Visual reconstruction
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Parallel and Deterministic Algorithms from MRFs: Surface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Lower and upper bounds for the allocation problem and other nonlinear optimization problems
Mathematics of Operations Research
A constant factor approximation algorithm for a class of classification problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Instant Recognition of Half Integrality and 2-Approximations
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
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
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Optimal Net Surface Problems with Applications
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Local Similarity Based Point-Pattern Matching
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
Methodologies and Algorithms for Group-Rankings Decision
Management Science
Parallelized segmentation of a serially sectioned whole human brain
Image and Vision Computing
Limited view CT reconstruction and segmentation via constrained metric labeling
Computer Vision and Image Understanding
On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows
International Journal of Computer Vision
Global optimization for first order Markov Random Fields with submodular priors
Discrete Applied Mathematics
Optimal estimation of deterioration from diagnostic image sequence
IEEE Transactions on Signal Processing
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A note on the discrete binary Mumford-Shah model
MIRAGE'07 Proceedings of the 3rd international conference on Computer vision/computer graphics collaboration techniques
Global optimization for first order Markov random fields with submodular priors
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Fast coupled path planning: from pseudo-polynomial to polynomial
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Minimization of monotonically levelable higher order MRF energies via graph cuts
IEEE Transactions on Image Processing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
Ranking sports teams and the inverse equal paths problem
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
A comparative study of energy minimization methods for markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
An efficient and effective tool for image segmentation, total variations and regularization
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
New algorithms for convex cost tension problem with application to computer vision
Discrete Optimization
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
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Problems of statistical inference involve the adjustment of sample observations so they fit some a priori rank requirements, or order constraints. In such problems, the objective is to minimize the deviation cost function that depends on the distance between the observed value and the modify value. In Markov random field problems, there is also a pairwise relationship between the objects. The objective in Markov random field problem is to minimize the sum of the deviation cost function and a penalty function that grows with the distance between the values of related pairs---separation function.We discuss Markov random fields problems in the context of a representative application---the image segmentation problem. In this problem, the goal is to modify color shades assigned to pixels of an image so that the penalty function consisting of one term due to the deviation from the initial color shade and a second term that penalizes differences in assigned values to neighboring pixels is minimized. We present here an algorithm that solves the problem in polynomial time when the deviation function is convex and separation function is linear; and in strongly polynomial time when the deviation cost function is linear, quadratic or piecewise linear convex with few pieces (where "e;few"e; means a number exponential in a polynomial function of the number of variables and constraints). The complexity of the algorithm for a problem on n pixels or variables, m adjacency relations or constraints, and range of variable values (colors) U, is O(T(n,m) + n log U) where T(n,m) is the complexity of solving the minimum s, t cut problem on a graph with n nodes and m arcs. Furthermore, other algorithms are shown to solve the problem with convex deviation and convex separation in running time O(mn log n log nU) and the problem with nonconvex deviation and convex separation in running time O(T(nU, mU). The nonconvex separation problem is NP-hard even for fixed value of U.For the family of problems with convex deviation functions and linear separation function, the algorithm described here runs in polynomial time which is demonstrated to be fastest possible.