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Digital Image Processing

Digital Image Processing. 7 Wavelets and Multiresolution Processing. Preview. 7.1 Background. Multiresolution Objects, which are of small size or of low contrast, require high resolution; Objects, which are of large size or of high contrast, often only require low resolution.

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Digital Image Processing

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  1. Digital Image Processing 7 Wavelets and Multiresolution Processing

  2. Preview

  3. 7.1 Background • Multiresolution • Objects, which are of small size or of low contrast, require high resolution; • Objects, which are of large size or of high contrast, often only require low resolution. • Statistics features

  4. 7.1 Background

  5. 7.1.1 Image pyramids

  6. 7.1.1 Image pyramids

  7. 7.1.2 Subband coding

  8. 7.1.2 Subband coding

  9. 7.1.2 Subband coding

  10. 7.1.3 The Haar transform • Principle • Basis functions of the Haar transform are the oldest and simplest known orthonormal wavelets. • Expression of the Haar transform T = HFH where F is an image, H is the Haar transform. • An instance of the Haar transform

  11. 7.1.3 The Haar transform

  12. 7.2 Multiresolution expansion • Series expansion • Scaling functions • Integer translation • Binary scaling

  13. 7.2 Multiresolution expansion

  14. 7.2 Multiresolution expansion • Wavelet functions • Definition • An example: the Haar wavelet function

  15. 7.2 Multiresolution expansion

  16. 7.3 Wavelet transform in one dimension • The wavelet series expansions • Expression • Approximation coefficients • Wavelet coeffients

  17. 7.3 Wavelet transform in one dimension • An example of the Haar wavelet series expansion

  18. 7.3 Wavelet transform in one dimension • The discrete wavelet transform • Definition

  19. 7.3 Wavelet transform in one dimension • The continuous wavelet transform • Definition • The inverse continuous wavelet transform

  20. 7.3 Wavelet transform in one dimension

  21. 7.4 The fast wavelet transform (skipped)

  22. 7.5 Wavelet transform in two dimension • Two dimensional scaling function (x, y) = (x) (y) • Two dimensional wavelet functions H(x, y) = (x) (y) V(x, y) = (x) (y) D(x, y) = (x) (y) • The scaled and translated basis functions

  23. 7.5 Wavelet transform in two dimension • Definition • The inverse discrete wavelet transform

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