Random Walk with Restart (RWR)

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19 Οκτ 2013 (πριν από 4 χρόνια και 26 μέρες)

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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.

2011
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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.


2011
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RWR 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?

9

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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n x n

n x 1

n x
1

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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Use of RWR






As restarting probability c decreases, coarser scale is
more emphasized in likelihood term.

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Energy minimization framework


Quadratic energy (cost) minimization:


similar to the formulation of RWR











( )

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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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