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
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
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
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