1. Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in N-D Images 2006. 9. 8 (Fri) Young Ki Baik, Computer Vision Lab.

2. 2 Interactive Graph Cuts for Segmentation References Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in N-D Images Yuri Y. Boykov, Marie-Pierre Jolly (ICCV 2001) An Experimental Comparison of Min-Cut/Max-Flow Algorithm for Energy Minimization in Vision Stefan Roth, Michael J. Black (PAMI Sept. 2004)

3. 3 Interactive Graph Cuts for Segmentation Contents Introduction Segmentation with energy minimization Graph-Cut based method Results Summary

4. 4 Interactive Graph Cuts for Segmentation Introduction Segmentation problem Grouping objects by some criteria, such that those within a group will respond similarly and those in a different group will respond differently. Whole objects“Segment 1”“Segment 2”

5. 5 Interactive Graph Cuts for Segmentation Introduction Automatic or Semi-automatic Fully automatic segmentation (which seems to) Never be perfect… Interactive segmentation (semi-auto) (is evaluated) More reliable…

6. 6 Interactive Graph Cuts for Segmentation Introduction Goal A general purpose interactive segmentation technique that divides and image into two segments: “object” and “background”.

7. 7 Interactive Graph Cuts for Segmentation Introduction Segmentation method Approximate solution Snake, Deformable templates Shortest path, Ration regions Intensity, Edge (locally minimum) Imperfect Global optimal solution MAP-MRF estimation (Graph-Cut) Reliable

8. 8 Interactive Graph Cuts for Segmentation Introduction Special features Quite stable and normally produces the same results regardless of particular seed positioning within the same image object. N-Dimensional segmentation such as video or 3D volume data Graph-Cut and User input (hard constraint) Energy function with hard constraints. Graph-cut algorithm to solve globally optimal problem for segmentation.

9. 9 Interactive Graph Cuts for Segmentation Segmentation Notation : arbitrary set of data elements : neighborhood set of all unordered pair Image N contain all unordered pairs of neighboring pixels (or voxels) under a standard 8-(or26) neighborhood system.

10. 10 Interactive Graph Cuts for Segmentation Segmentation Notation : binary vector or array Segmentation prob. = allocation prob. of proper value to A p Object Background

11. 11 Segmentation Cost function Interactive Graph Cuts for Segmentation Coefficient : relative importance Region properties term Boundary properties term

12. 12 Interactive Graph Cuts for Segmentation Segmentation Regional property term Individual penalties for assigning pixel p to “object” and “background”. may reflect on how the intensity of pixel p fits into a known intensity model (histogram) of object and background.

13. 13 Interactive Graph Cuts for Segmentation Segmentation Boundary property term = discontinuity penalty. is large when pixel p and q are similar. is close to zero when the two are very different. For the boundary

14. 14 Segmentation How to select A Test all case about A We don’t know when we find solution. Graph based method graph based method provides fast result. Interactive Graph Cuts for Segmentation

15. 15 Interactive Graph Cuts for Segmentation Graph-Cut based method Graph t a cut S

16. 16 Graph-Cut based method Graph Each edge is assigned a nonnegative weight. is set of edge that separate the terminals on the graph. Interactive Graph Cuts for Segmentation t a cut S

17. 17 Interactive Graph Cuts for Segmentation Graph-Cut based method Condition for feasible cut t s

18. 18 Interactive Graph Cuts for Segmentation Graph-Cut based method How to set the weight t s

19. 19 Interactive Graph Cuts for Segmentation Graph-Cut based method Finding min-cut To be specific, assume that a max-flow algorithm is used to determine the minimum cut on G. An Experimental Comparison of Min-Cut/Max-Flow Algorithm for Energy Minimization in Vision Stefan Roth, Michael J. Black (PAMI Sept. 2004) t a cut S

20. 20 Interactive Graph Cuts for Segmentation Graph-Cut based method Segmentation

21. 21 Interactive Graph Cuts for Segmentation Results Segmentation using Graph cuts in 2D

22. 22 Interactive Graph Cuts for Segmentation Results Segmentation using Graph cuts in 3D

23. 23 Interactive Graph Cuts for Segmentation Summary Contribution Well defined Cost function with hard constraint. Graph-cut algorithm to solve globally optimal problem with hard-constraint (user input) for segmentation