Download Wavelets and Image Processing, why bother?

Wavelets and Image
Processing, why bother?
Cn780
5/4/04
Tim McKenna
Outline
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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 Wavelets
Functional Form:
Mother:
The Children of the Mother:
where:
Compression
Lai et al 1999, Yale database
Compression in a Nutshell:
•DWT the image ->wavelet coefficients
•throw out the small coefficients
Foveated Vision
Space-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
Chang,Mallat&Yap 1999
Three Mother Wavelets:
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