-excesses are pushed towards the sink (T) -deficits are pulled towards the source (S) Active Graph Cuts O. Juan CERTIS, ENPC Marne-La-Vallée, France Y. Boykov University of Western Ontario London, Canada Video segmentation:  Recycles the cut of the previous frame  5 times faster than [1] (up to 11~20)  Speed is still correlated with Hausdorff distance Hierarchical segmentation:  Recycles the cut of the previous level  Guaranteed global optima, unlike [2]  … but no memory saving…  AlgorithmVentricle/TimeLung/Time MaxFlow [1]18.15ms26.47ms Active Cuts18.52ms19.98ms Hierarchical Active Cuts Level 2 : 0.70ms Level 1 : 0.61ms Level 0 : 8.59ms Total : 9.90ms Level 2 : 0.45ms Level 1 : 2.14ms Level 0 : 16.95ms Total : 19.54ms Result consistency:Decreasing cost cuts:  Intermediate cuts = local minima  Final cut = global minimum  [1] Boykov, Y., and Kolmogorov, V. An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. In Energy Minimization Methods in Computer Vision and Pattern Recognition (2001), pp. 359–374.  [2] Lombaert, H., Sun, Y., Grady, L., and Xu, C. A multilevel banded graph cuts method for fast image segmentation. In Proceedings of the Tenth IEEE International Conference on Computer Vision (2005), pp. 259–265.  [3] Kohli, P., and Torr, P. H. S. Effciently solving dynamic markov random fields using graph cuts. In Proceedings of the 10th IEEE International Conference on Computer Vision (2005), IEEE Computer Society, pp. 922–929.  [4] Goldberg, A. V., and Tarjan, R. E. A new approach to the maximum-flow problem. Journal of ACM 35, 4 (1988), pp. 921–940.  [5] Hochbaum, D. S. The pseudoflow algorithm and the pseudoflowbased simplex for the maximum flow problem. Lecture Notes in Computer Science 1412 (1998), pp. 325–337. Basic max-flow/min-cut algorithms: Initialization: Future work:  Estimation of the complexity (right now as in [1])  Exploration of Dynamic Trees  Comparison with [3] and [5]  Merging with [3]: "Dynamic Active Cuts"  Reusing flows, as in [3]  Iterative scheme  Video  Reusing cuts: this work  Hierarchical approach  Iterative scheme  Video  User interaction S  Speed is correlated with Hausdorff distance  Closer initialization implies faster convergence  Feasible flow [1]  Pre-flow [4] - excesses are pushed to the terminals  Pseudo-flow [5] - excesses are pushed towards passive deficits  initialized from a cut (if desired)  benefits from good initialization (available in early vision) A new min cut algorithm based on a symmetric "Push-Pull" design Benefits:  faster than state of the art [1]  produces a sequence of decreasing cost cuts Idea: Min-cut algorithms: S T S T - Inside Active Cuts: 2 possible approaches: Recycling Algorithm Trees (paths) FlowCut Push-Relabel [2] MaxFlow [1] Dynamic Cuts [4] Active Cuts Pseudo-Flow [5] S T - initial cut re-cutting T S T S T S deficit excess deficits excesses better cut T Active Cuts = symmetric Push-Pull: