ECE/OPTI533 Digital Image Processing class notes 256 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIPHOTOELECTRONIC NOISE
• Frame averaging
If available, average N frames of same object
If noise is independent frame-to-frame, variance will be reduced by
Requires multiple, co-registered frames
What will happen if the frames are not co-registered?
ση2 N⁄
ECE/OPTI533 Digital Image Processing class notes 257 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIsimulation example of frame averaging
N = 1σbackground = 19.86
σbackground = 13.98N = 2
σbackground = 11.47N = 3
σbackground = 9.92N = 4
ECE/OPTI533 Digital Image Processing class notes 258 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II• Low-pass smoothing
Reduces high-frequency noise
Smooths image
Set filter cutoff at about ρc ρc SNR 1==
10-4
10-3
10-2
10-1
100
101
102
103
0 0.1 0.2 0.3 0.4 0.5
frequency domain profile - noise image
poweramplitude
pow
er o
r am
plit
ude
spatial frequency (cycles/pixel)
ECE/OPTI533 Digital Image Processing class notes 259 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIideal low-pass filtered examples
ρc = 0.2
ρc = 0.1
ECE/OPTI533 Digital Image Processing class notes 260 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II• Sigma filter
Average selected pixels within moving window
Average only those pixels that are within a threshold difference ∆ from the DN of the center pixel, DNc
One type of “edge-preserving smoothing” algorithm
DNc ∆±
ECE/OPTI533 Digital Image Processing class notes 261 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIsigma filter near edges and lines
c
c
edge feature
5 x 5 window:
row m, column n
row m, column n+1
c
c
crow m, column n+2
line feature
only the green
pixels are
averaged for
the output
pixel c
ECE/OPTI533 Digital Image Processing class notes 262 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II• Nagao-Matsuyama filter
Calculate the variance of 9 subwindows within a 5 x 5 moving window
Output pixel is the mean of the subwindow with the lowest variance
The nine subwindows used in the Nagao-Matsuyama filter
c
c c c c
c c cc
ECE/OPTI533 Digital Image Processing class notes 263 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIExample of SAR (Synthetic Aperture Radar) noise filtering
original 5 x 5 LPF
ECE/OPTI533 Digital Image Processing class notes 264 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II
original 5 x 5 sigma (k=2)
ECE/OPTI533 Digital Image Processing class notes 265 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II
original Nagao-Matsuyama
ECE/OPTI533 Digital Image Processing class notes 266 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIImpulse Noise
• Salt and pepper noise DN is “outlier” relative to neighboring pixel DNs
• Use algorithms that compare test pixel to neighbors
ECE/OPTI533 Digital Image Processing class notes 267 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II• Noise cleaning
Set threshold ∆ = kσglobal
Noise Cleaning (pixels)
• DNneighbors = average DN (8-neighbors)
• If ,
• If ,
DN test DNneighbors– ∆> DN test DNneighbors=
DN test DNneighbors– ∆≤ DN test DN test=
Noise Cleaning (lines)
• DNneighbors = average DN (2-neighbors above and below)
• If ,
• If ,
DN test DNneighbors– ∆> DN test DNneighbors=
DN test DNneighbors– ∆≤ DN test DN test=
ECE/OPTI533 Digital Image Processing class notes 268 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II• Median filtering
Example of rank filtering
Output DN = median(DNwindow)
• Length of window must be odd
• Sort input DNs within window and select middle DN for output
median filter preserves 1-D edges
-5
0
5
10
15
-8 -6 -4 -2 0 2 4 6 8
input signal
1x3 median
amplit
ude
index
-5
0
5
10
15
-8 -6 -4 -2 0 2 4 6 8
input signal
1x3 LPF
amplit
ude
index
ECE/OPTI533 Digital Image Processing class notes 269 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IImedian filter removes impulse noise
-2
0
2
4
6
8
10
12
-8 -6 -4 -2 0 2 4 6 8
input signal
1x5 LPF
amplit
ude
index
-2
0
2
4
6
8
10
12
-8 -6 -4 -2 0 2 4 6 8
input signal
1x5 median
amplit
ude
index
median filter window length should be at least 2 x width impulse noise
-2
0
2
4
6
8
10
12
-8 -6 -4 -2 0 2 4 6 8
input signal
1x3 median
amplit
ude
index
ECE/OPTI533 Digital Image Processing class notes 270 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II“separable” 2-D median filter preserves 2-D edges
n
m
n
m
3 x 3 2-D median filter
n
m
3 x 3 2-D separable median filter
1 x 3 median filter along m, then 3 x 1 median filter along n
ECE/OPTI533 Digital Image Processing class notes 271 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIexample bad line removal with median filter (Schowengerdt, 1997)
single noisy partial scanline(Landsat MSS)
after 3 x 1 median filter
ECE/OPTI533 Digital Image Processing class notes 272 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIexample line drop removal
3 x 1 median filter
difference
ECE/OPTI533 Digital Image Processing class notes 273 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIMedian filter doesn’t work as well on photoelectronic noise
3 x 3 median filter
Why isn’t median filter effective for this type of noise?
ECE/OPTI533 Digital Image Processing class notes 274 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IISTRUCTURED NOISE
Periodic, stationary
• Periodicity means noise power is isolated into a few frequencies
• Difficulty is in detecting noise power “spikes”
• Visual detection works, but not practical for processing large number of images
Automated periodic, sta-tionary noise removal
• Apply “soft” (Gaussian) high-pass filter to noisy image to remove image components
• Threshold HPF-filtered spectrum to isolate noise frequency components
• Convert thresholded spectrum to 0 (noise) and 1 (non-noise) to create noise amplitude “notch” filter
• Apply filter to noisy image
ECE/OPTI533 Digital Image Processing class notes 275 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIexample Mariner 6 image (Rindfleish et al, 1971)
noisy image power spectrum
noise spikes
noise pattern
filtered image
ECE/OPTI533 Digital Image Processing class notes 276 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIexample automated periodic noise removal (Schowengerdt, 1997)
noise spikes
zeros in filter
high-pass filtered noisy image
notch-filtered image
notch filter
power spectrum
ECE/OPTI533 Digital Image Processing class notes 277 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE II
• Not really automated filter design
Two parameters must be supplied:
• width of Gaussian HPF
• power spectrum threshold for notch filter
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