Create Presentation
Download Presentation

Download Presentation
## The importance of phase in image processing

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**The importance of phase in image processing**Final thesis exam- 29/11/09 NikolaySkarbnik Under supervision of: Professor Yehoshua Y. Zeevi**Outline**• Introduction (Phase vs. Magnitude) • Global vs. Local phase • Local Phase based • Image segmentation • Edge detection • Applications • Rotated Local Phase Quantization**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.**Common image spectra**Lena image spectrum Natural Images statistical average spectrum[1]**Where is the data encoded?**2D Fourier magnitude 2D Fourier phase**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**Image segmentation- Gabor feature space**Magnitude based feature space Phase based feature space**Image segmentation- Clustering**K-means Clustering**How?**Brodatz Mosaics segmentation Tested mosaic Phase only Phase only [6] [7] Magnitude only Phase & Magnitude Phase & Magnitude [5] [6] [7]**Natural images segmentation**Tested image Phase only Phase only [6] [7] Phase & Magnitude Phase & Magnitude Magnitude only [6] [7] [5] All tests**Segmentation results- tables**Texture mosaics results Natural imagesresults Test images**Phase Congruency (PC) based Edge detection**[7] Even (cosine) and Odd (sine) components.**-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**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**Edge detectors-1D**Original Signal Edges via phase STD PC via**Edge detectors-1D**Original Signal AS Energy, Local Energy Sig. derivative 2D- PC?**Edge detection- Localized Phase Quantization error (LPQe)**scheme[9]**LPQe edge detector-1D**Original Signal LPQe**LMIe?**Edge detectors-2D Original Signal PC |LPQe|**Edge detectors- dealing with noise**Original Signal SNR 10[dB] |LPQe| PC Raw Canny [10] Canny thresholds**PC based application: Geodesic snakes segmentation**[11] Snakes?**2D LPQe based application: Detection of Man-Made**environment [13] Gray scale image LPQe edges map PC edges map Fractals?**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**Rotated Local Phase Quantization**• Imaginary{RLPQ}- blurred signal. • Blurring effect very similar to Box Blur.**Image primitives from Re{RLPQ}**Original image Kq>>2 Kq=3 Cartoon Kq=2 Edges Map**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!**Diffusion like results via RLPQ**RLPQ Heat Diffusion [14] Orig**TeD and edge preserving RLPQ**RLPQ Telegraph Diffusion [15] Iterative RLPQ**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).**Fin**Thank for your attention. Questions? Refs.