Correcting for not feasible values in reflectance function estimation using linear models

In this paper we present a method that, given the tristimulus values under a known illuminant, make it possible to compute a reflectance function that is in the range between 0 and 1 of physically admissible values without altering the corresponding tristimulus values. We represent the unknown reflectance function with a three-dimensional linear model. 1. INTRODUCTION A common problem in spectral imaging is the reconstruction of a reflectance spectrum starting from some experimental data, e.g. from suitable colorimetric measurements. Many of the techniques available for such reconstruction do not guarantee that the reconstructed reflectance will be physically feasible, that is, that all its values be in the interval [0,1]. Supposing that, starting from a colour, we have obtained a reflectance spectrum, and that this spectrum is not feasible, the problem is to obtain a feasible reflectance that generates the same colour. In other words, the problem that we are considering can be posed in its most general form as follows: given an illuminant, and a reflectance spectrum, find a feasible reflectance metameric, under the given illuminant, to the given reflectance.