Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002

Lecture Nine

Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.

DFT Filter Algorithms

operations N)) log M O(MN(log requires thisof All

y))(x,gRe((-1)y)g(x, 5.

DFTInvert v)),invDFT(G(uy)(x,g 4.

filtern convolutio Perform v)F(u, v)H(u, v)G(u, 3.

N/2)(M/2, v)(u,at Centered y))(x,fDFT( v)F(u, 2.

),((-1) y)(x,f .1

y x

yx

yxf

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

World’s Simplest Filter

Filter out average

H(u,v) = 0 (u,v)=(M/2,N/2)

1 otherwise

Called a notch filter

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Low and High Pass Filters

• Low pass filters, deemphasize high frequencies. Have less sharp detail. Averaging filters are low pass.

• High pass filters. Does opposite. Pictures should appear sharper. Laplacian filters are high pass.

In next picture, see effects of low pass and high pass filters. Looks like Gaussian filter.

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Impulse and Gaussian Functions(1)

Both yield real and simple DFTs. Both lead to different ideals.

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function theof value

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it howby defined ),(

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Impulse and Gaussian Functions(2)

gets.it as simple as

))2/()exp(-(uA v)H(u,

is DFT ts

))(2exp(2),(

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About

v

I

yxAyxh

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Three types of Low Pass Filters

• Ideal Low Pass Filters (ILPF)

• Butterworth Low Pass Filters (BLPF)

• Gaussian Low Pass Filters (GLPF)

Top draws strongest line in the sand, but has ringing effect. Bottom has no ringing effect, but draws weaker line in the sand.

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain