimization and Beyond via Dual Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision: Algorithms and Applications
Computer Vision: Algorithms and Applications
Improved Moves for Truncated Convex Models
The Journal of Machine Learning Research
Dynamic Programming and Graph Algorithms in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIFT Flow: Dense Correspondence across Scenes and Its Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
PAMPAS: real-valued graphical models for computer vision
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Transformation of General Binary MRF Minimization to the First-Order Case
IEEE Transactions on Pattern Analysis and Machine Intelligence
Faster Algorithms for Max-Product Message-Passing
The Journal of Machine Learning Research
Markov Random Fields for Vision and Image Processing
Markov Random Fields for Vision and Image Processing
Fast Inference with Min-Sum Matrix Product
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast memory-efficient generalized belief propagation
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Fast Approximate Energy Minimization with Label Costs
International Journal of Computer Vision
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
Exploiting inference for approximate parameter learning in discriminative fields: an empirical study
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Efficient belief propagation with learned higher-order markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Intrinsic dense 3D surface tracking
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Making the right moves: Guiding alpha-expansion using local primal-dual gaps
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Inference for order reduction in Markov random fields
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Efficient training for pairwise or higher order CRFs via dual decomposition
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Multi-label Moves for MRFs with Truncated Convex Priors
International Journal of Computer Vision
The generalized distributive law
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
IEEE Transactions on Information Theory
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
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimizing Energies with Hierarchical Costs
International Journal of Computer Vision
Fast dynamic programming for labeling problems with ordering constraints
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Revisiting uncertainty in graph cut solutions
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Superpixels via pseudo-Boolean optimization
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Learning to cluster using high order graphical models with latent variables
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
A graph cut algorithm for higher-order Markov Random Fields
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Efficient parallel message computation for MAP inference
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Viewpoint invariant 3D landmark model inference from monocular 2D images using higher-order priors
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Efficient nonlocal regularization for optical flow
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Hausdorff distance constraint for multi-surface segmentation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Dynamic programming for approximate expansion algorithm
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Simultaneous Cast Shadows, Illumination and Geometry Inference Using Hypergraphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Inference Methods for CRFs with Co-occurrence Statistics
International Journal of Computer Vision
A Fully-Connected Layered Model of Foreground and Background Flow
CVPR '13 Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition
Poselet Conditioned Pictorial Structures
CVPR '13 Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition
A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problems
CVPR '13 Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition
Fully-Connected CRFs with Non-Parametric Pairwise Potential
CVPR '13 Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition
Nonlinearly Constrained MRFs: Exploring the Intrinsic Dimensions of Higher-Order Cliques
CVPR '13 Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition
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In this paper, we present a comprehensive survey of Markov Random Fields (MRFs) in computer vision and image understanding, with respect to the modeling, the inference and the learning. While MRFs were introduced into the computer vision field about two decades ago, they started to become a ubiquitous tool for solving visual perception problems around the turn of the millennium following the emergence of efficient inference methods. During the past decade, a variety of MRF models as well as inference and learning methods have been developed for addressing numerous low, mid and high-level vision problems. While most of the literature concerns pairwise MRFs, in recent years we have also witnessed significant progress in higher-order MRFs, which substantially enhances the expressiveness of graph-based models and expands the domain of solvable problems. This survey provides a compact and informative summary of the major literature in this research topic.