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Boundary Extraction in Natural Images Using Ultrametric Contour Maps
Pablo Arbeláez Université Paris Dauphine
Presented byDerek Hoiem
What is segmentation?
What is segmentation?
• Segmentation is a result
What is segmentation?
• Segmentation is a result
• Segmentation is a process
Woman
Face
What is segmentation?
• Segmentation is a result
• Segmentation is a process
• Segmentation is a guide
Segmentation as a Guide
• Multiple Segmentations
Segmentation as a Guide
• Multiple Segmentations
• Hierarchy of Segmentations
Key Concepts/Contributions
• Hierarchical segmentation by iterative merging
• Ultrametric dissimilarities
• Thorough evaluation on BSDS
Hierarchical Segmentation
λ
3 Region Image Dendrogram
Contour Image
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 R1 or R2
λ
Ultrametric Contour Map
Region Dissimilarity
1. Dc(R1, R2): mean boundary contrast– contrast(x) = max L*a*b* diff within radius of x
2. Dg(R1, R2): mean boundary gradient– gradient(x) = Pb(x)
3. Da(R1): Area + α3 Scatter (in color space)
D(R1, R2) = [Dc(R1, R2) + α1 Dg(R1, R2)] · min{ Da(R1) , Da(R2) }α2
Learned Parameters: xi = 4.5 α1 = 5 α2 = 0.2 α3 = 0
Examples
Contrast
Contrast + Gradient
Contrast + Gradient + Region
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
• Martin et al. (Pb)• Canny edge detector• Hierarchical watersheds (using MFM for gradient)
[Najman and Schmitt 1996]• Variational (global energy minimization)
Pb
No Boundary
Boundary
[Martin Fowlkes Malik 2004]
Oriented Edges
Brightness Gradient
Color Gradient
Texture Gradient
Pb
Variational Method
[Koepfler Lopez Morel 1994]
Originally Wavelet-based Textons
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
Comparison
Results
Results
Best Results
http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html
Best Results
http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html
Best Results
http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html
Best Results
http://www.ceremade.dauphine.fr/~arbelaez/results-UCM/main.html
Median Results
Median Results
Median Results
Median Results
Worst Results
Worst Results
Worst Results
Worst Results
Hierarchies vs. Multiple Segmentations
Revising Segmentation