2d continuous wavelet transform
DESCRIPTION
2D Continuous Wavelet Transform. Heejong Yoo(ECE) April 26, 2001. Project Description. The idea of this project is from the software of Crit-tech.com(Psilets 3.0) ( www.crit-tech.com ). Project Description Understand 1D, 2D DWT(FWT_PO.m, FWT2_PO.m in WaveLab) - PowerPoint PPT PresentationTRANSCRIPT
2D Continuous Wavelet Transform
Heejong Yoo(ECE)
April 26, 2001
Project Description
The idea of this project is from the software of Crit-tech.com(Psilets 3.0) (www.crit-tech.com)
Project Description– Understand 1D, 2D DWT(FWT_PO.m, FWT2_PO.m in
WaveLab)– Understand 1D CWT(CWT.m in WaveLab)– Develop 2D CWT algorithm for image processing at fixed
scale
CWT & DWT
CWT DWT
1. Scale At any scale Dyadic scales
2. Translation At any point Integer point
3. Wavelet Any wavelet that satisfies minimum criteria
Orthogonal, biorthogonal, …
4. Computation Large Small
5. Detection Easily detects direction, orientation
Cannot detect minute object if not finely tuned
6. Application Pattern Recognition
Feature extraction
Detection
Compression
De-noising
Transmission
Characterization
Continuous Wavelet Transform
),()( 2 RLxf
dxs
bxxf
sbscwt )()(
1),(
)()(),( swwFswsCWT
In one dimension,
(time domain)
(frequency domain)
In two dimension,
),(),( 2 RLyxf dydxs
by
s
axyxf
sbascwt
),(),(
1),,( (time domain)
)2,1()2,1()2,1,( swswwwFswwsCWT (frequency domain)
We want to calculate 2D CWT in frequency domain(just like WaveLab)
When scale s is fixed,
)2,1()2,1()2,1( wwwwFwwCWT
2D Mexican Hat wavelet
)(2
122
22
)2(),(yx
eyxyx
Time domain)21(
2
122
22
)21(2)2,1(ww
ewwww
Frequency domain
2D Mexican Hat wavelet (Movie)low frequency high frequency
<Time Domain Wavelet> <Fourier Domain Wavelet>
)},({),( 21 yxFww
)(2
122
21
2
1
2
1
2
1
2
122
2
1
2
121
2
1
2
1
2
1
2
122
1
2
12
2
1
2
1
2
1
2
122
1
2
12
)(2
122
21
22
21
22
21
21
22
22
21
2
2
1
2
1
2
2
2
2
2
1
2
2
2
1
2
1
2
2
2
2
2
1
2
21
22
)(2
)2)(2(2
)2)()1(2()2)()1(2(
)()(2
)()()()(
))((2
))(())((
])2[()},({),(
ww
ww
wwww
yjwyxjwx
xjwxyjwyyjwyxjwx
yjwyxjwx
xjwxyjwyyjwyxjwx
yjwxjwyx
eww
ee
eeweew
dyeedxee
dxeedyeeydyeedxeex
dxdyeeee
dydxeeeeydxdyeeeex
dxdyeeeyxyxFww
GUI based 2D CWT
In general, low scale means high frequency, high scale means low frequency
In WaveLab, low scale means low frequency, high scale means high frequency
This program follows the WaveLab
Output Image Display
Fourier Domain Wavelet
4 different Input Image
Scale(1~100)
Wavelet Select
Crit-tech Psilets 3.0 Output (1)
Scale = 38
Scale =2
Scale =1
Crit-tech Psilets 3.0 Output (2)
Scale =48
Scale =3