Analysis of mean square errors of spectral reflectances recovered by multispectral cameras

Acquisition of the spectral reflectances of imaged objects through the use of sensor responses is important for color reproduction of images under various illuminations. The accuracy of the recovered spectral reflectances depends not only on the spectral sensitivities of sensors but also on the noise present in a device. For the first time, the mean square errors (MSE) between the measured and recovered spectral reflectances were separated into noise dependent and noise independent MSE based on the proposed model. Experiments were performed to study the influence of the bit-depth of the analog to digital conversion and of the sampling intervals over the visible wavelength on the MSE. It is shown that the sum of the theoretically calculated noise dependent and independent MSE agrees fairly well with the MSE of the spectral reflectances recovered by multispectral cameras. It is also confirmed that the noise dependent MSE increases with a decrease in the bit-depth and that the noise independent MSE increases with an increase in the sampling intervals. The separation of the MSE into noise dependent and independent MSE gives a powerful tool for the accurate image acquisition.