Segmentation with Pyramids

1
Segmentation with Pyramids

• Pyramid Linking

2
Segmentation

• Partitioning a digital image into multiple regions

3
Pyramids

• Regular and irregular structures

4
Relinking Connectivity Lost
Reassigning Vertex
Segmentation without connectivity preservation
5
Notation
?(v) Parent of v k(v) Childs of v (receptive
field) N(v) Neighbors of v k(?(v)) Vertices
in the same receptive field as v. Examples k(A)
c,d ?(e) B N(d) c, e ?2(f) A k(?(c)) c,d
6
Loss of Connectivity Parent Level

• 2 cases
• v is not neighbor of any vertex in k(Pnew). v
  may choose only a new parent from the set ?(N(v))
• v is an articulation point in its receptive
  field. If v is an articulation point it mustnt
  be reassigned.

7
Connectivity Higher Levels
8
Connectivity Preservation Results
Segmentation without connectivity preservation
Connectivity preserving segmentation
9
The Relinking Method

• Energy minimization
• Another criteria

10
Adaptive Construction of Successive Levels

• Clustering
• Vertices of lower level are partitioned into
  connected sets (clusters).
• Each cluster consists in a central vertex and its
  neighbors (Graph Decimation).
• Receptive field.
• Dissimilarities between vertices are represented
  by edge strength.

11
Edge Strength and areas

• Need to be corrected by an area factor

12
Creating a cluster

• Every vertex that is not in a cluster yet is
  given a label.
• Every vertex with higher label that its neighbors
  is chosen as new cluster center.
• A maximal subset of neighbors of every center are
  added (avoiding dissimilarities) to complete the
  cluster.

13
Results
14
Considering Boundary Information
As energy of the region (minimization)
Edges in any level of the graph represent
boundaries between regions so we want to maximize
the average edge strength
Combined score
15
Considering Boundary InformationEdge Strength
Combined dissimilarity measure
16
Final results

• Original image
• Segmentation (a.95)
• Segmentation (a.50)
• Segmentation (a.10)

17
Thanks for your attention