The importance of phase in image processing Final thesis exam-
29/11/09 Nikolay Skarbnik Under supervision of: Professor Yehoshua
Y. Zeevi
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Outline Introduction (Phase vs. Magnitude) Global vs. Local
phase Local Phase based Image segmentation Edge detection
Applications Rotated Local Phase Quantization
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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.
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Common image spectra Natural Images statistical average
spectrum [1] Lena image spectrum
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Where is the data encoded? 2D Fourier magnitude2D Fourier
phase
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The importance of phase in images [2]
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Short Time Fourier Transform ... FT
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Voice STFT spectrogram
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The importance of phase in voice STFT?
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Image reconstruction from phase [3].
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Global vs. Local schemes [4] Sliding window
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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?
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Image segmentation
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Image segmentation- Gabor Filters [5-7]
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Image segmentation- Gabor Wavelets
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Image segmentation- Filtering results
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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
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Edge detectors-1D Original Signal Edges via phase STD PC
via
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Edge detectors-1D Original Signal AS Energy, Local Energy Sig.
derivative 2D- PC?
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Radial HT detects Corners [9]
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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
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Edge detectors- dealing with noise Original Signal SNR 10[dB]
PC |LPQe| Raw Canny [10] Canny thresholds
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Influence of incorrect thresholds on Canny
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PC based application: Geodesic snakes segmentation [11]
Snakes?
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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
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1D LPQe based application: P&M anisotropic diffusion
[12]
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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]
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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.
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2D LPQe based application: Detection of Man-Made environment
Gray scale imageLPQe edges map Fractals? [13] PC edges map
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Phase quantization- how to, ?
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When quantized phase reconstruction is real? Real Thus to
result in a real signal the Quantization method Q must be
anti-symmetric:
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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
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Rotated Local Phase Quantization Imaginary{RLPQ}- blurred
signal. Blurring effect very similar to Box Blur.
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Blur from Im{RLPQ}
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Edges from Re{RLPQ} K q =2
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Cartoons from Re{RLPQ} K q =3
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Image primitives from Re{RLPQ} K q >>2 K q =3 K q =2
Edges Map Cartoon Original image
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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
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Diffusion like results via RLPQ Orig RLPQHeat Diffusion
[14]
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Original Lena Image
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TeD and edge preserving RLPQ RLPQTelegraph Diffusion [15]
Iterative RLPQ
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Iterative schemes- Localized RLPQ edges preserving Global
RLPQ
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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).
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