Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Calendar queues: a fast 0(1) priority queue implementation for the simulation event set problem
Communications of the ACM
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
The rectilinear Steiner arborescence problem is NP-complete
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
"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
Interactive Graph Cut Based Segmentation with Shape Priors
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Real-Time Tracking Using Level Sets
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
A Multilevel Banded Graph Cuts Method for Fast Image Segmentation
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
What Metrics Can Be Approximated by Geo-Cuts, Or Global Optimization of Length/Area and Flux
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
More-Than-Topology-Preserving Flows for Active Contours and Polygons
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Handbook of Mathematical Models in Computer Vision
Handbook of Mathematical Models in 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
An integral solution to surface evolution PDEs via geo-cuts
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Image segmentation by iterated region merging with localized graph cuts
Pattern Recognition
Global Interactions in Random Field Models: A Potential Function Ensuring Connectedness
SIAM Journal on Imaging Sciences
Smooth Chan-Vese segmentation via graph cuts
Pattern Recognition Letters
MRF reconstruction of retinal images for the optic disc segmentation
HIS'12 Proceedings of the First international conference on Health Information Science
A multiple object geometric deformable model for image segmentation
Computer Vision and Image Understanding
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Topology is an important prior in many image segmentation tasks. In this paper, we design and implement a novel graph-based min-cut/max-flow algorithm that incorporates topology priors as global constraints. We show that the optimization of the energy function we consider here is NP-hard. However, our algorithm is guaranteed to find an approximate solution that conforms to the initialization, which is a desirable property in many applications since the globally optimum solution does not consider any initialization information. The key innovation of our algorithm is the organization of the search for maximum flow in a way that allows consideration of topology constraints. In order to achieve this, we introduce a label attribute for each node to explicitly handle the topology constraints, and we use a distance map to keep track of those nodes that are closest to the boundary. We employ the bucket priority queue data structure that records nodes of equal distance and we efficiently extract the node with minimal distance value. Our methodology of embedding distance functions in a graph-based algorithm is general and can also account for other geometric priors. Experimental results show that our algorithm can efficiently handle segmentation cases that are challenging for graph-cut algorithms. Furthermore, our algorithm is a natural choice for problems with rich topology priors such as object tracking.