Image segmentation

Unit: 3
Image Segmentation
ET403:Principles of Image ProcessingET403:Principles of Image Processing
(Similarity Based Techniques)

Image Segmentation
 Group similar components (such as, pixels in an image,
image frames in a video) to obtain a compact
representation.
ET403:Principles of Image Processing
 Applications: Finding tumors, veins, etc. in medical images,
finding targets in satellite/aerial images, finding people in
surveillance images, summarizing video, etc.
 Methods: Thresholding, K-means clustering, etc.

Image Segmentation
 Segmentation algorithms for monochrome images generally
are based on one of two basic properties of gray-scale values:
 Discontinuity
 The approach is to partition an image based on abrupt changes in
gray-scale levels.
gray-scale levels.
 The principal areas of interest within this category are detection
of isolated points, lines, and edges in an image.
 Similarity
 The principal approaches in this category are based on
thresholding, region growing, and region splitting/merging.

Thresholding
 Suppose that an image, f(x,y), is composed of light objects on a
dark background, and the following figure is the histogram of the
image.
image with dark background
 Then, the objects can be extracted by comparing pixel values
with a threshold T.
and a light object

Thresholding
 One way to extract the objects from the background is to select
a threshold T that separates object from background.
 Any point (x,y) for which f(x,y) > T is called an object point;
otherwise the point is called a background point.
 When T is a constant applicable over an entire image, then the
above process is called as Global thresholding.
1 ( , )
( , )
0 ( , )
if f x y T
g x y
f f x y T

 


Thresholding
 When the value of T changes over an image
 Then that process is referred as Variable thresholding.
 Sometimes it is also termed as local or regional thresholding.
 Where, the value of T at any point (x,y) in an image depends
 Where, the value of T at any point (x,y) in an image depends
on properties of a neighborhood of (x,y).
 If T depends on the spatial coordinates (x,y) themselves, then
variable thresholding is often referred to as dynamic or
adaptive thresholding.

Thresholding

Multilevel Thresholding
 It is also possible to extract objects that have a specific intensity
range using multiple thresholds.
and two light objects
Extension to color images is straightforward: There are three color channels, in
each one specify the intensity range of the object… Even if objects are not
separated in a single channel, they might be with all the channels… Application
example: Detecting/Tracking faces based on skin color…

Multilevel thresholding
• A point (x,y) belongs
– to an object class if T1 < f(x,y)  T2
– to another object class if f(x,y) > T2
– to background if f(x,y)  T1
2
1 2
1
if ( , )
( , ) if ( , )
if ( , )
a f x y T
g x y b T f x y T
c f x y T


  
 

Role of Noise in Image Thresholding

Role of Illumination in Image Thresholding
 Non-uniform illumination may change the histogram in a
way that it becomes impossible to segment the image using
a single global threshold.
 Choosing local threshold values may help.

Role of Illumination in Image Thresholding

Basic Global Thresholding
Based on visual inspection of histogram
1. Select an initial estimate for T.
2. Segment the image using T. This will produce two groups of pixels: G1
consisting of all pixels with gray level values > T and G2 consisting of
pixels with gray level values  T
3. Compute the average gray level values 1 and 2 for the pixels in
regions G1 and G2
4. Compute a new threshold value
5. T = 0.5 (1 + 2)
6. Repeat steps 2 through 4 until the difference between the values of T
in successive iterations is smaller than a predefined parameter ΔT.

Note: the clear
valley of the
histogram and the
segmentation
between object and
background
background
Initially T= average intensity of image
T0 = 0
3 iterations
with result T = 125

1. Works well in situations where there is a reasonably clear
valley between the modes of the histogram related to
objects and background.
2. ΔT is used to control the number of iterations.
2. ΔT is used to control the number of iterations.
3. Initial threshold must be chosen greater than the minimum
and less than the maximum intensity level in the image
4. The average intensity of the image is a good initial choice
for T.

Basic Adaptive Thresholding
• subdivide original image into small areas.
• utilize a different threshold to segment each
subimages.
• since the threshold used for each pixel
• since the threshold used for each pixel
depends on the location of the pixel in terms
of the subimages, this type of thresholding is
adaptive.

Example : Adaptive Thresholding

Example : Adaptive Thresholding
How to solve this problem?

Further subdivision

• This method treats pixel values as probability density functions.
• The goal of this method is to minimize the probability of
misclassifying pixels as either object or background.
• There are two kinds of error:
– mislabeling an object pixel as background, and
Optimal Global and Adaptive Thresholding
– mislabeling an object pixel as background, and
– mislabeling a background pixel as object.

• Method for estimating thresholds that produce the
minimum average segmentation error.
• Let an image contains only two principal gray
regions.
regions.
• Let z represents the gray-level values.
• These can be viewed as random quantities, and the
histogram may be considered an estimate of their
probability density function (PDF), p(z).

