This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Modeling the Space of Camera Response Functions
October 2004 (vol. 26 no. 10)
pp. 1272-1282
Michael D. Grossberg, IEEE Computer Society
Many vision applications require precise measurement of scene radiance. The function relating scene radiance to image intensity of an imaging system is called the camera response. We analyze the properties that all camera responses share. This allows us to find the constraints that any response function must satisfy. These constraints determine the theoretical space of all possible camera responses. We have collected a diverse database of real-world camera response functions (DoRF). Using this database, we show that real-world responses occupy a small part of the theoretical space of all possible responses. We combine the constraints from our theoretical space with the data from DoRF to create a low-parameter empirical model of response (EMoR). This response model allows us to accurately interpolate the complete response function of a camera from a small number of measurements obtained using a standard chart. We also show that the model can be used to accurately estimate the camera response from images of an arbitrary scene taken using different exposures. The DoRF database and the EMoR model can be downloaded at http://www.cs.columbia.edu/CAVE.

[1] N. Asada, A. Amano, and M. Baba, Photometric Calibration of Zoom Lens Systems Proc. Int'l Conf. Pattern Recognition, vol. A, pp. 189-190, 1996.
[2] R. Basri and D.W. Jacobs, Photometric Stereo with General, Unknown Lighting Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 374-381, 2001.
[3] P.R. Burt and R.J. Kolczynski, “Enhanced Image Capture through Fusion,” Proc. Int'l Conf. Computer Vision, pp. 173-182, May 1993.
[4] B. Cabral, M. Olano, and P. Nemec, Reflection Space Image Based Rendering Computer Graphics, Proc. SIGGRAPH, pp. 165-170, 1999.
[5] Y.C. Chang and J.F. Reid, RGB Calibration for Color Image-Analysis in Machine Vision Proc. Int'l Conf. Image Processing, vol. 5, no. 10, pp. 1414-1422, Oct. 1996.
[6] P.E. Debevec and J. Malik, Recovering High Dynamic Range Radiance Maps from Photographs Computer Graphics, Proc. SIGGRAPH, pp. 369-378, 1997.
[7] P.E. Debevec, Rendering Synthetic Objects into Real Scenes Computer Graphics, Proc. SIGGRAPH, pp. 189-198, 1998.
[8] R. Duda, P. Hart, and D. Stork, Pattern Classification, second ed. New York: Wiley, 2000.
[9] H. Farid, Blind Inverse Gamma Correction Proc. Int'l Conf. Image Processing, vol. 10, no. 10, pp. 1428-1433, Oct. 2001.
[10] G.D. Finlayson, S.D. Hordley, and P.M. Hubel, Color by Correlation: A Simple, Unifying Framework for Color Constancy IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 11, pp. 1209-1221, Nov. 2001.
[11] P.E. Gill, W. Murray, M.A. Saunders, and M.H. Wright, Procedures for Optimization Problems with a Mixture of Bounds and General Linear Constraints ACM Trans. Math. Software, vol. 10, no. 3, pp. 282-298, 1984.
[12] P. Gill, W. Murray, and M. Wright, Numerical Linear Algebra and Optimization. vol. 1, Redwood City, Calif.: Addison-Wesley, 1991.
[13] M. Grossberg and S. Nayar, What Can Be Known About the Radiometric Response Function from Images? Proc. European Conf. Computer Vision, pp. 189-205, 2002.
[14] M. Grossberg and S. Nayar, What Is the Space of Camera Response Functions? Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2003.
[15] G. Healey and R. Kondepudy, Modeling and Calibrating CCD Cameras for Illumination-Insensitive Machine Vision SPIE Proc., Optics, Illumination, and Image Sensing for Machine Vision VI, vol. 1614, pp. 121-132, 1992.
[16] G. Healey and R. Kondepudy, "Radiometric CCD Camera Calibration and Noise Estimation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 3, pp. 267-276, Mar. 1994.
[17] B.K.P. Horn and M.J. Brooks, Shape from Shading. MIT Press, 1989.
[18] Eastman Kodak, Student Filmmaker's Handbook, 2002.
[19] E.H. Land and J.J. McCann, Lightness and Retinex Theory J. Optical Soc. of Am., vol. 61, no. 1, pp. 1-11, 1971.
[20] Q.T. Luong, P. Fua, and Y. Leclerc, The Radiometry of Multiple Images IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 1, pp. 19-33, Jan. 2002.
[21] B.C. Madden, Extended Intensity Range Image Technical Report 366, Grasp Lab, Univ. of Pennsylvania, 1993.
[22] S. Mann and R. Picard, Being‘Undigital’with Digital Cameras: Extending Dynamic Range by Combining Differently Exposed Pictures Proc. IS&T, Soc. for Imaging Science and Technology 46th Ann. Conf., pp. 422-428, 1995.
[23] S. Mann, Comparametric Equations with Practical Applications in Quantigraphic Image Processing Proc. Int'l Conf. Image Processing, vol. 9, no. 8, pp. 1389-1406, Aug. 2000.
[24] S. Mann, Comparametric Imaging: Estimating Both the Unknown Response and the Unknown Set of Exposures in a Plurality of Differently Exposed Images Proc. Conf. Computer Vision and Pattern Recognition, Dec. 2001.
[25] S. Marschner, S. Westin, E. Lafortune, and K. Torrance, Image-Based BRDF Measurement Applied Optics, vol. 39, no. 16, 2000.
[26] T. Mitsunaga and S.K. Nayar, “Radiometric Self Calibration,” Proc. Conf. Computer Vision and Pattern Recognition, vol. I, pp. 374-380, 1999.
[27] S. Narasimhan and S. Nayar, Removing Weather Effects from Monochrome Images Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 186-193, 2001.
[28] S.K. Nayar, K. Ikeuchi, and T. Kanade, Shape from Interreflections Int'l J. Computer Vision, vol. 6, no. 3, pp. 173-195, Aug. 1991.
[29] R. Ramamoorthi and P. Hanrahan, A Signal-Processing Framework for Inverse Rendering Computer Graphics, Proc. SIGGRAPH, pp. 117-128, 2001.
[30] Y. Tsin, V. Ramesh, and T. Kanade, Statistical Calibration of the CCD Imaging Process Proc. Int'l Conf. Computer Vision, vol. 1, pp. 480-487, 2001.
[31] R.J. Woodham, Photometric Method for Determining Surface Orientation from Multiple Images OptEng, vol. 19, no. 1, pp. 139-144, Jan. 1980.
[32] Y. Yu, P.E. Debevec, J. Malik, and T. Hawkins, Inverse Global Illumination: Recovering Reflectance Models of Real Scenes from Photographs Computer Graphics, Proc. SIGGRAPH, pp. 215-224, 1999.
[33] R. Zhang, P.-S. Tsai, J. Cryer, and M. Shah, Shape from Shading: A Survey IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 8, pp. 690-706, Aug. 1999.
[34] T. Zickler, P.N. Belhumeur, and D.J. Kriegman, Helmholtz Stereopsis: Exploiting Reciprocity for Surface Reconstruction Proc. European Conf. Computer Vision, 2002.

Index Terms:
Radiometric response function, camera response function, calibration, real-world response curves, empirical modeling, high-dynamic range, recovery of radiometry, nonlinear response, gamma correction, photometry, sensor modeling.
Citation:
Michael D. Grossberg, Shree K. Nayar, "Modeling the Space of Camera Response Functions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 10, pp. 1272-1282, Oct. 2004, doi:10.1109/TPAMI.2004.88
Usage of this product signifies your acceptance of the Terms of Use.