Wavelets and Image Processing, why bother

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Wavelets and Image Processing, why bother?

• Cn780
• 5/4/04
• Tim McKenna

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Outline

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

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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

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Gabor Wavelets
Functional Form
The Children of the Mother
Mother
where
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Compression
Lai et al 1999, Yale database

• Compression in a Nutshell
• DWT the image -gtwavelet coefficients
• throw out the small coefficients

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Foveated Vision

• Space-variant wavelet representation with a
  log-polar flavor.

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• Orthonormal Wavelet Bases (right) (scaling
  functions on left)
• Meyer
• Battle-Lemarie
• Battle-Lamarie
• Haar
• Daubechies
• other

Daubechies 1992
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Wavelets for a Vision
Chang,MallatYap 1999
Three Mother Wavelets
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from 1 dimension to 2
One-dimension foveation operator
Generalization to two dimensions
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Chang,MallatYap 1999
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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)

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WSQ
http//www.c3.lanl.gov/brislawn/FBI/OverCompress/
HowItWorks/howitworks.html
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• Discrete Wavelet Transform (DWT) Decomposition
• 64 subbands
• Variance varies

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Space-variant object recognition using wavelets