This document discusses frequency domain filtering for image sharpening. It begins by explaining the difference between spatial and frequency domain image enhancement techniques. It then describes the basic steps for filtering in the frequency domain, which involves taking the Fourier transform of an image, multiplying it by a filter function, and taking the inverse Fourier transform. The document discusses sharpening filters specifically, noting that high-pass filters can be used to sharpen by preserving high frequency components that represent edges. It provides examples of ideal low-pass and high-pass filters, and Butterworth and Gaussian filters. Laplacian filters are also introduced as a common sharpening filter that uses an approximation of second derivatives to detect and enhance edges.

1. 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

2. 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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3. 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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4. Basic steps for filtering in
the frequency domain
4
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5. 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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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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13. 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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14. 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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15. 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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16. 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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17. 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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18. Sharpening Filters:
Laplacian
The Laplacian is defined as:
(dot product)
Approximate
derivatives:
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19. Sharpening Filters:
Laplacian (cont’d)
Laplacian Mask
detect zero-crossings
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20. 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!
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21. REFERENCE VIDEOS
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22. References Videos
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23. 10/25/16
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THANK YOU