The importance of phase in image processing Final thesis exam-
29/11/09 Nikolay Skarbnik Under supervision of: Professor Yehoshua
Y. Zeevi
Slide 3
Outline Introduction (Phase vs. Magnitude) Global vs. Local
phase Local Phase based Image segmentation Edge detection
Applications Rotated Local Phase Quantization
Slide 4
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.
Slide 5
Common image spectra Natural Images statistical average
spectrum [1] Lena image spectrum
Slide 6
Where is the data encoded? 2D Fourier magnitude2D Fourier
phase
Slide 7
The importance of phase in images [2]
Slide 8
Short Time Fourier Transform ... FT
Slide 9
Voice STFT spectrogram
Slide 10
The importance of phase in voice STFT?
Slide 11
Image reconstruction from phase [3].
Slide 12
Global vs. Local schemes [4] Sliding window
Slide 13
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 ImageLocal phase rec.Global phase
rec.Comparison chart Reconstruction from phase?
Slide 14
Image segmentation
Slide 15
Image segmentation- Gabor Filters [5-7]
Slide 16
Image segmentation- Gabor Wavelets
Slide 17
Image segmentation- Filtering results
Slide 18
Image segmentation- Gabor feature space Magnitude based feature
space Phase based feature space
PC and AS Local Energy (PC)- AS Energy- AS, HT, PC and Zero
crossing are interconnected PC E AS
Slide 32
Edge detectors-1D Original Signal Edges via phase STD PC
via
Slide 33
Edge detectors-1D Original Signal AS Energy, Local Energy Sig.
derivative 2D- PC?
Slide 34
Radial HT detects Corners [9]
Slide 35
2D PC2D AS No unique definition for the multidimensional HT or
AS exists. Most general 2D HT definition is radial HT- H(w 1,w 2
)=() ( sufficient for edges detection ). sufficient for edges
detection For now, 2D PC is defined via combination of several 1D
PCs in different orientations. A truly multidimensional PC?
Edge detection via local Magnitude impairment Original Signal
LMIe- magnitude quantization LMIe- magnitude noise LPQe
Slide 41
Edge detectors- dealing with noise Original Signal SNR 10[dB]
PC |LPQe| Raw Canny [10] Canny thresholds
Slide 42
Influence of incorrect thresholds on Canny
Slide 43
PC based application: Geodesic snakes segmentation [11]
Snakes?
Slide 44
Intensity Based Classical Snakes Let C(p) = { x(p),y(p) }, be a
parameterized curve, p [0,1] Deform the initial curve towards a
boundary to be detected y x C(p) Euler-LagrangeSteepest
Descent
Slide 45
1D LPQe based application: P&M anisotropic diffusion
[12]
Slide 46
Man-mades detection via Fractals Fractals are mathematical
objects defined by B.B Mandelbrot Natural objects usually self
similarity Able to easily generate and represent natural-like
shapes Each part of the image has different fractal dimensions,
-> feature space. [13]
Slide 47
Man-mades detection via Fractals Grayscale levels represent the
height of the surface. The area is measured at different scales to
check the fractal model fit, according to: The 3 fractal model
parameters are calculated for each pixel: the fractal Dimension D,
the constant F and the model fit error.
Slide 48
2D LPQe based application: Detection of Man-Made environment
Gray scale imageLPQe edges map Fractals? [13] PC edges map
Slide 49
Phase quantization- how to, ?
Slide 50
Slide 51
Slide 52
When quantized phase reconstruction is real? Real Thus to
result in a real signal the Quantization method Q must be
anti-symmetric:
Slide 53
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
Slide 54
Rotated Local Phase Quantization Imaginary{RLPQ}- blurred
signal. Blurring effect very similar to Box Blur.
Slide 55
Blur from Im{RLPQ}
Slide 56
Edges from Re{RLPQ} K q =2
Slide 57
Cartoons from Re{RLPQ} K q =3
Slide 58
Image primitives from Re{RLPQ} K q >>2 K q =3 K q =2
Edges Map Cartoon Original image
Slide 59
Localized K q Edges carry information, thus preserving edges
during RLPQ is vital. Means localized, signal dependent K q !
||LPQe|| KqKq Input image Edges Detection Signal dependent RLPQ TeD
like results
Slide 60
Diffusion like results via RLPQ Orig RLPQHeat Diffusion
[14]
Slide 61
Original Lena Image
Slide 62
TeD and edge preserving RLPQ RLPQTelegraph Diffusion [15]
Iterative RLPQ
Slide 63
Iterative schemes- Localized RLPQ edges preserving Global
RLPQ
Slide 64
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. Gilboa FaB,
V. Ratner TeD).
Slide 65
References 1.A. V. Oppenheim, and J. S. Lim, The importance of
phase in signals, Proceedings of the IEEE, vol. 69, no. 5, pp.
529-541, 1981. 2.A. Torralba, and A. Oliva, Statistics of natural
image categories, Network, vol. 14, no. 3, pp. 391-412, Aug, 2003.
3.J. Behar, M. Porat, and Y.Y. Zeevi. Image reconstruction from
localized phase, IEEE Transactions on Signal Processing, Vol. 40,
No. 4, pp. 736743, 1992. 4.G. Michael, and M. Porat, "Image
reconstruction from localized Fourier magnitude," Proceedings 2001
International Conference on Image Processing. pp. 213-16. 5.A. C.
Bovik, M. Clark, and W. S. Geisler, Multichannel texture analysis
using localized spatial filters, Pattern Analysis and Machine
Intelligence, IEEE Transactions on, vol. 12, no. 1, pp. 55-73,
1990. 6.A. K. Jain, and F. Farrokhnia, Unsupervised texture
segmentation using Gabor filters, Pattern Recognition, vol. 24, no.
12, pp. 1167-1186, 1991. 7.H. Tanaka, Y. Yoshida, K. Fukami et al.,
Texture segmentation using amplitude and phase information of Gabor
filters, Electronics and Communications in Japan, Part 3
(Fundamental Electronic Science), vol. 87, no. 4, pp. 66-79, 2004.
8.A. P. N. Vo, S. Oraintara, and T. T. Nguyen, "Using phase and
magnitude information of the complex directional filter bank for
texture image retrieval," Proceedings 2007 IEEE International
Conference on Image Processing, ICIP 2007. pp. 61-4.
Slide 66
References 9.J. A. Davis, D. E. McNamara, D. M. Cottrell et
al., Image processing with the radial Hilbert transform: theory and
experiments, Optics Letters, vol. 25, no. 2, pp. 99- 101, 2000.
10.N. Skarbnik, C. Sagiv, and Y. Y. Zeevi, "Edge Detection and
Skeletonization using Quantized Localized phase," Proceedings of
2009 European Signal Processing Conference, EUSIPCO-09. 11.M. Kass,
A. Witkin, and D. Terzopoulos, "Snakes: Active contour models."
International Journal of Computer Vision. v. 1, n. 4, pp. 321-331,
1987. 12.P. Perona, and J. Malik, Scale-Space and Edge Detection
Using Anisotropic Diffusion, IEEE Trans. Pattern Anal. Mach.
Intell., vol. 12, no. 7, pp. 629-639, 1990. 13.M. J. Carlotto, and
M. C. Stein, A method for searching for artificial objects on
planetary surfaces, Journal of the British Interplanetary Society,
vol. 43, no. 5, pp. 209-16, 1990. 14.V. Ratner, Y. Y. Zeevi, and
Ieee, "Telegraph-diffusion operator for image enhancement." IEEE
International Conference on Image Processing (ICIP 2007), pp.
525-528, 2007.
