Ligiero Zeca Performance e Antropologia de Richard Schechner
Resolution Loss without Optical Blur Tali Treibitz Alex Golts Yoav Y. Schechner Technion, Israel 1.
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Transcript of Resolution Loss without Optical Blur Tali Treibitz Alex Golts Yoav Y. Schechner Technion, Israel 1.
Resolution Loss without
Optical Blur
Tali Treibitz
Alex Golts
Yoav Y. Schechner
Technion , Israel
1
14
airlightA
( , ) ( , ) ( ) ( , )D
I x y L x y t z A x y
object
0
1
z
ze
scatteringdirect transmission
D
object radiance
Lobject
total intensity
I
A
0 z
1 ze
Schechner, Narasimhan, Nayar
Haze
object( ) ( ) ( ) ( )I l t A x x x x
airlightobject transmittance
Schechner et al., Applied Optics ‘03
15
Pointwise Degradations
object( )I lx
object
( )x t ( )x A
pointwise attenuation:
vignetting
atmosphere attenuation
additive component:
reflection
glare
path radiance
( )x n
noise
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
17
Pointwise Degradations
object( )I lx
object
( )x t ( )x A
pointwise attenuation
( )x n
noise
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
reduce SNR even if known
additive (positive) bias
18
Noise: Object size matters?19
Noise: Object size matters?
0.5
20
1
Noise: Object size matters?21
1.5
Noise: Object size matters?22
depends on:
noise level
object background intensity difference
object size
quantify this dependency!
Prior art: resolution limits due to optical blur
here: no optical blur
Visibility Under Noise23
Previous criteria• Is there something there?• Is it a tank?• What type is it?
Johnson charts:
identification recognition orientation detection
7 3.5 1.2 0.75 tank
minimum line pairs for 50% success
NIIRS- National Image Interpretability Rating Scales
Identify the wing configuration (e.g., straight, swept, delta) of all large aircraft (e.g., 707, CONCORD, BEAR, BLACKJACK). ..
Detect large hangars at airfields. Detect large static radars (e.g., AN/FPS-85, COBRA DANE, PECHORA, HENHOUSE), Detect military training areas...
Detect a medium-sized port facility and/or distinguish between taxi-ways and runways at a large airfield.
Interpretability of the imagery is precluded by obscuration, degradation, or very poor resolution
Identify small light-toned ceramic insulators that connect wires of an antenna. Identify vehicle registration numbers (VRN) on trucks. Identify screws and bolts on missile components. ..
0
1
2
3
9
pattern visible
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
24
Where is the Cutoff?
0.1 0.5
10
0.5
pattern visible
pattern invisible calculated analytically!
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
Input SNR
noise
| ( ) |
S u
25
(frequency)u
0.1 0.5
10
0.5
(frequency)
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
u
26
Cutoff Per Success Rate
success rate 50%
cutoffu
1
Input SNR
noise
| ( ) |
S u
Noise Suppression in the HVS
Theoretical Neuroscience, Dayan & Abbott
frequency (cycles/degree)
response of receptive field
low noise
high noise
We derive: fundamental analytical model
Model: simple linear denoising
not a denoising method
28
SNR Improvement by Averaging
WH
/W
signal
noise
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
output
input
SNRC(u,W)=
SNR- SNR change after averaging
29
Different Sizes of Windows
too big for signal too small for noise
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
30
Averaging by Optimal Window
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
31
SNR Improvement by Averaging
outputmax input( ) SNR u SNR
depends on frequency!
u
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
max ( )C u
same plot for a Gaussian filter
32
Output SNR
0.1 0.5
6.5
0.32
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
cutoffu
output 1SNR output 0.5SNR
Input SNR
noise
| ( ) |
S u
(frequency)u
1
33
Cutoff Per Success Rate
0.1 0.5
0.32
success rate 70%
success rate 40%
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
Input SNR
(frequency)ucutoffu6.5
noise
| ( ) |
S u
34
Vision Success is Probabilistic
SNR=2/3
SNR determines chances of visibility
visible invisible
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
35
Success within a Confidence Interval
( ) prob N S xSN
68%
0 22
- success rate
SNRTreibitz & Schechner, Recovery Limits in Pointwise Degradations
0.68
Object is visible if ( )N Sx
…depends on SNR and..
( )xN
36
25
Success within a Confidence Interval
- success rate
SNRTreibitz & Schechner, Recovery Limits in Pointwise Degradations
what is the probability for correct detection?
depends on SNR object pixel
background pixel
visibility is kept if edge keeps sign
background object ( ) ( ) x x prob N N S
%(sign kept) - %(wrong sign)
noisyclear
0.5
0.1 0.5
6.5
0.32
system input SNR
cutoffu
Determining Resolution Limits
cutoff for ρ=70% success
frequency
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
noise
| ( ) |
S u
37
Pointwise Degradations
object( )I lx ( )x t ( )x A
pointwise attenuation:
vignetting
atmosphere attenuation
additive component:
reflection
glare
haze
( )x n
noise
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
38
Noise Model
2 2 / I g
2 200 I
Nikon D100
2
photon noise dominates
39
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
Detector (pixel)
50% quantum efficiency
Schechner
Photon (shot) Noise9
Electrons
Photon
or
e{nothing
either
50% quantum efficiency
Schechner
10
Photons
Electrons
e{nothing
e e
either
Photon (shot) Noise
object background| | , ( )
SSNR = S l l t x
SNR per size (frequency)
object background| | ,
SSNR = S l l
objectl
backgroundl
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
backgroundlobjectl
41
Resolution Limits in Haze
distance [km]
limit due to pixel size
limit due to atmosphere
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
minimal visible object size[m]
cutoffu
reciprocal to
42
0.1 0.5
10
0.5
(frequency)
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
u
43
Cutoff Per Success Rate
success rate 50%
cutoffu
1
Input SNR
noise
| ( ) |
S u
Haze in the Galilee
Treibitz & Schechner, Recovery Limits in Pointwise Degradations
average of 50 framesraw frame
limit due to noise and not blur
44
What now?
What are the reconstruction limits?
What is the minimal detectable object size?
What camera noise properties are acceptable for detection?
…
45
Imaging in Haze
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
46
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
Haze Through a Polarizer
best polarized image
47
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
single frame- used by photographers
Haze Through a Polarizer
increased exposure time
best polarized image
48
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
two frames- Schechner et al.
Dehazing using a Polarizer
post-processing 2 frames
best polarized image
worst polarized image
49
goal: object detection local contrast stretch- OK
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
Is it worth using a polarizer?
unpolarized image
best polarized
image
post-processing 2 frames
rarely!under the constraint of equal acquisition time
50
degree of polarization
( , ) 1( ) ( , )
2 2
D x y pI x, y A x ymin
0,1p
Using a Single Polarized Image
Best polarized image
I min
51
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
SNR ComparisonIunpolarized Ibest
52
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
p
A Single Saturated Frame
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
SNRpolarized
SNRunpolarized
maximal value in nature
53
SNR ComparisonIunpolarized Ibest
equal acquisition time
technical details
in the paper
acquisition time = exposure time X number of frames
54
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
Same Total Acquisition Time
p<0.4in our experiments
SNRpolarized
SNRunpolarized
maximal value in nature
p
55
Experiment
Wide field of view
bestI
average of 2 frames
unpolarizedI
Treibitz & Schechner, Polarization- Beneficial for Visibility Enhancement?
same total acquisition time
56
dehazing
tbest tworst
1 p
p
1 p
p
SNR ComparisonIunpolarized
technical details
in the paper
optimal exposures
equal acquisition time
57
Advantages of Polarization
distance map
• contrast stretch in non-uniform distances
• restoring color• compensating for attenuation
58
• Freq cutoff – due to noise – without imaging blur
• Relation between cutoff and success rate
• Application: limits in pointwise degradations
Limits in Pointwise Degradations
• Case study of performance trade-offs
59