The University of
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CS
4487/9587
Algorithms for Image Analysis
Segmentation (2D)
Acknowledgements: Alexei Efros, Steven Seitz
The University of
Ontario
CS 4487/9587
Algorithms for Image Analysis
Segmentation (2D)
Blobs
•
Need for blobs
•
Extracting blobs
–
Thresholding, region growing, mean

shift
–
Minimum spanning trees
Object extraction
•
Intelligent scissors (also known as
live

wire
)
•
Snakes
•
Region+boundary methods
Local, greedy, and global processing
Extra Reading: Sonka at.al. Ch. 5
Gonzalez and Woods, Ch. 10
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HW assignment 1
2D image segmentation
•
Live

wire (based on
Dijkstra
algorithm for shortest
paths on a graph)
•
Implement and experiment on
many images
•
Compare
with local/greedy methods
•
Some useful code libraries and sample images will
be posted within a couple of days
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Goal: Extract “Blobs”
What are “blobs”?
•
Regions of an image that are somehow coherent
Why?
•
Object extraction, object removal, compositing, etc.
•
…but are “blobs” objects?
•
No, not in general
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Blob’s coherence
Simplest way to define blob coherence is as
similarity in brightness or color:
The tools become blobs
The house, grass, and sky make
different blobs
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Why is this useful?
AIBO
RoboSoccer
(VelosoLab)
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Ideal Segmentation
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Result of Segmentation
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Thresholding
Basic segmentation operation:
mask(x,y) = 1 if im(x,y) > T
mask(x,y) = 0 if im(x,y) < T
T is threshold
•
User

defined
•
Or automatic
Same as
histogram
partitioning:
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Sometimes works well…
What are potential
Problems?
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…but more often not
Adaptive thresholding
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Region growing
Is this same as global threshold?
•
Start with initial set of pixels
K
(initial seed(s))
•
Add to pixels
p
in
K
their neighbors
q
if
Ip

Iq < T
•
Repeat until nothing changes
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Region growing
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What can go wrong
with region growing ?
Region growth may “leak”
through a single
week spot
in the boundary
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Region growing
See region
leaks
into sky
due to a weak boundary
between them
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Due to Pedro
Felzenszwalb
and Daniel Huttenlocher
Motivating example
This image has three
perceptually distinct regions
Difference along border between A and
B is less then differences within C
A
C
B
Q: Where would
image thresholding
fail?
Q: Where would
region growing
fail?
A: Region A would be divided in two sets and
region C will be split into a large number
of arbitrary small subsets
A: Either A and B are merged or region C is
split into many small subsets
Also, B and C are merged
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Color

Based Blob Segmentation
Automatic Histogram Partitioning
•
Given image with N colors, choose K
•
Each of the K colors defines a region
–
not necessarily contiguous
•
Performed by computing color histogram, looking for
modes
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Finding Modes in a Histogram
How Many Modes Are There?
•
Easy to see, hard to
compute
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Mean Shift [
Comaniciu & Meer]
1.
Initialize random seed, and fixed window
2.
Calculate center of gravity ‘
x
’ of the window (
the“mean
”)
3.
Translate the search window to the mean
4.
Repeat Step 2 until convergence
Iterative
Mode Search
x
o
x
x
mode
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Mean

Shift
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Mean

shift results
More Examples
:
http://www.caip.rutgers.edu/~comanici/segm_images.html
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Issues:
Although often useful, all these approaches
work only some of the time, and are considered
rather “hacky”.
Can’t even handle our tiger:
Problem is that blobs != objects!
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Extracting objects
How could this be done?
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Extracting objects
Many approaches proposed
•
color cues
•
region cues
•
contour cues
We will consider a few of these
Today:
•
Intelligent Scissors (contour

based)
–
E. N. Mortensen and W. A. Barrett,
Intelligent Scissors for Image
Composition
, in ACM Computer Graphics (SIGGRAPH `95), pp. 191

198,
1995
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Intelligent Scissors
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Intelligent Scissors
Approach answers a basic question
•
Q: how to find a path from seed to mouse that follows
object boundary as closely as possible?
•
A: define a path that stays as close as possible to edges
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Intelligent Scissors
Basic Idea
•
Define edge score for each pixel
–
edge pixels have low cost
•
Find lowest cost path from seed to mouse
seed
mouse
Questions
•
How to define costs?
•
How to find the path?
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Path Search (basic idea)
Graph Search Algorithm
•
Computes minimum cost path from seed to
all
other
pixels
Note: diagonal “paths”
are scaled by a factor
.
…
Why?
3 sets of nodes
•
Free
•
Active
•
Done
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Segmentation should be
Invariant
to Image Rotation
After object rotation
L
Path’s cost along the top boundary
Path’s cost along the top

left boundary
After diagonal links are adjusted by
2
2
2
2
2
2
2
2
2
2
2
2
image gradient scores
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Instead of nodes, image gradient scores
can be assigned directly to graph edges
Graph
•
node for every pixel
p
•
link between every adjacent pair of pixels
e=(p,q)
•
cost
w(e)
for each link
Note: each
link
has a cost
•
this is a little different than the figure before where
each pixel (graph node) had a cost
p
q
Treat the image as a graph
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Defining edge costs
Treat the image as a graph
Want to hug image edges:
how to define cost of a link?
p
q
•
the link should follow the intensity edge
–
want intensity to change rapidly to the link
•
the cost of edge should be small when the
difference of intensity to the link is large
T
T
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Defining edge costs
p
q
First, estimate image derivative in the direction
orthogonal to the edge
Use finite differences (or cross

