1. 2D Continuous Wavelet Transform Heejong Yoo(ECE) April 26, 2001

2. Project Description The idea of this project is from the software of Crit- tech.com(Psilets 3.0) (www.crit-tech.com)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

3. CWT & DWT CWTDWT 1. ScaleAt any scaleDyadic scales 2. TranslationAt any pointInteger point 3. WaveletAny wavelet that satisfies minimum criteria Orthogonal, biorthogonal, … 4. ComputationLargeSmall 5. DetectionEasily detects direction, orientation Cannot detect minute object if not finely tuned 6. ApplicationPattern Recognition Feature extraction Detection Compression De-noising Transmission Characterization

4. Continuous Wavelet Transform In one dimension, (time domain) (frequency domain) In two dimension, (time domain) (frequency domain) We want to calculate 2D CWT in frequency domain(just like WaveLab) When scale s is fixed,

5. 2D Mexican Hat wavelet Time domainFrequency domain

6. 2D Mexican Hat wavelet (Movie) low frequency  high frequency

8. 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 ImageScale(1~100) Wavelet Select

9. Crit-tech Psilets 3.0 Output (1)

10. Scale = 38

11. Scale =2

12. Scale =1

13. Crit-tech Psilets 3.0 Output (2)

14. Scale =48

15. Scale =3