1. Boundary Extraction in Natural Images Using Ultrametric Contour Maps Pablo Arbeláez Université Paris Dauphine Presented by Derek Hoiem

2. What is segmentation?

3. Segmentation is a result

4. What is segmentation? Segmentation is a result Segmentation is a process Woman Face

5. What is segmentation? Segmentation is a result Segmentation is a process Segmentation is a guide

6. Segmentation as a Guide Multiple Segmentations

7. Segmentation as a Guide Multiple Segmentations Hierarchy of Segmentations

8. Key Concepts/Contributions Hierarchical segmentation by iterative merging Ultrametric dissimilarities Thorough evaluation on BSDS

9. Hierarchical Segmentation λ 3 Region ImageDendrogram Contour Image

10. Ultrametric Contour Map Ultrametric –Definition: D(x,y) <= max{ D(x,z), D(z,y) } The union R 12 of two regions R 1 and R 2 must have >= distance to adjacent region R 3 than either R 1 or R 2 λ

11. Ultrametric Contour Map

12. Region Dissimilarity 1.D c (R 1, R 2 ): mean boundary contrast –contrast(x) = max L*a*b* diff within radius of x 2.D g (R 1, R 2 ): mean boundary gradient –gradient(x) = Pb(x) 3.D a (R 1 ): Area + α 3 Scatter (in color space) D(R 1, R 2 ) = [D c (R 1, R 2 ) + α 1 D g (R 1, R 2 )] · min{ D a (R 1 ), D a (R 2 ) } α2α2 Learned Parameters: x i = 4.5 α 1 = 5 α 2 = 0.2 α 3 = 0

13. Examples Contrast Contrast + Gradient Contrast + Gradient + Region

14. Algorithm Summary Create Initial Contours: –Extrema in gray channel form regions –Assign pixels to regions based on above ultrametric Iteratively merge regions –Keep adjacency/distance matrix

15. Comparison Martin et al. (Pb) Canny edge detector Hierarchical watersheds (using MFM for gradient) [Najman and Schmitt 1996] Variational (global energy minimization)

16. Pb No Boundary Boundary [Martin Fowlkes Malik 2004] Oriented Edges Brightness Gradient Color Gradient Texture Gradient

17. Pb

18. Variational Method [Koepfler Lopez Morel 1994] Originally Wavelet-based Textons

19. Comparison MFM: Martin et al. (Pb) Canny: Canny edge detector WS: Hierarchical watersheds (using MFM for gradient) [Najman and Schmitt 1996] MS: Variational (global energy minimization) Edge-BasedRegion-Based

20. Comparison

21. Results

23. Best Results http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html

24. Best Results http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html

25. Best Results http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html

26. Best Results http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html

27. Median Results

31. Worst Results

35. Hierarchies vs. Multiple Segmentations

36. Revising Segmentation