its very useful for students. Sharpening process in spatial domain Direct Manipulation of image Pixels. The objective of Sharpening is to highlight transitions in intensity The image blurring is accomplished by pixel averaging in a neighborhood. Since averaging is analogous to integration. Prepared by M. Sahaya Pretha Department of Computer Science and Engineering, MS University, Tirunelveli Dist, Tamilnadu.

1. Prepared by
T. Sathiyabama
M. Sahaya Pretha
K. Shunmuga Priya
R. Rajalakshmi
Department of Computer Science and Engineering,
MS University, Tirunelveli
10/26/2016 8:17 AM 1

2. Definition
Direct Manipulation of image Pixels.
The objective of Sharpening is to highlight transitions
in intensity
The image blurring is accomplished by pixel averaging
in a neighborhood.
Since averaging is analogous to integration.
10/26/2016 8:17 AM 2

3. Some Applications
Photo Enhancement
Medical image visualization
Industrial defect detection
Electronic printing
Autonomous guidance in military systems
10/26/2016 8:17 AM 3

4. Foundation
Sharpening Filters to find details about
Remove blurring from images.
Highlight edges
We are interested in the behavior of these derivatives
in areas of constant gray level(flat segments), at the
onset and end of discontinuities(step and ramp
discontinuities), and along gray-level ramps.
These types of discontinuities can be noise points,
lines, and edges.
10/26/2016 8:17 AM 4

5. Definition for a first derivative
Must be zero in flat segments
Must be nonzero at the onset of a gray-level step or ramp
Must be nonzero along ramps
A basic definition of the first-order derivative of a one-dimensional
function f(x) is
(Diff b/w subsequent values & measures the rate of change of the
function)
10/26/2016 8:17 AM 5
)()1(
f
xfxf
x




6. Definition for a second derivative
Must be zero in flat areas
Must be non zero at the onset and end of a gray-level step
or ramp
Must be zero along ramps of constant slope
We define a second-order derivative as the difference
(the values both
before& after the
current value)
10/26/2016 8:17 AM 6
)(2)1()1(2
2
xfxfxf
x
f




7. First and second-order derivatives in digital form => difference
The 1st-order derivative is nonzero along the entire ramp,
while the 2nd-order derivative is nonzero only at the onset and
end of the ramp.
The response at and around the point is much stronger for the
2nd- than for the 1st-order derivative.
10/26/2016 8:17 AM 7
)()1( xfxf
x
f



)(2)1()1(
)]1()([)]()1([2
2
xfxfxf
xfxfxfxf
x
f





8. Gray-level profile
10/26/2016 8:17 AM 8
660 1 2 30 0 2 2 2 2 23 3 3 3 30 0 0 0 0 0 0 0 7 7 5 5
7
6
5
4
3
2
1
0

9. Derivative of image profile
10/26/2016 8:17 AM 9
0 0 0 1 2 3 2 0 0 2 2 6 3 3 2 2 3 3 0 0 0 0 0 0 7 7 6 5 5 3
0 0 1 1 1-1-2 0 2 0 4-3 0-1 0 1 0-3 0 0 0 0 0-7 0-1-1 0-2
0-1 0 0-2-1 2 2-2 4-7 3-1 1 1-1-3 3 0 0 0 0-7 7-1 0 1-2
first
second

10. 2nd derivatives for image
Sharpening
 2-D 2nd derivatives => Laplacian
10/26/2016 8:17 AM 10
2
2
2
2
2
y
f
x
f
f






),(4)]1,()1,(),1(),1([
)],(2)1,()1,([
)],(2),1(),1([2
yxfyxfyxfyxfyxf
yxfyxfyxf
yxfyxfyxff



=>discrete formulation

11. Implementation






),(),(
),(),(
),( 2
2
yxfyxf
yxfyxf
yxg
),(2
yxf
10/26/2016 8:17 AM 11
If the center coefficient is negative
If the center coefficient is positive
Where f(x,y) is the original image
is Laplacian filtered image
g(x,y) is the sharpen image

