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