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Radiometric Nonidealities: A Unified Framework

1. Dept. Elect. Eng. Technion – Israel Institute of Technology. Radiometric Nonidealities: A Unified Framework. Anatoly Litvinov , Yoav Y. Schechner. Support: Ollendorff Foundation (BMBF), GIF. 2. Spatial Non-Uniformity. Iris. camera.

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Radiometric Nonidealities: A Unified Framework

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  1. 1 Dept. Elect. Eng. Technion – Israel Institute of Technology Radiometric Nonidealities:A Unified Framework Anatoly Litvinov , Yoav Y. Schechner Support: Ollendorff Foundation (BMBF), GIF

  2. 2 Spatial Non-Uniformity Iris camera A. Litvinov & Y. Schechner, radiometric nonidealities

  3. Spatial Non-Uniformity Temporal Non-Uniformity: Automatic Gain Control (AGC) gain time iris Litvinov, Schechner, radiometric nonidealities

  4. G AGC Automatic Gain Control (AGC) A. Litvinov & Y. Schechner, radiometric nonidealities

  5. 3 Image Mosaicing Standard seam removal: “feathering” Duplaquet (98) Burt; Adelson (83) Soderblum et. al (78) Jia; Tang (03) Shum; Szeliski (00) Levin; Zomet; Peleg; Weiss (04) Not addressing the root of inconsistencies A. Litvinov & Y. Schechner, radiometric nonidealities

  6. 4 Nonlinear Radiometric Response electronic readout light intensity FillfactoryCMOSchip

  7. 5 Image Intensifier Nonlinear Radiometric Response Phosphor screen: nonlinear Photo cathode CCD Accelerating potential Fiber optic coupler A. Litvinov & Y. Schechner, radiometric nonidealities

  8. 42 The Eye Spatial non-uniformity Radiometric response Auto gain A. Litvinov & Y. Schechner, radiometric nonidealities

  9. 6 Prior Techniques Pre-calibrations Based on edge detection Lin et al. (04) Spatial non-uniformity estimation Combined AGC and radiometric response Only radiometric response Standard target Integrating sphere Only spatial non-uniformity Exposure variations Debevec; Malik (98) Mann; Picard (95) Only radiometric response Mitsunaga; Nayar (99) Only radiometric response Only spatial non-uniformity Schechner; Nayar (01) not including spatial non-uniformity Mann; Mann (01) Kim; Pollefeys (04) Candocia; Mandarino (05) AND OTHERS …

  10. visible mismatch Spatial non-uniformity pre-calibration Integrating Sphere 97 % - not accurate enough A. Litvinov & Y. Schechner, radiometric nonidealities

  11. 7 non-uniformity AGCnonlinearity We Achieve : spatial non-uniformity Blind estimation of: light intensity electronic readout pixel A. Litvinov & Y. Schechner, radiometric nonidealities

  12. 8 non-uniformity AGCnonlinearity Without “seam-removal” steps Blind estimation of: light intensity electronic readout pixel A. Litvinov & Y. Schechner, radiometric nonidealities

  13. 10 Camera Model M(x) E G r(I) A. Litvinov & Y. Schechner, radiometric nonidealities

  14. r -1 log log{r[v(x)]} = log(G) + log[M(x)] + log[I(x)] -1 ρ(v) - m(x) – g = i gain grayscale value of x irradiance of pixel x spatial non-uniformity of x radiometric response r[ ] G M(x) v(x) = I(x) m(x) ρ(v) g i A. Litvinov & Y. Schechner, radiometric nonidealities

  15. 12 i i s i N 1 B = g ρ(v) - m(x) – g = i 1 g F ρ (0) 1 -1 -1 1 -1 -1 ρ (255) 1 -1 -1 m (x=1) = 1 -1 -1 m (x=N) 1 -1 -1 1 -1 -1 1 -1 -1 A. Litvinov & Y. Schechner, radiometric nonidealities

  16. 13 Bs = i B γs = γi γ ^ ρ(v)= γρ (v) ^ -1 r (v)= [r(v)] -1 ^ γ ^ m(x)= γm(x) exp M(x)= M(x) ^ ^ γ g = γg G = G f f f f A. Litvinov & Y. Schechner, radiometric nonidealities

  17. 14 An Image Invariance ^ log I = γlog I A. Litvinov & Y. Schechner, radiometric nonidealities

  18. 15 Nevertheless … Mutually Consistent A. Litvinov & Y. Schechner, radiometric nonidealities

  19. 16 Frame: p Frame: k m(x) : log of mask at pixel x r(v) : log of inverse-radiometric response ρ(v ) -ρ(v ) - m(x ) + m(x ) - g + g = 0 p p k k p k g:log of gain at frame f : f ρ(v ) – m(x ) - g= log[I(x)] k k k ρ(v ) – m(x )-g= log[I(x)] p p p A. Litvinov & Y. Schechner, radiometric nonidealities

  20. g 1 ρ(v ) -ρ(v ) - m(x ) + m(x ) - g + g = 0 p p k k p k g F ρ (0) 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1 ρ (255) m (x=1) -1 1 -1 1 -1 1 = 0 1 -1 -1 1 -1 1 m (x=N) 1 -1 -1 1 -1 1 Rs = 0 A. Litvinov & Y. Schechner, radiometric nonidealities

  21. Experiment: AGC, Vignetting, Gamma 17 radiometric response transmittance (vignetting) amplifier gain 1 1 irradiance 4 0 pixel 0 graylevel 460 255 0 frame (time) 1 15

  22. Rs = 0 SVD solution Null space of R s= 0 s =[ ρ= const , m =const , g =const ] 1 2 3 T A. Litvinov & Y. Schechner, radiometric nonidealities

  23. Trivial Solutions electronic readout r light intensity ρ(v) = const exp light intensity r -1 electronic readout A. Litvinov & Y. Schechner, radiometric nonidealities

  24. hist hist hist Entropy Maximization A. Litvinov & Y. Schechner, radiometric nonidealities

  25. 18 1 0 460 A Unified Framework Image invariance ^ log I = γlog I 4 1 0 1 0 15 255 Anatoly Litvinov Yoav Schechner

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