Spectral responsivity estimator for color vision systems: Filter selection and noise effect

The determination of spectral responsivities for machine vision systems plays a significant role in analyzing and predicting their color imaging performance. A filter-based optical system, called the spectral responsivity estimator, is developed in this paper. The design objective of the optical system is to effectively select a limited number of spectral (or broadband) filters to characterize the spectral features of color imaging processes which are contaminated by noise, so that the spectral response functions can be estimated with satisfactory accuracy. In this paper, a theoretical study is first presented to pave the way for this work, and then we propose a filter selection algorithm based on the technique of orthogonal-triangular (QR) decomposition with column pivoting, called the QRCP method. This method involves QR computations and a column permutation process, which determines a permutation matrix used to conduct subset (or filter) selection. Experimental results reveal that the proposed technique is truly consistent with the theoretical study on filter selections. As expected, the optical system with filters selected using the QRCP method is much less sensitive to noise than are those which use other spectral filters obtained using different selections. It turns out that our approach is an effective way to implement an optical system for estimating the spectral responsivities of color vision systems.