Random Walk with Restart (RWR)
for Image Segmentation
Sungsu
Lim
AALAB, KAIST
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.
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RWR for image segmentation
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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.
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RWR for image segmentation
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Random walk with restart
Example of RW
What if we star
t at a different
node?
Start node
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RWR for Classification
RW with start no
des being labeled
points in class A
RW with start n
odes being labele
d points in class B
Nodes frequented more by RW(A)
belongs to class A, otherwise they b
elong to B
Simple idea: use RW for classification
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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.
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Generative Model
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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?
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Random Walk with Restart
The walk distribution
r
satisfies a simple equation:
Transition matrix
(relevance vector)
Seed vector
(start nodes)
“Keep

going”
probability
(damping factor)
Restart
probability
Equivalent to the
well

known Googl
e
PageRank
if all n
odes are start nod
es! (
e
is uniform)
Ranking
vector
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RWR for image segmentation
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n x n
n x 1
n x
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Example of RWR
Iterative update until convergence
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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
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RWR for image segmentation
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Use of RWR
As restarting probability c decreases, coarser scale is
more emphasized in likelihood term.
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RWR for image segmentation
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Energy minimization framework
Quadratic energy (cost) minimization:
similar to the formulation of RWR
( )
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RWR for image segmentation
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Experimental Results
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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)
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