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Wavelets and Image Processing, why bother?

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

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Wavelets and Image Processing, why bother?

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  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: Mother: The Children of the Mother: where:

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

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

  7. Orthonormal Wavelet Bases (right) (scaling functions on left) • Meyer • Battle-Lemarie • Battle-Lamarie • Haar • Daubechies • other Daubechies 1992

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

  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

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