Post on 14-Dec-2015
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Real-Time Compressive Tracking
Contents
• Phase shifting• Phase shift encoding• Phase shift decoding
• Issue• Inter reflection
• Micro Phase shifting• Disambiguation• experiments
Phase shifting Phase shift encodingThree image structured light I1(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y) - 2π/3]I2(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y)]I3(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y) + 2π/3]I1(x,y) : first image I2(x,y) : seond image I3(x,y) : third imageI’(x,y) : average intensity I’’(x,y) : intensity modula-tion θ(x,y) : phase
Phase shifting Phase shift encodingEx) I’(x,y) = 125 I’’(x,y) = 125I1(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y) - 2π/3]I2(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y)]I3(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y) + 2π/3]
θ(x,y) I1(x,y) I2(x,y) I3(x,y) π/6 125 233 16π/3 187 187 0π/2 233 125 162π/3 250 62 625π/6 233 16 125π 187 0 187
Phase shifting Phase shift decoding
I1(x,y) I2(x,y) I3(x,y) θ(x,y) 125 233 16 π/6187 187 0 π/3233 125 16 π/2250 62 62 2π/3233 16 125 5π/6187 0 187 π
Phase shifting Phase shift decoding
I1(x,y) = 1(x,y) + N(x,y) 1 = true intensityN(x,y) = noise
Camera imageProjector image
1(x,y)
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Phase shift decoding– If the noise is same in the three camera images, noise doesn’t matter.
Phase shifting
= =
I1(x,y) = 1(x,y) + N(x,y) I2(x,y) = 2(x,y) + N(x,y) I3(x,y) = (x,y) + N(x,y)
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Phase shifting
,
pixel pixel
θ(π)
θ(π)
Input phase output phase
ambiguous I1(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y) - 2π/3]I2(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y)]I3(x,y) = I’(x,y) + I’’(x,y)cos[θ(x,y) + 2π/3]θ ( x , y )= tan−1 √3( I1 (x , y ) −I3 ( x , y ))
2∗I 2 (x , y ) − I1( x , y )− I3( x , y )
Input phase
Output phase
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Phase shifting
frequency (w)
am
plit
ude
Broad Frequency Band
wmax wmean wmin
Unambiguous but NoisyAccurate but Ambiguous
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Inter reflection
Issue
camera
projector
Inter reflections
P
Q
R
time
Inter reflections
Direct Radiance
radia
nce
scene
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Inter reflection
Issue
camera
projector
Inter reflections
P
Q
R
time
Inter reflections
Direct Radiance
radia
nce
scene Phase Error
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Inter reflection
Issue
camera
projector
Inter reflections
P
Q
R
scene
=
Inter reflection
Illumination pattern
light transport coefficients
×
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Inter reflection
Issue
camera
projector
Inter reflections
P
Q
R
scene
=
Inter reflection
Illumination pattern
light transport coefficients
×
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Inter reflection
Issue
camera
projector
Inter reflections
P
Q
R
scene
=
Inter reflection
Illumination pattern
light transport coefficients
×
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Inter reflection
Issue
camera
projector
Inter reflections
P
Q
R
scene
=
Inter reflection
Illumination pattern
light transport coefficients
×
: light transport coefficients about P point : illumination pattern
N
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Inter reflection
Issue
= Inter reflection
*
illumination pattern light transport coeffi-cients
pixels pixels
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Inter reflection
Issue
frequency frequency
×
projected patterns
= Inter reflection
illumination pattern light transport coefficients
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Inter reflection
Issue
frequency frequency
×
projected patterns
= Inter reflection
illumination pattern light transport coefficients
Micro phase shifting
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Micro Phase shifting
wmax wmean wmin
frequency (w)
am
plit
ude
How Can We Disambiguate Phase Without Low Frequency Patterns?
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Micro Phase shifting
period :𝑝 pixels
correspondence :𝐶 pixels
𝐶=𝑛𝑝+𝑞
phase :𝑞 pixels
number of periods (unknown)
Phase disambiguation
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Phase disambiguation
Micro Phase shifting
𝑝1
𝐶
𝑞1 𝑝 𝑓
𝐶
𝑞 𝑓 𝑝𝐹
𝐶
𝑞𝐹
𝐶=𝑛1𝑝1+𝑞1
unknown known
𝐶=𝑛𝐹𝑝𝐹+𝑞𝐹
unknown known
𝐶=𝑛𝑓 𝑝 𝑓 +𝑞𝑓
unknown known
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Phase disambiguation– Chinese remainder theorem
• There exists an integer solving the below system of simultaneousCongruence, if , , are positive integers which are pairwise relatively prime.
Pairwise relatively prime : are pairwise relatively prime if gcd(, gcd(, ) = gcd(, ) = 1. (gcd : greatest common divisor)
Micro Phase shifting
𝐶=𝑛1𝑝1+𝑞1 𝐶=𝑛𝐹𝑝𝐹+𝑞𝐹𝐶=𝑛𝑓 𝑝 𝑓 +𝑞𝑓
Ex) =3, =2, =5, =3, =7, =2C = 2 x 35 x 2 + 3 x 21 x 1 + 2 x 15 = 233 ≡ 23 (mod 105).
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Micro Phase shifting Experiments
– Ceramic bowl
Conventional Phase Shifting
Micro Phase Shifting[Our]