1. http://www.hiroshima-cu.ac.jp/ Computer Graphics Laboratory, Hiroshima City University All images are compressed.

2. http://www.hiroshima-cu.ac.jp/ Computer Graphics Laboratory, Hiroshima City University Interactive shadow removal from a single image using hierarchical graph cut Daisuke Miyazaki Yasuyuki Matsushita Katsushi Ikeuchi

3. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Motivation

4. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Prior work multiple single automatic interactive Weiss 01; Matsushita et al. 04 Finlayson et al. 04; Fredembach & Finlayson 06; Tappen et al. 05; Baba et al. 04; Arbel & Hel-Or 07; Nielsen & Madsen 07 Wu et al. 07

5. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Contribution Prior Smoothness Graph cut Alpha expansion User satisfaction Robust Intuitive Fast

6. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Algorithm flow InputOver-segmentationLazy snapping Shadow removal InitialInteractionOutput 1 1 2 2 3 3 4 4 5 5 6 6

7. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Shadow matte Prior of shadowless image Prior of shadow image Smoothness of shadowless image Smoothness of shadow image Solve

8. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Prior of shadowless image Likelihood P appropriatelargesmall

9. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Prior of shadow image smalllargeappropriate L0.7-NormL1-NormL2-Norm

10. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Smoothness of shadowless image smalllargeappropriate

11. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Smoothness of shadow image smalllargeappropriate

12. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Smoothness shadow 0 1 Interactive parameter optimization Smoothness shadowless Prior shadowless Prior shadow 0 0.25 0 0.4 0.7 Init Initial 1st 2nd 3rd 4th 5th 6th

13. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Approach based on alpha expansion Alpha expansionHierarchical graph cut alpha=2 alpha=2,4,... alpha=4 3 15 2 4 1 1 3 5 5 1 1 3 5 5 3 51 2 1 2 3 5 4 5 4 1 2 1 2 5 4

14. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Hierarchical structure 32 1648 8244056 8 162432404856 163248 8 162432404856 163248 20

15. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Graph construction example paq  

16. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Algorithm Alpha expansionHierarchical graph cut 1.A = {{0}, {32}, {16}, {48}, {8, 40}, {24, 56}, {4, 20, 36, 52}, {12, 28, 44, 60},..., {3, 7, 11,..., 63}} 2.for i = 0 to 11 do a.for all nodes&edges do I. II.add nodes&edges using & b.solve max-flow/min-cut problem 3.Iterate 2 until convergence 1.A = {0, 1, 2,..., 63} 2.for i = 0 to 63 do a.for all nodes&edges do I. II.add nodes&edges using & b.solve max-flow/min-cut problem 3.Iterate 2 until convergence

17. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Output of Hierarchical graph cut Stereo matching [Art] Stereo matching [Laundry] Image restoration Shadow removal InputGround truthIshikawa 2003  expansion Hierarchical cut

18. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Speed of hierarchical graph cut Stereo matching [Art] Stereo matching [Laundry] Image restoration Shadow removal Speed-up  6.8  11.4  16.6  3.4 Error difference+4.6%+3.0%-0.4%+0.0% Hierarchical graph cut Alpha expansion [sec] Iteration 250 7 Energy 0 1.1  10 7 1.7  10 6 1.5  10 6

19. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Incremental improvement InputTruthFinlayson 2004Wu 2007InitialInteractive [Ours] Error Number of strokes for parameter optimization50 Finlayson 2004 Wu 2007 Ours

20. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University 0 strokes (param. opt.) 1.4 sec  1 strokes2.1 sec  6 strokes Natural images 1.2 sec  4 strokes

21. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University 2.0 sec  12 strokes1.5 sec  2 strokes Natural images 1.9 sec  15 strokes1.5 sec  8 strokes

22. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University 5.8 sec  27 strokes2.8 sec  40 strokes Natural images 6.3 sec  32 strokes2.0 sec  26 strokes

23. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Aerial images

24. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Conclusions Hierarchical graph cut Cost functionUser interaction

25. http://www.hiroshima-cu.ac.jp/ CG Lab, Hiroshima City University Discussions Cost function User interaction Hierarchical graph cut

26. http://www.hiroshima-cu.ac.jp/ Computer Graphics Laboratory, Hiroshima City University (c) Daisuke Miyazaki 2009 All rights reserved. http://www.cg.info.hiroshima-cu.ac.jp/ Daisuke Miyazaki, Yasuyuki Matsushita, Katsushi Ikeuchi, "Interactive shadow removal from a single image using hierarchical graph cut," Lecture Notes in Computer Science (Proc. Asian Conference on Computer Vision), vol. 5994, part 1, 2009.