Diapositive 1

1
Active Graph Cuts
O. Juan CERTIS, ENPC Marne-La-Vallée,
France juan_at_certis.enpc.fr
Y. Boykov University of Western Ontario London,
Canada yuri_at_csd.uwo.ca
A new min cut algorithm based on a symmetric
"Push-Pull" design
Idea

• initialized from a cut (if desired)
• benefits from good initialization (available in
  early vision)

Benefits

• faster than state of the art 1
• produces a sequence of decreasing cost cuts

• excesses are pushed towards the sink (T)
• deficits are pulled towards the source (S)

Basic max-flow/min-cut algorithms
Initialization
Min-cut algorithms
T
2 possible approaches

• Feasible flow 1
• Pre-flow 4
• - excesses are pushed to the terminals
• Pseudo-flow 5
• - excesses are pushed towards passive deficits

excesses
Recycling Algorithm Trees (paths) Flow Cut
Push-Relabel 2 ?
MaxFlow 1 ?
Dynamic Cuts 4 ? ?
Active Cuts ? ? ?
Pseudo-Flow 5 ?

• Reusing flows, as in 3
• Iterative scheme
• Video
• Reusing cuts this work
• Hierarchical approach
• Iterative scheme
• Video
• User interaction

deficits
S
Active Cuts symmetric Push-Pull
Hierarchical segmentation
Result consistency
Decreasing cost cuts
Inside Active Cuts
initial cut
Algorithm Ventricle/Time Lung/Time
MaxFlow 1 18.15ms 26.47ms
Active Cuts 18.52ms 19.98ms
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
better cut

• Speed is correlated with Hausdorff distance
• Closer initialization implies faster convergence

• Recycles the cut of the previous level
• Guaranteed global optima, unlike 2
• but no memory saving ?

re-cutting

• Intermediate cuts local minima
• Final cut global minimum

Video segmentation
Future work

• Recycles the cut of the previous frame
• 5 times faster than 1 (up to 1120)
• Speed is still correlated with Hausdorff distance

• Estimation of the complexity (right now as in
  1)
• Exploration of Dynamic Trees
• Comparison with 3 and 5
• Merging with 3 "Dynamic Active Cuts" ?

• 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. 359374.
• 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. 259265.
• 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. 922929.
• 4 Goldberg, A. V., and Tarjan, R. E. A new
  approach to the maximum-flow problem. Journal of
  ACM 35, 4 (1988), pp. 921940.
• 5 Hochbaum, D. S. The pseudoflow algorithm and
  the pseudoflowbased simplex for the maximum flow
  problem. Lecture Notes in Computer Science 1412
  (1998), pp. 325337.