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Boundary Extraction in Natural Images Using Ultrametric Contour Maps. Pablo Arbel á ez Universit é Paris Dauphine Presented by Derek Hoiem. What is segmentation?. What is segmentation?. Segmentation is a result. Face. Woman. What is segmentation?. Segmentation is a result

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boundary extraction in natural images using ultrametric contour maps

Boundary Extraction in Natural Images Using Ultrametric Contour Maps

Pablo Arbeláez

Université Paris Dauphine

Presented by

Derek Hoiem

what is segmentation1
What is segmentation?
  • Segmentation is a result
what is segmentation2

Face

Woman

What is segmentation?
  • Segmentation is a result
  • Segmentation is a process
what is segmentation3
What is segmentation?
  • Segmentation is a result
  • Segmentation is a process
  • Segmentation is a guide
segmentation as a guide
Segmentation as a Guide
  • Multiple Segmentations
segmentation as a guide1
Segmentation as a Guide
  • Multiple Segmentations
  • Hierarchy of Segmentations
key concepts contributions
Key Concepts/Contributions
  • Hierarchical segmentation by iterative merging
  • Ultrametric dissimilarities
  • Thorough evaluation on BSDS
hierarchical segmentation

λ

Hierarchical Segmentation

3 Region Image

Dendrogram

Contour Image

ultrametric contour map

λ

Ultrametric Contour Map
  • Ultrametric
    • Definition: D(x,y) <= max{ D(x,z), D(z,y) }

The union R12 of two regions R1 and R2 must have >= distance to adjacent region R3 than either R1or R2

region dissimilarity
Region Dissimilarity
  • Dc(R1, R2): mean boundary contrast
    • contrast(x) = max L*a*b* diff within radius of x
  • Dg(R1, R2): mean boundary gradient
    • gradient(x) = Pb(x)
  • Da(R1): Area + α3 Scatter (in color space)

α2

D(R1, R2) = [Dc(R1, R2) + α1 Dg(R1, R2)] · min{ Da(R1), Da(R2)}

Learned Parameters: xi = 4.5 α1 = 5 α2 = 0.2 α3 = 0

examples
Examples

Contrast

Contrast + Gradient

Contrast + Gradient + Region

algorithm summary
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
comparison
Comparison
  • Martin et al. (Pb)
  • Canny edge detector
  • Hierarchical watersheds (using MFM for gradient) [Najman and Schmitt 1996]
  • Variational (global energy minimization)
slide16
Pb

Brightness Gradient

Oriented Edges

Color Gradient

Texture Gradient

No Boundary

Boundary

[Martin Fowlkes Malik 2004]

variational method
Variational Method

Originally Wavelet-based Textons

[Koepfler Lopez Morel 1994]

comparison1
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-Based

Region-Based

best results
Best Results

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

best results1
Best Results

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

best results2
Best Results

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

best results3
Best Results

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