Micro Phase Shifting 2014-07-01 Se-Hoon, Park -Mohit Gupta and Shree K. Nayar, CVPR2012.

Micro Phase Shifting

2014-07-01Se-Hoon, Park

- Mohit Gupta and Shree K. Nayar, CVPR2012

2

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

5

Phase shift encoding

Phase shifting

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I1 I2 I3

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

12

Inter reflection

Issue

camera

projector

Inter reflections

P

Q

R

time

Inter reflections

Direct Radiance

radia

nce

scene Phase Error

13

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

×

15

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

17

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

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Micro Phase shifting Experiments

– Ceramic bowl

point

projector

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Micro Phase shifting Experiments

– Ceramic bowl

Conventional Phase Shifting

Micro Phase Shifting[Our]

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Micro Phase shifting Experiments

– Lemon

point

projector

subsurface scacttering

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Experiments– Lemon

Micro Phase shifting

Conventional Phase Shifting

Micro Phase Shifting[Our]

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Experiments– Shiny Metal Bowl

Micro Phase shifting

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Experiments– Shiny Metal Bowl

Micro Phase shifting

Conventional Phase Shifting

Micro Phase Shifting[Our]