On submodular function minimization
Combinatorica
A new approach to the maximum flow problem
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
On active contour models and balloons
CVGIP: Image Understanding
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Curvature-driven flows: a variational approach
SIAM Journal on Control and Optimization
Variational algorithms and pattern formation in dendritic solidification
Journal of Computational Physics
Fast algorithms for parametric scheduling come from extensions to parametric maximum flow
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Mathematical Techniques for Efficient Record Segmentation in Large Shared Databases
Journal of the ACM (JACM)
SIAM Review
A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
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
Introduction to Algorithms
What Energy Functions Can Be Minimized via Graph Cuts?
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Discrete Applied Mathematics
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
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
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Experimental evaluation of parametric max-flow algorithms
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
An integral solution to surface evolution PDEs via geo-cuts
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
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
Minimization of monotonically levelable higher order MRF energies via graph cuts
IEEE Transactions on Image Processing
Image denoising with a constrained discrete total variation scale space
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
A Spatial Regularization Approach for Vector Quantization
Journal of Mathematical Imaging and Vision
Convex and Network Flow Optimization for Structured Sparsity
The Journal of Machine Learning Research
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
WBIR'12 Proceedings of the 5th international conference on Biomedical Image Registration
Segmentation with non-linear regional constraints via line-search cuts
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Bregmanized Domain Decomposition for Image Restoration
Journal of Scientific Computing
Supervised feature selection in graphs with path coding penalties and network flows
The Journal of Machine Learning Research
Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem
Journal of Mathematical Imaging and Vision
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In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409---422, 2006) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26---33, 2003). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Almgren et al. (SIAM Journal on Control and Optimization 31(2):387---438, 1993) and Luckhaus and Sturzenhecker (Calculus of Variations and Partial Differential Equations 3(2):253---271, 1995), and show how the corresponding problems can be solved with sub-pixel accuracy using Parametric Maximum Flow techniques. This provides interesting algorithms for computing crystalline curvature motion, possibly with a forcing term.