Random Walk with Restart (RWR) for Image Segmentation

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

2. 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 sinceuser 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. 10 9 12 2 8 1 11 3 4 6 5 7 Random walk with restart

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. 10 9 12 2 8 1 11 3 4 6 5 7 Example of RWR Iterative update until convergence n x 1 n x 1 n x n RWR for image segmentation 11

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

13. 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. Experimental Results RWR for image segmentation

16. 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