Image process - Image segmentation-Ch10.ppt

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Image processing  understanding
Preprocess
Image acquisition, restoration, and enhancement
Intermediate process
Image segmentation and feature extraction
High level process
Image interpretation and recognition

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Why Image segmentation ?
Image segmentation is used to separate an image into constituent
parts based on some image attributes.
Benefit
1. Image segmentation reduces huge amount of unnecessary
data while retaining only importance data for image analysis
2. Image segmentation converts bitmap data into better
structured data which is easier to be interpreted

What is Image Segmentation
 It is a process that partitions R(image) into n
sub regions, such that
Ri is a connected set
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Ways of Image Segmentation
1. Similarity properties
2. Discontinuity of pixel properties Discontinuity:
Intensity change
at boundary
Similarity:
Internal
pixels share
the same
intensity

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Point detection
 We can use Laplacian masks
for point detection.
 Laplacian masks have the largest
coefficient at the center of the mask
while neighbor pixels have an
opposite sign.
 This mask will give the high response to the object that has the
similar shape as the mask such as isolated points.
 Notice that sum of all coefficients of the mask is equal to zero.
This is due to the need that the response of the filter must be zero
inside a constant intensity area
-1 -1
-1
8
-1
-1
-1
-1
-1
-1 0
0
4
-1
-1
0
-1
0

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Point detection
Point detection can be done by applying the thresholding function:


 


otherwise
0
)
,
(
1
)
,
(
T
y
x
f
y
x
g
Laplacian image After thresholding
X-ray image of the
turbine blade with
porosity

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Line detection
 For a simple line detection, 4 directions that are mostly
used are Horizontal, +45 degree, vertical and –45 degree.

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Binary wire
bond mask
image
Absolute value
of result after
processing with
-45 line detector
Result after
thresholding
Line detection

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Edges
Generally, objects and background have different intensities. Therefore,
Edges of the objects are the areas where abrupt intensity changes occur.

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Ideal Ramp & its derivative
Original image

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Gray level
profile
The 1st
derivative
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-5
-4
-3
-2
-1
0
1
2
3
4
5
x 10-3
The 2nd
derivative
Smooth step edge & its derivative

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Derivative
operator is a high
pass filter and
thus enhances
noise.
Edge responses
are buried by
noise.
f(x)
AWGN = 0.1
AWGN = 1.0
AWGN = 10
dx
df
2
2
dx
f
d
Noisy Edges and Derivatives

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)
,
( y
x
f
y
f


x
f


y
f
x
f





Example: Image gradient

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Laplacian of Gaussian(LoG), Marr- Hildrath
Edge detection







 






 




2
2
2
2
4
2
2
2
2
)
,
(



y
x
e
y
x
y
x
G
LOG image
5x5 LOG
mask
Surface plot of
LOG, Looks like
a “Mexican
hat”
Cross section
of LOG

Marr-Hildrath Edge detection
 Filter the image with an n x n
Gaussian low pass filter.
 Compute the laplacian of the
image.
 Find the zero crossings of the
image
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It generates responses that may not correspond
edges called False edges
Localization error may be sever at curved edges

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Marr-Hildrath Edge detection

Difference of Gaussian(DoG)
 Marr & Hildrath suggested that using ratio of
1.6:1 preserves the basic characteristics and
closer approximation to LoG.
 Zero crossings of LoG and DoG will be the
same when above value of σ is used.
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Difference of Gaussian(DoG)

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Canny edge detection
Complex algorithm but performance is superior.
3 basic objectives
 Low error rate
 Edge points should be well localized
 Single Edge point response

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Smoothing the image with a circular 2D Gaussian.
Let f(x,y) input image and G(x,y) denotes Gaussian







 


2
2
2
2
)
,
(

y
x
e
y
x
G
)
,
(
)
,
(
)
,
( y
x
f
y
x
G
y
x
fs 


 Compute image gradient & direction
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 Fs is generated using gradient, M(x,y)
contains wide ridges around local
maxima.
 Next step is to thin ridges.
 One approach nonmaxima
suppression.
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 Nonmaxima suppression
 Find the direction dk closest to α(x,y)
 If the value of M(x,y) is less than at least
one of its neighbours along dk , let gN(x,y)
=0, otherwise gN(x,y) = M(x,y)
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P2 P3
P9
P5
P8
P6
P1
P4
P7
Edge normal

 gN(x,y) is nonmaxima suppressed
image.
 Next step to threshold the gN(x,y) to
reduce false edges.
 Use of hysteresis thresholding: two
thresholds, TL and TH
gNH(x,y) = gN(x,y) ≥ TH
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gNL(x,y) = gN(x,y) ≥ TL
 gNH(x,y) has very few nonzero pixels
than gNL(x,y).
 Nonzero pixels of gNH also contained in
gNL
gNL(x,y) = gNL(x,y) - gNH(x,y)
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 Depending on the values of TH, edges in gNH have gaps.
Longer edges are formed using following procedure.
 Locate next unvisited edge pixel p, in gNH
 Mark as valid edge pixels all the weak pixels in gNL
that are connected to p, using 8 connectivity.
 If all nonzero pixels in gNH have been visited go to
next step else return to first step
 Set to zero all pixels in gNL that were not marked as
valid edge pixels
 Append all nonzero pixels from gNL to gNH
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Edge Linking & Boundary Detection
 Local Processing
 To analyze the each pixel in a small
neighborhood about every pixel.
 Consider the strength and gradient vector
 An edge pixel with coordinates (s,t) in Sxy is
similar to pixel at (x,y) if
 E and A are positive threshold for magnitude
and angle.
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 Compute garident magnitude and angle arrays,
M(x,y) & α(x,y) for f.
 Form binary image g, whose value at (x,y) is
given by
 Scan the rows of g and fill all gaps in each row
that do not exceed specified length k.
 To detect gap in any other direction, rotate g by
that angle and apply above step. Rotate the
result back by negtive of that angle.
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 TM = 30% of
maximum gradient
 A =90o
 TA = 45o

 Given n points, we want to find subsets of these
points that lie on straight lines.
 Find all lines determined by every pair of
points
 Then find all subsets of points that are close
to particular lines
 Approach involves finding n(n-1)/2 = n2
lines
and then n3
comparisons.
 Alternative approach proposed by Hough[1962].
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Global Processing using Hough Transform

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 xy plane is transformed to ab plane(Parameter space).
 All the points on the line have lines in parameter space
that intersect at (a’, b’).

