We have measured the spectral sensitivity functions for 28 cameras, including professional DSLRs, point-and-shoot, industrial and mobile cameras (i.e.Nokia N900), using a monochromator and a spectrometer PR655. At each wavelength, the camera spectral sensitivity in RGB channels is calculated by c(λ) = d(λ)/(r(λ)⋅t(λ)), where d is the raw data recorded by the camera, r is the illuminant radiance measured by the spectrometer, and t is the exposure time of the camera. All other settings (i.e., ISO and aperture) remained the same during the measurement for each camera. The procedure is repeated across the whole visible wavelength from 400 to 720nm with an interval of 10nm.

The spectral sensitivity of 28 cameras are measured in our database, including professional DSLRs, point-and-shoot, industrial and mobile cameras. Statistical analysis of these measurements shows the space of camera spectral sensitivities is two-dimensional. This statistical model is useful to recover camera spectral sensitivities from a single image with regular broadband reflective color targets.

The need for statistics prior when estimating the camera spectral sensitivities. Direct inversion suffers even with a small amount of noise (1%) due to the low dimensionality of spectral reflectance of real-world objects. The subscripts m and e stand for the measured and estimated camera spectral sensitivities.

A camera satisfies the Luther condition if its spectral sensitivity function is a linear transformation of the CIE-1931 2-degree color matching function. The Luther condition can be evaluated by the RMS error between C_2deg and T⋅C, C_2deg are the CIE-1931 2-degree color matching functions, and C are the measured camera spectral sensitivities. Color difference (CIEDE00) is calculated between C_2deg and T⋅C under CIE D65 illuminant and the 1269 Munsell color chips. Ideally, spectral RMS and color differences are zero if a camera perfectly satisfies the Luther condition. Overall, most cameras have a deviation from the Luther condition, especially for the two industrial cameras.

The principal components of camera spectral sensitivities. The three columns represent the R/G/B channels, respectively. We performed PCA on 28 cameras including Canon Nikon, SONY etc. The 1st principal component accounts for over 95% of total variance for all three channels, and the first two principal components accounts for over 97% of total variance. Thus, we model camera spectral sensitivity functions as two-dimensional functions.

(a) The measured spectrum of a daylight. (b) The spectral reflectance of a color checker DC. (c) The captured image (glossy and duplicate patches are removed to avoid overweighting certain colors). (d) The recovered spectral sensitivities with known daylight spectrum. By using a daylight model, we can recover both the daylight spectrum (e) and the camera spectral sensitivities (f). The subscripts m and e in (d) and (f) stand for the measured and estimated camera spectral sensitivities, respectively.

(a) Fourier basis, (b) polynomial basis, and (c) radial basis. The results are worse than that of using the PCA model. The subscripts m and e stand for the measured and estimated camera spectral sensitivities, respectively.

A-PCA model, B-Fourier basis, C-radial basis and D-polynomial basis with the ground truth (E). A color checker is rendered under D65 with camera spectral sensitivities recovered using these basis functions, and converted to sRGB. The average color difference between the renderings (from A to D) and the ground truth (E) are 1.59, 3.54, 2.43 and 7. The gain of the imaging system remains the same for all four basis functions.

The images are rendered to sRGB based on the measured (top row) and estimated (bottom row) camera spectral sensitivities of Canon 60D. (a) face, (b) beads, and (c) peppers are from the multispectral image database [25]. The values in the parentheses are the average color difference (CIEDE00) between the bottom and top images in each column. For all three examples, the color difference is close to one, indicating a close color match.

CC is put in the scene to locate the white point. The estimated camera spectral sensitivity of Canon5D Mark II is used to calculate T. Left column: The captured image; Middle column: the corrected image based on T, and Right column: the corrected image by dividing the white point (without using T). The images are rendered in sRGB color space.