Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.
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Transcript of Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.
![Page 1: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/1.jpg)
Lecture Nine
Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.
![Page 2: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/2.jpg)
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
![Page 3: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/3.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 4: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/4.jpg)
World’s Simplest Filter
Filter out average
H(u,v) = 0 (u,v)=(M/2,N/2)
1 otherwise
Called a notch filter
![Page 5: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/5.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 6: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/6.jpg)
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.
![Page 7: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/7.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 8: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/8.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 9: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/9.jpg)
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 ),(
00
1
0
1
000
Copies
yxsyyxxyxs
yx
M
x
N
y
![Page 10: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/10.jpg)
Impulse and Gaussian Functions(2)
gets.it as simple as
))2/()exp(-(uA v)H(u,
is DFT ts
))(2exp(2),(
222
22222
About
v
I
yxAyxh
![Page 11: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/11.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 12: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/12.jpg)
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.
![Page 13: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/13.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 14: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/14.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 15: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/15.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 16: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/16.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 17: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/17.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 18: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/18.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 19: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/19.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 20: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/20.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 21: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/21.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 22: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/22.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 23: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/23.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 24: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/24.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 25: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/25.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 26: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/26.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 27: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/27.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 28: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/28.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 29: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/29.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 30: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/30.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 31: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/31.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 32: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/32.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain
![Page 33: Lecture Nine Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bfba1a28abf838ca0145/html5/thumbnails/33.jpg)
Chapter 4Image Enhancement in the
Frequency Domain
Chapter 4Image Enhancement in the
Frequency Domain