1 1 2 2
1 2
( ) ( ) ( )
1
p z P p z P p z
P P
 
 
P1: probability that a random pixel
with value z is an object pixel.
P2: probability that a random pixel
Is a background pixel

Probability of erroneously


T
dzzpTE )()( 21


T
dzzpTE )()( 12
)()()( 2112 TEPTEPTE 

Minimum error
0
))()(()( 2112



TEPTEPdTdE
Differentiating E(T) with respect to T (using Leibniz’s rule) and
equating the result to 0
02112

dTdT
)()( 2211 TpPTpP 
find T which makes
if P1 = P2 then
the optimum threshold
is where the curve
p1(z) and p2(z) intersect

Gaussian density
Example: use PDF = Gaussian density : p1(z) and p2(z)
2
1
2
1
( )
2
1
1
1
( )
2
z
p z e


 



2
2
2
2
( )
2
2
2
1
( )
2
z
p z e


 



where
• 1 and 1
2 are the mean and variance of the Gaussian density
of one object
• 2 and 2
2 are the mean and variance of the Gaussian density
of the other object

Gaussian density
2
1
2
1
2
2
( )
2
1
1
( )
1
( )
2
1
T
T
p T e



 





)()( 2211 TpPTpP 
2
2
2
( )
2
2
2
1
( )
2
T
p T e


 




Quadratic equation
)(2
0
2
12
2
21
2
2
2
1
2
B
Awhere
CBTAT





)/ln(22
)(2
2112
2
2
2
1
2
1
2
2
2
2
2
1
1221
PPC
B














1
2
21
2
21
ln
2 P
P
T

 if P1 = P2 or  = 0 then
the optimal threshold
is the average of the
means

Region-Based Segmentation
ET403:Principles of Image ProcessingET403:Principles of Image Processing

• Basic Formulation
, ..., n,iRb
RRa
i
i
n



21region,connectedais)(
)(
1i
jfor iFALSE)RP(Re
, ..., n,iTRUE)P(Rd
jiRRc
ji
i
ji
i



)(
21for)(
j,andiallfor)( 
P(Ri) is a logical predicate property defined over the points in set Ri
ex. P(Ri) = TRUE if all pixel in Ri have the same gray level

 Region Growing
 Region growing is a procedure that groups pixels or
subregions into larger regions.
 The simplest of these approaches is pixel aggregation,
which starts with a set of “seed” points and from these
grows regions by appending to each seed points those
grows regions by appending to each seed points those
neighboring pixels that have similar properties (such as
gray level, texture, color, shape).
 Region growing based techniques are better than the
edge-based techniques in noisy images where edges are
difficult to detect.

Region Growing
select all seed points with gray level 255
criteria:
1. the absolute gray-
level difference
between any pixel
and the seed has to
be less than 65
2. the pixel has to be 8-
connected to at least
connected to at least
one pixel in that
region (if more, the
regions are merged)

Region Growing
select all seed points with gray level 255
criteria:
1. the absolute gray-level
difference between any pixel
and the seed has to be less
than 65
than 65
2. the pixel has to be 8-
connected to at least one
pixel in that region (if more,
the regions are merged)

Histogram of fig 10.40 a)
used to find the criteria of the
difference gray-level between
each pixels and the seeds

 Region Splitting
 Region growing starts from a set of seed points.
 An alternative is to start with the whole image as a single region
and subdivide the regions that do not satisfy a condition of
homogeneity.
 Region Merging
 Region merging is the opposite of region splitting.
 Start with small regions (e.g. 2x2 or 4x4 regions) and merge the
regions that have similar characteristics (such as gray level,
variance).
 Typically, splitting and merging approaches are used iteratively.

Region splitting and merging
Quadtree
1. Split into 4 disjoint quadrants any region Ri for which
P(Ri) = FALSE
2. Merge any adjacent region Rj and Rk for which
P(Ri  Rk ) = TRUE
3. Stop when no further merging or splitting is possible.

Example
P(Ri) = TRUE if at least 80% of the pixels in Ri have the property |zj-mi|  2i,
where
zj is the gray level of the jth pixel in Ri
mi is the mean gray level of that region
i is the standard deviation of the gray levels in Ri

Example: Apply the split and merge technique to segment
the image shown in fig. below.
Figure: Image
R1 R2
R4R3
R1 R2

Quadtree Representation
R
R2R1

Figure: Image

Solution:
Figure(b): step-1
R1
R3 R4
R2
Figure(a): Image
Figure(b): step-1
Figure(c): step-2 Figure(d): step-3
R1
R4
R31
R21
R32
R33 R34
R23
R22
R24

Quadtree Representation
R
R4R3R2R1
R22 R23
R21 R24
R32 R33
R31
R34

R1 R2
R4R3

More Complex Segmentation Methods
• Snakes
• Level Sets
• Graph Cuts
• Generalized PCA
17/09/2016
Copyright G.D. Hager
• Generalized PCA

Snakes
17/09/2016
Images taken from
http://www.cs.bris.ac.uk/home/xie/content.htm

Level Sets
17/09/2016
Images taken from
http://www.cgl.uwaterloo.ca/~mmwasile/cs870/

Graph Cuts
17/09/2016
Images taken from efficient graph-based segmentation paper

GPCA (Rene Vidal)
17/09/2016
Human GPCA

Image segmentation

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