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1. Image
Segmentation

2. Topic’s to be covered
 Introduction to Image analysis and segmentation
 Detection of Discontinuity
 Point, line, edge and combined detection..
 Edge linking and boundary detection
 Local processing, hough transform, graph-theoretic
technique..
 Thresholding
 Global thresholding, Optimal thresholding, threshold
selection..
 Region oriented segmentation
 Region growing, Region splitting and merging..

3. Introduction
 Image analysis:-
Techniques for extracting information from an
image.
 Segmentation is the first step for image analysis.
 Segmentation is used to subdivide an image into its
constituent parts or objects.
 This step determines the eventual success or failure
of image analysis.

4. Introduction
 Generally, the segmentation is carried out only up to
the objects of interest are isolated. e..g. face
detection.
 The goal of segmentation is to simplify and/or
change the representation of an image into
something that is more meaningful and easier to
analyze.

5. 5
Image Segmentation - 1
 Extracting information form an image
 Step 1: segment the image ->objects or regions
 Step 2 : describe and represent the segmented
regions in a form suitable for computer
processing
 Step 3 : image recognition and interpretation
Image analysis – HLIP

6. Image Segmentation
 Segmentation divides an image into its constituent
regions or objects.
 Segmentation of images is a difficult task in image
processing. Still under research.
 Segmentation allows to extract objects in images.
 Segmentation is unsupervised learning.
 Model based object extraction, e.g., template
matching, is supervised learning.

7. Classification of the Segmentation
techniques
Image
Segmentation
Discontinuity Similarity
e.g.
- Point Detection
- Line Detection
- Edge Detection
e.g.
- Thresholding
- Region Growing
- Region splitting &
merging

8. Detection of Discontinuities
 There are three kinds of discontinuities of intensity:
points, lines and edges.
 The most common way to look for discontinuities is to
scan a small mask over the image. The mask determines
which kind of discontinuity to look for.







9
1
9
9
2
2
1
1 ...
i
i
i z
w
z
w
z
w
z
w
R

9. Point Detection
 Based on Masking…
 Find response R.
 The emphasis is strictly to detect points. That is,
differences those are large enough to be considered as
isolated points.
 So, compare and separate based on
 Where R = Response of convolution
T = Non negative threshold value
-1
-1
8 -1
-1
-1 -1
-1 -1
R T


10. Point Detection(Example)

11. Line Detection
 Only slightly more common than point detection is to find
a one pixel wide line in an image.
 For digital images the only three point straight lines are
only horizontal, vertical, or diagonal (+ or –45).

12. Line Detection
-1
2
2 -1
2
-1 -1
-1 -1
-1
-1
2 -1
-1
-1 2
2 -1
-1
-1
2 -1
-1
2 -1
-1 2
2
-1
2 2
-1
-1 -1
-1 -1
Horizontal Line 45 degree inclined
Line
Vertical Line -45 degree inclined
Line

13. Line Detection(Cont.)

14. Edge detection
 Edge detection is an image processing technique
for finding the boundaries of objects within images. It
works by detecting discontinuities in brightness.
 Edge detection is used for image segmentation and
data extraction in areas such as image processing,
computer vision, and machine vision.

15. 15
 Definition
 An edge is a set of connected pixels that lie on the
boundary between two regions
 The difference between edge and boundary, pp.68
 Edge detection steps
 Compute the local derivative
 Magnitude of the 1st derivative can be used to detect
the presence of an edge
 The sign of the 2nd derivative can be used to
determine whether an edge pixel lies on the dark or
light side of an image
 Zero crossing of the 2nd derivative is at the midpoint of
a transition in gray level, which provides a powerful
approach for locating the edge.
Edge detection

16. 16
Edge detection (cont’)

17. 17
Edge detection (cont’)

18. 18
 Use gradient for image differentiation
 The gradient of an image f(x,y) at point (x,y) is
defined as
 Some properties about this gradient vector
 It points in the direction of maximum rate of change of image at (x,y)
 Magnitude
 angle
Gradient operators
T
y
x
y
f
x
f
G
G
f 

































x
y
y
x
y
x
G
G
y
x
G
G
G
G
f
mag
1
2
2
tan
)
,
(
)
(


19. 19
Edge operator

20. 20
 Advantages : providing both differencing and a
smooth effect and slightly superior noise
reduction characteristics.
Sobel edge operator

21. 21
Edge detection example

22. 22
Edge detection example (cont’)

23. 23
 A second order
derivative
 Problems
 Very sensitive to noise
 Detect double edges
 Can’t detect edge
direction
 Usage
 Find the location of
edge using zero-
crossing property
2
2
2
2
2
y
f
x
f
f







Laplacian edge operator

24. 24
 Edge detection by gradient operations tends to
work well when
 Images have sharp intensity transitions
 Relative low noise
 Zero-crossing approach work well when
 Edges are blurry
 High noise content
 Provide reliable edge detection
discussion

25. 25
Gradient operators – examples
Zero-Crossing:
Advantages:
noise reduction capability;
edges are thinner.
Drawbacks:
edges form numerous closed loops
(spaghetti effect);
computation complex.

