Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
The theory and practice of Bayesian image labeling
International Journal of Computer Vision
Markov random field modeling in computer vision
Markov random field modeling in computer vision
Image quilting for texture synthesis and transfer
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms
International Journal of Computer Vision
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Graphcut textures: image and video synthesis using graph cuts
ACM SIGGRAPH 2003 Papers
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
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Interactive digital photomontage
ACM SIGGRAPH 2004 Papers
"GrabCut": interactive foreground extraction using iterated graph cuts
ACM SIGGRAPH 2004 Papers
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Bi-Layer Segmentation of Binocular Stereo Video
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
ACM SIGGRAPH 2005 Papers
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
A New Framework for Approximate Labeling via Graph Cuts
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Efficient Belief Propagation for Early Vision
International Journal of Computer Vision
Comparison of energy minimization algorithms for highly connected graphs
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
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
Estimating Optimal Parameters for MRF Stereo from a Single Image Pair
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
On the Spatial Statistics of Optical Flow
International Journal of Computer Vision
Efficient inference with cardinality-based clique potentials
Proceedings of the 24th international conference on Machine learning
ACM SIGGRAPH 2007 papers
A new graph cut-based multiple active contour algorithm without initial contours and seed points
Machine Vision and Applications
Programmable aperture photography: multiplexed light field acquisition
ACM SIGGRAPH 2008 papers
Inter-Image Statistics for 3D Environment Modeling
International Journal of Computer Vision
Stylized black and white images from photographs
NPAR '08 Proceedings of the 6th international symposium on Non-photorealistic animation and rendering
On partial optimality in multi-label MRFs
Proceedings of the 25th international conference on Machine learning
Efficiently solving convex relaxations for MAP estimation
Proceedings of the 25th international conference on Machine learning
Modeling the World from Internet Photo Collections
International Journal of Computer Vision
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
MAP-Inference for Highly-Connected Graphs with DC-Programming
Proceedings of the 30th DAGM symposium on Pattern Recognition
Scene Reconstruction Using MRF Optimization with Image Content Adaptive Energy Functions
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
GeoS: Geodesic Image Segmentation
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Search Space Reduction for MRF Stereo
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Two-dimensional generalisations of dynamic programming for image analysis
Statistics and Computing
Fast image blending using watersheds and graph cuts
Image and Vision Computing
Stereo Matching Using Population-Based MCMC
International Journal of Computer Vision
Improving Border Localization of Multi-Baseline Stereo Using Border-Cut
International Journal of Computer Vision
Convex Multi-class Image Labeling by Simplex-Constrained Total Variation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Focusing generalizations of belief propagation on targeted queries
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Many-pairs mutual information for adding structure to belief propagation approximations
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Bilayer representation for three dimensional visual communication
Journal of Visual Communication and Image Representation
Composition of a dewarped and enhanced document image from two view images
IEEE Transactions on Image Processing
Coarse-to-fine stereo vision with accurate 3D boundaries
Image and Vision Computing
A Framework for Long Distance Face Recognition Using Dense - and Sparse-Stereo Reconstruction
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
A Study of Parts-Based Object Class Detection Using Complete Graphs
International Journal of Computer Vision
Spatially Varying Mixtures Incorporating Line Processes for Image Segmentation
Journal of Mathematical Imaging and Vision
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
Simulating classic mosaics with graph cuts
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
Automatic segmentation of blood vessels from dynamic MRI datasets
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Scale selection for anisotropic diffusion filter by Markov random field model
Pattern Recognition
Approximating weighted Max-SAT problems by compensating for relaxations
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
MRF labeling with a graph-shifts algorithm
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Labeling irregular graphs with belief propagation
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
International Journal of Sensor Networks
Robust stereo matching with improved graph and surface models and occlusion handling
Journal of Visual Communication and Image Representation
User-assisted ink-bleed reduction
IEEE Transactions on Image Processing - Special section on distributed camera networks: sensing, processing, communication, and implementation
Image segmentation by MAP-ML estimations
IEEE Transactions on Image Processing
Fast interactive image segmentation by discriminative clustering
Proceedings of the 2010 ACM multimedia workshop on Mobile cloud media computing
Graph cut based inference with co-occurrence statistics
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Rolled fingerprint construction using MRF-based nonrigid image registration
IEEE Transactions on Image Processing
Probabilistic multi-class scene flow segmentation for traffic scenes
Proceedings of the 32nd DAGM conference on Pattern recognition
Visual enhancement of old documents with hyperspectral imaging
Pattern Recognition
Collective Inference for Extraction MRFs Coupled with Symmetric Clique Potentials
The Journal of Machine Learning Research
Solving MRFs with higher-order smoothness priors using hierarchical gradient nodes
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part I
Modeling complex scenes for accurate moving objects segmentation
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Learning of graphical models and efficient inference for object class recognition
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Solving multilabel MRFs using incremental α-expansion on the GPUs
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
Comparison of energy minimization algorithms for highly connected graphs
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Recovering depth map from video with moving objects
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part II
Answering table queries on the web using column keywords
Proceedings of the VLDB Endowment
Minimizing Energies with Hierarchical Costs
International Journal of Computer Vision
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Brush-and-drag: a multi-touch interface for photo triaging
MobileHCI '12 Proceedings of the 14th international conference on Human-computer interaction with mobile devices and services
User-Centric Learning and Evaluation of Interactive Segmentation Systems
International Journal of Computer Vision
Pose invariant approach for face recognition at distance
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Contraction moves for geometric model fitting
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Analytical dynamic programming matching
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
Going with the flow: pedestrian efficiency in crowded scenes
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Window annealing for pixel-labeling problems
Computer Vision and Image Understanding
A hybrid matching algorithm based on contour and motion information for depth estimation
Proceedings of the 7th International Conference on Ubiquitous Information Management and Communication
Toward parts-based scene understanding with pixel-support parts-sparse pictorial structures
Pattern Recognition Letters
Simultaneous image interpolation for stereo images
Signal Processing
Inference Methods for CRFs with Co-occurrence Statistics
International Journal of Computer Vision
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One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Random Fields (MRF's), the resulting energy minimization problems were widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods—graph cuts, LBP, and tree-reweighted message passing—as well as the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at http://vision.middlebury.edu/MRF.