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