Boundary Extraction in Natural Images Using Ultrametric Contour Maps
description
Transcript of Boundary Extraction in Natural Images Using Ultrametric Contour Maps
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