Image segmentation Thresholding Otsu's Method

1. 1. Introduction
What is segmentation?
Three major ways to do.
Thresholding
Edge-based segmentation
Region-based segmentation

2. Thresholding
Finding histogram of gray level intensity.
Basic Global Thresholding
Otsu’s Method
Multiple Threshold
Variable Thresholding

3. Edge-based segmentation
Using mask to detect edge in image by convolution.
Basic Edge Detection
The Marr-Hildreth edge detector(LoG)
Watersheds

4. Region-based segmentation
Finding region, but not finding edge.
Region Growing

5. 2. Thresholding
Basic Global Thresholding
1) Select an initial To
2) Segment image use:
3) Compute the average intensity
and for the pixels in and .
7) Compute a new threshold:
8) Until the difference between values of T is smaller than a predefined parameter.
{ 1 if f(x,y)
0 if f(x,y) T( , ) T
g x y ≥
≤=
1m
2m
1 2
1
( )
2
T m m= +

6. Otsu’s Method
{0,1,2,…,L-1} , L means gray level intensity

M*N is the total number of pixel.
denote the number of pixels with intensity
we select a threshold , and use it to
classify : intensity in the range and :
 ,
 ,
 , it is global variance.
in i
0 1 2 1... LMN n n n n −= + + + +
( ) ,0 1T k k k L= < < −
1C 2C[0, ]k [ 1, 1]k L+ −
1
0
( )
k
i
i
P k p
=
= ∑
1
2 1
1
( ) 1 ( )
L
i
i k
P k p P k
−
= +
= = −∑
1 1 2 2 GP m P m m+ = 1 2+ =1P P
( )
1
22
G
0
=
L
G i
i
i m pσ
−
=
−∑

7. 
it is between-class variance
 ,
it is a measure of separability between class.


For x = 0,1,2,…,M-1 and y = 0,1,2…,N-1.
Using image Smoothing/Edge to improve Global Thre
shold
2 2
B 1 2 1 2( ) ( )k P P m mσ = − =
2
1
1 1
( ( ) ( ))
( )(1 ( ))
Gm P k m k
P k P k
−
−
2
B
2
G
( )
=
kσ
η
σ
2 2
B B
1
( ) max ( )
o k L
k kσ σ∗
≤ ≤ −
=
{1 if f(x,y) k*
0 if f(x,y) k*( , )g x y ≥
≤=
0 ( *) 1kη≤ ≤
Smoothing Edge
detection
What situation is
more suitable for the
method
Large object we
are interested.
Small object we
are interested

8. Multiple Threshold
 As Otsu’s method, it takes more area and k*





Disadvantage: it becomes too complicate when number of ar
ea more than three.
2 2 2 2
B 1 1 2 2 3 3( ) ( ) ( )G G GP m m P m m P m mσ = − + − + −
1 1 2 2 3 3 GP m P m P m m+ + =
1 2 3+ +P =1P P
1 2
2 * * 2
B 1 2 B 1 2
1
( , ) max ( , )
o k k L
k k k kσ σ
< < < −
=
2 * *
* * B 1 2
1 2 2
G
( , )
( , )
k k
k k
σ
η
σ
=

9. Variable Thresholding
1) Image partitioning
.
)It works when the objects of interest and the backgro
und occupy regions of reasonably comparable size. If
not , it will fail.

10. Watersheds
Algorithm:
 , g(s,t) is intensity.
n= min+1 to n = max +1. And let T[n]=0, others 1.
 , is minimum point beneath n.
[ ] {( , ) | ( , ) }T n s t g s t n= <
1
[ ] ( )
R
n i
i
C n C M
=
= U ( )n iC M

11. Markers
External markers:
Points along the watershed
line along highest points.
Internal markers:
(1) That is surrounded higher points .
(2) Points in region form a connected component
(3) All points in connected component have the same
intensity.

12. Region-based segmentation
Region Growing

13. Region-based segmentation
Region Growing
Algorithm:
a. Choose a random pixels
b. Use 8-connected and threshold to determine
c. Repeat a and b until almost points are classified.