Micro Phase Shifting

1. Micro Phase Shifting 2014-07-01 Se-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

3. Phase shifting • Phase shift encoding Three 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]

4. Phase shifting • Phase shift encoding Ex) I’(x,y) = 125 I’’(x,y) = 125 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]

5. Phase shifting • Phase shift encoding 5

6. Phase shifting • Phase shift decoding

7. Phase shifting • Phase shift decoding 1 = true intensity N(x,y) = noise 1(x,y) I1(x,y) = 1(x,y) + N(x,y) Projector image Camera image

8. Phase shifting • Phase shift decoding • If the noise is same in the three camera images, noise doesn’t matter. 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) = =

9. Phase shifting Input phase 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] ambiguous , Output phase Input phase output phase θ (π) θ (π) pixel pixel

10. Phase shifting AccuratebutAmbiguous UnambiguousbutNoisy wmax wmean wmin Broad Frequency Band amplitude frequency (w)

11. Issue • Inter reflection camera Direct Radiance Inter reflections scene Q P radiance R Inter reflections time projector

12. Issue • Inter reflection camera Direct Radiance Inter reflections scene Phase Error Q P radiance R Inter reflections time projector

13. Issue • Inter reflection camera Inter reflection scene Q = P Illumination pattern light transport coefficients R Inter reflections projector

14. Issue • Inter reflection camera Inter reflection scene Q = P Illumination pattern light transport coefficients R Inter reflections projector

15. Issue • Inter reflection camera Inter reflection scene Q = P Illumination pattern light transport coefficients R Inter reflections projector

16. Issue • Inter reflection camera Inter reflection scene Q = N P Illumination pattern light transport coefficients R Inter reflections : light transport coefficients about P point : illumination pattern projector

17. Issue • Inter reflection illumination pattern light transport coefficients Inter reflection = * pixels pixels

18. Issue • Inter reflection projected patterns illumination pattern light transport coefficients Inter reflection = frequency frequency

19. Issue • Inter reflection projected patterns illumination pattern light transport coefficients Inter reflection = frequency frequency Micro phase shifting

20. Micro Phase shifting wmax wmean wmin amplitude frequency (w) How Can We Disambiguate Phase WithoutLow FrequencyPatterns?

21. Micro Phase shifting • Phase disambiguation number of periods (unknown)

22. Micro Phase shifting • Phase disambiguation unknown known unknown known unknown known

23. Micro Phase shifting • Phase disambiguation • Chinese remainder theorem • There exists an integer solving the below system of simultaneous Congruence, 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) • Ex) =3, =2, =5, =3, =7, =2 • C = 2 x 35 x 2 + 3 x 21 x 1 + 2 x 15 = 233 ≡ 23 (mod 105).

24. Micro Phase shifting • Experiments • Ceramic bowl

25. Micro Phase shifting • Experiments • Ceramic bowl point projector

26. Micro Phase shifting • Experiments • Ceramic bowl Conventional Phase Shifting Micro Phase Shifting [Our]

27. Micro Phase shifting • Experiments • Lemon subsurface scacttering point projector

28. Micro Phase shifting • Experiments • Lemon Conventional Phase Shifting Micro Phase Shifting [Our]

29. Micro Phase shifting • Experiments • Shiny Metal Bowl

30. Micro Phase shifting • Experiments • Shiny Metal Bowl Conventional Phase Shifting Micro Phase Shifting [Our]