1. Wavelets and Image Processing, why bother? Cn780 5/4/04 Tim McKenna

2. Outline Multiresolution Analysis using Wavelets Compression Wavelets for a Vision The FBI Fingerprint Database Space-variant object recognition using wavelets

3. Multiresolution Analysis Using Wavelets The claim by R.G.Daugman concerning the receptive field profile of neurons in visual cortex - “These turn out, for about 97% of the neurons, to be very closely described as 2D Gabor wavelets”

4. Gabor Wavelets Functional Form: The Children of the Mother: where: Mother:

5. Compression Compression in a Nutshell: DWT the image ->wavelet coefficients throw out the small coefficients Lai et al 1999, Yale database

6. Foveated Vision Space-variant wavelet representation with a log-polar flavor.

7. Orthonormal Wavelet Bases (right) (scaling functions on left) 1.Meyer 2.Battle-Lemarie 3.Battle-Lamarie 4.Haar 5.Daubechies 6.other Daubechies 1992

8. Wavelets for a Vision Three Mother Wavelets: Chang,Mallat&Yap 1999

9. from 1 dimension to 2 One-dimension foveation operator: Generalization to two dimensions:

10. Chang,Mallat&Yap 1999

11. The FBI Fingerprint Database Single print ~ 1/2megabyte, (768x768) Target rate desired.75bits/pixel JPEG at that compression rate was “blocky” Used wavelet transform/scalar quantization (WSQ)

12. WSQ http://www.c3.lanl.gov/~brislawn/FBI/OverCompress/HowItWorks/howitworks.html

13. Discrete Wavelet Transform (DWT) Decomposition 64 subbands Variance varies

14. Space-variant object recognition using wavelets