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The importance of phase in image processing

The importance of phase in image processing

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The importance of phase in image processing

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  1. The importance of phase in image processing Final thesis exam- 29/11/09 NikolaySkarbnik Under supervision of: Professor Yehoshua Y. Zeevi

  2. Outline • Introduction (Phase vs. Magnitude) • Global vs. Local phase • Local Phase based • Image segmentation • Edge detection • Applications • Rotated Local Phase Quantization

  3. Introduction • Phase is an important signal component, which is often ignored in favor of magnitude. • Phase is sufficient for image segmentation, edges detection etc… • Phase manipulations result in various useful effects.

  4. Common image spectra Lena image spectrum Natural Images statistical average spectrum[1]

  5. Where is the data encoded? 2D Fourier magnitude 2D Fourier phase

  6. The importance of phase in images[2]

  7. The importance of phase in voice STFT?

  8. Reconstruction from phase? Global and Local phase [3] • Localized phase is sufficient for exact image reconstruction. • Single iteration of Localized (sub-signal) phase is sufficient image content recognition. • Globalised (whole signal) phase requires many iterations for the same tasks. Original Image Local phase rec. Global phase rec. Comparison chart

  9. Image segmentation

  10. Image segmentation- Gabor Filters [5-7]

  11. Image segmentation- Gabor Wavelets

  12. Image segmentation- Filtering results

  13. Image segmentation- Gabor feature space Magnitude based feature space Phase based feature space

  14. Image segmentation- Clustering K-means Clustering

  15. How? Brodatz Mosaics segmentation Tested mosaic Phase only Phase only [6] [7] Magnitude only Phase & Magnitude Phase & Magnitude [5] [6] [7]

  16. Natural images segmentation Tested image Phase only Phase only [6] [7] Phase & Magnitude Phase & Magnitude Magnitude only [6] [7] [5] All tests

  17. Segmentation results- tables Texture mosaics results Natural imagesresults Test images

  18. Edge detection

  19. Analytical Signal and Hilbert Transform

  20. Phase Congruency (PC) based Edge detection [7] Even (cosine) and Odd (sine) components.

  21. -Freq. comp. 1 -Freq. comp. 2 -Freq. comp. 3 -Freq. comp. 4 Im{FT[x]} -Freq. comp. 1 -Freq. comp. 2 -Freq. comp. 3 -Freq. comp. 4 Im{FT[x]} Re{FT[x]} Re{FT[x]} PC Edge detection

  22. Im{FT[x]} Im{FT[x]} -Freq. comp. 1 -Freq. comp. 2 -Freq. comp. 3 -Freq. comp. 4 -Freq. comp. 1 -Freq. comp. 2 -Freq. comp. 3 -Freq. comp. 4 Re{FT[x]} Re{FT[x]} PC Edge detection (cont.) PC ? AS

  23. Edge detectors-1D Original Signal Edges via phase STD PC via

  24. Edge detectors-1D Original Signal AS Energy, Local Energy Sig. derivative 2D- PC?

  25. Edge detection- Localized Phase Quantization error (LPQe) scheme[9]

  26. LPQe edge detector-1D Original Signal LPQe

  27. LMIe? Edge detectors-2D Original Signal PC |LPQe|

  28. Edge detectors- dealing with noise Original Signal SNR 10[dB] |LPQe| PC Raw Canny [10] Canny thresholds

  29. PC based application: Geodesic snakes segmentation [11] Snakes?

  30. 1D LPQe based application: P&M anisotropic diffusion [12]

  31. 2D LPQe based application: Detection of Man-Made environment [13] Gray scale image LPQe edges map PC edges map Fractals?

  32. Phase quantization- how to, ?

  33. Phase quantization- how to, ?

  34. Phase quantization- how to, ?

  35. Rotated Local Phase Quantization • Only asymmetric quantization scheme results in a non complex signal. • Therefore the Rotated Quantization scheme resulting signal is complex for all values • Meaningful Real and Imaginary components Proof

  36. Rotated Local Phase Quantization • Imaginary{RLPQ}- blurred signal. • Blurring effect very similar to Box Blur.

  37. Blur from Im{RLPQ}

  38. Edges from Re{RLPQ} Kq=2

  39. Cartoons from Re{RLPQ} Kq=3

  40. Image primitives from Re{RLPQ} Original image Kq>>2 Kq=3 Cartoon Kq=2 Edges Map

  41. Input image Edges Detection Kq ||LPQe|| Signal dependent RLPQ TeD like results Localized Kq • Edges carry information, thus preserving edges during RLPQ is vital. • Means→ localized, signal dependent Kq!

  42. Diffusion like results via RLPQ RLPQ Heat Diffusion [14] Orig

  43. TeD and edge preserving RLPQ RLPQ Telegraph Diffusion [15] Iterative RLPQ

  44. Conclusions • We have shown that use phase can replace magnitude in various algorithms (segmentation, edges detection, etc…) and sometimes result in a better performance. • We have shown that common signal/image processing tasks such as: HP filtering and  can be achieved via localized phase manipulations. • Our RLPQ output (simultaneous cartoonization and edge detection) visually similar to results achieved by diffusion schemes (P&M, G. GilboaFaB, V. RatnerTeD).

  45. Fin Thank for your attention. Questions? Refs.