lecture nine figures from gonzalez and woods, digital image processing, copyright 2002

Lecture Nine

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

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

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.

Frequency Domain

Impulse and Gaussian Functions(1)

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

impulse theoflocation at the

function theof value

),(),(),(

functionsother with convolves

it howby defined ),(

Copies

yxsyyxxyxs

Impulse and Gaussian Functions(2)

gets.it as simple as

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

is DFT ts

))(2exp(2),(

yxAyxh

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.

Frequency Domain

lecture nine figures from gonzalez and woods, digital image processing, copyright 2002

Documents

image enhancement

thefrequency domainchapter

thefrequency domainlow

thefrequency domainimpulse

digital image processing

effects of low pass

averaging filters

laplacian filters