Pigment mapping allows the classification and estimation of the abundances of pigments in paintings. The information learned becomes extremely important for conservators, who are then able to decide the best strategies in the conservation of the artefacts. When the goal is to restore a painting, it is also important to know what the effects of the newly introduced materials are. To fulfil this purpose, a proper mixing model must be defined. We propose a framework to perform pigment mapping on the hyperspectral image of an experimental painting realised for the occasion, with the goal of rendering a colour image using the concentrations retrieved from the mapping. Contrarily to spectral unmixing tasks, where subtractive models prevailed, hybrid models have the advantage of outputting more accurate colours in this workflow