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(λ) is the raw data recorded by the camera, r(λ) is the illuminant radiance measured by the spectrometer, and t(λ) 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.

It is known that common color targets such as a colorchecker cannot be used directly to recover camera spectral sensitivities under conventional illumination (e.g., daylight, tungsten, fluorescent). This is because the intrinsic dimensionality of real-world objects' reflectance is about 8, which is less than the number of unknowns in camera spectral sensitivities. Direct inversion is not reliable, even with a small amount of noise (1%).

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 C2deg and TC, C2deg are the CIE-1931 2-degree color matching functions, and C are the measured camera spectral sensitivities. Color difference (CIEDE00) is calculated between C2deg and TC 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 Canon cameras, Nikon cameras, and all 28 cameras. 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 sensitiv- ities 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 [11]) 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.