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Nonlinear Camera Response Functions and Image Deblurring : Theoretical Analysis and Practice

Nonlinear Camera Response Functions and Image Deblurring : Theoretical Analysis and Practice. Yu-Wing Tai , Xiaogang Chen, Sunyeong Kim, Seon Joo Kim, Feng Li, Jie Yang, Jingyi Yu, Yasuyuki Matsushita, Michael S. Brown. Presentation by Seungwoo Lee 2012. 5. 9. Teaser!.

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Nonlinear Camera Response Functions and Image Deblurring : Theoretical Analysis and Practice

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  1. Nonlinear Camera Response Functions and Image Deblurring: Theoretical Analysis and Practice Yu-Wing Tai, Xiaogang Chen, Sunyeong Kim, Seon Joo Kim, Feng Li, Jie Yang, Jingyi Yu, Yasuyuki Matsushita, Michael S. Brown Presentation by Seungwoo Lee 2012. 5. 9.

  2. Teaser! • The Power of ‘CRF’ in Image Deblurring Original No CRF consideration Proper CRF correction (This paper)

  3. 0 255 Camera Pipeline PSF CRF

  4. PSF • PSF (Point Spread Function) Spread of light coming from a point source Scene Image Intensity Intensity PSF X axis X axis PSF

  5. CRF • CRF (Camera Response Function) “Secret Recipe” of a Camera RAW CRF Sony Canon Nikon

  6. CRF • 188 CRF curves of real cameras from DoRF Kodak Ektachrome-100plus Green Cannon Optura 1 Kodak DCS 315 Green Kodak Ektachrome-64 Green 0.9 Sony DXC-950 Agfachrome CTPrecisa100 Green 0.8 Agfachrome RSX2 050 Blue 0.7 Agfacolor Futura 100 Green Agfacolor HDC 100 plus Green 0.6 Agfacolor Ultra 050 plus Green 0.5 Intensity Agfapan APX 025 0.4 Agfa Scala 200x 0.3 Fuji F400 Green Fuji F125 Green 0.2 g gamma curve, =0.6 Kodak Max Zoom 800 Green 0.1 g gamma curve, =1.0 Kodak KAI0372 CCD g gamma curve, =1.4 0 Kodak KAF2001 CCD g gamma curve, =1.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Irradiance * DoRF : Database of response functions (DoRF) created by Grossberg and Nayar

  7. Impact of CRF • Image Deblurring using PSF PSF

  8. Impact of CRF • PSF Estimation from edge profiles Image Edge Profile Estimated PSF

  9. Impact of CRF • But, Non-linear CRF corrupts the linearity Estimated PSF Non-linear CRF Invalid PSF

  10. Impact of CRF • PSF kernels with linear CRF and nonlinear CRF Linear CRF Nonlinear CRF

  11. Impact of CRF • Invalid PSF messes up Deblurring Algorithm Non-linear CRF No CRF Deblurring Deblurring

  12. CRF Estimation • Two algorithms are proposed • CRF approximation with a known PSF • CRF estimation with a unknown PSF

  13. CRF Estimation • CRF approximation with a known PSF Input Constraints Output CRF best describes PSF Edge Profiles . CRF 5th order Polynomial Boundary constraint CRF(0) = 0 CRF(1) = 1 PSF Monotonic constraint CRF(k) < CRF(k+1)

  14. CRF approximation with known PSF • CRF-PSF model 1D PSF value (1≦i≦m) Number of selected blurred edge profiles (dark  bright) Number of selected blurred edge profiles (bright  dark) Minimum intensity value Intensity range (max-min)

  15. CRF approximation with known PSF • Approximation Model Polynomial of degree d (e.g. 5) Heviside step function Maximum intensity level (e.g. 255 for 8 bit image) Boundary constraint (100) Monotonic constraint (10)

  16. CRF Estimation • CRF estimation with a unknown PSF Assumption Input Constraints Output All edge profiles have the same shape Initial CRF CRF 5th order Polynomial Edge Profiles All edges are linearly dependant (Rank-1) Update Boundary constraint CRF(0) = 0 CRF(1) = 1 Update CRF Monotonic constraint CRF(k) < CRF(k+1)

  17. CRF estimation with unknown PSF • CRF-PSF model Number of selected blurred edge profiles (dark  bright) Number of selected blurred edge profiles (bright  dark) Minimum intensity value Intensity range (max-min)

  18. CRF estimation with unknown PSF • Additional Constraints • Linearity of CRF  Rank minimization problem Length of edge profiles Total number of observation matrix (=number of groups of edge profiles) Weight given to each observation matrix (e.g. more edge profiles  more weight) Singular values of

  19. CRF estimation with unknown PSF • Final objective function • Solve by non-linear least squares fitting

  20. Experiments

  21. Experiments Original Image

  22. Experiments Edge Profiles Estimated CRF

  23. Experiments Without Proper CRF (Gamma Correction) Using Estimated CRF (This Paper)

  24. References • Yu-Wing Tai et al, Nonlinear Camera Response Functions and Image Deblurring: Theoretical Analysis and Practice, TPAMI 2013 • Michael S. Brown, Modeling the Digital Camera Pipeline : From RAW to sRGB and Back, NUS Lecture Slides • Paul E. Debevec, Recovering High Dynamic Range Radiance Maps from Photographs, SIGGRAPH 1997.

  25. Summary • Analysis on the effect of the CRF • New CRF estimation algorithms for known/unknown PSF cases Non-linear CRF No CRF Deblurring Deblurring

  26. Thanks • Any question?

  27. Inconsistency by nonlinear CRF • Variables • Blur Inconsistency

  28. Inconsistency by nonlinear CRF • Claims • In uniform intensity regions, Γ=0 • If the blur kernel K is small and the CRF f is smooth, Γ≈0 in low frequency regions • Γ can be large at high frequency high contrast regions.

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