1 / 30

Digital image processing Digital image transforms

Digital image processing Digital image transforms. 4. DIGITAL IMAGE TRANSFORMS 4.1. Introduction 4.2. Unitary orthogonal two-dimensional transforms Separable unitary transforms 4.3. Properties of the unitary transforms

aurora-david
Download Presentation

Digital image processing Digital image transforms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Digital image processing Digital image transforms 4. DIGITAL IMAGE TRANSFORMS 4.1. Introduction 4.2. Unitary orthogonal two-dimensional transforms Separable unitary transforms 4.3. Properties of the unitary transforms Energy conservation Energy compaction; the variance of coefficients De-correlation Basis functions and basis images 4.4. Sinusoidal transforms The 1-D discrete Fourier transform (1-D DFT) Properties of the 1-D DFT The 2-D discrete Fourier transform (2-D DFT) Properties of the 2-D DFT The discrete cosine transform (DCT) The discrete sine transform (DST) The Hartley transform 4.5. Rectangular transforms The Hadamard transform = the Walsh transform The Slant transform The Haar transform 4.6. Eigenvectors-based transforms The Karhunen-Loeve transform (KLT) The fast KLT The SVD 4.7. Image filtering in the transform domain 4.8. Conclusions

  2. Digital image processing Digital image transforms

  3. Digital image processing Digital image transforms

  4. Digital image processing Digital image transforms

  5. Digital image processing Digital image transforms

  6. Digital image processing Digital image transforms

  7. Digital image processing Digital image transforms  Basis functions and basis images KLT Haar Walsh Slant DCT Basis functions (basis vectors) Basis images (e.g.): DCT, Haar, ….

  8. = + = + + + + + + + + + + + + + … + Keeping only 50% of coefficients

  9. Digital image processing Digital image transforms

  10. Digital image processing Digital image transforms

  11. Digital image processing Digital image transforms

  12. Digital image processing Digital image transforms

  13. Digital image processing Digital image transforms

  14. Digital image processing Digital image transforms

  15. Digital image processing Digital image transforms

  16. Digital image processing Digital image transforms

  17. Digital image processing Digital image transforms

  18. Digital image processing Digital image transforms Basis vectors for the Walsh-Hadamard transform

  19. Digital image processing Digital image transforms Original image Ordered Hadamard Non-ordered Hadamard

  20. Digital image processing Digital image transforms

  21. Digital image processing Digital image transforms

  22. Digital image processing Digital image transforms Applying the Haar transform at block level (e.g. 2×2 pixels blocks => Hr[2×2]): Rearrange coefficients: Block transform: Applying the Haar transform at block level for a 4×4 pixels blocks => Hr[4×4]: Rearrange coefficients: Block transform:

  23. Digital image processing Digital image transforms

  24. Digital image processing Digital image transforms

  25. 3 eigenimages and the individual variations on those components KLT (PCA) Eigenimages – examples: Facial image set Corresponding “eigenfaces” Face aproximation, from rough to detailed, as more coefficients are added

  26. Digital image processing Digital image transforms

  27. DFT DFT = sinc 2-D for the square + cst. (for noise) LPF 2-D IDFT Original image = (white square, grey background) + aditive noise

  28. The 2-D spectrum of the image and the filters applied: In the regions corresponding to the vertical lines frequencies Noisy image; periodic noise as vertical lines Image restoration through filtering

  29. Digital image processing Digital image transforms

More Related