Active Cuts for Real-Time Graph Partitioning in Vision

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Active Cuts for Real-Time Graph Partitioning in
Vision
Active Cuts, un algorithme de GraphCut adapté à
la Vision
Olivier Juan (CERTIS, ENPC) Joined work with Yuri
Boykov (University of Western Ontario)
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Outline

• Existing algorithms
• Context Motivations
• Description of the new algorithm
• New concepts
• Guidelines
• Experiments
• Segmentation
• Dynamic Segmentation
• Hierarchical Segmentation
• Conclusions

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Existing Methods (1/2)

• Feasible Flow (Ford Fulkerson 62, Dinic 70)
• Flow Conservation Law
• For each edge, flow does not exceed its capacity
• Total amount of inflow that enters each node
  should be equal to the amount of outflow that
  leaves the node
• Preflow (introduced by Karzanov 74,
  GoldbergTarjan 85)
• Relaxation of the Conservation Law
• Any node can have a positive flow excess
• Excess Inflow-Outflow 0

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Augmenting Path Algorithms

• Algorithm FordFulkerson 62
• While there exists a path between source and sink
  in the residual graph
• Take such path
• Send as much flow as possible along the selected
  path
• Update the residual graph
• Complexity O(EC)
• Alternatives
• Shortest Augmenting Path O(VE2)
• Maximum Capacity Augmenting Path
• Dinics Augmenting Path O(EV2)
• Boykov-Kolmogorov O(VEC)

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BoykovKolmogorov Algorithm
FordFulkerson Bottleneck any path is good,
even the longest !
Shortest Augmenting Path Bottleneck search of
the shortest path over the graph
Relaxing
Relaxing
Any path is good ! Heuristics to use a short one !
BoykovKolmogorov Trick Use of a dual dynamic
tree structure to maintain a short path
relationship
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Push Relabel

• Algorithm Cormen, GolbergTarjan 85
• While there is some active node (excess gt 0),
  push this excess using Push Step
• Admissible edge edge connecting the current
  node p with another node q with a label just
  below L(p) L(q) 1
• Push step
• Push as much flow as possible over outgoing
  admissible edges
• If some excess remains do Relabel
• Relabel step
• Increase the label to the minimum label 1 of
  the reachable nodes
• Initialization
• Label distance to the sink or V for the
  source
• Nodes connected to the source are excessed by
  t-link saturation
• Heuristics Global relabeling, Gap relabeling,
• Complexity O(V3) or O(EV2) or even a little bit
  better

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Existing Methods (2/2)
Feasible Flow Based Preflow Based
Unsymmetric Augmenting Path Push Relabel
Symmetric Boykov-Kolmogorov ?
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New Concepts (1/2)

• Push-Pull
• Excess node e Outflow Inflow gt 0
• They are pushed over outgoing edges towards the
  sink
• Deficit node d Outflow Inflow lt 0
• They are pulled over incoming edges towards the
  source
• Use of a dual dynamic tree for connectivity
  selection
• A tree is rooted at a terminal
• A tree spans all nodes reachable from a root
• All edges included in a tree are non-saturated

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New Concepts (2/2)

• Initialization with a given cut
• But How

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Stuck ? Better Cut

• The new cut or better cut in dotted line has a
  lower cost than the previous one.
• Cost(New Cut) Cost(Previous Cut) - Flow Stuck
• Sequence of decreasing cost cuts.

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Equivalence Deficit/t-link

• The same scheme is available for excess

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Better Cut

• Reconnect stuck deficit to the Sink and stuck
  excess to the Source
• Complete the tree
• And so on

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Effect of Initialization

• Concentric initializations show that running
  time is correlated to the distance between
  initialization and optimal solution.

Closest initialization Fastest convergence
Radius
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Sequence of cuts
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Video Segmentation

• ActiveCuts is in mean 5 times faster than BK (up
  to 11)
• Speed is also correlated to Hausdorff distance

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Hierarchical Segmentation
Algorithm Ventricle/Time Lung/Time
MaxFlow (BK) 18.15ms 26.47ms
ActiveCut 18.52ms 19.98ms
Hierarchical ActiveCut 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

• Recycle the previous level cut
• No lost of global optima as in Banded GraphCut

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Contributions Conclusions

• A new algorithm for solving s/t mincut problem
• Takes advantage of a good initial cut
• (Pre-Segmentation, Dynamic or Hierarchical
  Segmentation, etc)
• Faster than standard Maxflow algorithm
• Outputs a sequence of decreasing cost cuts
• Useful for iterative/learning scheme
• Could be combine with Dynamic GraphCut
  (KohliTorr05) to speed up the convergence
• Need to improve our dynamic tree structure ???

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Questions ?