12. Definition of 2nd derivatives in
filter mask
900 rotation
invariant
450 rotation
invariant
(include
Diagonals)
4 -
-
-
- -
- - -
-
---
8
10/26/2016 8:17 AM 12

13. Implementation
10/26/2016 8:17 AM 13

14. Implementation
10/26/2016 8:17 AM 14
Filtered = Conv(image,mask)

15. Implementation
10/26/2016 8:17 AM 15
filtered = filtered - Min(filtered)
filtered = filtered * (255.0/Max(filtered))

16. Implementation
10/26/2016 8:17 AM 16
sharpened = image + filtered
sharpened = sharpened - Min(sharpened )
sharpened = sharpened * (255.0/Max(sharpened ))

17. Algorithm
1. Using Laplacian filter to original image
2. And then add the image result from step 1 and the
original image
3. We will apply two step to be one mask
10/26/2016 8:17 AM 17
),(4)1,()1,(),1(),1(),(),( yxfyxfyxfyxfyxfyxfyxg 
)1,()1,(),1(),1(),(5),(  yxfyxfyxfyxfyxfyxg

18. Result of Algorithm
10/26/2016 8:17 AM 18
-1
-1
5 -1
-1
0 0
0 0
-1
-1
9 -1
-1
-1 -1
-1 -1

19. Laplacian filtering: example
10/26/2016 8:17 AM 19
Original image Laplacian filtered image

20. Unsharp masking
 A process to sharpen images consists of
subtracting a blurred version of an image from
the image itself. This process, called unsharp
masking, is expressed as
),(),(),( yxfyxfyxfs 
),( yxfs
10/26/2016 8:17 AM 20
),( yxf),( yxf
Where denotes the sharpened image obtained by unsharp
masking, an is a blurred version of

21. High-boost filtering
 A high-boost filtered image, fhb is defined at any
point (x,y) as
1),(),(),(  AwhereyxfyxAfyxfhb
),(),(),()1(),( yxfyxfyxfAyxfhb 
10/26/2016 8:17 AM 21
),(),()1(),( yxfyxfAyxf shb 
This equation is applicable general and does not state explicity how
the sharp image is obtained

22. High-boost filtering and Laplacian
 If we choose to use the Laplacian, then we know
fs(x,y)






),(),(
),(),(
2
2
yxfyxAf
yxfyxAf
fhb
10/26/2016 8:17 AM 22
If the center coefficient is negative
If the center coefficient is positive
-1
-1
A+4 -1
-1
0 0
0 0
-1
-1
A+8 -1
-1
-1 -1
-1 -1

23. The Gradient (1st order derivative)
 First Derivatives in image processing are
implemented using the magnitude of the
gradient.
The gradient of function f(x,y) is























y
f
x
f
G
G
f
y
x
10/26/2016 8:17 AM 23

24.  The magnitude of this vector is given by
yxyx GGGGfmag  22
)(
-1 1
1
-1
Gx
Gy
This mask is simple, and no isotropic. Its result
only horizontal and vertical.
10/26/2016 8:17 AM 24

25. Robert’s Method
 The simplest approximations to a first-order
derivative that satisfy the conditions stated in
that section are
2
68
2
59 )()( zzzzf 
6859 zzzzf 
z1 z2 z3
z4 z5 z6
z7 z8 z9
Gx = (z9-z5) and Gy = (z8-z6)
10/26/2016 8:17 AM 25

26.  These mask are referred to as the Roberts cross-
gradient operators.
-1 0
0 1
-10
01
10/26/2016 8:17 AM 26

27. Sobel’s Method
 Using this equation
)2()2()2()2( 741963321987 zzzzzzzzzzzzf 
-1 -2 -1
0 0 0
1 2 1 1
-2
10
0
0-1
2
-1
10/26/2016 8:17 AM 27

28. Gradient: example
defectsoriginal(contact lens) Sobel gradient
 Enhance defects and eliminate slowly changing background
10/26/2016 8:17 AM 28

29. 10/26/2016 8:17 AM 29
Thank You to all my viewers