1 / 14

What can be Known about the Radiometric Response from Images?

What can be Known about the Radiometric Response from Images?. Michael Grossberg and Shree Nayar CAVE Lab, Columbia University Partially funded by NSF ITR Award. ECCV Conference May, 2002, Copenhagen, Denmark. I. Irradiance. u. Response = Gray-level. Radiometric Response Function.

gen
Download Presentation

What can be Known about the Radiometric Response from Images?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. What can be Known about the Radiometric Response from Images? Michael Grossberg and Shree Nayar CAVE Lab, Columbia University Partially funded by NSF ITR Award ECCV Conference May, 2002, Copenhagen, Denmark

  2. I Irradiance u Response = Gray-level Radiometric Response Function Response function: f(I)=u Scene Radiance: R Image Plane Irradiance: I Response: u 0 255 Inverse response function: g g(u)=I

  3. Gray-levels: Image D Gray-levels: Image C k 3 Gray-levels: Image B k 2 Gray-levels: Image A k 1 k k k 1 2 3 Response Recovery from Images Exposure Ratios I Irradiance u Response uB uA Recovery Algorithms: S. Mann and R. Picard, 1995, P. E. Debevec, and J. Malik, 1997, T. Mitsunaga S. K. Nayar 1999, S. Mann 2001, Y. Tsin, V. Ramesh and T. Kanade 2001

  4. I Irradiance u Response k k k 1 2 3 How is Radiometric Calibration Done? Images at Different Exposures Corresponding Gray-levels Inverse Response g, Exposure Ratio k Geometric Correspondences Recovery Algorithms • We find: • All ambiguities in recovery • Assumptions that break them We eliminate the need for geometric correspondences: Static Scenes Dynamic Scenes

  5. Constraint on irradiance I: IB= kIA Constraint on g: g(uB)=kg(uA) IB Brighter image Filter IA Darker image T Constraint Equations • Brightness Transfer Function T: • uB=T(uA) • Constraint on g in terms of T g(T(uA))=kg(uA)

  6. Exposure ratio k known Constraint makes curve self-similar I kg(uA) = g(T(uA)) 1 g(T(uA)) kg(uA) Irradiance 1/k g(uA) u uA T-1(1) 0 T(uA) 1 Gray-levels How Does the Constraint Apply?

  7. I Irradiance u 0 T-1(1) 1 Gray-levels Self-Similar Ambiguity:Can We Recover g? Choose anything here • Conclusions: • Constraint gives no information in [T-1(1),1] • Regularity assumptions break ambiguity • Known k: only Self-similar ambiguity 1 and copy 1/k 1/k2 1/k3

  8. Exponential Ambiguity: Can We Recover g and k ? Inverse Response Function gγ Brightness Transfer Function T Exposure ratio k=21/3 I k=21/2 k=2 γ=1/3 Gray-level Image B Irradiance γ=1/2 k=22 T(M)=2M γ=1 k=23 γ=2 γ=3 U Response Gray-level Image A T(u) = g -1(kg(u)) = g -γ(k- γgγ(u)) = T(u) We cannot disambiguate (gγ, kγ) from (g, k) using T!

  9. Gray-level Image B Gray-level Image A Obtaining the Brightness Transfer Function (S. Mann, 2001) Registered Static Images at Different Exposures Brightness Transfer Function 2D-Gray-level Histogram Gray-level Image B Regression Gray-level Image A Scenes must be static.

  10. Gray-level Image B Gray-level Image A Brightness Transfer Function without Registration Unregistered Images at Different Exposures Brightness Histograms Brightness Transfer Function Gray-level Image B Histogram Specification Gray-level Image A Scenes may have motion.

  11. How does Histogram Specification Work? Cumulative Area (Fake Irradiance) Histogram Equalization Histogram Equalization Histogram Specification Gray-levels in Image A Gray-levels in Image B Histogram Specification = Brightness Transfer Function

  12. 1 1 Recovered Response 0.9 0.9 0.8 0.8 1 0.7 0.7 0.9 0.6 0.6 0.8 Irradiance Irradiance Irradiance Macbeth Chart Data 0.5 0.5 0.7 0.4 0.4 0.6 0.3 0.3 0.5 0.2 0.2 0.4 0.1 0.1 0.3 0 0 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 Red Response Green Response Blue Response 0 Results: Object Motion Recovered Inverse Radiometric Response Curves

  13. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 Recovered Response 0.9 0.8 0.7 0.6 Macbeth Chart Data 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Results: Object and Camera Motion Recovered Inverse Radiometric Response Curves Irradiance Red Response Irradiance Red Irradiance Blue Irradiance Green Irradiance Green Response Irradiance Blue Response

  14. Exposure ratio k known Self-similar Ambiguity Need assumptions on g and k to recover g Recovery of g from T Self-similar Ambiguity + Exponential Ambiguity Exposure ratio k unknown Conclusions: What can be Known about Inverse Response g from Images? • A2: In theory, we can recover exposure ratio directly from Brightness Transfer Function T • A3: Geometric correspondence step eliminated allowing recovery in dynamic scenes: • A1:

More Related