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Image Segmentation by Branch-and- Mincut

Image Segmentation by Branch-and- Mincut. Victor Lempitsky Andrew Blake Carsten Rother. An example. 0. 0. s. 1. 1. image from UIUC car dataset. [Hammer 64] [Greig, Porteous, Seheult 89]. p. q. . . Standard “graph cut” segmentation energy [Boykov, Jolly 01] :. F p =1, B p =0.

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Image Segmentation by Branch-and- Mincut

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  1. Image Segmentation by Branch-and-Mincut Victor LempitskyAndrew Blake Carsten Rother

  2. An example 0 0 s 1 1 image from UIUC car dataset [Hammer 64] [Greig, Porteous, Seheult 89] p q ... ... Standard “graph cut” segmentation energy [Boykov, Jolly 01]: Fp=1, Bp=0 Ppq t Fp=0, Bp=1 [Freedman, Zhang 05], [Ali, Farag, El-Baz 07],...

  3. A harder example image from UIUC car dataset Ppq 0 1 Optimal x min x, ω Optimal ω

  4. Energy optimization ω –global parameter (ω ∊ Ω0) Optimization options: • Choose reasonable ω, solve for x[Freedman, Zhang 05], [Pawan Kumar, Torr, Zisserman’ObjCut 05], [Ali, Farag, El-Baz 07] .... • Alternate between x and ω (EM) [Rother, Kolmogorov, Blake’ GrabCut 04], [Bray, Kohli, Torr’PoseCut 06], [Kim, Zabih 03].... • Optimize continuously [Chan, Vese 01], [Leventon, Grimson, Faugeras 00], [Cremers, Osher, Soatto 06], [Wang, Staib 98]... • Exhaustive search pairwise potentials (costs) ≥ 0 constant unary potentials (costs) ....shape priors, color distribution/intensity priors (Chan-Vese, GrabCut)...

  5. Our approach along x dimension along ω dimension • Extremely large, structured domain • Specific “graph cut” function • Low-dimensional (discretized) domain • Function of the general form Branch-and-bound Mincut Branch-and-Mincut [Gavrila, Philomin 99], [Lampert, Blaschko, Hofman 08], [Cremers, Schmidt, Barthel 08]

  6. Search tree Ω0 Ω0

  7. Bounding the energy: an example Fp=0, Bp=1 min Fp=1, Bp=0 ω1 ω2 Fp=0, Bp=0

  8. The lower bound s p q Ω t Computable with mincut!

  9. Lower bound • Monotonic increase towards leaves • Tightness at leaf nodes:

  10. Lower bound: example precomputed computed at runtime

  11. Branch-and-Bound Standard best-first branch-and-bound search: lowest lower bound B C A Small fraction of nodes is visited additional speed-up from “reusing” maxflow computations [Kohli,Torr 05]

  12. Results: shape prior 30,000,000 shapes Exhaustive search: 30,000,000 mincuts Branch-and-Mincut: 12,000 mincuts Speed-up: 2500 times (30 seconds per 312x272 image)

  13. Results: shape prior Left ventricle epicardium tracking (work in progress) Original sequence No shape prior Our segmentation Shape prior from other sequences 5,200,000 templates ≈20 seconds per frame Speed-up 1150 Data courtesy: Dr Harald Becher, Department of Cardiovascular Medicine, University of Oxford

  14. Result: shape prior Can add feature-based detector here UIUC car dataset

  15. Results: Discrete Chan-Vese functional cb c_p cf Chan-Vese functional [Chan, Vese 01]: ∊ [0;255]x[0;255]: quad-tree clustering Global minima of the discrete Chan-Vese functional: Speed-up 28-58 times

  16. Performance Sample Chan-Vese problem:

  17. Results: GrabCut • ω corresponds to color mixtures • [Rother, Kolmogorov, Blake’ GrabCut 04] uses EM-like search • Branch-and-Mincut searches over 65,536 starting points E = -618 E = -624 (speed-up 481) E = -628 E = -593 E = -584 (speed-up 141) E = -607

  18. Conclusion • ̶ good energy to integrate low-level and high-level knowledge in segmentation. • Branch-and-Mincut framework can find its global optimum efficiently in many cases • Ongoing work: Branch-and-X algorithms Branch-and-bound Mincut Dynamic Programming C++ code at http://research.microsoft.com/~victlem/

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