Visual reconstruction
Parallel and Deterministic Algorithms from MRFs: Surface Reconstruction
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
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Contour and Texture Analysis for Image Segmentation
International Journal of Computer Vision
Bayesian image restoration and segmentation by constrained optimization
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Quantitative Measures of Change based on Feature Organization: Eigenvalues and Eigenvectors
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
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
Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
Graph Partitioning by Spectral Rounding: Applications in Image Segmentation and Clustering
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
"Ratio Regions": A Technique for Image Segmentation
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem
Operations Research
Image segmentation with ratio cut
IEEE Transactions on Pattern Analysis and Machine Intelligence
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One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. MRF formulates many total variation and other optimization criteria used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is not due to the power of the model. Rather it is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. We describe here an implementation of a very efficient polynomial time algorithm, which is provably fastest possible, delivering the optimal solution to the MRF problem, Hochbaum (2001). It is demonstrated here that many continuous models, common in image segmentation, have a discrete analogs to various special cases of MRF. As such they are solved optimally and efficiently, rather than with the use of continuous techniques such as PDE methods that can only guarantee convergence to a local minimum. The MRF algorithm is enhanced here demonstrating that the set of labels can be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Modifications in the set of labels (colors), for instance, are executed instantaneously. Several theoretical results on the properties of the algorithm are proved here and are demonstrated for examples in the context of medical and biological imaging.