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Equation of the line in polar form

35

 Hough transform approach is as follows:
 Obtain binary edge image
 Specify subdivisions in the ρθ plane.
 Examine the counts of accumulator cells
for high level pixel concentrations.
 Examine the relationship between pixels
in a chosen cell.
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37

Thresholding
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 The simplest approach
to segment an image.
If f (x, y) > T then
f (x, y) = 0
else f (x, y) = 255

 Intensity thresholding is directly related to the
width and depth of the valley separating
histogram. Key factors affecting the valleys are:
 The separation between peaks
 Noise contents in the image.
 Relative size of objects and background.
 Uniformity of the illumination source.
 Uniformity of the reflectance property of the image.
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Thresholding

Role of noise in thresholding
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Role of illumination & Reflectance
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Basic Global thresholding
 Following steps for this purpose
 Select an initial estimate for the global threshold T.
 Segment the image using following eqn
. This will produce
two groups of pixels G1 and G2.
 Compute the average intensity values m1 and m2 for the
pixels in G1 and G2.
 Compute a new threshold value:
 Repeat Steps 2 through 4 until the difference between
values of T in successive iterations is smaller than ∆T
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Optimum Global Thresholding using “Otsu”
 Thresholding may be viewed as decision theory
problem.
 Otsu's method tries to maximize between class
variance.
 Let L distinct intensity levels in a digital image of
size M x N image.
 Suppose, T(k) = k, 0<k<L-1, threshold the input
image in class C1 and C2. C1 consists of all pixels in
the range [0,k] and C2 in the range of [k+1, L-1].
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 Probability that pixel is assigned to class C1
given as P1(k) and occurring of class C2 given
by P2(k)
 Mean intensity value of pixels assigned to C1
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 Mean intensity value of pixels assigned to C2
 Average Intensity up to level K
 Average Intensity of the entire image
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 We can obtain from preceding results
P1m1 + P2m2 = mG and P1 + P2 = 1
 “goodness” of threshold at level k
 Global variance can be defined as follows
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 Between class variance(σ2
B) is defined as
follows
 Farther the two means m1 and m2, we have
larger σ2
B
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 σ2
G is Constant and is a measure of separability.
 Objective: Determine k which maximizes between
class variance.
 Once k* has been obtained, segment the image.
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Otsu’s method: summary
 Compute normalized histogram of the image.pi
 Compute cumulative sums, P1(k)
 Compute the cumulative means, m(k)
 Compute the global intensity mean mG
 Compute between class variance σ2
B
 Obtain otsu’s threshold k* which maximizes σ2
Bif
maximum is not unique, obtain by averaging.
 Obtain separability measure η*
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Otsu’s method
Threshold in c: 169
Threshold in d: 181
η = 0.467

Smoothing to improve global thresholding
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How/when Smoothing fails in segmentation

Use of edges to improve global
thresholding
 Chance of selecting good “threshold” are enhanced
if histogram peaks are tall, narrow, symmetric and
separated by deep valleys.
 Process can be summarized as follows:
1. Compute Edge map image as either magnitude of gradient or
absolute value of laplacian of f(x, y)
2. Specify threshold value T
3. Threshold the image from step 1 using threshold of step 2 to
produce binary image gT(x, y). This image is used as mask
image.
4. Compute a histogram using only the pixels in f(x, y) that
correspond to the locations of 1 valued pixels in gT(x, y).
5. Use histogram from step 4 to segment f(x, y) globally using
method like ‘otsu’.
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Use of edges to improve global
thresholding

Multiple Thresholds
 Arbitrary number of thresholds, in case of K
classes
 K classes are separated by k-1 thresholds
whose values are k1
*
,k2
*
,….kk-1
*
that maximize
56

 3 classes consisting of three intensity levels,
between class variance is given by
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Multiple Thresholds

 We know that
 we can find optimum thresholds by
 Thresholded image is given by
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Multiple Thresholds
a,b,c are valid intensity values

 Separabilty measure for one threshold can be
extended directly to multiple thresholds.
 σ2
G is total image variance.
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Multiple Thresholds

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Multiple Thresholds
K*
1=80
K*
2=177

Region based Segmentation
 Region growing
 It is a procedure that groups pixels into
larger regions based on predefined criteria
for growth.
 Start with a set of “seed” points and from
these grow regions by appending to each
seed those nearer pixels that are similar in
criteria to seed.
 Criteria depends on the type of image.
61

Region growing
 Region growing algorithm based on 8 connectivity
is as follows:
 Find all connected components in S(x, y) and erode each
connected component to one pixel; label all such pixels found
as 1. All other pixels in S are labeled as 0.
 Form an image fQ such that, at a pair of coordinates (x, y), let
fQ(x, y) = 1 if the input image satisfies the given predicate, Q
at those coordinates; otherwise, fQ(x, y) = 0.
 Let g be an image formed by appending to each seed point in S
all the 1 valued points in fQ that are 8-connected to that seed
point.
 Label each connected component in g with a different region
label. This is the segmented image.
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Image process - Image segmentation-Ch10.ppt

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