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Constrained Optimization on Hierarchies of partitions Bangalore Ravi KIRAN CAOR Ecoles Des Mines 16 Jan 2015 B Ravi Kiran Constrained Optimization on Hierarchies 1

Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

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Page 1: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Constrained Optimization on Hierarchies of partitions

Bangalore Ravi KIRAN CAOR Ecoles Des Mines

16 Jan 2015

B Ravi Kiran Constrained Optimization on Hierarchies 1

Page 2: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Overview

B Ravi Kiran Constrained Optimization on Hierarchies 2

Page 3: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Braid of Partitions

B Ravi Kiran Constrained Optimization on Hierarchies 3

Page 4: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Generalizing Parent-Child Relations

B Ravi Kiran Constrained Optimization on Hierarchies 4

Page 5: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Braid: Composing hierarchies

B Ravi Kiran Constrained Optimization on Hierarchies 5

Page 6: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Composing Hierarchies

B Ravi Kiran Constrained Optimization on Hierarchies 6

Page 7: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Braid: Composing hierarchies

B Ravi Kiran Constrained Optimization on Hierarchies 7

Page 8: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Why Braids

B Ravi Kiran Constrained Optimization on Hierarchies 8

No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Page 9: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Comparing Segmentations

B Ravi Kiran Constrained Optimization on Hierarchies 9

Page 10: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Constraint Partition Sets: Braid Structure

B Ravi Kiran Constrained Optimization on Hierarchies 10

Page 11: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

h-increasingness on BOP

B Ravi Kiran Constrained Optimization on Hierarchies 11

S

Page 12: Bangalore Ravi KIRAN - GitHub Pages€¦ · B Ravi Kiran Constrained Optimization on Hierarchies 8 No single GT is a refinement of the mean-shift segmentation, but their suprema are!

Highlights

B Ravi Kiran Constrained Optimization on Hierarchies 12