Optimal Spectral Sampling for Color Imaging

Abstract

I consider the problem of numerically computing tristimulus values for a given spectral power density. In particular, I examine the use of interpolatory quadrature rules for the solution of this problem. A good deal of effort has gone into creating tables of weights and abcissas for solving this problem [3]. Wallis [2] has proposed a more sophisticated approach using Gauss quadrature rules. I show that the performance of these techniques can be improved in a well-defined sense, and derive a method based on a new class of quadrature rules. These rules give optimal performance in the sense that they maximize the overall degree of precision while simultaneously minimizing the number of function evaluations.