26. Edge Detection
Robert’s Mask Prewitt Operator
Sobel Operator Laplacian
-1 0
0 1
-1
0
0
1
-1 -1 -1
0 0 0
1 1 1
-1 0 1
-1 0 1
-1 0 1
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1
-1 -1 -1
-1 8 -1
-1 -1 -1

27. Edge Detection(Example)

28. Edge Detection(Example)

29. Edge Linking and Boundary Detection
Local Processing
 Two properties of edge points are useful for edge linking:
 the strength (or magnitude) of the detected edge points
 their directions (determined from gradient directions)
 This is usually done in local neighborhoods.
 Adjacent edge points with similar magnitude and
direction are linked.
 For example, an edge pixel with coordinates (x0,y0) in a
predefined neighborhood of (x,y) is similar to the pixel at
(x,y) if
threshold
e
nonnegativ
a
:
,
)
,
(
)
,
( 0
0 E
E
y
x
y
x
f 
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threshold
angle
nonegative
a
:
,
)
,
(
)
,
( 0
0 A
A
y
x
y
x 



30. Edge Linking and Boundary Detection
 Intensity discontinuity can be utilized to find
boundary.
 The lagging part of boundary detection using
intensity discontinuity is that the boundary may not
be completely defined because of
 Noise
 Breaks in boundary due to non-uniform illumination
 So, after edge detection, edge linking process is
carried out to assemble edge pixels into meaningful
boundary

31. Need of Edge
Linking
The boundary is not
complete in edge
detection (bottom figure).

32. 1) Edge Linking – Local Processing
 Analyze every pixel in small neighborhood that has
undergone edge detection.
 For same characteristics (point is on same edge or
not), two principal properties used are
 Strength of response of the gradient operator
 The direction of gradient.
( , ) ( ', ')
f x y f x y T
  
( , ) ( ', ')
x y x y A
 
 

33. Thresholding
 Assumption: the range of intensity levels covered by
objects of interest is different from the background.
Single threshold Multiple threshold






T
y
x
f
T
y
x
f
y
x
g
)
,
(
if
0
)
,
(
if
1
)
,
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34. Thresholding
 Thresholding can be viewed as an operation that
involves tests against a function T of the form:
)]
,
(
),
,
(
,
,
[ y
x
f
y
x
p
y
x
T
T 
where p(x,y) denotes
some local property of this point.

35. Thresholding
 When T depends only on f(x,y) 
global threshold
 When T depends on both f(x,y) and p(x,y) 
local threshold
 When T depends on x and y (in addition) 
dynamic threshold

36. Thresholding
The Role of Illumination

37. Thresholding
The Role of Illumination
(a) (c)
(e)
(d)
)
,
(
)
,
(
)
,
( y
x
r
y
x
i
y
x
f 
)
,
( y
x
i
)
,
( y
x
r

38. Thresholding
Basic Global Thresholding

39. Thresholding
Basic Global Thresholding

40. Thresholding
Basic Adaptive Thresholding

41. Thresholding
Basic Adaptive Thresholding
How to solve this problem?

42. Thresholding
Basic Adaptive Thresholding
Answer: subdivision

43. Thresholding
Optimal Global and Adaptive Thresholding
 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
 mislabeling a background pixel as object.

44. Thresholding
Use of Boundary Characteristics

45. Thresholding
Thresholds Based on Several Variables
Color image

46. Region-Based Segmentation
 Edges and thresholds sometimes do not give
good results for segmentation.
 Region-based segmentation is based on the
connectivity of similar pixels in a region.
 Each region must be uniform.
 Connectivity of the pixels within the region is very
important.
 There are two main approaches to region-based
segmentation: region growing and region
splitting.

47. Region-Based Segmentation
Basic Formulation
 Let R represent the entire image region.
 Segmentation is a process that partitions R into
subregions, R1,R2,…,Rn, such that
where P(Rk): a logical predicate defined over the points in
set Rk
For example: P(Rk)=TRUE if all pixels in Rk have the same
R
Ri
n
i

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1
(a)
j
i
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i
R
R j
i 

 ,
and
all
for
(c) 
n
i
Ri ,...,
2
,
1
region,
connected
a
is
(b) 
n
i
R
P i ,...,
2
,
1
for
TRUE
)
(
(d) 

j
i
j
i R
R
R
R
P and
regions
adjacent
any
for
FALSE
)
(
(e) 


48. Region-Based Segmentation
Region Growing

49. Region-Based Segmentation
Region Growing
 Fig. 10.41 shows the histogram of Fig. 10.40 (a). It is
difficult to segment the defects by thresholding methods.
(Applying region growing methods are better in this case.)
Figure 10.41
Figure 10.40(a)

50. Region-Based Segmentation
Region Splitting and Merging
 Region splitting is the opposite of region growing.
 First there is a large region (possible the entire image).
 Then a predicate (measurement) is used to determine
if the region is uniform.
 If not, then the method requires that the region be split
into two regions.
 Then each of these two regions is independently tested
by the predicate (measurement).
 This procedure continues until all resulting regions are
uniform.

51. Region-Based Segmentation
Region Splitting
 The main problem with region splitting is determining
where to split a region.
 One method to divide a region is to use a quadtree
structure.
 Quadtree: a tree in which nodes have exactly four
descendants.

52. Region-Based Segmentation
Region Splitting and Merging
 The split and merge procedure:
 Split into four disjoint quadrants any region Ri for which
P(Ri) = FALSE.
 Merge any adjacent regions Rj and Rk for which
P(RjURk) = TRUE. (the quadtree structure may not be
preserved)
 Stop when no further merging or splitting is possible.