Wavelets and Image Processing, why bother?
Cn7805/4/04
Tim McKenna
Outline
• Multiresolution Analysis using Wavelets
• Compression
• Wavelets for a Vision
• The FBI Fingerprint Database
• Space-variant object recognition using wavelets
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”
Gabor WaveletsFunctional Form:
The Children of the Mother:
where:
Mother:
Compression
Compression in a Nutshell:•DWT the image ->wavelet coefficients•throw out the small coefficients
Lai et al 1999, Yale database
Foveated VisionSpace-variant wavelet representation with a log-polar
flavor.
Orthonormal Wavelet Bases (right) (scaling functions on left)
1. Meyer
2. Battle-Lemarie
3. Battle-Lamarie
4. Haar
5. Daubechies
6. other
Daubechies 1992
Wavelets for a
Vision
Three Mother Wavelets:Chang,Mallat&Yap 1999
from 1 dimension to 2
One-dimension foveation operator:
Generalization to two dimensions:
Chang,Mallat&Yap 1999
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)
WSQ
http://www.c3.lanl.gov/~brislawn/FBI/OverCompress/HowItWorks/howitworks.html
Discrete Wavelet Transform (DWT) Decomposition
•64 subbands
•Variance varies
Space-variant object recognition using wavelets