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Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in N-D Images

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

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Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in N-D Images

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

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

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

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

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

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

  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. 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. Interactive Graph Cuts for Segmentation • 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.

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

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

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

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

  19. a cut t 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) S

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

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

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

  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

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