Post on 20-Feb-2016
description
Boundary Extraction in Natural Images Using Ultrametric Contour Maps
Pablo Arbeláez Université Paris Dauphine
Presented byDerek Hoiem
What is segmentation?
• Segmentation is a result• Segmentation is a process• Segmentation is a guide
Key Concepts/Contributions
• Hierarchical segmentation by iterative merging
• Ultrametric dissimilarities
• Thorough evaluation on BSDS
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
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
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
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