The importance of phase in image processing

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.