We examine the problem of building quantitative elemental maps from X-ray absorption images (radiography). As we suggested in a previous publication in Microbeam Analysis, factorial analysis of correspondence is shown to be an optimal method, in the least squares sense, for solving the multilinear equation system given by Beer's law: it relates to an efficient description of the problem in the concentration phase space. We explain how factorial analysis is related to singular value decomposition and we give a complete description of the algorithm. The method can be applied to any multilinear analytical technique as well. Programs are written in C and Mathematica® languages. Academic users may obtain the relevant software (source and code) as freeware directly from the authors.