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DIGITAL IMAGE PROCESSINGTOPIC: FREQUENCY DOMAIN FILTER
IMAGE SHARPENING
Submitted To - Mrs.G.Murugeswari M.Tech.,Assistant ProfessorDepartment of Computer Science & EngineeringM.S.UniversityAbishekapattiSubmitted By -
T.Arul RajA.D.BibinM.KalidassM.SaravananM.Phil (CSE)M.S University
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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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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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Basic steps for filtering in the frequency domain
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Basics of filtering in the frequency domain1. 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.
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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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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 FiltersThe Butterworth high pass filter is given as:
where n is the order and D0 is the cut off distance as before
nvuDDvuH 2
0 )],(/[11),(
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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)
Approximatederivatives:
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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!
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REFERENCE VIDEOS
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References Videos
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THANK YOU