1. Random Walk with Restart (RWR) for Image Segmentation
Sungsu Lim
AALAB, KAIST

2. RWR for image segmentation
Computer vision: make machine to see or to understand/ interpret the scenes (images & videos) like human do.
Image segmentation is one of the most challenging issues in computer vision.
Two major difficulties of conventional algorithms: weak boundary problem & texture problem.
Semi-supervised segmentation approaches are preferred since user inputs can reduce the ambiguity in images.
RWR for image segmentation

3. Random Walks for Image Segmentation
RW (L. Grady, PAMI2006): In image segmentation, random walks are used to determine the labels (i.e., “object” or “background”) to associate with each pixel.
K-way image segmentation: given user-defined seeds indicating regions of the image belonging to k objects. Each seed specifies a location with a user-defined label.
We can use hitting time or commute time as relevance score between two nodes (seed and unlabeled pixel).
By assigning each pixel to the label for which the best value is calculated.
RWR for image segmentation

4. Random walk with restart1 4 3 2 5 6 7 9 10 8 11 12
ICDM2006 Dec, 18-22, HongKong

5. Example of RW What if we start at a different node? Start node
RWR for image segmentation

6. RWR for Classification
Simple idea: use RW for classification
RW with start nodes being labeled points in class A
RW with start nodes being labeled points in class B
Nodes frequented more by RW(A) belongs to class A, otherwise they belong to B

7. RWR for Image Segmentation
Limitation of RW: only considers the local relationship between the pixel and that border. (more prone to hit popular nodes)
RWR (Kim, Lee and Lee, ECCV2008): a new generative image segmentation algorithm based on Random Walks with Restart (Pan,Yang and Faloutsos, KDD2004)
Most previous semi-supervised image segmentation algorithms focus on the inter-label discrimination, but it introduce a generative model for image segmentation.
RWR for image segmentation

8. Generative Model

9. Random Walk with Restart
Imagine a network, and starting at a specific node, you follow the edges randomly.
But (perhaps you’re afraid of wondering too far) with some probability, you “jump” back to the starting node (restart!).
If you record the number of times you land on each node, what would that distribution look like?

10. Random Walk with Restart
The walk distribution r satisfies a simple equation:
Transition matrix (relevance vector)
Seed vector
(start nodes)
Equivalent to the well-known Google PageRank if all nodes are start nodes! (e is uniform)
“Keep-going” probability (damping factor)
Ranking vector
Restart probability
RWR for image segmentation

11. RWR for image segmentation
Example of RWR
Iterative update until convergence 1 4 3 2 5 6 7 9 10 8 11 12
n x 1
n x n
n x 1
RWR for image segmentation 11
ICDM2006 Dec, 18-22, HongKong

12. Use of RWR Linear solution: It can be reformulated as ( )
( )
It considers all relations at all scales in the image.
As t increases weight becomes smaller.
Weighted average of all probability
Restart probability
RWR for image segmentation

13. RWR for image segmentation
Use of RWR
As restarting probability c decreases, coarser scale is more emphasized in likelihood term.
RWR for image segmentation

14. Energy minimization framework
Quadratic energy (cost) minimization:
similar to the formulation of RWR
( )
RWR for image segmentation

15. RWR for image segmentation
Experimental Results
RWR for image segmentation

16. RWR for image segmentation
Applications
1. Data-Driven RWR (Kim, Lee and Lee, ICIP2009)
It use the restart probability matrix. The restarting probability of each pixel depend on its edgeness, generated by Canny edge detector.
2. High-order RWR (multi-layer graph model)
RWR for image segmentation