correlation filters)
1

1

1

1
1
1
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Defining edge costs
p
q
Second, use some penalty function
g( )
assigning low
penalty to large directional derivatives and large
penalty to small derivatives
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Defining edge costs
p
q
Finally, cost of en edge
e
should be local contrast
score adjusted by the edge length
Why?
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Defining edge costs
When computing the shortest path we approximate a
contour
C
minimizing continuous geometrically
meaningful functional
Cost of one edge
Cost of a PATH
Integral of contrast penalty along the contour
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(see Cormen et.al. “
Introduction to Algorithms
”, p.595)
Dijkstra’s shortest path algorithm
0
5
3
1
3
3
4
9
2
link cost
1.
init node costs to
, set
p
= seed point, cost(
p
) =
0
2.
expand
p
as follows:
for each of
p
’s neighbors
q
that are not expanded
•
set cost(
q
) = min( cost(
p
) +
c
pq
, cost(
q
) )
ALGORITHM
3 sets of nodes
•
Free
•
Active
•
Done
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Dijkstra’s shortest path algorithm
4
1
0
5
3
3
2
3
9
5
3
1
3
3
4
9
2
1
1
1.
init node costs to
, set
p
= seed point, cost(
p
) =
0
2.
expand
p
as follows:
for each of
p
’s neighbors
q
that are not expanded
•
set cost(
q
) = min( cost(
p
) +
c
pq
, cost(
q
) )
–
if
q
’s cost changed, make
q
point back to
p
•
put
q
on the ACTIVE list (if not already there)
ALGORITHM
3 sets of nodes
•
Free
•
Active
•
Done
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Ontario
Dijkstra’s shortest path algorithm
4
1
0
5
3
3
2
3
9
5
3
1
3
3
4
9
2
1
5
2
3
3
3
2
4
1.
init node costs to
, set
p
= seed point, cost(
p
) =
0
2.
expand
p
as follows:
for each of
p
’s neighbors
q
that are not expanded
•
set cost(
q
) = min( cost(
p
) +
c
pq
, cost(
q
) )
–
if
q
’s cost changed, make
q
point back to
p
•
put
q
on the ACTIVE list (if not already there)
3.
set
r
= node with minimum cost on the ACTIVE list
4.
repeat Step 2 for
p
=
r
ALGORITHM
3 sets of nodes
•
Free
•
Active
•
Done
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Ontario
Dijkstra’s shortest path algorithm
3
1
0
5
3
3
2
3
6
5
3
1
3
3
4
9
2
4
3
1
4
5
2
3
3
3
2
4
1.
init node costs to
, set
p
= seed point, cost(
p
) =
0
2.
expand
p
as follows:
for each of
p
’s neighbors
q
that are not expanded
•
set cost(
q
) = min( cost(
p
) +
c
pq
, cost(
q
) )
–
if
q
’s cost changed, make
q
point back to
p
•
put
q
on the ACTIVE list (if not already there)
3.
set
r
= node with minimum cost on the ACTIVE list
4.
repeat Step 2 for
p
=
r
ALGORITHM
3 sets of nodes
•
Free
•
Active
•
Done
The University of
Ontario
Dijkstra’s shortest path algorithm
3
1
0
5
3
3
2
3
6
5
3
1
3
3
4
9
2
4
3
1
4
5
2
3
3
3
2
4
2
1.
init node costs to
, set
p
= seed point, cost(
p
) =
0
2.
expand
p
as follows:
for each of
p
’s neighbors
q
that are not expanded
•
set cost(
q
) = min( cost(
p
) +
c
pq
, cost(
q
) )
–
if
q
’s cost changed, make
q
point back to
p
•
put
q
on the ACTIVE list (if not already there)
3.
set
r
= node with minimum cost on the ACTIVE list
4.
repeat Step 2 for
p
=
r
ALGORITHM
3 sets of nodes
•
Free
•
Active
•
Done
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Path Search (basic idea)
A
B
Dijkstra algorithm

processed nodes (distance to A is known)

active nodes (front)

active node with the smallest distance value
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Dijkstra’s shortest path algorithm
Properties
•
It computes the minimum cost path from the seed to every
node in the graph. This set of minimum paths is represented
as a
tree
•
Running time, with N pixels:
–
O(N
2
) time if you use an active list
–
O(N log N) if you use an active priority queue (heap)
–
takes < second for a typical (640x480) image
•
Once this tree is computed once, we can extract the optimal
path from any point to the seed in O(N) time.
–
it runs in real time as the mouse moves
•
What happens when the user specifies a new seed?
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Livewire extensions
Directed graphs
Restricted search space
•
Restricted domain (e.g. near
a priori
model)
•
Restricted backward search
Different edge weight functions
•
Image

Edge strength
•
Image

Edge Curvature
•
Proximity to known approximate model/boundary
Multi

resolution processing
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Results
http://www.cs.washington.edu/education/courses/455/03wi/projects/project1/artifacts/index.html
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