Sharpening using frequency Domain Filter

DIGITAL IMAGE PROCESSING
TOPIC: FREQUENCY DOMAIN FILTER
IMAGE SHARPENING
Submitted To -
Mrs.G.Murugeswari M.Tech.,
Assistant Professor
Department of Computer Science & Engineering
M.S.University
Abishekapatti
Submitted By -
T.Arul Raj
A.D.Bibin
M.Kalidass
M.Saravanan
M.Phil (CSE)
M.S University
10/25/16

What Is Image
Enhancement?
Image enhancement is the process of making images more
useful
The reasons for doing this include:
– Highlighting interesting detail in images
– Removing noise from images
– Making images more visually appealing
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2

Spatial & Frequency Domains
There are two broad categories of image enhancement
techniques
– Spatial domain techniques
– Direct manipulation of image pixels
– Frequency domain techniques
– Manipulation of Fourier transform or wavelet transform of an image
For the moment we will concentrate on techniques that
operate in the spatial domain
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3

Basic steps for filtering in
the frequency domain
4
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Basics of filtering in the
frequency domain
1. multiply the input image by (-1)x+y
to center the
transform to u = M/2 and v = N/2 (if M and N are even
numbers, then the shifted coordinates will be integers)
2. computer F(u,v), the DFT of the image from (1)
3. multiply F(u,v) by a filter function H(u,v)
4. compute the inverse DFT of the result in (3)
5. obtain the real part of the result in (4)
6. multiply the result in (5) by (-1)x+y
to cancel the
multiplication of the input image.
5
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Sharpening
– Edges and fine detail characterized by sharp transitions in
image intensity
– Such transitions contribute significantly to high frequency
components of Fourier transform
– Intuitively, attenuating certain low frequency components
and preserving high frequency components result in
sharpening
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6

Sharpening Filter Transfer
Function
– Intended goal is to do the reverse operation of low-pass
filters
– When low-pass filer attenuates frequencies, high-pass filter
passes them
– When high-pass filter attenuates frequencies, low-pass filter
passes them
( , ) 1 ( , )hp lpH u v H u v= −
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Blurring masks
A blurring mask has the following properties.
– All the values in blurring masks are positive
– The sum of all the values is equal to 1
– The edge content is reduced by using a blurring mask
– As the size of the mask grow, more smoothing effect will take
place
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Derivative masks
A derivative mask has the following properties.
– A derivative mask have positive and as well as negative values
– The sum of all the values in a derivative mask is equal to zero
– The edge content is increased by a derivative mask
– As the size of the mask grows , more edge content is increased
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Relationship between blurring mask and
derivative mask with high pass filters and low
pass filters:
The relationship between blurring mask and derivative mask
with a high pass filter and low pass filter can be defined
simply as.
– Blurring masks are also called as low pass filter
– Derivative masks are also called as high pass filter
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High pass frequency components
and Low pass frequency components
– High pass frequency
components and Low
pass frequency
components
– the low pass frequency
components denotes
smooth regions.
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Ideal low pass
This is the common example
of low pass filter.
When one is placed
inside and the zero is placed
outside , we got a blurred
image. Now as we increase
the size of 1, blurring would
be increased and the edge
content would be reduced.
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Ideal High pass filters
This is a common example
of high pass filter.
When 0 is placed
inside, we get edges, which
gives us a sketched image.
An ideal low pass filter in
frequency domain is given
below.
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Butterworth High Pass
Filters
The Butterworth high pass filter is given as:
where n is the order and D0 is the cut off distance as before
n
vuDD
vuH 2
0 )],(/[1
1
),(
+
=
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Butterworth High Pass Filters
(cont…)
Results of
Butterworth
high pass
filtering of
order 2 with
D0 = 15
Results of
Butterworth
high pass
filtering of
order 2 with
D0 = 80
Results of Butterworth high pass
filtering of order 2 with D0 = 30
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Gaussian Low pass Filter
– The concept of filtering and low pass
remains the same, but only the
transition becomes different and
become more smooth.
– The Gaussian low pass filter can be
represented as
– Note the smooth curve transition,
due to which at each point, the value
of Do, can be exactly defined.
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Gaussian high pass filter
– Gaussian high pass filter has the same concept as ideal high
pass filter, but again the transition is more smooth as
compared to the ideal one.
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Sharpening Filters:
Laplacian
The Laplacian is defined as:
(dot product)
Approximate
derivatives:
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Sharpening Filters:
Laplacian (cont’d)
Laplacian Mask
detect zero-crossings
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20 Conclusion
– The aim of image enhancement is to improve the
information in images for human viewers, or to provide
`better' input for other automated image processing
techniques
– There is no general theory for determining what is `good'
image enhancement when it comes to human perception.
If it looks good, it is good!
10/25/16

Sharpening using frequency Domain Filter

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